UNIVERSITY OF NAIROBI

Transcription

1 UNIVERSITY OF NAIROBI FINAL YEAR PROJECT PROJECT INEX: MFO 06/05 COMPUTER AIE ESIN CASE STUY: COMPOUN EAR TRAIN PRESENTE BY: MAKAU CARLOS VAATI- F8//00 MBUUA SAMUEL KARITA- F8/5897/00 MWENWA NICHOLAS MBATHA- F8//00 SUPERVISOR: PROF. M. F. OUORI APRIL, 05 PROJECT REPORT SUBMITTE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWAR OF THE BACHELOR OF SCIENCE EREE IN MECHANICAL ENINEERIN EPARTMENT OF MECHANICAL & MANUFACTURIN ENINEERIN

2 ECLARATION STUENTS This report is our original work and has not een pulished or presented for award of any degree in any university/college there efore. Signed ate NICHOLAS MWENWA MBATHA Signed ate CARLOS MAKAU VAATI Signed ate MBUNUA SAMUEL KARITA SUPERVISOR This report has een suitted y the aove students for exaination with y approval as a university lecturer and supervisor of the project. Signed. ate PROF M.F. OUORI i

3 EICATION We would like to dedicate this project to our faily eers, for the years of patience, support and guidance towards our education. ii

4 ACKNOWLEEMENTS We take this opportunity to express our gratitude to all those who otivated, encouraged and helped us in the project work. We specially would like to express our sincere gratitude to our supervisor PROF M.F. OUORI for the aterial he ade availale to us, advice and guidance in every step in the entire project writing process. His dedication and friendly supervision contriuted highly to our succession this project. Special thanks to our friends and other eers of the epartent of Mechanical & Manufacturing Engineering for eing so supportive and helpful in every possile way. Finally we would like to take this chance to express our appreciation to our faily eers. Their continuous love and support gave us the strength for pursuing our drea. od less you all. MWENWA M., MAKAU V.& MBUUA K. iii

5 LIST OF FIURES Fig.. Phases of the esign Process Fig.. Priitive ears Made of Wood..6 Fig.. Spur ears in Mesh...7 Fig.. Helical ears..7 Fig.. Crossed Helical ears 8 Fig..5 Straight Bevel ears...8 Fig..6 Spiral Bevel ears..8 Fig..7 Hypoid Ring ear () and Pinion ear ().. 8 Fig..8 Axes of Bevel Hypoid and Wor rives.8 Fig..9 Wor and Wheel...9 Fig..0 Rack-and-Pinion..9 Fig.. Rack-and-Pinion on Radial rilling Machine 0 Fig.. oule Helical ears in a Ceent Mill...0 Fig.. Siple ear Trains... Fig.. Copound ear Train. Fig..5 Reverted ear Train. Fig..6 Epicyclic ear Train. Fig..7 ear Train for a Manual Winch.. Fig..8 Friction Wheels and Spur earing..5 Fig..9 ear Teeth Noenclature 6 iv

6 Fig.. Scheatic of a Reverted Two Stage ear Train. Fig.. Forces Acting Between Two Meshing ear Wheels.8 Fig.. Scheatic of a Non-reverted Two Stage ear Train.. Fig.. Forces Acting Between Two Meshing ear Wheels 0 Fig..5 ear Train for a Manual Winch.5 Fig..6 Scheatic of a Reverted Two Stage ear Train 7 Fig..7 Scheatic of a Non-reverted Two Stage ear Train.55 Fig.8.rawing done using AutoCA inventor..59 Fig.. raphical user interface..68 Fig... Case study- run- progra...7 Fig...Case study- run- progra (Non- reverted copound gear train). 86 v

7 LIST OF TABLES Tale. Recoended Maxiu Speed Reduction Ratio in a Single Stage.. 6 Tale. Recoended Maxiu Speed Reduction Ratio in a Single Stage. 9 Tale. Case study values 5 Tale. Recoended Maxiu ear Ratios in a Single Stage 7 Tale.5 ear Teeth Systes.. 8 Tale.6 Standard Modules in Millieters.. 8 Tale.7 Velocity Factors..5 Tale.8 ear diensions..5 Tale.9 Recoended Maxiu Speed Reduction Ratio in a Single Stage 55 Tale.0 ear diensions...58 Tale. Volues. 58 vi

8 Tale of Contents ECLARATION... i EICATION... ii ACKNOWLEEMENTS... iii LIST OF FIURES... iv LIST OF TABLES... vi ABSTRACT... ix CHAPTER ONE..... INTROUCTION.....STATEMENT OF THE PROBLEM OBJECTIVES.....JUSTIFICATION OF THE ESIN ENINEERIN ESIN AS A PROBLEM SOLVIN TOOL esign Tools and Resources Coputer Aided esign (C.A.)... CHAPTER TWO LITERATURE REVIEW Introduction to ears...5. ear Trains.... ear Noenclature...5 CHAPTER THREE LITREATURE REVIEW FOR THE ESIN OF AN OPTIMUM TWO STAE REVERTE AN NON- REVERTE COMPOUN EAR TRAIN..... INTROUCTION... PART A..... OPTIMAZATION THEORY FOR A TWO STAE REVERTE COMPOUN EAR TRAIN.... A) Ojective Function..... THE CONSTRAINTS...5 (i) eoetrical Constraints...5 (ii) Kineatical Constraints...6 (iii) Strength Constraints...7. THE OPTIMIZATION MOEL... vii

9 PART B....5 OPTIMIZATION THEORY FOR A TWO STAE NON-REVERTE COMPOUN EAR TRAIN.... A) Ojective Functions THE CONSTRAINTS...8 i) eoetric Constraints...8 ii) Kineatical Constraints...8 iii) Strength Constraints THE OPTIMIZATION MOEL....8 CASE STUY THE REVERTE EAR TRAIN THE NON-REVERTE EAR TRAIN AUTOCA RAWIN OF A REVERTE COMPOUN EAR TRAIN...59 CHAPTER EVELOPMENT OF COMPUTER AIE PRORAM FOR THE OPTIMIZATION MOEL INTROUCTION ESIN PROCESS ALORITHIM USE IN MATLAB Optiied reverted copound gear coand line Matla algorith Optiied non reverted copound gear coand line Matla algorith RAPHICAL USER INTERFACE (UIs) THE REVERTE COMPOUN EAR TRAIN ( UI )COE THE NON REVERTE COMPOUN EAR TRAIN ( UI )COE ISCUSSION RECOMMENATIONS CONCLUSIONS...9 REFERENCES...9 viii

10 ABSTRACT This project involves study and design of the reverted and non-reverted two stage copound gear train of iniu weight.a case study of a anual winch was analyed with the ain ai of deterining which of the two will e of iniu optiu volue hence iniu weight given that the face widths of all the gear wheels in the trains are equal. The speed of the input shaft was, =0.6 rads/s and the power to e transitted eing kw. The design process involved utiliation of optiiation theory, geoetrical constraints, kineatic constraints, and strength constraints which included ea strength and wear strength analysis. It was found that in order to avoid ending failure, the odule and the face width of the gear is adjusted so that the ea and wear strength was greater than the load to e transitted. Fro calculation force to e transitted, Ft was 00 Newton while the ea strength and wear strength were 975.8N and N respectively. By use of MATLAB, an algorith was developed to deterine gear paraeters required for the gear design such as the inter-stage gear ratio, face width, centre distance, allowale iniu ending stress of the gear aterial and optiu volue for the gear aterial. A source code was created and an executale raphical -User Interface (UI) developed as it is easy to use, efficient and tie saving during design. For power transission of kW, input shaft of 5.7 Rp and a speed reduction of :7 for reverted two stage gear train the iniu volue fro the calculation was. while the value fro the progra was. the difference was found to e which is.7%. For a non-reverted two stage gear train of sae power transission, sae input shaft speed and sae overall gear ratio the iniu fro the calculation was. while the value fro the progra was.. The difference was found to e ix

11 CHAPTER ONE.. INTROUCTION In odern daily work routines either in our doestic chores or in industrial workplaces, anual lifting of oth heavy and light loads is a coon practice. These practices of anual lifting have een characteried y high input undertakings in ters of laor, energy and tie investents. This has proven to e detriental to health of the individuals due to poor work ergonoics exhaustion, inefficiencies and strenuous tasks involved. Although different loads have their own way of lifting, ost of the have to e hooked to the equipent through a winch of rope for appropriate lifting. Thus an efficient lifting echanis is required. Over the years, lifting activities were heavily dependent on anual laor. uring this period various echaniss such as pulleys and gears were used...statement OF THE PROBLEM. Lifting of loads, heavy or light is a paraount undertaking in any industrial and doestic activities. Many of the activities are econoically vital and require etter, efficient and faster lifting echaniss. Owing to the fact that Kenya is a third world country with low power production and connectivity and generally low incoe per capita, any people have resorted to inefficient echanis of anually lifting loads which are dead slow, risky and exhaustive aong other liitations. For instance70% of the country has water scarcity and people have dug water wells to help itigate the prole, however fetching of water has een tedious involving risky echaniss. An attept to overcoe this challenge calls for design of an efficient lifting echanis, which is locally availale and affordale for the coon people. This will help iprove their output significantly.

12 .. OBJECTIVES To study the theory underlying the design of gears and copound gear trains. To design a locally availale two stage copound gear train of iniu weight for anual winch application. esign and optiie a two-stage copound gear train considering the following ultiojective functions: Miniiation of the overall weight. Maxiiation of Power transitted... JUSTIFICATION OF THE ESIN For efficient safe lifting activities, then expensive, large and heavy installation of lifting/hoisting achinery will e required. This is however, expensive for local people who earn living fro such work and their incoe is low. On the other hand, the cheapest and availale echaniss are slow, heavy and inefficient hence low production rates. Hence there is a need for design of locally availale lifting echaniss..5. ENINEERIN ESIN AS A PROBLEM SOLVIN TOOL To design is either to forulate a plan for the satisfaction of a specified need or to solve a prole. If the plan results in the creation of soething having a physical reality, then the product ust e functional, safe, reliale, copetitive, usale, anufacturale, and arketale. esign is a highly innovative process that requires the right aount of inforation to enale appropriate decision aking. ecisions are soeties ade tentatively, with the right reserved to adjust as ore ecoes known. The engineer asically ecoes responsile with a decisionaking, prole-solving role. A designer s personal resources of creativeness, counicative aility, and prole solving skill are intertwined with knowledge of technology and first principles. Engineering tools such as atheatics, statistics, coputers, graphics, and languages are necessary skills in engineering design. esign is a counication-intensive activity in which oth words and pictures are used, and written and oral fors are eployed. Engineers have to counicate effectively and work with people of any disciplines. These are iportant skills, and an engineer s success depends on the. The coplete design process can e split into six stages as represented and descried elow. Phases of design process. Identification of need: The need in this case is to study the theory underlying the design of gears and copound gear trains.

13 . efinition of prole: To design, with the aid of the digital coputer, a copound gear train for a anual winch application, in all its detail.. Synthesis: This will involve calculations and the CA drawing of the relevant diensions of the proposed design.. Analysis and optiiation: The proposed design will e analyed and this ay require the construction of a odel to siulate the real product. 5. Evaluation: This process involves the testing of the prototype to deterine if the design really eets the needs and to eploy every design consideration so that they are satisfied. 6. Presentation: This is the final design process after all the possile iterations have een done and the product satisfies the design ojectives. It can then e presented for anufacture. Fig.. Phases of the esign Process

14 .5. esign Tools and Resources Roust coputer software packages provide tools of iense capaility for the design, analysis and siulation of echanical coponents. The resource and tool suggested to e applied for coputational and design visualiation is a coputer aided design software that allows designs fro which conventional two-diensional orthographic views with autoatic diensioning can e produced. In addition, the engineer always needs technical inforation, either in the for of asic science/engineering ehavior or the characteristics of specific off-theshelf coponents. The resources range fro science/engineering textooks to anufacturers rochures or catalogues. Major Categories of esign Considerations Traditional Considerations. Materials. eoetry. Operating conditions. Cost Modern Considerations. Safety. Ecology. Quality of life 5. Availaility 6. Produciility 7. Coponent life Miscellaneous Considerations. Reliaility and aintainaility. Ergonoics and aesthetics. Assely and disassely. Analysis

15 .6. Coputer Aided esign (C.A.) Coputer aided design is the practice of engineering design where roust coputer software packages are used for design. Engineering is a wide discipline of science which involves various ranches/fields of practices such as nuclear, echanical, civil and structural and any ore. Each field of practice in engineering involves various scientific theories, calculations, forulas, equipents of use and other properties. The use of coputers in engineering design enales the pre-prograing and custoiation aility of engineering aspects into a progra/dataase of various properties for use. It is here where software packages (such as Matla, AutoCA, Autodesk Investor, ProEngineer) take advantage of the coputer s aility to store, process data and retrieve inforation. A designer descries the proposed design and then displays it on the coputer onitor as an output iage, user interface or even a plot. esign changes can e ade quickly and inexpensively at this point. Furtherore, CA can also e used to create accurate, three diensional (-) geoetry/shape, dataases, produce a ill of aterials and eliinate the need for a prototype, or create a prototype via stereo-lithography. Thus CA can reduce concept-toproduction tie, hence iproving copetitiveness. However it is iportant to recognie the highly efficient ethod of concurrent engineering. An Institute for efense Analysis report (986) defines concurrent engineering (CE) as a systeatic approach to integrated, concurrent design of products and their related processes. CE requires teawork and coordination involving research and developent engineers, designers, anufacturing engineers and technicians and personnel fro other functions. The focus is on product-ased teas rather than on departents. With CE different aspects of product design and developent can e carried out siultaneously. Thus, CE is a parallel process, while the traditional process is a series approach. Proles soeties result fro lack of co-ordination in the traditional approach. CE attepts to eliinate such proles in the concept and design phase.

16 CHAPTER TWO.0LITERATURE REVIEW.. Introduction to ears ears are copact, positive-engageent, power transission eleents that are used to deterine the speed, torque, and direction of rotation of driven achine eleents. This for of transission is possile ecause of the rigidity of the aterial fro which the gear wheels are ade. Fro the kineatical point of view, gear wheels ay e assued to e copletely rigid, such that there is no deforation whatsoever when the gear wheel is sujected to force. Thus the kind of transission of otion that occurs in gear drives is known as a positive drive in which there should e no loss of otion at all. This is as opposed to elt drives, for instance, in which loss of otion ay occur due to creep, slip or oth creep and slip of the elt relative to the pulleys. The slipping of a elt or rope is a coon phenoenon in the transission of otion or power etween two shafts, y use of these devices. The effect of slipping is to reduce the velocity ratio of the syste. In precision achines, in which a definite speed ratio is of iportance (as in watch echanis), positive drive is achieved y use of gears or toothed wheels. ears are also used to adjust the direction of rotation. For instance, in the differential etween the rear wheels of a car, the power is transitted y a shaft that runs down the center of the car, and the differential has to turn that power through 90 degrees in order to apply it to the wheels... History and developent of gears. In the fourth century B.C., Aristotle entioned in his writings that gears were eing used very coonly in any applications. Archiedes originated the use of wor gearing y 87- B.C. In his writing in 8 B.C., Vitruvius, a ilitary engineer, also descried a nuer of gear applications such as the water wheel and grain ill. Leonard da Vinci used ultitudes of gears in various echaniss that he developed y hi around 500 A.. reek and Roan literature show extensive usage of gears for forward otion. Toothed gears used in the clocks of Cathedrals and other ecclesiastical uildings were also used during the iddle ages. In the 8th century, the Industrial Revolution in England led to the usage of cycloidal gears in clocks, irrigation devices, water ills and powered achines.the industrialiation of the west ade a ig ipact on gear technology which is the key to odern developents and the rapid advanceents in gear technology. Currently gear trains are widely used in all kinds of echaniss and achines fro can openers to aircraft carriers. Whenever a change in the speed or torque of a rotating device is needed, a gear train will usually e used. 5

17 ears of various sies and styles are readily availale fro any anufactures. Asseled gearoxes with particular ratios are also stock ites. Fig.. Priitive ears Made of Wood.. Types of gears. ear types ay e grouped into five ain categories: Spur, Helical, Bevel, Hypoid, Wor and wor gear, Rack and pinion and Herringone gears. Typically, shaft orientation, efficiency, and speed deterine which of these types should e used for a particular application. I. Spur ears Spur gears have straight teeth cut parallel to the rotational axis. The tooth for is ased on the involute curve. Their design accoodates ostly rolling, rather than sliding, contact of the tooth surfaces. Since less heat is produced y this rolling action, the echanical efficiency of spur gears is high, often up to 99%. Spur gears are the least expensive to anufacture and the ost coonly used, especially for drives with parallel shafts. 6

18 II. Helical ears Fig.. Spur ears in Mesh Helical gearing differs fro spur in that helical teeth are cut across the gear face at an angle, rather than eing parallel to the axis of rotation of the gear wheels. Thus, the contact line of the eshing teeth progresses across the face fro the tip at one end to the root at the other end, reducing the noise and viration that are characteristics of spur gears. Also, several teeth are in contact at any one tie, producing a ore gradual loading of the teeth that reduces wear sustantially. Fig.. Helical ears 7

19 Fig.. Crossed Helical ears III. Bevel ears Unlike spur and helical gears, which have teeth cut fro a cylindrical lank, evel gears have teeth cut on a conical surface. Bevel gears are used when input and output shaft centerlines intersect. Teeth are usually cut at an angle so that the shaft axes intersect at Fig..5 Straight Bevel ears Fig..6 Spiral Bevel ears 8

20 IV. Hypoid ears Hypoid gears resele spiral-evels, ut the shaft axes of the pinion and driven gear do not intersect. This configuration allows oth shafts to e supported at oth ends. Fig..7 Hypoid Ring ear () and Pinion ear () In hypoid gears, the eshing point of the pinion with the driven gear is aout idway etween the central position of a pinion in a spiral-evel and the extree top and otto position of a wor. This geoetry allows the driving and driven shafts to continue past each other so that end-support earings can e ounted. V. Wor and Wor ear Sets Fig..8 Axes of Bevel Hypoid and Wor rives Wor gear sets, consist of a screw-like wor (coparale to a pinion) that eshes with a larger gear, usually referred to as a wheel. The wor acts as a screw, several revolutions of which pull 8

21 the wheel through a single revolution. In this way, a wide range of speed ratios up to a reduction of :60 and higher can e otained fro a single stage. VI. Rack and Pinion Fig..9 Wor and Wheel A straight ar with teeth cut straight across is known as a rack. Basically, this rack is considered to e a spur gear unrolled and laid out flat. Thus, the rack and pinion is a special case of spur gearing. The rack-and-pinion is useful in converting rotary otion to linear and vice versa. Rotation of the pinion produces linear travel of the rack. Conversely, oveent of the rack causes the pinion to rotate. The rack-and-pinion is used extensively in achine tools, lift trucks, power shovels, and other heavy achinery where rotary otion of the pinion drives the straight-line action of a reciprocating part. Fig..0 Rack-and-Pinion 9

22 VII. Herringone ears Fig.. Rack-and-Pinion on Radial rilling Machine oule-helical or herringone gears are fored y joining two helical gears of identical pitch and diaeter ut of opposite hand on the sae shaft. The advantage copared to a helical gear is the internal cancellation of its axial thrust loads since each hand half of the herringone gear has an oppositely directed thrust load. Thus no thrust earings are needed other than to locate the shaft axially. They are used in high power applications such as ship drives where the frictional losses fro axial loads will e prohiitive. Fig.. oule Helical ears in a Ceent Mill 0

23 . ear Trains In order to transit power fro one shaft to another, two or ore gears are ade to esh with each other. Such a coination is known as a gear train or train of toothed wheels. The nature of the train used depends upon the velocity ratio required, the relative position of the axes of shafts and the relative directions of rotation of the shafts. A gear train ay consist of spur, evel or spiral gears Types of gear trains: Following are the different types of gear trains, depending upon the arrangeent of wheels:. Siple gear train,. Copound gear train,. Reverted gear train, and. Epicyclic gear train. In the first three types of gear trains, the axes of the shafts over which the gears are ounted are fixed relative to each other. But in case of epicyclical gear trains, the axes of the shafts on which the gears are ounted ay ove relative to a fixed axis.. Siple ear Train When there is only one gear on each shaft, as shown in Fig..the train is known as siple gear train. The gears are represented y their pitch circles. When the distance etween the two shafts is sall, the two gears and are ade to esh with each other to transit otion fro one shaft to the other, as shown in Fig.. (a). Since the gear drives the gear, therefore gear is known as the driver and the gear is known as the driven. It ay e noted that the otion of the driven gear is opposite to the otion of driving gear. Fig.. Siple ear Trains

24 . Copound ear Train When there is ore than one gear on a shaft, as shown in Fig.., the train is known as a copound train of gear. Fig.. Copound ear Train In a siple train of gears, idle gears do not affect the speed ratio of the syste. But these gears are useful in ridging over the space etween the driver and the driven. But whenever the distance etween the driver and the driven or follower has to e ridged over y interediate gears and at the sae tie a great (or uch less) speed ratio is required, then the advantage of interediate gears is intensified y providing copound gears on interediate shafts. In this case, each interediate shaft has two gears rigidly fixed to it so that they ay have the sae speed. One of these two gears eshes with the driver and the other with the driven or follower attached to the next shaft as shown in Fig.... Reverted ear Train When the axes of the first gear (i.e. first driver) and the last gear (i.e. last driven) are co-axial, then the gear train is known as a reverted gear train as shown in Fig..5.

25 . Epicyclic ear Train Fig..5 Reverted ear Train In an epicyclic gear train, the axes of the shafts, over which the gears are ounted, ay ove relative to a fixed axis. A siple epicyclic gear train is shown in Fig..6 where a gear A and the ar C have a coon axis at O aout which they can rotate. The gear B eshes with gear A and has its axis on the ar at O, aout which the gear B can rotate. If the ar is fixed, the gear train is siple and gear A can drive gear B or vice- versa, ut if gear A is fixed and the ar is rotated aout the axis of gear A (i.e. O), then the gear B is forced to rotate up on and around gear A. Such a otion is called epicyclic and the gear trains arranged in such a anner that one or ore of their eers ove upon and around another eer is known as anepicyclic gear trains (epieans upon and cyclic eans around).

26 Fig..6 Epicyclic ear Train The epicyclic gear trains are useful for transitting high velocity ratios with gears of oderate sie in a coparatively sall space. The epicyclic gear trains are used in the ack gear of lathe, differential gears of the autooiles, hoists, pulley locks and wrist watches, aong other applications. We shall liit the scope of this project to the design of a two stage copound gear train of iniu weight (see Fig..6). Handle L Crank Ar Shaft Rope ru Bearing ear Train Load Fig..7 ear Train for a Manual Winch

27 . ear Noenclature The ters defined here are generally applicale to gears. The pitch circle is an iaginary circle upon which all calculations are ased. Kineatically, two eshing gears ay e likened to two interacting friction wheels whose diaeters are equal to the pitch circle diaeters of the corresponding gears (See Fig..8). The pitch circles of eshing gears roll on each other without slipping. Fig..8 Friction Wheels and Spur earing The pitch circle diaeter is the diaeter of the pitch circle of a gear or pinion. The pinion is the saller of two eshing gears. The larger gear is often referred to siply as gear. The addenduha is the radial distance fro the pitch circle to the top of the tooth (to the addendu circle). See Fig..9. The dedenduhd is the radial distance fro the pitch circle to the otto of the tooth space (to the dedendu circle). The outside diaeter o The root diaeter r The whole depthht Thush h h. t a d is the diaeter of the addendu circle. Thus o ha. is the diaeter of the root circle, thus r hd. is the total height of the tooth or the total depth of the tooth space. The working depthhk is the distance that a tooth projects into the ating tooth space. Thus, if the addenda of the ating gears are equal then h h. k a The root circle is also known as the dedendu circle. 5

28 Addendu Circle Top Land Face Width Fillet Radius Face Addendu edendu Tooth Thickness Circular Pitch Width of Space Pitch Circle Flank Botto Land edendu Circle Clearance Circle Clearance Fig..9 ear Teeth Noenclature The clearancehc is the distance etween the top of a tooth and the otto of the ating tooth space. The clearance can also e descried as the aount y which the addendu of a given gear exceeds the addendu of its ating gear. Thus, if the addenda of the ating gears are equal then h h h. c d a The circular pitch is the distance, along the pitch circle, fro a point on one tooth to a corresponding point on an adjacent tooth. Therefore, if the nuer of teeth on a gear wheel is denoted y then p c. Since is an irrational nuer, the circular pitch is not a convenient quantity fro the point of view of easureent. The odule is the ratio of the pitch circle diaeter of a gear wheel to the nuer of teeth on the gear wheel. Thus. It therefore follows that p c and that the circular pitch and the oduleare really easures of the sae quantity, to different scales. The odule has the diensions of length and it can e conveniently taken as an indication of gear tooth sie. ear wheels of equal odule have teeth of roughly the sae sie regardless of their pitch circle diaeters. The diaetral pitchpd was ore coonly used in the past than it is at present. It is the ratio of the nuer of teeth on a gear wheel to the pitch circle diaeter of the gear wheel. Thus. The odule and the diaetral pitch cannot actually e p d p c p c 6

29 easured on the gear wheel itself; they ust e calculated fro easureents of and. However, these two quantities do not include the irrational nuer. The acklashb of a pair of eshing teeth is the aount y which the width of a tooth space exceeds the thickness of the ating tooth, on the pitch circles. A sall aount of acklash is usually desirale, or necessary, ut if it is excessive the gears will rattle under light loads or when running idle. The chordal addenduhac the pitch circle that spans the width of a tooth. Thus: is the radial distance fro the top of a tooth to the chord of h ac h a cos 90 Chordal addendu is required when easuring chordal thickness. The chordal thicknesstc sin 90 0 circle. Thus t c gear teeth. 0 is the thickness of a tooth, easured along a chord of the pitch. Chordal thickness is required in easuring the finished The face of the tooth is that portion of the tooth surface etween the pitch cylinder and the addendu cylinder. The flank of the tooth is that portion of the tooth surface etween the pitch cylinder and the root cylinder. For a spur gear, the face widthw is the lengthwise width of the teeth in the direction parallel to the axis of rotation of the gear wheel.. systes of gear teeth These are standards that specifies the relationship involving addendu, dedendu, working depth, tooth thickness and pressure angle. The following four systes of gear teeth are coonly used in practice. The coposite syste-used for general purpose gears. It s stronger ut has no interchangeaility and is now osolete. The full depth involute syste-was developed for use with gear hos for spur and helical gears. The full depth involute syste-the increase of the pressure angle fro to 0 results in a stronger tooth, ecause the tooth acting as a ea is wider at the ase. The stu involute syste-has strong teeth to take heavy loads. 7

30 ear aterials and gear anufacturing. Materials used to produce gears ay include steel which is the ost coon aterial, and various non-ferrous aterials including plastics and coposites.manufacturing ethods include: achining, forging, casting, staping, powder etallurgy techniques, and plastic injection olding. Of these, achining is the ost coon anufacturing ethod used. ear achining is classified into two categories: ear enerating ear For-Cutting ear generating involves gear cutting through the relative otion of a rotating cutting tool and the generating, or rotational, otion of the work piece. The two priary generating processes are hoing and shaping. Hoing: uses a helically fluted cutting tool known as a ho. Both the ho and the work piece rotate as the ho is fed axially across the gear lank. Hoing is liited to producing external gear teeth on spur and helical gears. It can e perfored on a single gear lank, ut also allows for stacking of ultiple work pieces, thus increasing production rates. Shaping: produces gears y rotating the work piece in contact with a reciprocating cutting tool. The cutter ay e pinion shaped, a ulti-tooth rack-shaped cutter, or a single-point cutting tool. ear for-cutting uses fored cutting tools that have the actual shape, or profile that is desired in the finished gear. The two priary for-cutting ethods are roaching and illing. Broaching is the fastest ethod of achining gears and is perfored using a ulti-tooth cutting tool known as a roach. Each tooth on the roach is generally higher than the preceding tooth. As a result, the depth of cut increases with each tooth as the roaching operation progresses. Broaching is typically used to produce internal gear teeth. External teeth can e roached using pot roaching. In this process a hollow roaching tool, called the pot, is used to cut the gear teeth. Milling is a asic achining process which uses the relative otion etween a rotating, ulti-edge cutter and a work piece to cut individual gear teeth. A variation of the process, called gashing, is used to produce large, coarse pitch gears. ashing is used on heavyduty illing achines and involves plunging the rotating cutter into a lank for rapid etal reoval. 8

31 .5 EAR FINISHIN After anufacturing, gears require a nuer of finishing operations. Finishing operations include heat treatent and final diensional and surface finishing. This finishing can e accoplished using: Shaving rinding Honing Shaving is perfored with a cutter having the exact shape of the finished gear tooth. Only sall aounts of aterial are reoved y a rolling and reciprocating action. The process is fast ut generally expensive due to the cost of achinery and tooling. Shaving is typically perfored prior to heat treating. rinding soeties serves as an initial gear production process, ut is ost often eployed for gear finishing. rinding is classified as either for grinding or involute-generation grinding. For grinding uses wheels having the exact shape of the tooth spacing. The grinding wheels are either vitrified-ond wheels, which require periodic redressing, or Cuic Boron Nitride (CBN) wheels, which can last hundreds of ties longer than vitrified wheels without dressing. Involutegeneration grinding refers to a grinding wheel or wheels used to finish the gear tooth y axially rotating the work piece while it is reciprocated in an angular direction, which in turn is deterined y the type of gear eing finished. This type of grinding is perfored either interittently or continuously. Interittent grinding uses tooth profiles dressed on cup wheels, or on one or two single-ri wheels. Each tooth is ground individually, and then the next is indexed to the wheel. Continuous grinding uses grinding wheels with the rack profile dressed helically on the outside diaeter. Both the grinding wheel and the work turn in tied relationship for continuous finishing. Honing involves the eshing of the gear teeth in a cross axis relationship with a plastic, arasive ipregnated gear shaped tool. The tool traverses the tooth surface in a ack and forth oveent parallel to the work piece axis. Honing polishes the gear tooth surface and can e used to correct inor errors in gear tooth geoetry..6 ear drives advantages and disadvantages. The following are the advantages/disadvantages of the gear drive as copared to other drives, i.e. elt and chain drives 9

32 Advantages High power transission efficiency Copact and easy to install Can e used to transit large aount of power Constant velocity ratio Unlike elt drives they do not slip isadvantages They are costly when copared to other drives They have liited centre distance They error in cutting teeth ay cause virations and noise during operation. 0

33 CHAPTER THREE.0 LITREATURE REVIEW FOR THE ESIN OF AN OPTIMUM TWO STAE REVERTE AN NON-REVERTE COMPOUN EAR TRAIN... INTROUCTION Concept of optiiation and decision theory can play an iportant role in all stages the design process. The optiiing design theory and ethodology will e illustrated through a gear train transission. ear train transissions present a very iportant group of achine eers, which are utilied in a great nuer of engineering fields and which ust satisfy very rigorous technical requireents regarding reliaility, efficiency, precise anufacturing of gears, earing, etc. Optiiation can e realied when design consideration and constraints are incorporated into the design. uring the design process, our ojective is to arrive at an optiu design using volue of aterial used to anufacture the gears (excluding shafts and keyways) and the of inial centre distance C thus resulting to a iniied package sie.

34 PART A.. OPTIMAZATION THEORY FOR A TWO STAE REVERTE COMPOUN EAR TRAIN. A) Ojective Function. A scheatic diagra of a reverted two stage copound gear train is illustrated in Fig... C C Fig.. Scheatic of a Reverted Two Stage ear Train For the reverted copound gear train, the input and output shafts ust e co-axial and therefore: C C =C () Moreover, it is coon practice to ake eshing gear wheels e of equal face widths. We shall assue this to e so, at least initially. In that case: () In Fig.., the nuers of teeth on the gear wheels are denoted y,, and. Further, let us denote the corresponding gear wheel pitch diaeters y,, and. Then, y definition, the odules of the gear wheels are deterined as follows:

35 ; ; ; () As is well known, the odules of eshing gear wheels ust e equal. Therefore: () Now, the centre distances in the two stages ay e expressed as follows: ; C C (5) Fro equations (), (), () and (5), it follows that: (6) The intra-stage gear ratios are deterined as follows: (7) Thus, fro equations (6) and (7), one otains the following: (8) The volue of aterial required for the gear wheels ay e estiated to e the su of the volues of the pitch cylinders of the gear wheels. Thus: V (9) Fro equations () and (9), the following is readily otained: V (0) Fro the definitions of the intra-stage gear ratios, it follows that:

36 and () Thus, fro equations (0) and (), the following is readily otained: V () Now, according to F.Oduori (00), a two-stage reverted copound gear train will e of iniu weight, and therefore of iniu volue for a given aterial, if: () Therefore, fro equations () and (), the following can e readily otained: V () Moreover, fro the definition of odule, it follows that: (5) Therefore: V (6) Equations (6) ay e re-written in diensionless for as follows:

37 5 V V (7) At this stage, let us introduce the following notation for noralied volue and noralied face widths, as a atter of convenience:,, and V V V V n n n n (8) Then equations (7) ay e re-written as follows: V V n n n n (9) The aove will e the ojective function to e iniied... THE CONSTRAINTS (i) eoetrical Constraints According to Juvinall (98) and Marshek (0), the face width of a gear wheel should lie etween 9 and ties the odule of the gear wheel. In the present case, this constraint ay e expressed atheatically, as follows: 9 9 n n (0) Furtherore, according to Juvinall and Marshek (0), gear wheels with standard 0 degree teeth should not have less than 8 teeth. This is the condition for avoiding undercutting for gear wheels that are produced y a generation process and is atheatically correct so long as the pinion eshes with a rack. However, according to Budynas and Nisett (0), the nuer of teeth on a pinion that will avoid interference is deterined as follows:

38 p i k sin i i sin () In the aove equation, i is the angular velocity ratio for a pair of eshing gear wheels, k is a factor that is equal to for standard full-depth teeth and 0. 8 for stu teeth, is the pressure angle and p is the required nuer of teeth on the pinion, in order to avoid interference. Forfull-depth teeth, if we ake 6 and constraint ay e stated as follows: i , we find that 6 p Matheatically, this () (ii) Kineatical Constraints Budynas and Nisett (0) recoend that the speed reduction ratio in a single stage of a copound gear train should not exceed : 0. Oonishi (988) recoends that the speed reduction ratio in a single stage e liited as shown in Tale, elow. Tale. Recoended Maxiu Speed Reduction Ratio in a Single Stage Type of gear Low speed High speed Source: Oonishi (988) Spur :7 :5 Bevel :5 : We shall liit the axiu speed reduction ratio in a single stage to e : 6. Bearing in ind that the gear train eing designed is a speed reducer, this leads to constraints that ay e stated atheatically as follows: () 0.67 and 0.67 The intra-stage gear ratios ust take on such values as to otain the required overall gear ratio of the train. This constraint ay e expressed as follows: () 6

39 (iii) Strength Constraints The odules and the face widths of all the gear wheels in the train ust e deterined so as to otain teeth of adequate strength. If the power and the speed at the input shaft are known, we can start y considering the ea strength of the gear teeth on the input pinions. a)bea strength. According to the original Lewis equation (Lewis, 89; Budynas and Nisett, 0), gear tooth ending stress is given y: F t (5) In the aove equation, Ft is known as the transitted force, p is the circular pitch and y is known as the tooth for factor. Now, fro their definitions, the circular pitch and the odule are related as follows: py p (6) Therefore, fro equations (5) and (6), the following can e readily otained: F y (7) t Now, let us introduce the following notation: Y y (8) Then, fro equations (7) and (8) the following can e readily otained: F Y (9) Figure. shows the pitch circles of a pinion and a gear in esh, along with the forces and torques that act upon the two gear wheels. T is the input torque at the pinion shaft and T is the load torque acting upon the shaft carrying the larger gear. It can e seen in Fig.. that: t T Ft (0) 7

40 F T F F t r F F F t r F F cos sin T F r F t Fig.. Forces Acting Between Two Meshing ear Wheels The power input at the pinion shaft is denoted H and can e expressed as follows: H T () Let us denote the pitch line velocity of the input pinion yu. Then we can write the following: u () Fro equations (0), () and (), we can write the following: H F t () u Fro equations (8), (9) and (), we can write the following: H u Y n Y () Siilarly, for the output stage pinion gear, we can write the following: 8

41 9 n Y Y u H (5) If we denote the allowale ending stress of the gear aterial y a, then we can write the following: Y u H n a (6) Siilarly, assuing that all the gear wheels in the train are ade of the sae aterial, we can write the following: Y u H n a (7) The pitch-line velocities, u and u, ay e expressed in ters of the input shaft rotational velocity as follows: u u (8) Thus, fro equations (6), (7) and (8), we can write the following: Y H Y H n a n a (9) ) Wear strength. According to Buckingha (99) and Oonishi (988), the liiting wear load for eshing gear teeth is given y: g p g p p v t KK F (0)

42 0 In the aove equation: K is the contact stress factor (N/ ), v K is the velocity factor (N/ ), p is the pitch circle diaeter () of the pinion in the pair of eshing gears, p is the face width () of the pinion in the pair of eshing gears, g, p are the nuers of teeth on the larger gear and the pinion, respectively, in the pair of eshing gears. Adapting this equation to the load on the input stage pinion, we can write the following: KK F v t () By using equations (7), (5), () and (), we can write the following: KK u H v () Siilarly, for the output stage pinion, we can write the following: KK u H v () Fro equations (8), () and (), we can write the following: KK u H n v () KK u H n v (5)

43 . THE OPTIMIZATION MOEL We shall deonstrate the optial design routine y designing a gear train that can transit kw of power at an input speed of 5.7 rp and with an overall speed reduction ratio of :8. The optiiation odel can e stated as follows. Miniie the following ojective function: f ( x) x x x x x x n x x or or x x n (6) Since the required overall gear reduction ratio is :8, we can apply the following nonlinear equality constraint: x x 8 (7) Note that for equation (7) to hold true, if we set x 6 then x and vice versa. Therefore, the iniiation should also e suject to the following linear inequality constraints: 9 x 6 x x x Equation (6) is an interpretation of equation (9), equation (7) is an interpretation of equation () while equations (8) are interpretations of equations (0), () and (). (8) a) Analytical solution. A closer look at equations (6), (7) and (8) reveals that the iniu value of f (x) e realied if the variales x and x take on the iniu possile values that they are constrained to take. Thus we can readily assign the following values: can only

44 x (9) 9 and x 6 The iniiation prole can then e reduced to the following. Miniie the following ojective function: x x x g( x) x (50) The iniiation should e suject to the following nonlinear equality constraint: x x 8 (5) Moreover, the iniiation should also e suject to the following linear inequality constraints: x x 6 6 (5) We can now otain an analytical solution to the prole, as follows. Using equations (50) and (5), we can readily otain the following single equation, in a single variale: 8 g( x) x x x x (5) For g(x) as expressed in equation (5) to have a iniu value, it follows fro the differential calculus that: Hence: d dx g( x) x 68x 0 x x x 0; x.6 (5) Fro equations (5) and (5), it follows that: x x.6 (55) Note that the solution given in equation (55) satisfies oth the nonlinear constraint of (5) and the linear constraints of equation (5). Thus, the gear train will e of iniu volue if:

45 x x x x x (56) Note that the odules of the gears in the first and the second stages of the gear train still have to e deterined efore the diensions and the tooth proportions of all the gears can e deterined. eterination of the odules will e done y considering gear tooth strength.

46 PART B.5 OPTIMIZATION THEORY FOR A TWO STAE NON-REVERTE COMPOUN EAR TRAIN. The scheatic diagra of a non-reverted two stage copound gear train is illustrated in Fig., elow. C C Fig.. Scheatic of a Non-reverted Two Stage ear Train For the non-reverted copound gear train, the centre distance fro the input shaft axis to the output shaft axis is given y: C () C C Moreover, it is coon practice to ake eshing gear wheels e of equal face widths. In that case: ()

47 A) Ojective Functions eterine the paraeters of the gear train nuers of teeth and intra-stage gear ratios,, odules, face widths that will iniie the total volue V of aterial used for the gear wheels (excluding shafts and other eleents), as well as the centre distance C. The design ust also satisfy all geoetrical, kineatical and strength requireents (constraints). In Fig., the nuers of teeth on the gear wheels are denoted,, and. Further, let us denote the corresponding gear wheel pitch diaeters y,, and. Then the odules of the gear wheels can e deterined as follows: ; ; ; As is well known, the odules of eshing gear wheels ust e equal. Therefore: () Now, the centre distances in the two stages ay e expressed as follows: C ; C Fro equations (), (), () and (5), it follows that: C () (5) (6) The intra-stage gear ratios can e deterined as follows: (7) Thus, fro equations (6) and (7), one can otain the following: 5

48 6 C (8) The volue of aterial required for the gear wheels ay e estiated to e the su of the volues of the pitch cylinders of the gear wheels. Thus: V (9) Fro equations () and (9), the following is readily otained: V (0) Fro the definitions of the intra-stage gear ratios, it follows that: and () Thus, fro equations (0) and (), the following is readily otained: V () Now, according to Oduori (00), a two-stage non reverted copound gear train will e of iniu volue for a given aterial, if: () Therefore, fro equations () and (), the following can e readily otained: V (a) Alternatively:

49 7 V () Moreover, fro the definition of odule, it follows that: (5) Therefore: V (6) Equation (6) ay e re-written in diensionless for as follows: V (7) At this stage, let us introduce the following notation for noralied volue and noralied face widths, as a atter of convenience:, V V n n (8) Then equation (7) ay e re-written as follows: V n n (9) Equation (9) will e one of the ojective functions to e iniied.

50 .6.THE CONSTRAINTS i) eoetric Constraints According to Juvinall (98), the face width of a gear wheel should lie etween 9 and ties the odule of the gear wheel. In the present case, this constraint ay e expressed atheatically, as follows: 9 9 n n Furtherore, according to Juvinall (98), gear wheels with standard 0 degree teeth should not have less than 8 teeth. This is the condition for avoiding undercutting for gear wheels that are produced y a generation process and is atheatically correct so long as the pinion eshes with a rack. However, according to Budynas and Nisett (008), the nuer of teeth on a pinion that will avoid interference is deterined as follows: k p sin i i () sin i In the aove equation, i is the speed ratio for a pair of eshing gear wheels, k is a factor that is equal to for standard full-depth teeth and 0. 8 for stu teeth, is the pressure angle and p is the nuer of teeth on the pinion. For full-depth teeth, if we ake 6 and i (0) 0 0, we find that 6. Matheatically, for the prole under consideration, this constraint ay e p stated as follows: 6 6 () ii) Kineatical Constraints Budynas and Nisett (008) recoend that the speed reduction ratio in a single stage of a copound gear train should not exceed : 0. Oonishi (988) recoends liiting the speed reduction in a single stage as shown in Tale.. 8

51 Tale. Recoended Maxiu Speed Reduction Ratio in a Single Stage Type of gear Low speed High speed Source: Oonishi (988) Spur :7 :5 Bevel :5 : We shall liit the axiu speed reduction in a single stage to e : 7. Bearing in ind that the gear train eing designed is a speed reducer, this leads to constraints that ay e stated atheatically as follows: 0. and 0. () The intra-stage gear ratios ust take on such values as to otain the required overall gear ratio of the train. This constraint ay e expressed as follows: () iii) Strength Constraints The odules and the face widths of all the gear wheels in the train ust e deterined so as to otain teeth of adequate strength. If the power and the speed at the input shaft are known, we can start y considering the ea strength of the gear teeth on the input pinions. a) Bea strength. ear tooth ending stress is given y: F t (5) py In the aove equation, Ft is known as the transitted force, p is the circular pitch and y is known as the tooth for factor. Now, fro their definitions, the circular pitch and the odule are related as follows: p (6) Therefore, fro equations (5) and (6), the following can e readily otained: Now, let us introduce the following notation: F y (7) t 9

52 Y y (8) Then, fro equations (7) and (8) the following can e readily otained: F Y (9) t The figure elow shows the pitch circles of a pinion and a gear in esh, along with the forces and torques that act upon the two gear wheels. T is the input torque at the pinion shaft and T is the load torque acting upon the shaft carrying the larger gear. It can e seen in figure. elow that: T Ft (0) F T F F t r F F F t r F F cos sin T F r F t Fig.. Forces Acting Between Two Meshing ear Wheels The power input at the pinion shaft is denoted H and can e expressed as follows: H () T Let us denote the pitch line velocity of the input pinion yu. Then we can write the following: 0

53 u Fro equations (0), () and (), we can write the following: () H F t () u Fro equations (8), (9) and (), we can write the following: H u Y n Y Siilarly, for the output stage pinion gear, we can write the following: H u Y n Y () (5) If we denote the allowale ending stress of the gear aterial y following: n a, then we can write the H a (6) Y u Siilarly, assuing that all the gear wheels in the train are ade of the sae aterial, we can write the following: H a (7) Y u n The pitch-line velocities, u and u, ay e expressed in ters of the input shaft rotational velocity as follows: u u (8) Thus, fro equations (6), (7) and (8), we can write the following:

54 Y H Y H n a n a (9) ) Wear strength. According to Buckingha and Oonishi, the liiting wear load for eshing gear teeth is given y: g p g p p v t KK F (0) Adapting this equation to the load on the input stage pinion, we can write the following: KK F v t () By using equations (7), (5), () and (), we can write the following: KK u H v () Siilarly, for the output stage pinion, we can write the following: KK u H v () Fro equations (8), () and (), we can write the following: KK u H n v () KK u H n v (5)

55 .7THE OPTIMIZATION MOEL We shall deonstrate the optiu design routine y designing a gear train that can transit kW of power at an input speed of 5.7 rp and with an overall speed reduction ratio of :8. The optiiation odel can e stated as follows. Miniie the following ojective function: f ( x) x x x x, x x x n x x (6) Since the required overall gear reduction ratio is :8, we can apply the following nonlinear equality constraint: x x 8 (7) Note that for equation (7) to hold true, if we set x 6 then x and vice versa. Therefore, the iniiation should also e suject to the following linear inequality constraints: 9 x 6 x x x Equation (6) is an interpretation of equation (9), equation (7) is an interpretation of equation () while equations (8) are interpretations of equations (0), () and (). (8) a) Analytical solution. A closer look at equations (6), (7) and (8) reveals that the iniu value of f (x) e realied if the variales x and x take on the iniu possile values that they are constrained to take. Thus we can readily assign the following values: can only

56 x (9) 9 and x 6 The iniiation prole can then e reduced to the following. Miniie the following ojective function: x g ( x) x (50) x The iniiation should e suject to the following nonlinear equality constraint: x x 8 (5) Moreover, the iniiation should also e suject to the following linear inequality constraints: x x 6 6 (5) We can now otain an analytical solution to the prole, as follows. Using equations (50) and (5), we can readily otain the following single equation, in a single variale: g( x) x x 8 x x (5) For g(x) as expressed in equation (5) to have a iniu value, it follows fro the differential calculus that: d dx x 8 x 8 g( x) x x 0 In the aove equation, x cannot e ero. Therefore: x 8 x 0; 8 j; x j (5) In equation (5) the solution is iaginary. This eans that an analytical solution to this prole, y use of the differential calculus, is not possile.

57 .8 CASE STUY A scheatic of the gear train is shown in the Fig., elow. Handle L Crank Ar Shaft Rope ru Bearing ear Train Load Fig..5 ear Train for a Manual Winch Tale. Case study values Effort to e applied at the handle y a single operator, F, (Newtons) 7 Load to e hoisted, W, (Newtons) 5,000 Length of the crank ar, L, (etres) 0.5 Efficiency of the power train,, (diensionless) 0.8 or 80% Cranking velocity, v, i (etres per second) 0. iaeter of the wire rope, d r, (illietres) 6 Source:-The taulated data was taken as a case study for a anual winch application. The torque applied to the crank ar, y a single operator, is deterined as follows: T i FL N 5

58 According Rudenko, a siultaneity factor of 0.8 is applicale when two operators turn the winch siultaneously. Therefore, for two operators, the input torque is deterined as follows: T i N The rotational speed at the input shaft is deterined as follows: i v i L The diaeter of the rope dru is deterined as follows: 0.6 rad 06 0dr The torque required to lift the load is deterined as follows: T o W 000 N The input power and the output power are related as follows: T o o T Now the overall gear ratio (speed transforation ratio) is deterined as follows: o i Ti T i i s.57 6

59 .8. THE REVERTE EAR TRAIN C C Fig..6 Scheatic of a Reverted Two Stage ear Train For a reverted copound gear train, the intra-stage gear ratios should all e equal. Therefore: 6.5 Since this is a low speed device, spur gears can e used with the aove speed ratio in a single stage. See Tale, elow. Tale. Recoended Maxiu ear Ratios in a Single Stage Type of ear Low Speed Operation High Speed Operation Spur :7 :5 Bevel :5 : Source: Oonishi Miniu nuer of teeth on the pinion in order to avoid interference To avoid interference, the point of contact etween the two teeth is always on the involute profiles of oth the teeth. According to Budynas and Nisett (008), the nuer of teeth required in the pinion in order to avoid interference is given y: 7

60 p i k sin i i sin In the aove expression: The value of the factor k is unity for standard full depth teeth and 0.8 for stu teeth. i is the speed ratio in the is the pressure angle i th stage of the gear train. p is the nuer of gear teeth on the pinion. Tale.5 ear Teeth Systes Serial Nuer Syste of ear Miniu Nuer of Teeth on Pinion 0 Coposite 0 Full depth involute Full depth involute Stu involute Source: R.S.Khuri The 0 0 stu involute is a strong tooth to take heavy loads ecause the tooth acting as ea is wider at ase. This tooth syste shall e used in this design. esign for ea strength Let the iniu nuer of teeth on the pinion e 6. The preferred standard odules are the following: Tale Tale.6 Standard Modules in Millieters p Preferred Next Choice Source: Shigley

61 eterination of odule. Taking the nuer of teeth on the pinion to e 6. For a anual winch that is operated y two persons, the transitted force at the input stage is deterined as follows: F t Ti The input power is deterined as follows: Ti H i T i i Watts The aove input power is supplied y two persons. The output power is deterined as follows: H o H i Watts The nuer of teeth on the larger gear in the first stage is deterined as follows: teeth According to the Lewis equation, the transitted force for adequate ea strength is given y the following relation: In the aove expression: F c y c is the allowale cyclic ending stress for the given aterial, is the face width of the gear, in illietres, is the odule of the gear teeth, in illietres, y is the Lewis for factor. t For the 0 0 stu teeth syste y Source:A textook of Machine y R.S.Khuri,J.K.upta 9

62 Therefore, for a pinion with 6 teeth: 0.8 y The face width of the gear is constrained to lie etween 9 and odules. Taking the face width to e equal to odules: If the gear aterial is taken to e a ray Cast Iron FC 0 (Japanese Industrial Standard) then: (ray cast iron FC 0,has a high caron content that akes it easy to elt, weld, achine and cast using coon etalworking processes. ray iron contains graphite flakes that provide a high level of staility and iniie shrinking during the casting process. The etallurgy of gray iron also akes it resistant to corrosion and low cost aking it ideal for our choice). c 88 MPa 88 N The transitted force can e expressed as follows: F t Ti Ti Therefore: Let us choose a standard odule of.5 illietres. We can now calculate the suitale face width as follows: 50

63 According to Juvinall(98) the face width of a gear wheel should lie etween 9 and tines the odule.i.e 9 Therefore a face width of will e used. With the aove gear diensions, the allowale transitted force will e: F ta N According to the aove results, the actual transitted force is 00 Newtons. Since F F t ta, the teeth will have adequate ea strength. esign against wear strength The axiu load that gear teeth can carry, without preature wear, depends upon the radii of the curvature of the tooth profiles and on the elasticity and surface fatigue liits of the aterials. The axiu or the liiting load for satisfactory wear of gear teeth is otained y using the following equation, which is known as thebuckingha equation. For external gears the equation takes the following for Source :Buckingha and Oonishi. F w KK p v g p g In the aove equation: Fw p is the liiting wear load in MPa or Newtons per square illietre, is the pitch circle diaeter of the pinion, in illietres, is the face width of the pinion in illietres, 5

64 p and g are the nuers of teeth on the pinion and the larger gear, respectively. The quantity denoted y K is known as the load stress factor and it is deterined as follows: K es sin. E p E g In the aove expression: es is the surface endurance liit in MPa, is the pressure angle, E p and E g MPa. The quantity denoted y are the oduli of elasticity of the pinion and the larger gear, respectively, in Kv is the velocity factor and the values are given in the Tale elow. Tale.7 Velocity Factors Application Pitch-line Velocity, v Velocity Factor, K v Type of Finish Low Speed Cut ear v5 s Mediu Speed Surface Finished ear v 5~0 s v v Machining Shaping Mediu Speed Cut ear v 0~ 0 s 5 Machined and 5 v round The anual winch is a low speed application and the velocity factor is deterined as follows:. 05 K v. 05 v 5

65 Fro the results otained in designing for ea strength: Tale.8 ear diensions. Z=Z Z=Z = v = Therefore:.5656 Q K v For rey Cast Iron FC 0 = 60MPa = = 0MPa = 0 Source:A textook of Machine esign y R.S.Khuri and J.K upta. = 60 sin = 6.5 = =.7 =.97 5

66 5 = = 55.98N The actual transitted force is 00 Newtons. Since Fw F t, the teeth will have adequate wear strength. The volue of aterial required for the gear wheels ay e estiated to e the su of the volues of the pitch cylinders of the gear wheels. Thus: V V = [0.0( ) + 0.0( )] =

67 .8. THE NON-REVERTE EAR TRAIN C C Fig..7 Scheatic of a Non-reverted Two Stage ear Train Tale.9 Recoended Maxiu Speed Reduction Ratio in a Single Stage Type of gear Low speed High speed Source: Oonishi (988) Spur :7 :5 Bevel :5 : For low speed spur gear, the axiu speed reduction in a single stage is :7. Bearing in ind that the gear train eing designed is a speed reducer, this leads to constraints that ay e stated atheatically as follows: () 0. and 0. The intra-stage gear ratios ust take on such values as to otain the required overall gear ratio of the train. This constraint is expressed as follows: 55

68 =. = 0.05 fro the exaple aove. = 0. = = 0.6 The transitted force can e expressed as follows: Therefore:. F 0.00 t Ti Ti Let us choose a standard odule of.5 illietres. We can now calculate the suitale face width as follows: According to Juvinall (98) the face width of a gear wheel should lie etween 9 and ties the odule. i.e 9 Therefore a face width of will e used. With the aove gear diensions, the allowale transitted force will e: F ta N 56

69 According to the aove results, the actual transitted force is 00 Newtons. Since F F t ta, the teeth will have adequate ea strength. esign against wear strength. F w p g KK v p g =.5 6 = 56 = = = 6 7 = + = 6 + =.75 = = N The transitted force Ft (00N) is less than wear strength ( ) for the first stage, hence the wear strength will e adequate. = = 0.6 = = = 98 + = =.79 = = 589.N The actual transitted force is 00 Newtons. 57

70 Since F t Fw, the teeth will have adequate wear strength for the second stage,. The volue of aterial required for the gear wheels ay e estiated to e the su of the volues of the pitch cylinders of the gear wheels. Thus: Tale.0 ear diensions. Z V V V 0.0 = Tale. Volues Type of ear Train Miniu Volue Two-stage Reverted Copound ear Train Two-stage Non-Reverted Copound ear Train

71 .9 AUTOCA RAWIN OF A REVERTE COMPOUN EAR TRAIN. Z L Z Z Z RUM Fig.8.rawing done using AutoCA inventor. 59

72 CHAPTER.0 EVELOPMENT OF COMPUTER AIE PRORAM FOR THE OPTIMIZATION MOEL.. INTROUCTION The design of the optiu copound gear follows a series of steps that guide the designer, ased on the ojective function iniiation analysis presented in the preceding chapter, to arrive at the optiu design required. This is then followed y the selection of the suitale, roust coputer progra fro which the correct algorith is generated for this particular project,we shall use MATLAB 0 prograing language to generate our algorith.. ESIN PROCESS STEP : Identify the power to e transitted y the gear train. ear drives are used to change the speed or direction of otion fro a prier over such as a otor to an output point that carries a load. In the process, the gear drive transits power. The power to e transitted plays a ig role in the deterination of the gear tooth ending stress, so that design against gear tooth failure is also taken care of. STEP : State the overall gear ratio,. The overall gear ratio is a necessary requireent, so that the nuer of stages to e eployed can e deterined.as a rough guideline, a train value of up to 0: can e otained with one pair of eshing gears. For instance, in a two stage copound gear train, each stage can e assigned a value equal to the square root of the overall train value. If the stage ratio so otained fails to eet the ration, a three stage copound gear should e conteplated and so on. Since our design liits us to only two stages, the overall gear ratio would then e useful in the deterination of the interstage gear ratios. STEP : State the speed of the input shaft,. The speed of the input shaft would e useful in the deterination of the interstage gears speeds (or angular velocities) and the final output speed y aking use of the interstage gear ratios. For the pinion gear, (rad/s) where, speed of the input shaft in rp. 60

73 STEP: Select the value of the noralied face width,. This is the ratio of the gear face width, to its odule, i.e.. It s a geoetric constraint whose nuerical values lies etween 9 and (9 ). STEP 5: Select the nuer of teeth, on the input pinion gear. This gives the nuer of teeth on a pinion gear that will avoid interference. Interference ay only e avoided if the point of contact etween the two teeth is always on the involute profiles of oth the teeth. STEP 6: eterine y differentiation, the iniu value of the ojective function,. The ojective function g( x) x x x x should e evaluated at iniu or critical points.fro the preceding analysis,the iniu value of x is siply the square root of the overall gear ratio,. STEP 7: Calculate the interstage gear ratios,. This is deterined fro the inverse of the iniu value of i.e. =. STEP 8: Calculate the pitch diaeter, of the pinion gear. Fro the preceding gear tooth noenclature, diaetrical pitch, is given y ; = (Teeth per inch) Since diaetral pitch is used only with U.S. Units, it is expressed as teeth per inch. STEP 9.Miniu pitch diaeter,. This is coputed y finding the quotient of the pinion diaeter, i.e. and the interstage gear ratio = STEP 0: Calculate the angular velocity =. This is the product of the angular velocity and interstagegear ratio. = (Rad/s) 6

74 STEP.Calculate the angular velocity,. This is now the speed of the output shaft. = (rad/s) = ( ) (Rp). STEP :Calculate the nuer of teeth of the output gear. Nuer of teeth of output gear = STEP :Calculate the odule of the gear wheels,. The odule of a gear wheel is given y; Μ = pitch diaeter nuer of teeth But for this particular optiiation prole, the odule of the gear wheels is the sae at each stage = ; =. STEP : Calculate the tooth face width, = = (c). This is the product of the noralied face width and the odule of the gear teeth i.e. = STEP 5: Calculate the MINIMUM VOLUME OF MATERIAL for the gears, V. The noralied volue is given y the expression V V = = 6

75 STEP 6: Calculate the MINIMUM CENTRE ISTANCE,C. The centre distance,c(= = ), is a function of the pitch diaeters of the gear wheels. = = Since this is a reverted copound gear train,at iniu volue, a iniu centre distance shall have siultaneously een attained. Therefore = STEP 7: Calculate the allowale ending stress of the aterial,. This is a strength constraint eant to protect the gear against tooth failure, It liits on the type of gear aterial to e used in ters of strength. a n H Y u Where =. = h 6

76 . ALORITHIM USE IN MATLAB An algorith is a self-contained step-y-step set of operations to e perfored. Algoriths exist that perfor calculation, data processing, and autoated reasoning. An algorith is an effective ethod that can e expressed within a finite aount of space and tie and in a welldefined foral language for calculating a function. Starting fro an initial state and initial input (perhaps epty), the instructions descrie a coputation that, when executed, proceeds through a finite [5] nuer of well-defined successive states, eventually producing "output" and terinating at a final ending state. The transition fro one state to the next is not necessarily deterinistic; soe algoriths, known as randoied algoriths, incorporate rando input. MATLAB is the high-level language and interactive environent used y illions of engineers and scientists worldwide. It lets you explore and visualie ideas and collaorate across disciplines including signal and iage processing, counications, control systes, and coputational finance. The MATLAB faily of progras include the ase progra plus a variety of tooloxes,a collection of special files called M-files that extend the functionality of the ase progra. The MATLAB environent can e descried as an interactive environent as a single line coands can e entered and executed,the results displayed and oserved,and then a second coand can e executed that interacts with the results fro the first coand that reain in eory. This eans that you can type coands at the atla propt and get answers iediately, which is very useful for siple proles. When a coand is entered that doesn t eet the coand rules, an error essage is displayed. The corrected coand can then e entered. While this interactive, line-y-line execution of Matla coands is convenient for siple coputational tasks, a process of preparation and execution of progras called scripts is eployed for ore coplicated coputational tasks. A script is list of MATLAB coands,prepared within a text editor. Matla then executes a script y reading a coand fro the script file, executing it, and then repeating the process on the next coand in the script file. Errors in the syntax of coand are detected when Matla attepts to execute the coand. A syntax error essage is displayed and execution of the script is halted. When the syntax errors are encountered, the user ust edit the script file to correct the error and then direct Matla to execute the script again. The literature algorith discussed in the section.can e written in Matla syntax script,and e executed in the coand window in a step y-step sequence,with the results produced at the end of each coand line. 6

77 .. Optiied reverted copound gear coand line Matla algorith. clc,clear foratshort%this coand alloys only up to 5 decial digits noralied_face_width=input('enter noralied face width:'); %propts the user to enter the value of noralied face width n=noralied_face_width overall_gear_ratio=input('enter the overall gear ratio:'); =overall_gear_ratio optiu_variale=sqrt(); x=optiu_variale inter_stage_gear_ratio=x =inter_stage_gear_ratio iniu_nuer_of_teeth_on_pinion_gear=input('enter iniu nuer of teeth on the pinion gear:'); =iniu_nuer_of_teeth_on_pinion_gear iniu_pitch_dia=(*.5) =iniu_pitch_dia iniu_pitch_dia=/ =iniu_pitch_dia speed_of_input_shaft=input('enter speed of input shaft,rpm:'); N=speed_of_input_shaft angular_velocity=(*pi*n)/60 w=angular_velocity angular_velocity=*w w=angular_velocity nuer_of_teeth=/ =nuer_of_teeth angular_velocity=*w w=angular_velocity %odule=/ =*.5; 65

78 %=odule iniu_face_width=n*.5 =iniu_face_width =n*.5 iniu_center_distance=(+)/ c=iniu_center_distance optiu_volue=pi/**(^+^) power_to_e_transitted=input('enter power to e transitted(kw):') H=power_to_e_transitted tooth_for_factor=0.5-(0.9/) y=tooth_for_factor allowale_ending_stress=*h*0^/(pi*n*.5^*0^-6*y*w*).. Optiied non reverted copound gear coand line Matla algorith clc,clear forat short%this coand alloys only up to 5 decial digits noralied_face_width=input('enter noralied face width:'); %propts the user to enter the value of noralied face width n=noralied_face_width overall_gear_ratio=input('enter the overall gear ratio:'); =overall_gear_ratio optiu_variale=sqrt(0.8795*); x=optiu_variale inter_stage_gear_ratio=x =inter_stage_gear_ratio =*.68 %=inter_stage_gear_ratio %inter_stage_gear_ratio=*.68 iniu_nuer_of_teeth_on_pinion_gear=input('enter iniu nuer of teeth on the pinion gear:'); =iniu_nuer_of_teeth_on_pinion_gear 66

79 = =/ =/ iniu_pitch_dia=(*.5) =iniu_pitch_dia = iniu_pitch_dia=.5* =iniu_pitch_dia =.5* speed_of_input_shaft=input('enter speed of input shaft,rpm:'); N=speed_of_input_shaft angular_velocity=(*pi*n)/60 w=angular_velocity angular_velocity=*w w=angular_velocity %nuer_of_teeth=/ %=nuer_of_teeth angular_velocity=*w w=angular_velocity %odule=/ %=*.5; %=odule iniu_face_width=n*.5 =iniu_face_width =n*.5 iniu_center_distance=(+)/ c=iniu_center_distance optiu_volue=pi/*(*(^+^)+*(^+^)) power_to_e_transitted=input('enter power to e transitted(kw):') H=power_to_e_transitted tooth_for_factor=0.5-(0.9/) y=tooth_for_factor allowale_ending_stress=*h*0^/(pi*n*.5^*0^-6*y*w*) 67

80 . RAPHICAL USER INTERFACE (UIs). The script file we have written has no interaction with the user,except y eans of the occasional input stateent. Modern users, however, have grown accustoed to ore sophisticated interaction with progras, y eans of windows containing enus, uttons, drop-down lists, etc. This way of interacting with a progra is called a graphical user interface, or UI for short(pronounced gooey ) as opposed to a text user interface y eans of coand-line ased input stateents. Fig.. raphical user interface. MATLAB has a facility called UIE (raphical User Interface evelopent Environent) for creating and ipleenting UIs. UIE stores a UI in two files which are generated the first tie you save or run the UI: A FI-file, with extension.fig, that contains a coplete description of the UI layout and the UI coponents, such as push uttons, axes, panels, enus, and so on. The FIfile is a inary file and you cannot odify it except y changing the layout in UIE. Note that a FI-file is a kind of MAT-file. An M-file, with extension., that contains the code that controls the UI, including the callacks for its coponents. Callack functions are written y you and deterine what action is taken when you interact with a UI coponent. UIE callack function prototype for each UI coponent you create. You then use the Editor to fill in the details. 68

81 .. THE REVERTE COMPOUN EAR TRAIN ( UI )COE function varargout = optiueartrain(varargin) % OPTIMUMEARTRAIN MATLAB code for optiueartrain.fig % OPTIMUMEARTRAIN, y itself, creates a new OPTIMUMEARTRAIN or raises the existing % singleton*. % % H = OPTIMUMEARTRAIN returns the handle to a new OPTIMUMEARTRAIN or the handle to % the existing singleton*. % % OPTIMUMEARTRAIN('CALLBACK',hOject,eventata,handles,...) calls the local % function naed CALLBACK in OPTIMUMEARTRAIN.M with the given input arguents. % % OPTIMUMEARTRAIN('Property','Value',...) creates a new OPTIMUMEARTRAIN or raises the % existing singleton*. Starting fro the left, property value pairs are % applied to the UI efore optiueartrain_openingfcn gets called. An % unrecognied property nae or invalid value akes property application % stop. All inputs are passed to optiueartrain_openingfcn via varargin. % % *See UI Options on UIE's Tools enu. Choose "UI allows only one % instance to run (singleton)". % % See also: UIE, UIATA, UIHANLES % Edit the aove text to odify the response to help optiueartrain % Last Modified y UIE v.5 07-Apr-05 ::58 % Begin initialiation code - O NOT EIT gui_singleton = ; gui_state = struct('gui_nae', filenae,... 'gui_singleton', gui_singleton,... 'gui_layoutfcn', [],... 'gui_callack', []); if nargin && ischar(varargin{}) gui_state.gui_callack = strfunc(varargin{}); end if nargout [varargout{:nargout}] = gui_ainfcn(gui_state, varargin{:}); else gui_ainfcn(gui_state, varargin{:}); end % End initialiation code - O NOT EIT % --- Executes just efore optiueartrain is ade visile. 69

82 function optiueartrain_openingfcn(hoject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hoject handle to figure % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % varargin coand line arguents to optiueartrain (see VARARIN) % Choose default coand line output for optiueartrain handles.output = hoject; % Update handles structure guidata(hoject, handles); % UIWAIT akes optiueartrain wait for user response (see UIRESUME) % uiwait(handles.figure); % --- Outputs fro this function are returned to the coand line. function varargout = optiueartrain_outputfcn(hoject, eventdata, handles) % varargout cell array for returning output args (see VARAROUT); % hoject handle to figure % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % et default coand line output fro handles structure varargout{} = handles.output; function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end 70

83 function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end % --- Executes on utton press in pushutton. function pushutton_callack(hoject, eventdata, handles) % hoject handle to pushutton (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) 7

84 angular_velocity=*pi*strnu(get(handles.textox,'string'))/60 set(handles.textox6,'string',angular_velocity); optiu_variale=sqrt(strnu(get(handles.textox,'string'))); set(handles.textox,'string',optiu_variale); %interstage=/x; %inter_stage_gear_ratio=/strnu(get(handles.textox,'string')); function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox5_Callack(hOject, eventdata, handles) % hoject handle to Textox5 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox5 as text % strdoule(get(hoject,'string')) returns contents of Textox5 as a doule % --- Executes during oject creation, after setting all properties. function Textox5_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox5 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called 7

85 % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox6_Callack(hOject, eventdata, handles) % hoject handle to Textox6 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox6 as text % strdoule(get(hoject,'string')) returns contents of Textox6 as a doule % --- Executes during oject creation, after setting all properties. function Textox6_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox6 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox7_Callack(hOject, eventdata, handles) % hoject handle to Textox7 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox7 as text % strdoule(get(hoject,'string')) returns contents of Textox7 as a doule % --- Executes during oject creation, after setting all properties. function Textox7_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox7 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. 7

86 if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end % --- Executes on utton press in pushutton. function pushutton_callack(hoject, eventdata, handles) % hoject handle to pushutton (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) =.5*strnu(get(handles.Textox,'string')) set(handles.textox,'string',) iniu_face_width=strnu(get(handles.textox,'string'))*.5; set(handles.textox8,'string',iniu_face_width) nuer_of_teeth=strnu(get(handles.textox,'string'))/strnu(get(handles.textox5,'string')) set(handles.textox7,'string',nuer_of_teeth) y=0.5-(0.9/strnu(get(handles.textox,'string'))) allowale_ending_stress=*strnu(get(handles.textox,'string'))*0^/(pi*s trnu(get(handles.textox,'string'))*strnu(get(handles.textox0,'string '))^*0^- 6*y*strnu(get(handles.Textox6,'string'))*strnu(get(handles.Textox,'st ring'))) set(handles.textox9,'string',allowale_ending_stress) iniu_center_distance=(strnu(get(handles.textox,'string'))+strnu(get (handles.textox,'string')))/ set(handles.textox7,'string',iniu_center_distance) %optiu_volue=pi/*strnu(get(handles.textox,'string'))*strnu(get(han dles.textox,'string'))^/*(+/strnu(get(handles.textox5,'string'))^) optiu_volue=pi/*((strnu(get(handles.textox8,'string'))*((strnu(get(h andles.textox,'string'))^+(strnu(get(handles.textox,'string'))^)))) ) set(handles.textox8,'string',optiu_volue) function Textox8_Callack(hOject, eventdata, handles) % hoject handle to Textox8 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox8 as text % strdoule(get(hoject,'string')) returns contents of Textox8 as a doule % --- Executes during oject creation, after setting all properties. function Textox8_CreateFcn(hOject, eventdata, handles) 7

87 % hoject handle to Textox8 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end Fig... Case study- run- progra. 75

88 .. THE NON REVERTE COMPOUN EAR TRAIN ( UI )COE function varargout = optiueartrain(varargin) % OPTIMUMEARTRAIN MATLAB code for optiueartrain.fig % OPTIMUMEARTRAIN, y itself, creates a new OPTIMUMEARTRAIN or raises the existing % singleton*. % % H = OPTIMUMEARTRAIN returns the handle to a new OPTIMUMEARTRAIN or the handle to % the existing singleton*. % % OPTIMUMEARTRAIN('CALLBACK',hOject,eventata,handles,...) calls the local % function naed CALLBACK in OPTIMUMEARTRAIN.M with the given input arguents. % % OPTIMUMEARTRAIN('Property','Value',...) creates a new OPTIMUMEARTRAIN or raises the % existing singleton*. Starting fro the left, property value pairs are % applied to the UI efore optiueartrain_openingfcn gets called. An % unrecognied property nae or invalid value akes property application % stop. All inputs are passed to optiueartrain_openingfcn via varargin. % % *See UI Options on UIE's Tools enu. Choose "UI allows only one % instance to run (singleton)". % % See also: UIE, UIATA, UIHANLES % Edit the aove text to odify the response to help optiueartrain % Last Modified y UIE v.5 9-Apr-05 :5:59 % Begin initialiation code - O NOT EIT gui_singleton = ; gui_state = struct('gui_nae', filenae,... 'gui_singleton', gui_singleton,... 'gui_layoutfcn', [],... 'gui_callack', []); if nargin && ischar(varargin{}) gui_state.gui_callack = strfunc(varargin{}); end if nargout [varargout{:nargout}] = gui_ainfcn(gui_state, varargin{:}); else gui_ainfcn(gui_state, varargin{:}); end % End initialiation code - O NOT EIT % --- Executes just efore optiueartrain is ade visile. function optiueartrain_openingfcn(hoject, eventdata, handles, varargin) 76

89 % This function has no output args, see OutputFcn. % hoject handle to figure % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % varargin coand line arguents to optiueartrain (see VARARIN) % Choose default coand line output for optiueartrain handles.output = hoject; % Update handles structure guidata(hoject, handles); % UIWAIT akes optiueartrain wait for user response (see UIRESUME) % uiwait(handles.figure); % --- Outputs fro this function are returned to the coand line. function varargout = optiueartrain_outputfcn(hoject, eventdata, handles) % varargout cell array for returning output args (see VARAROUT); % hoject handle to figure % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % et default coand line output fro handles structure varargout{} = handles.output; function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox_Callack(hOject, eventdata, handles) 77

90 % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end % --- Executes on utton press in pushutton. function pushutton_callack(hoject, eventdata, handles) % hoject handle to pushutton (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) angular_velocity=*pi*strnu(get(handles.textox,'string'))/60 78

91 set(handles.textox6,'string',angular_velocity); optiu_variale=sqrt(0.8795*strnu(get(handles.textox,'string'))); set(handles.textox,'string',optiu_variale); %interstage=/x; %inter_stage_gear_ratio=/strnu(get(handles.textox,'string')); function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox5_Callack(hOject, eventdata, handles) % hoject handle to Textox5 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox5 as text % strdoule(get(hoject,'string')) returns contents of Textox5 as a doule % --- Executes during oject creation, after setting all properties. function Textox5_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox5 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called 79

92 % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox6_Callack(hOject, eventdata, handles) % hoject handle to Textox6 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox6 as text % strdoule(get(hoject,'string')) returns contents of Textox6 as a doule % --- Executes during oject creation, after setting all properties. function Textox6_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox6 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox7_Callack(hOject, eventdata, handles) % hoject handle to Textox7 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox7 as text % strdoule(get(hoject,'string')) returns contents of Textox7 as a doule % --- Executes during oject creation, after setting all properties. function Textox7_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox7 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) 80

93 end set(hoject,'backgroundcolor','white'); % --- Executes on utton press in pushutton. function pushutton_callack(hoject, eventdata, handles) % hoject handle to pushutton (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) =sqrt(0.8795*strnu(get(handles.textox,'string'))) set(handles.textox5,'string',) =.5*strnu(get(handles.Textox,'string')) set(handles.textox,'string',) = set(handles.edit,'string',) =*.685 set(handles.edit9,'string',) =strnu(get(handles.textox,'string'))/ set(handles.edit0,'string',) =.5* set(handles.edit,'string',) iniu_face_width=strnu(get(handles.textox,'string'))*.5; set(handles.textox8,'string',iniu_face_width) nuer_of_teeth_=strnu(get(handles.textox,'string'))/strnu(get(handl es.textox5,'string')) set(handles.textox7,'string',nuer_of_teeth_) y=0.5-(0.9/strnu(get(handles.textox,'string'))) allowale_ending_stress=*strnu(get(handles.textox,'string'))*0^/(pi*s trnu(get(handles.textox,'string'))*strnu(get(handles.textox0,'string '))^*0^- 6*y*strnu(get(handles.Textox6,'string'))*strnu(get(handles.Textox,'st ring'))) set(handles.textox9,'string',allowale_ending_stress) iniu_center_distance=(strnu(get(handles.textox,'string'))+strnu(get (handles.textox,'string')))/ set(handles.textox7,'string',iniu_center_distance) %optiu_volue=pi/*strnu(get(handles.textox,'string'))*strnu(get(han dles.textox,'string'))^/*(+/strnu(get(handles.textox5,'string'))^) %optiu_volue=pi/*((strnu(get(handles.textox8,'string'))*((strnu(get( handles.textox,'string'))^+(strnu(get(handles.textox,'string'))^))) )) %set(handles.textox8,'string',optiu_volue) 8

94 p=((strnu(get(handles.textox,'string'))^+(strnu(get(handles.textox,'string'))^))) q=((strnu(get(handles.edit,'string'))^+(strnu(get(handles.edit,'stri ng'))^))) r= (pi/)*(strnu(get(handles.textox8,'string'))) optiu_volue=r*(p+q) set(handles.textox8,'string',optiu_volue) function Textox8_Callack(hOject, eventdata, handles) % hoject handle to Textox8 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox8 as text % strdoule(get(hoject,'string')) returns contents of Textox8 as a doule % --- Executes during oject creation, after setting all properties. function Textox8_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox8 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox9_Callack(hOject, eventdata, handles) % hoject handle to Textox9 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox9 as text % strdoule(get(hoject,'string')) returns contents of Textox9 as a doule % --- Executes during oject creation, after setting all properties. function Textox9_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox9 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB 8

95 % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox0_Callack(hOject, eventdata, handles) % hoject handle to Textox0 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox0 as text % strdoule(get(hoject,'string')) returns contents of Textox0 as a doule % --- Executes during oject creation, after setting all properties. function Textox0_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox0 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. 8

96 if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end % --- Executes on utton press in pushutton. function pushutton_callack(hoject, eventdata, handles) % hoject handle to pushutton (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) iniu_pitch_dia=strnu(get(handles.textox,'string'))/strnu(get(hand les.textox5,'string')) set(handles.textox,'string',iniu_pitch_dia); angular_velocity=strnu(get(handles.textox5,'string'))*strnu(get(handles.textox6,'string')) set(handles.textox5,'string',angular_velocity) angular_velocity=strnu(get(handles.textox5,'string'))*strnu(get(handles.textox5,'string')) set(handles.textox6,'string',angular_velocity) function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text 8

97 % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox_Callack(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox as text % strdoule(get(hoject,'string')) returns contents of Textox as a doule % --- Executes during oject creation, after setting all properties. function Textox_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox5_Callack(hOject, eventdata, handles) % hoject handle to Textox5 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox5 as text % strdoule(get(hoject,'string')) returns contents of Textox5 as a doule 85

98 % --- Executes during oject creation, after setting all properties. function Textox5_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox5 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox6_Callack(hOject, eventdata, handles) % hoject handle to Textox6 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox6 as text % strdoule(get(hoject,'string')) returns contents of Textox6 as a doule % --- Executes during oject creation, after setting all properties. function Textox6_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox6 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox7_Callack(hOject, eventdata, handles) % hoject handle to Textox7 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox7 as text % strdoule(get(hoject,'string')) returns contents of Textox7 as a doule % --- Executes during oject creation, after setting all properties. function Textox7_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox7 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB 86

99 % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function Textox8_Callack(hOject, eventdata, handles) % hoject handle to Textox8 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of Textox8 as text % strdoule(get(hoject,'string')) returns contents of Textox8 as a doule % --- Executes during oject creation, after setting all properties. function Textox8_CreateFcn(hOject, eventdata, handles) % hoject handle to Textox8 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function edit9_callack(hoject, eventdata, handles) % hoject handle to edit9 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of edit9 as text % strdoule(get(hoject,'string')) returns contents of edit9 as a doule % --- Executes during oject creation, after setting all properties. function edit9_createfcn(hoject, eventdata, handles) % hoject handle to edit9 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. 87

100 if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function edit0_callack(hoject, eventdata, handles) % hoject handle to edit0 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of edit0 as text % strdoule(get(hoject,'string')) returns contents of edit0 as a doule % --- Executes during oject creation, after setting all properties. function edit0_createfcn(hoject, eventdata, handles) % hoject handle to edit0 (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end function edit_callack(hoject, eventdata, handles) % hoject handle to edit (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of edit as text % strdoule(get(hoject,'string')) returns contents of edit as a doule % --- Executes during oject creation, after setting all properties. function edit_createfcn(hoject, eventdata, handles) % hoject handle to edit (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end 88

101 function edit_callack(hoject, eventdata, handles) % hoject handle to edit (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles structure with handles and user data (see UIATA) % Hints: get(hoject,'string') returns contents of edit as text % strdoule(get(hoject,'string')) returns contents of edit as a doule % --- Executes during oject creation, after setting all properties. function edit_createfcn(hoject, eventdata, handles) % hoject handle to edit (see CBO) % eventdata reserved - to e defined in a future version of MATLAB % handles epty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white ackground on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hoject,'backgroundcolor'), get(0,'defaultuicontrolbackgroundcolor')) set(hoject,'backgroundcolor','white'); end Fig...Case study- run- progra (Non- reverted copound gear train). 89