Design and Analysis of 2 - Speed gearbox for Bicycles

Design and Analysis of 2 - Speed gearbox for Bicycles Venu Akhil Kumar Parakala, Lucky Purushwani SMBS, VIT University, Chennai Campus, Vandalur-kelambakam road, Chennai-600127 ABSTRACT This paper sees the implementation of the transmission system of a common road vehicle to a bicycle. The design and analysis have been performed on a normal bicycle with standard dimensions. The gears used for the design are also standardized from those available in the market. The end results that we achieved is reduced effort by 57% for the rider, increase in speed at low pedalling rpm to around 138% and higher Torque by 133%. The transmission will be a small gear box attached to the pedalling shaft which will transmit power to the output shaft connected to the sprocket via a normal chain. A Factor of Safety of 5.68 has been obtained on analysis of design, thereby rendering our design safe for use. Keywords :- Bicycle Gearbox, Solidworks Modelling of Gearbox, GB ANSYS Analysis, Application of gears, Speed- Torque Converter and Gearbox stress strain analysis 1. INTRODUCTION There are two basic mechanisms of gear shifting in bicycles, either the cable moves a derailleur (front or rear) that physically moves a chain from one sprocket to another, or (simply put) it changes which gears are engaged inside the hub gears, the dis-advantage of this method is that the chain might slip from one gear to another at high speeds and sometimes leads to the chain coming off the sprockets, as experienced by most riders in practical situations. The other mechanism is by using non-electronic hub gears that change without cables, either by back-pedalling (duo-matic) or mechanical speed dependent (e.g SRAM Automatix), but this method is a bit expensive. So, to counter these problems we came up with a new design. In this paper we have designed a constant gear mesh for a bicycle. It consists of a gear box which has two gear ratios. A dog clutch engages with any of the output gears and provide the rotation to the output shaft. This is done to reduce the rider effort and help achieve a better output. A small gear box consisting of two gear ratios are mounted on the pedalling area. The input shaft of the gear box is connected to the pedal. By the use of idling gears we couple the input shaft to the output shaft. The output shaft is connected to the driving sprocket. The mechanism of shifting the gears consists of a dog clutch which is mounted on the splined portion of the output shaft. The gears are initially mounted on bearing to rotate freely on the shaft unless the dog clutch is engaged. Output shaft also consist of the spline on which dog clutch is free to rotate over the spline. Dog clutch is shifted by the help of brake wire which is connected to both ends of dog clutch. So say you want to shit the Dog clutch left to mesh with left gear then pressing the left brake will increase the tension in the brake wire and hence cause the Dog clutch to shift leftwards. Now, the gear and Dog clutch are meshed using synchro-mesh rings (the same as in the case of cars). Using the pre-determined gear ratios of 2.33:1 we have decreased the effort required by 57 % and output torque was increased by 133 %. With the gear ratio of 0.42:1 we will be able to achieve 138 % increase in output speed. This helps the rider by providing him greater torques, say during a hill climb or by providing a high speed at low pedalling speeds, say during plain road driving. Thus, he has to apply less effort for the same result and hence causes less fatigue. 2.STEPS INVOLVED Calculation of required gear sizes according to space constraints and required reduction in pedal effort. The standard gear sizes are chosen using the PSG Design Data Book. Checking the design constraints. Design of gears, shaft, cycle frame, bearing and sprockets is done using Solidworks. Assembly of all the components is done. Simulation and stress analysis using ANSYS has been done on every component, also keeping in mind the factor of safety. Volume 3, Issue 7, July 2015 Page 5

3.TECHNICAL SPECIFICATIONS 3.1 Gear dimensions Input gears: Gear 1 = 105 mm, Gear 2 = 45 mm Idling gear: Gear 3 (x 2) = 45 mm Output gears: Gear 4 = 45 mm, Gear 5 = 105 mm Module: 1.5 Gear ratios: 1st gear = 2.33:1, 2nd gear = 0.42: 1 3.2 Standards Used Bearing specifications ISO 15:2011 EN24 material used for frame ISO 9001: 2008 Alloy steel used for gear ISO `410-77I 4300-4.CALCULATIONS No. of teeth in large gear = 70 No. of teeth in pinion gear = 30 1st Gear ratio = 70/30 = 2.33:1 2nd Gear ratio = 30/70 = 0.42:1 Increase in output torque in 1st gear = (2.33T T)/T * 100 = 133% Reduction in effort in 1st gear = (2.33F F)/2.33F * 100 = 57% Increase in speed in 2nd gear = (N 0.42N)/0.42N * 100 = 138 5. SOLIDWORKS MODEL Figure1. Complete assembly of the cycle frame and gear box. Figure2. Sectional view of the gear box. Volume 3, Issue 7, July 2015 Page 6

The above two figures, i.e. Figure 1 and Figure 2 have been designed in Solidworks, a popular designing software among designers known for its simplicity, high design accuracy and analysis features. Figure 1 shows our gearbox will be installed in the available space. While, Figure2 gives a better view of the internal section of the gearbox. As it can be seen in Figure2 the centre gear in lowermost row of gears is our Dog Clutch while the gears on its left and right are the two gears that it connects with to give the desired speed and torque ratios. Say, the dog clutch moves to your left to connect with the left gear, then the immediate left gear being large will rotate at low speeds while the gears meshed to it being smaller rotate much faster than it giving us the increased speed. Now the vice-versa happens when the Dog clutch meshes with the right gear giving us a high Torque at the output. 6. SIMULATION RESULTS USING ANSYS Ansys is a popular software used for analysis purposes, it contains many predefined analysis that can be applied according to the boundary conditions involved in a design 6.1Pedalling Shaft- This simulation is for the input shaft and we obtain the factor of safety of the shaft material which is comes out to be 5.68, using the Ansys FOS. We calculated the force that acts on the shaft and we apply the load accordingly and then we ran the simulation to obtain the result. Factor of Safety obtained = 5.68 from Figure3. Figure3. Calculation of factor of safety 6.2 Shear Stress Analysis- This ANSYS simulation shows the shear stress that is induced on the surface of the input shaft and then after the simulation we obtained the maximum shear stress to be 86.39MPa from Figure4. Figure 4. Shear stress analysis on pedalling shaft Volume 3, Issue 7, July 2015 Page 7

Induced shear stress = 76 MPa x 5.6 = 425.6 MPa Allowable shear stress = 850 MPa Induced stress < Allowable shear stress The above is a must condition for a design to be considered as safe. 6.3 Total Input shaft deformation- This simulation result shown in Figure5 shows total deformation of the input shaft when we apply the load and the boundary conditions. The total input shaft deformation comes around 3.5*10-5 m. Figure5. Deformation analysis on pedalling shaft 6.4 Output Shaft- This simulation result show the factor of safety of the output shaft material which is comes out to be 6.14 as shown in Figure6. Figure6.Calculation of factor of safety Factor of Safety obtained = 6.14 6.5 Maximum Shear stress- This simulation result shows the maximum shear stress induced on output shaft when we apply the load on the input shaft. The maximum induced shear stress comes out to be 79.70MPa from Figure7. Volume 3, Issue 7, July 2015 Page 8

Figure7.Shear stress analysis on output shaft Induced shear stress = 79.7 MPa x 6.14 = 489.358 MPa Allowable shear stress = 850 MPa Induced stress < Allowable shear stress Again, the condition for a safe design has been met. 6.6 Total Output shaft deformation- This ANSYS simulation result shows total deformation on output shaft when we apply load and boundary condition. The maximum displacement comes out to be 5.29*10-5 m. Figure8.Deformation analysis on output shaft 6.7 Total deformation of Gear mesh system This ANSYS simulation result shows the total deformation in case of gear mesh system when we apply load and boundary condition. The maximum deformation is seen in the teeth of the smaller gear, which is around 2.86*10-6 m as shown in Figure9 given below. Volume 3, Issue 7, July 2015 Page 9

Figure9.Deformation analysis on gear system Induced shear stress = 80 MPa x 6.14 = 491.2 MPa Allowable shear stress = 850 MPa Induced stress < Allowable shear stress 7.DESIGN CONSTRAINTS Size of the gear box designed was made such that it does not interfere with the legs of the rider. Also, the proposed design should be ergonomic and must fit in the normal area without taking up too much additional space. Gears box has been chosen such that they do not increase the weight of the bicycle drastically. Gears has been designed in such a way that there is no drastic change in pedalling speed required. 8.CONCLUSIONS The Advantages of the design are - There is no chain slipping like in conventional gear cycle because there is no chain movement and the shifting only requires the shifting of the Dog clutch. This method can be used for more gear ratios and made customized as per the desired ratios by adding respective gears. Driver effort has been reduced while improving speed and power delivered. The limitations of the design are The costs will be higher than a conventional gear cycle. The design may cause confusion to a beginner due to the additional 2 brake wire controls along with the standard brakes control. 9.RESULTS The gear box for the bicycle has been designed according to the design constraints and keeping in mind the safety of the rider. The material EN 24 has been chosen such that it keeps the weight of the gear box to minimum and simultaneously provides strength for continuous loading cycles. As seen above the Design boosts the Torque by 133%, and increases speed by 138% leading to an overall reduction in effort required by 57%. According to the simulation results from ANSYS, the induced stress on the gear box components is lesser than the allowable stress of the material. The FOS of the pedalling shaft comes out to be around 5.68 and that of the output shaft around 6.14. Thus, we can infer that the design of this constant gear mesh system for bicycle will not fail at high loads and at the same time ease the input required by a the rider. REFERENCES [1.] Chinmay Kirtane Sachin Ghodke Dr.Shailaja Kurode Dr.Prakash A.K,Gear Shift Schedule Optimization and Drive Line Modeling for Automatic Transmission, Proceedings of the 1st International and 16th National Conference on Machines and Mechanisms (inacomm2013), IIT Roorkee, India, Dec 18-20 2013. Volume 3, Issue 7, July 2015 Page 10

[2.] JunQiang Xi JianMin MengHuiYan Chen,Research on Shifting Control Method of Positive Independent Mechanical Split Path Transmission for the Starting Gear, Mathematical Problems in Engineering Volume 2013 (2013), Article ID 191574. [3.] Hariharan_ME_Thesis, SPUR GEAR TOOTH STRESS ANALYSIS AND STRESS REDUCTION USING STRESS REDUCING GEOMETRICAL FEATURES, Thapar Institute of Engg. & Tech., 2006. [4.] Fredette.L and Brown.M, Gear Stress Reduction Using Internal Stress Relief Features, Journal of Mechanical Design, vol. 119, pp. 518-521, 1997. [5.] M. Naveena Reddy1 Dr. B.S.R.Murthy, GEOMETRIC MODELING OF ELLIPTICAL GEAR DRIVES, International Journal of Advanced Engineering Research and Studies. [6.] Ali Raad Hassan, Contact Stress Analysis of Spur Gear Teeth Pair, World Academy of Science, Engineering and Technology 58 2009. [7.] Mr. A. Gopi chand M.TECH(Ph.D) Prof. A.V.N.L. Sharma K. Pavan Kumar K. Sainath I. Aravind, Design of Spur Gear and its Tooth profile, International Journal of Engineering Research and Applications (IJERA). Books: [8.] Joseph Edward Shigley, Mechanical Engineering Design, McGraw Hill, 1986. [9.] PSG Design Data Book. Websites [10.] www.mit.edu [11.] www.wikipedia.org [12.] http://www.roymech.co.uk/useful_tables/drive/gears.html [13.] http://www.gearsandstuff.com/gear_ [14.] http://nptel.iitm.ac.in/courses/iit-madras/machine_design_ii/pdf/2_3.pdf Volume 3, Issue 7, July 2015 Page 11