Theory of Machines II EngM323 Laboratory User's manual Version I Table of Contents Experiment /Test No.(1)... 2 Experiment /Test No.(2)... 6 Experiment /Test No.(3)... 12 EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 1
Title: Gear Train Test Description: Experiment /Test No.(1) Experiment/Test Description In the following experiments the speed ratio is the subject being studied. Nevertheless some account will be taken of the direction of rotation as this can be changed independently of the speed ratio. Test Objectives: There are two main purposes for using a train of gears. The most important is to establish a speed ratio between two rotating shafts: the other is to transfer rotation from one axis to another with or without a change in the direction of rotation (that is clockwise or anticlockwise) Only simple spur gears will be used, although an introduction to the principles of epicyclic gear trains is included in an, elementary form. Hence there are several aspects of the application of gears and gear trains to be learned by doing this experiment.. Theoretical Background: - Gear train (Lecture) - Compound gears (Lecture) - Epicyclic gear train (Lecture) Equipment and tools: Experiment/Test Activities - The unit comes fully assembled with the spares (spare pin for compound gears and spare spacer on rear gear pin) situated onto the unit itself. No further assembly work is required other than preparing the unit for the first experiment. Gear train apparatus EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 2
- A pivoted arm mounted on a horizontal base carries three movable gear pins on which four interchangeable spur gears can be arranged. All gears can be pinned together in order to assemble a compound gear train using the small pins supplied. - The pivoting arm can be locked in position for gear train work using the locking device at the non rotating end of the arm. Alternatively it can be rotated about its pivot to simulate the planet arm of an epicyclic gear system. The spur gears have 40, 60, 80 and 100 teeth and a module of 1. - The arm has a series of threaded holes into which each gear pin mounts. The series of holes allows many ratios to be made up from the gears supplied. All gears and gear pins have been checked for free running when fixed to the arm, but a light drop of oil from time to time will ensure continuous free running. - 3 spacer blocks are provided to ensure all gears mesh at the correct height when running in a compound gear train arrangement. A spare spacer and joining pin are supplied. At the rear of the base is a locating pin with wing nut for securing any spare gears and spacers when not being used. Test Procedure: There are two separate experiments to be performed on this apparatus, one on gear trains and the other an introduction to epicyclic gears. 1. Simple gear trains Simple gear trains - Assemble a two wheel gear train with the 80 tooth wheel as the driver: on the fixed pivot as shown in the image above. - Ensure the arm is in its locked position. Add the 40 tooth gear as the 'driven follower' so that it meshes with the driver gear. - A spacer will be required on top of both gears as shown. Mark the teeth of both gears at the point where they mesh using a pencil. - Turn the driver through one revolution clockwise (+ve) and note how many full revolutions (and parts of a revolution) the driven follower wheel completes. - As an alternative keep turning the driver through enough complete revolutions for the two marks to come together again, and note the corresponding number of complete turns of the driven wheel. - Record the direction in which the driven follower wheel rotates. EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 3
- Repeat the above procedure using the 60 and 100 tooth gear wheels, in turn, as the driven followers. Three wheel gear train - Next assemble a three wheel gear train as in the image above with the 80 tooth as the driver and the 60 tooth wheel at the end of the train and the 40 tooth in the middle of the two (idler). Spacers will be required on top of all" gears as shown above. - Note the initial positions of marks on the driver and final wheel of the train, and then determine the turns ratio by rotating the driver 1 revolution clockwise (+ve). Also note the direction of rotation of the final wheel when the driver turns clockwise. Repeat the above procedure with the 100 tooth gear as the 'final'. 2. Compound gear trains Compound gear trains - Position the 100 tooth gear as the driver with a spacer on top of it. Join the 40 and 60 tooth gears using the small pins supplied, to create a compound gear, with the 40 tooth gear uppermost and the 6Otooth gear lowermost and meshing with the 100tooth driver. - Add the 80 tooth gear so that it meshes with the 4Otooth gear. A spacer underneath the 80 tooth gear will be required. EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 4
Test Results: Compare the experimental results with the theoretical predictions For the three gears train, The compound gear train is resolved in a similar manner. Let the first driver and follower be designated A and B, and the second set C and D. Then Conclusion: - Comments:. EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 5
Experiment /Test No.(2) Title: CAM AND FOLLOWER SPECIFICATIONS Test Description: Experiment/Test Description A vertical stem attached to an aluminum base plate has a fixed spigot on which the reamed hole in each cam is mounted while the cam is turned by hand. The fixed spigot for the cams is at the centre of a circular protractor numbered 0 to 360 both clockwise and anti-clockwise. Above the cam is a guided push rod at the bottom of which the various designs of follower are attached. At the top of the push rod a 50 mm travel dial gauge is located into the side of the grooved extrusion so that the initial reading of the dial gauge can be pre-set. To the left of the vertical stem is a mounting containing a protractor bracket with a 100 mm long lever to hold the roller follower on the cam. Each cam has a second hole, which enables a pointer assembly to be temporarily attached to it. The assembly carries a pointer to indicate the cam rotation on the circular protractor. Test Objectives: - Determine the follower displacement against angular rotation of a cam. - Drive the velocity and acceleration diagrams - Study of uniform motion cam with a roller follower. - Comparison of a roller follower and lever roller follower on a tangent cam - Comparison of a range of followers on an eccentric circular cam - Comparison of SHM and constant acceleration cams with a roller follower Theoretical Background: - CAM design, UA, (Lecture) - CAM design, SHM, (Lecture) - CAM design, UV, (Lecture) Experiment/Test Activities Equipment and tools: Equipment of the experiment: - Extruded base and vertical pillar - SHM, UV, UA cams - followers include roller, knife edge, offset - Angular protractor graduated from 0 to 360 deg. in 1deg increments - Dial gauge with 50 mm travel, 0.01 mm resolution EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 6
Test Procedure: Experiment set-up 1. Mount the pointer on the tangent cam at the small end and fit the two parts on the fixed spigot while lifting the roller follower out of the way. Set the pointer to zero on the protractor. Adjust the position of the dial gauge to give a reading of 1.00 (for a final fine adjustment use the movable scale of the dial gauge). 2. Rotate the cam clockwise by 150 increments up to 1200 taking readings of the push rod displacement at each position. Then take readings every 5 of rotation up to 240. Finally revert to 15 increments to complete one revolution of the cam. 3. Remove the roller follower :from the push rod and lift the rod up to lodge it on the bottom guide. Fix the lever follower in position and attach the roller to the threaded hole at the end of the lever. With the cam stationed at 0 rest the roller on the edge of the cam and zero the pointer on the lever rotation scale. Note whether the roller is exactly in line with 0 o on the cam or not as this will affect the symmetry of the readings. 4. Rotate the cam for one revolution by 15 increments, reading the angular displacement of the lever at each step. Test Results: - Plot the push rod displacement against the cam rotation on a full scale graph. If the lever roller follower was used plot the angular displacement on the same graph (the scale used for mm can be used for degrees). - Draw what appear to be good curves through the points. Bear in mind that the lever rotation is a crude measurement (perhaps to 0.25 o ) compared with the dial gauge readings. EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 7
Recording the displacement of the follower EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 8
SHM - CAM - If it is required to study the velocity and acceleration of the push rod there are two methods both entailing a lot of calculation. Assuming the cam was being driven at a constant speed then it follows that the cam rotation scale is also time to some scale. Hence the velocity of the push rod is the gradient of the plotted graph. A crude estimate might be made by drawing tangents to the graph curve at various points to permit a velocity against rotation (time) graph to be constructed. The exercise would then have to be repeated to obtain an acceleration graph which would obviously be very approximate. Alternatively use could be made of first differences between the displacement readings whereby EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 9
Uniform Velocity CAM EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 10
Conclusion: Uniform Acceleration CAM - CAM profiles can be experimentally verified, more accurate profiles can be obtained using fine recording resolution. Comments: One disadvantage experimentally is that friction in bearings may affect displacement, force and energy measurements. The other is that large changes in dimension (geometry) of models must be accommodated if possible. Results can be improved by using stiffer models and larger loads, but this reduces visual effects such as curvature of beams and may make the experiment less manageable. EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 11
Title: Dynamic Balancing Test Description: Experiment /Test No.(3) Experiment/Test Description The experiment model enables to reproduce, visualize, analyze and measure vibration phenomena linked to unbalanced wheels, all whilst simulating the functioning of a balancing machine. Test Objectives: - Training the students to calculate the unbalancing of rotating masses. - Practice the students to record the measured strain data, in order to identify the vibration resulting from rotating masses. - Balance unbalanced system of rotating masses in different planes. Theoretical Background: - Balancing of rotating masses in single plane (Lecture) - Balancing of rotating masses in multi-plane (Lecture) - calculating the force and moment balance (Lecture) Equipment and tools: Experiment/Test Activities A rotor assembly, made up of a shaft and four platforms, mounted on a flexible connection with the support manually rotated. One-off loads can be fixed on these platforms in order to unbalance or rebalance the system. More other different non-balanced parts can be fixed on the rotor in place of the first platform. Principal diagram of the model EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 12
Shaft : length between shaft bearings: L = 180 mm weight = 0.65 kg Platforms: Experiment set-up Platforms : PI and P4 are identical, so are P2 and P3. The platforms P2 and P3 consist of an interior rim on which balanced weights can be stuck on. Diameter : 180 mm Thickness: 10 mm Weight : PI and P4 : 660 g P2 and P3 : 780 g Platform position (data by their y-axes marked (O,X,Y,Z) : PI : YI = -240 mm P2 : Y2 = -160 mm P3 : Y3 = 160 mm P4 : Y4 = 240 mm Position of weight fastening holes : r = 80 mm r' = 40mm Sticking radius for weights on P2 and P3 : R = 90 mm Test Procedure: - The base plate of the experimental bench has 4 drilled holes so it can be fixed onto a support or on the ground. This support can be a wooden housing filled with sand or with another material to give it a substantial weight. If the experimental bench is not withheld by a fixed and very rigid support, it is possible that the sensors will measure the deplacements (interfering vibrations) not caused by the system studied. Wrong measurements lead to false calculations and no reasoning can then be applied to the experiments carried out. EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 13
- install the software "Instacal" by running the setup.exe file situate in the folder 'Acquisition card.' It is possible that at the end of the software installation you have to reboot your computer. - To run the program Instacal program from the menu Start / Program / Measurement Computing - Connect the flex linked to the bench at the subd15 terminal 'SENSOR IN' on the EX175 unit. - Connect the EX175 unit (sub D9 terminal 'ANALOG OUT') to the PCI-DAS08 card, in the PC, using the subd9- subd37 cable. - Use the 2 remaining subd9-subd9 and subd15-subd15 cables to connect to the EX175 unit at the EI616 strain gauge testing drive. - Place a bob weight on the same platform and in the same position as for the simulation using the VIBROTOR software: Platform P3 Weight 30g, Position: r = 80cm, a =0 - Click on 'Excitation of the resultant type -Weaken the spring blades by exerting a force equally spaced on the two shaft bearings. -Allow the rotor and shaft assembly to vibrate Test Results: The software interface should like as, SIMULATION FROM VIBROTOR SOFTWARE -Start the acquisition (Button 'start acquisition'), The movement of the shaft bearings is shown in actual time on the screen. EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 14
Measured vibration Also the rotation speed is shown in the momentary zone. Stabilization must be carried out at a speed higher than about 100 t/min at the measuring speed in order to obtain a good measurement. the Speed at which the measurement is released is given in the measurement zone. Once the measurement has been done (during the measurement around 180 ms), the screen shows the maximum amplitude measured in Newtons for each channel (load on the shaft bearing A and B), as well as the phase difference associated with 'zero' platforms. Conclusion: The graph shows the variation of the horizontal load component for the shaft bearing A and B, as well as the curve 'toptour', the corresponding peak from zero of the platform. The phase difference shown for the shaft bearings A and B is calculated from the 'blip', phase difference 0, the value from the signal period is equal to the time passed between the two blips. Comments: EngM323 Theory of Machines II Instructor: Dr. Nada A. A. Page 15