02 May QuestionDesign Of Mechanical Components Project
Question
Design Of Mechanical Components Project
Proposed Project: MANUAL TRANSMISSION DESIGN
BACKGROUND:
The basic transmission is connected to an engine shaft. Inside the transmission, this shaft is in turn connected to another shaft (layshaft) via two gears. The layshaft is in turn connected to a differential drive shaft (which is the main shaft that eventually runs the wheels of the car) through a series of another set of gears. The engine power causes the engine shaft to turn at a specified velocity (rpm = revolutions per minute) which in turn causes the other shafts to turn and eventually cause the vehicle to move. Thus, a set of four gears is needed to cause the car to run at a specified velocity and there are five sets of these gears inside the transmission, each one designed to cause the vehicle to move at specified speeds. When a person switch the lever (commonly known as “switching gears”), he/she is actually switching a set of four gears and thus he/she changes the velocity of the vehicle. A full five speed transmission requires five sets of four gears in addition to an extra set of gears to account for the reverse speed of the vehicle. The design of this basic transmission is time consuming. There are some issues that an engineer has to resolve: a) The required velocity (rpm) for the differential drive shaft has to be met, b) the engine shaft has to align properly with the differential drive shaft (otherwise the transmission will jam and collapse during high velocities), c) the gears have be reliable and not interfere with each other d) the shafts have to be able to withstand the loads imposed upon them and not bend, etc.
This basic transmission is designed in four stages. The first stage deals with determining the dimensions of the appropriate set of gears that will meet the needed requirements: a) correct power output (rpm is related to power) at each gear shift b) maintaining the alignment of the transmission shafts. The second stage deals with determining the material that will be used to make these gears. This including analyzing the points of possible gear failure and analyzing the gears for possible interference. (Basically, we want to ensure a smooth operation, reduce wear and tear, and design a reliable system.) The third stage consists of analyzing only the reverse gear set. This set is different from the other sets and it requires it own set of calculations to determine whether the vehicle will operate nicely while in reverse. (If not properly designed, the vehicle can speed up so fast in reverse that it can crash into something.) The fourth stage consists of analyzing the loads imposed on the shafts. (The shafts should not bend or break during the operation of the transmission.)
Part I-GEAR SELECTION FOR DIFFERENT GEAR MODES
For this particular transmission, the engine is 3.50 Hp engine that provides 4000 rpm. Transmission shaft length = 4 feet, differential drive length is 6 feet. Bending Strength <= bending strength of material selected, contact strength <= allowable contact strength of material. The first part of the project is the selection of four set of gears that will provide the correct rpm output in the differential shaft. Note that that the distance between the differential shafts and the layshaft for all four set of gears have to be the same. Note that for two gears to mesh, they have to have the same Pd.
When the stick shift is selects the first gear, the driven shaft output should be 1300 +- 200 rpm.
When 2nd gear is selected, the driven shaft output should be 1900 +- 200 rpm.
When 3rd gear is selected, the driven shaft output should be 2500 +- 200 rpm.
When 4rth gear is selected, the driven shaft output should be 3000 +- 200 rpm
When 5th gear is selected, the driven shaft output should be 3500 +- 200 rpm
a) For each pair of gears compute the contact ratio (should be >=1.2) and check for gear interference.
Part II-STRESS ANALYSIS ON GEARS
For each gear selected, compute:
b) Tangential Force, Radial Force, Normal Force, Torque.
c) Check that Face width of gear tooth falls in 8/Pd < F<16/Pd range to minimize alignment problems. You can estimate Face width by F=12/Pd.
For the input pinion/gear pair,
d) compute the bending stress using Equation 9.16 and compute the contact stress number using equation 9.23. This gear set is expected to be under the most stress.
e) Determine the appropriate material for the input set of gears. Table 9.9 and Table 9.10 specifies the allowable bending stress numbers and allowable contact stress numbers for different materials. Equation 9.25 and 9.26 adjust these allowable stress numbers to account for safety factor, reliability, and design life. Reliability should be 0.9999. Operational use is five day per week operation, for two hours.
f) For the material chosen for part e) determine the safety factor for the pinion, for the gear the material chosen for bending stress. Determine the safety factor for the pinion and for the gear based on the material chosen for contact stress. (Refer to page 399).
PART 3-DESIGNING THE REVERSE GEAR SET.
a) Once you have found all the set of gears needed for every one of the gear selection modes, the design of the reverse gear can begin. As you may have noticed, all the previous set of gears caused the differential shaft to rotate in one direction. Now it is time to make this shaft shift in the opposite direction and you can do this by inserting a trio of gears labeled A, B, and C. Select a trio of gears that will have the same equivalent “c” value as given by the following equation:
C= (da/2 + db + dc/2) where da, db, and dc are the diameters of the pitch circles for gears A, B, and C respectively. Try to select a set of gears where the output rpm is minimized. (If this transmission was in your car, you wouldn’t want the car to go crazy on you each time you shifted to reverse.).
b) Test these trio set of gears for contact strength, bending strength, interference, and CR ratio. Test a pair of gears at a time.
c) Determine the volume of each gear (including the ones that are not part of the reverse trio set). The diameter of the pitch circle can be used to estimate the volume of the cylinder with width w (from part II). The diametrical pitch (Pd) tells how many teeth are per diametral pitch. So if you have N teeth, you know that they are situated along a circumference =2*pi*r. The side of each tooth is therefore (pi*(pitch dimaeter))/N. The width is w (from part II). You can model each tooth as a box with the height = 2*a where “a” is the addendum a=(1/Pd)
d) Once you find the entire volume for each gear, find its weight. This weight will obviously depend on the material chosen and will be modeled as a static load on the shafts (Part IV of transmission design).
PART IV—FINAL PART OF TRANSMISSION PROJECT.
After selecting the gears to move the vehicle forward and the reverse gear set, the final project involves analyzing the shafts for the loads that will be subjected to.
a) The Engine shaft will be under the stress of one set of gears. Decide what material the shaft will be made out. Model the weight of this shaft made out of this material as a distributed load. Model the load exerted by the gears on the shaft due to rotation and to weight of the gears. Create the necessary L(x) , V(x), and M(x) equations for one x-y plane and then for the x-z plane and construct the T(x) equations for this shaft. All these equations needed to be plotted using the singularity function. Apply the Soydenberg Criteria to determine if this shaft will be strong enough to hold the loads. Create the associated v(x) (deflection diagram) to determine the amount of deflection too.
b) Repeat part a for the other two shafts. In order to be complete, all shafts should be able to pass the Soydenberg Cr
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