Question

power = 3 kW
if need any more information please ask !!!

You are the designer and you have been asked to design a speed reducer (gearbox) that will take power from the shaft of an electric motor rotating at 1500 rpm and deliver it to a machine that is to operate at approximately at 200 rpm Assume that you have decided to use spur gears to transmit the power [A power equal to the last one digits of your student number in kilowatts, eg. Power-3 kW for a student # 2012298043, if the last digit is zero you can take the digit before the last digt] and you are proposing to use a two stage speed reducer like the one shown in Figure 1. PinionA Gear D Shaft 1 Shaft 3 IN OUT 75 mm 75 mm Shaft 2 Pinion C Gear B Housing Figure 1 Speed Reduction Gear Box Layout The input shaft (shaft-1) is coupled to the motor shaft. The first gear of the gear train is mounted on this shaft and rotates at the same speed as the motor (nn-n" 1500 rpm) Gear- A drives the mating gear (gear-B) which is larger, causing the speed of rotation of shaft-cd to be slower than shaft-1. It is noted that the speed is not yet down to 200 rpm as desired. [That helps explain the need for a double-reduction train set. This is because a compact gearbar is needed!] The next step is to mount a third gear (gear-C) on shaft-2 and mate it with gear-D mounted on the output shaft (shaft-3). With proper sizing of all four gears, you should be able to obtain an output speed equal or quite close to the desired speed [not = ~205 rpm.] Each of the shafts are supported by two ball or roller bearings that need to be specified by you [there are six bearings to be selected by the designer!) An overall reliability of 95 %, and a design life of 20000 h are desired Important parameters of each gear o The number of teeth, o The size of the teeth as indicated by the module, m [mm.] a The face width of the teeth, F [mm.] (FAB is not necessarily equal to Fco) o The pitch diameter (dp)for each of the gears, [mm.] o The means of attaching the gear to its shaft (such as: keys and keyways) o The means of locating the gear axially on the shaft (collars, retaining rings etc.) The degree of precision of the gear teeth (You will need to decide on Qv based on the pitch line velocity V of the pair (Noting that VAB VcD) o SOME MAJOR TASKS EXPECTED FROM YOU AS A DESIGNER: Determining the number of teeth for each gear: Knowledge of kinematic analysis of geared mechanisms is required. You will refer to your Class-Notes and Chapter 12 of your text, and understand the concept of 'velocity ratio' and leam the techniques of designing double-reduction gear trains. 1. Analyzing the forces on gears and shafts: Force analyses are to be made based on the power transmitted by the gear system. You will need to determine the loads acting on the teeth of each gear pair, i.e. the transmitted load Wt, and the radial load Wr need to be determined for each gear pair. For example, for gear pairAB. (W) AB, and (WAB and for the pair formed by gears C and D, (W) cD, and (W) co, must be calculated and shown on their respective shafts. (You may start with taking Ф-20) 2. 3. Determining the stress acting on the gear teeth and selection of material to withstand these stresses safely are other important tasks. You may take a factor of safety of 2 for this purpose. These will require the determination of face width F and the module m for each pair. This may require a trial-and-error approach. (recall that pitch diameter ofa gear is: d = m N) 4. You must also be able to draw the shear and bending moment diagrams, as well as drawing the free-body diagrams and calculating the reactions at the supports (Statics) A good understanding of the subject matter covered in Chapters 3 and 10, as well as within your class-notes. Since the shafts must be able to accommodate all the elements within the range of the supports, you must assign proper length dimensions for each of the shafts, considering the arrangement of the elements and allowing space for the width of each bearing. (This is important and should be checked later, as the width of the items will finally be decided.) Based on the given data and the reactions found, you will select bearings for each of the supports. You will need to choose an appropriate load application factor, chapter 11. In this selection, the design life, the design speed, and reliability requirements should all be considered. Note that the speeds of the shafts are not the same Based on the given data and the reactions found, you will select bearings for each of the supports. You will need to choose an appropriate load application factor, chapter 11. In this selection, the design life, the design speed, and reliability requirements should all be considered Note that the speeds of the shafts are not the same. 5. 6. From the bending moment diagrams obtained in task # 4, and after calculating the torque transmitted by each one of the shafts, you will select materials for the shafts and design the shafts. A factor of safety of 2.0 seems to be appropriate. Note that the diameter of the shaft will not be constant. There wll be some keyways and/or shoulders on each of the shaft creating stress concentration, which need to be considered. Trial and error approaches, therefore, may need to be followed. 7. You are to size the keys and keyways for the application, which also requires selection of materials for the intended application. [Chapter 7 in your textbook] A scaled drawing of the entire system will have to show all elements of the gearbox including its housing 8. 9. Make a tabular summary of your results. Grade Sheet 25 points Gears design: Load determination is reasonable Bending and wear factors of safety are minimized. Gears face width, m and Qv are reasonable. Material selection is discussed. Shaft center-distance constraints met. Contact Ratio acceptable. Bearing design: Bearing forces correctly resolved Bearing sizes are consistent with other calculations Correct procedure used to find Fe and C1o- Co criteria met. Shaft design: Fatigue and yield factors of safety are met Stress concentrations are included. Shaft material selection discussed Shafts fit the bearings Shafts constrained axially Bearings constrained axially to the shafts. Ke: Comect c Correct calculation method used for shear and crushing Slot size and depth reasonable. Factors of safety are adequate. Weakest link is an appropriate fail-safe Housing Housing is reasonable to make as a prototype. Designed so that all components can fit and be assembled. Feet designed to hold bottom of box to frame. Bolt holes sized appropriately in mm. Bolt size and grade selection for mm

Answer 1

By approximation and to make the calculations smooth I've taken no of teeth on Gear A as 60 and Gear B as 90. By using gear ratios I've determined the following, $T_A=60$,
TB = 90
, $T_C=20$, $T_D=100$ calculations in the image below.

6 2 7

Next is determining the size of gears, Gears A and B need to be of the same face width and C, D should have same face width, i.e.,
FA = FB = 25mm
and
20mm
(by trial and to easy with calculations)

First is the pitch diameter, p, below are the calculations for the same (for the module, m, I've referred Machine Design Data Book by V B Bhandari)

module, m- loo 2 mm her CD eeT 20

Since the minimum no of teeth are 20 (>17) we can go with $20^o$ full depth involute system which is widely used thus manufactured at low cost as tooling is easy to acquire.

Gear Data is as follows

Dimension	Value
Addendum	$h_a=m=2mm$
Dedendum	$h_f=1.25m=2.5mm$
Clearance	-0.25m 0.5mum
Working Depth	$h_k=2m=4mm$
Whole Depth	h 2.25m 4.5mm
Tooth Thickness	$s=1.5708m=3.1416mm$
Tooth Space	1.5708m-3.1416mmm
Tooth Fillet	$0.4m=0.8mm$

After gears, it is the shafts and keys/keyways that are to be determined.

Shaft 1 and 3 can have a higher diameter than Shaft 2 as the smallest Gear C on it is only 40mm in diameter, so having a diameter of 22mm (standard size from databook) would be optimal, and other two would be good at 44mm (standard size from databook).

For both of these, the keys/keyways are as follows

Shaft size\dimension	key width	key depth	keyway depth in the shaft	keyway depth in gear	key length
22mm	6mm	6mm	3.5mm	2.8mm	18mm
44mm	14mm	9mm	5.5mm	3.8mm	36mm

Due to the time constraint more than this can't be covered in one go, to save time submit this data and you can go further into the designing the gearbox.

The data which has not been calculated is obtained from Machine Design Data Book by V B Bhandari except the determination of gear ratio between Gear A and B.