Question: Problem StatementThe Figure $1$below shows an electric motor driving a machine by means of three straight tooth spur gears required to have $16,32,$and $24$teeth with a diametral pitch of $8.$An idler gear is used to facilitate the smooth transmission of motion between gears and ensure that the output shaft rotates in the desired direction without changing

Problem Statement

The Figure $1$below shows an electric motor driving a machine by means of three straight tooth spur gears required to have $16,32,$and $24$teeth with a diametral pitch of $8.$An idler gear is used to facilitate the smooth transmission of motion between gears and ensure that the output shaft rotates in the desired direction without changing the speed ratio. The idler shaft is supported by bearings A and B $$as shown. The input shaft experiences a maximum $($operational$)$torque of $100$lb$.$in and angular speed of $1700$rpm$.$The gearset should have a $10-$year lifespan with $1-$shift operation. During operations, the gear temperature could reach maximum of $350$F$.$Utilize AGMA standard full$-$depth teeth to design a spur gearset. You are required to select suitable material and full$-$depth teeth parameters to ensure a minimum safety factor of $2$and $2$against bending and pitting failure, respectively.

Figure $1$illusterates the setup, where the electric motor is used to drive the machine through the idler gear.

Figure $1$: Electric motor, idler gear, bearings, and machine shafts.

The following assumptions and limitations must be applied during the design process.

The gear set is made of spur gears of commercial quality level $($the designer should take into consideration operating speed$).$

The gear set output and input nature of load should be carefully considered based on operation.

Assume $20$pressure angle and diametral pitch of $8.$

Both pinion and gear are made from the same material and hardness.

Interference must be avoided.

The minimum safety factor against bending and pitting should be $2$and $2,$respectively$.$

The minimum reliability is $0\mathrm{.}99,$and the gearset should have a $10-$year lifespan with $1-$shift operation.

f$.$Draw the free body diagram showing forces acting on the pinion, idler and gear. $\{$Hint: Refer to Shigley Ex$.13-7$for typical sketches$\}.$

g$.$Estimate the pinion, idler and gear diameters:

h$.$Estimate the required gear unit enclosure spacing by calculating center distance, volume, and deciding accordingly.

$6.$ The minimum safety factor against bending and pitting should be $2$ and $\backslash (\backslash$sqrt$\{\}2\backslash ),$ respectively.

$7.$ The minimum reliability is $0\mathrm{.}99,$ and the gearset should have a $10-$year lifespan with $1-$shift operation.

$8.$ During operations, the gear temperature could reach maximum of $\backslash (350^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$

Steps to solution:

a$.$ List the design constraints provided.

b$.$ List all assumptions or relevant information that must be identified to start the solution.

c$.$ Locate and indicate the input and output shaft gears in Figure $1.$

d$.$ From Figure $1,$ which one of the gears is the idler? Indicate on the sketch in c$.$

What are the benefits of using an idler in gear design? What are the limitations$?$