(Solved): We need to perform some analysis on the helical gears of the gearbox shown below. 1- We intend to i ...

We need to perform some analysis on the helical gears of the gearbox shown below. 1- We intend to increase the rotation rate from the input to our output 42 times. The first gearset has a gear ratio of 7 and the second gearset has a ratio of 6 . The gears have a normal module of $2.5\mathrm{mm}$, a normal pressure angle of ${?}_n=20^{?}$, and a helix angle of $?=30^{?}$. a. Calculate the traverse pressure angle of these gears. Using this info calculate the minimum number of teeth required for the pinion to avoid interference in the gears. Calculate the maximum number of teeth of the gear to avoid interference. b. The input and output shafts must be in the same line. We need to minimize the size of our gearbox. Determine the number of teeth for all four gears in the gearbox. c. Assuming the input power is $2\mathrm{kW}$ at a rate of $150\mathrm{rpm}$, calculate the loads in the $\mathrm{radial}/\mathrm{axial}/\mathrm{tangent}$ directions for both paired gearsets $(W_t=W_r=W_a=$ ?). d. Using the AGMA method, we need to determine this gearbox's minimum safety factor. Assume that we will make all the gears with the same face width of $32\mathrm{mm}$. In this analysis, we will consider both teeth' bending and pitting failures. The gears are made of induction-hardened grade 2 steel. We are seeking a reliability of 0.99 for $10^8$ cycles. You may use the following given values for your calculation, you need to calculate all other factors and variables for the AGMA method. $K_o=1,K_H=1.2,K_B=1,Y_{?}=1,Z_R=1,Z_W=1\text{. }$