Gears

Question 1

Diametral Pitch

Accepted Answer

$P_d=\frac{T}{D}=\frac{1}{m}

Question 2

Module

Accepted Answer

$m=\frac{D}{T}=\frac{1}{P_d}

Question 3

Circular Pitch

Accepted Answer

$P_c=\frac{πD}{T}=πm

Question 4

PcPd Relation

Accepted Answer

$π=P_cP_d

Question 5

Circular Pitch With Backlash

Accepted Answer

$P_c=2t+B

Question 6

Tooth Thickness With Backlash

Accepted Answer

$t=\frac{P_c-B}{2}

Question 7

Contact Ratio

Accepted Answer

$C.R.=\frac{\sqrt{(R_o^2-R_b^2)_g}+\sqrt{(R_o^2-R_b^2)_p}-csin	heta}{P_ccos	heta}

Question 8

Center Distance

Accepted Answer

$C=\frac{D_g\pm D_p}{2}$

Question 9

Center Distance Given $P_d

Accepted Answer

$C=\frac{T_g \pm T_p}{2P_d}

Question 10

Center Distance Given $P_c

Accepted Answer

$C=\frac{P_c(T_g \pm T_p)}{2π}

Question 11

Center Distance Given Module

Accepted Answer

$C=\frac{m(T_g \pm T_p)}{2}

Question 12

Whole Depth

Accepted Answer

$W_h=a+d=W_r+c

Question 13

Working Depth

Accepted Answer

$W_r=2a

Question 14

Clearance

Accepted Answer

$c=d-a

Question 15

Power and Tangential Torque

Accepted Answer

Peanut $T=F_tr_{driver}

Question 16

Total Load

Accepted Answer

$F_{tot}=\sqrt{F_a^2+F_t^2+F_r^2}

Question 17

Radial Load and Pressure Angle

Accepted Answer

$F_r=F_ttan\phi$ $tan\phi=\frac{F_r}{F_t}

Question 18

Axial Load and Helix Angle

Accepted Answer

$F_a=F_ttan\psi$ $tan\psi=\frac{F_a}{F_t}

Question 19

Normal Pressure Angle Relation

Accepted Answer

$tan\phi_N=tan\phi cos\psi

Question 20

Normal Circular Pitch

Accepted Answer

$P_{cN}=P_ccos\psi

Question 21

Normal Diametral Pitch

Accepted Answer

$P_{dN}=\frac{P_d}{cos\psi}

Question 22

Power Worm Gears and Torque

Accepted Answer

$P=F_{tw}V_w=\frac{NT}{factor}$ $T=F_{tw}r_w

Question 23

Worm Helix Angle

Accepted Answer

$\psi=tan^{-1}\left(\frac{L}{πD_w}\right)$ L=nP n= single, double, triple

Question 24

Separating Force

Accepted Answer

$F_s=F_{tw}\left(\frac{sin\phi_N}{sin\psi cos\phi_N +fcos\psi}ight)

Question 25

Tangential Force of Worm

Accepted Answer

$F_{tg}=F_s\left(\frac{cos\psi cos\phi_N - fsin\psi}{sin\phi_N}ight)

Question 26

Cone Pitch Angle

Accepted Answer

$tanamma_p=\frac{sin	heta}{SR+cos	heta}

Question 27

Theta in Cone Pitch

Accepted Answer

$	heta=amma_p+amma_g

Question 28

Cone Pitch Angle (θ= 90°)

Accepted Answer

$tan\gamma_p=\frac{1}{SR}$ $90°=amma_g+amma_p

Question 29

Cone Distance

Accepted Answer

$L=\frac{1}{2}\sqrt{D_g^2+D_p^2}

Question 30

Face Width

Accepted Answer

$b=\frac{L}{3}$ $b=\frac{10}{P_d}$ whichever is lower

Question 31

Bevel Gear Axial Force

Accepted Answer

$F_a=F_ttan\phi sinamma_p

Question 32

Bevel Gear Radial Force

Accepted Answer

$F_r=F_ttan\phi cosamma_p

Question 33

Torque Bevel Gear

Accepted Answer

$T=F_tr_{mean}

Question 34

Mean Radius Bevel

Accepted Answer

$r_{mean}=\frac{D_p-bsinamma_p}{2}

Question 35

Outside Diameter for Pinion

Accepted Answer

$D_{op}=2a+2$ $D_{op}=\frac{N_p+2}{P_d}

Question 36

Tooth Thickness Backlash zero

Accepted Answer

$t=\frac{P_c}{2}

Question 37

Root Diameter PinionBack

Accepted Answer

$D_{rp}=D_g-2a

Question 38

Root Diameter Gear

Accepted Answer

$D_{rg}=D_g-2d

Question 39

Outside Diameter for Gear

Accepted Answer

$D_{og}=\frac{N_p+2}{P_d}$ $D_{og}=D_g+2a

Question 40

Backlash

Accepted Answer

$B=S-T$ $B=\frac{0.03}{P_d}$ to $\frac{0.04}{P_d}$ $0.035/P_d

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