Belts, Chain and Sprockets, & Screws

$v=πDN

$V_a=πDN(1\pm\%slip)$
$V_a=V(1\pm\%slip)

$L=2c+\frac{π}{2}(D_2+D_1)+\frac{(D_2-D_1)^2}{4c}

$\theta=180°\pm2sin^{-1}\left(\frac{D_2-D_1}{2c}\right)$

$\theta≈π\pm\left(\frac{D_2-D_1}{c}\right)

$L=2c+\frac{π}{2}(D_2+D_1)+\frac{(D_2+D_1)^2}{4c}

$\theta=180°+2sin^{-1}\left(\frac{D_2-D_1}{2c}\right)$

$\theta≈π+\left(\frac{D_2-D_1}{c}\right)

$\frac{F_1}{F_2}=e^{f\theta}

$\frac{F_1-F_c}{F_2-F_c}=e^{f\theta}

$F_c=\frac{mv^2}{r}=\rho btv^2$

$\rho=0.035\frac{lb}{in^3} (leather)

$F_{net}=F_1-F_2=F_1(1-e^{-f\theta})

$F_{net}=(F_1-F_c)(1-e^{-f\theta})$
$F_{net}=(F_1-F_c)-(F_2-F_c)

$S_t=\frac{F_1}{bt}

$P=\frac{NT}{factor}=F_{net}V

$D_1N_1=D_2N_2

$T_1N_1=T_2N_2

$D_1=\frac{P}{sin\left(\frac{180}{T_1}\right)}

$D_2=\frac{P}{sin\left(\frac{180}{T_2}\right)}

$C=D_2+\frac{D_1}{2}$ inches

$C_p=\frac{C}{P}$ pitches

$SR=\frac{N_1}{N_2}=\frac{T_2}{T_1}

$L=L_pP$ (in)

$L_p=2C_p+\frac{T_2+T_1}{2}+\frac{(T_2-T_1)^2}{40C_p}$
(pitches)

$D_m=\frac{D_o+D_i}{2}

$D_m=D_o-h$
$D_m=D_i+h

$h=\frac{1}{2}Ptan(60)

$P=\frac{1}{TPI}

$L=nP$
$L=P$(single)
$L=2P$(double)
$L=3P$(triple)

$v=LN

$tan\lambda=\frac{L}{πD_m}

$F_a=\frac{S_y}{6}A_s^{1.5}$
$F_a=CA_r^{1.418}

$S_w=\frac{S_y}{6}A_s^{0.5}$
$S_w=CA_r^{0.418}

5000 (carbon steel)
10000 (bronze)
15000 (alloy steel)

$S_{sr}=\frac{16T}{πD_i^3}$
$S_{sr}=\frac{F_a}{πD_itn}

$S_c=\frac{F_a}{\frac{π}{4}(D_o^2-D_i^2)n}

$S_t=\frac{F_a}{A_r}

$T=\frac{WD_m}{2}tan(\lambda \pm \beta)

$T_c=f_cWr_c$
$T_c=\frac{f_cWD_c}{2}

$\beta=tan^{-1}\left(\frac{f}{cos\phi}\right)

$\lambda=tan^{-1}\left(\frac{L}{πD_m}\right)

Square = 0°
ACME = 14.5°
Traoezoidal = 15°
American = 30°
Butress = 45°

$T=T+T_c

$e=\frac{P_o}{P_i}=\frac{Wv}{\frac{NT}{factor}}$
$e=\frac{tan\lambda}{tan(\lambda \pm \beta)+\frac{f_cD_c}{D_m}}$
$e=\frac{tan\lambda}{\frac{cos\phi tan\lambda \pm f}{cos\phi \pm ftan \lambda}+\frac{f_cD_i}{D_m}}

$D_r=D_o-P