I am going to design a bowling machine. In this design, I'm going to use two motors that are being placed vertically and their shaft are attached with two horizontal identical wheels with a space of ball in between these two wheels.
The wheen diameter is
360mm and the weight is
3kg each. the ball is
75mm dia and the weight is
160 grams. I need to calculate torque and rpm required to throw the ball at
170km/h velocity. The cricket pitch length is
22 meter = 2200mm
The required acceleration is a need to throw the ball at
$v^2=u^2+2fs$ where intial velocity is $u=0$
So, $f = v^2/2s$
accleration $f = 50m/s^2 $
The force required $ F = ma$ where $m =$ total weight of two wheels + wight of ball $= 6+0.160$ $= 6.016$ kg.
So, $F = 308N$ i.e, $154N$ in each wheel.
Assume rubber to leather kinetic friction $u = 0.4$ it's not actually
kinetic Frictional force $Fr = 1.4 * 154 = 215.6$
Required torque $Ta = F * r$ $= 215.6 * (0.36/2) = 36.8 Nm$
If the linear velocity of the ball is $v=47.22m/s$ The velocity of the ball is an average velocity of two-wheel $v = (v1+v2)/2$
for the maximum velocity of the ball with no spin, the velocity of two-wheel must be the same.
so, $v1 = v = v2$
ao, the angular velocity of each wheel should be $v = d × w × 0.001885$
So, $w = v/(d * 0.001885)$RPM
Please let me know I am right or wrong?