How much force exerted by ball pushed between two spinning wheels?

[MHassaan]

Hi everyone,

I am making a project involving shooting a tennis-sized ball by means of an automated mechanism. I have two horizontal wheels which are at the same height from the ground, and are spinning in opposite directions via motors. There is a space between them, a bit smaller than the ball which is to be pushed through them.

The mechanism works like this: the wheels are spinning at a very high speed (around 3000RPM), and when the ball is pushed between them, it will be squeezed and will shoot out at high speed.

Now here's the problem:
I need to choose the material of the wheels and the width of the shafts spinning them so as to minimize the amount of lateral displacement caused when the ball is squeezed through so the mechanism doesn't fall apart. The ball is quite hard (in fact, it is a cricket ball). In order to do so, I will need to know the force exerted by the ball on the wheels when they attempt to squeeze it, and will then make sure the materials are chosen to withstand this force.

Can anyone give me a push in the right direction regarding the calculations involved? I need to work out the aforementioned force. I know it is not a simple calculation by any means, so any hints will be appreciated.

 

[Mech_Engineer]

This design sounds like a pretty standard ball launcher (tennis or baseball), but 3000 rpm is way too fast. Take a second look at how fast your want the ball to be going and assume a launcher wheel speed of more like 50-100 rpm; then you can calculate how large the wheels will need to be.

For how much force is needed to compress the ball I would set up a test rig to measure force as a function of compression on a sample of cricket balls.

 

[MHassaan]

I need the ball to have a maximum speed of 160kph. To achieve that I need a minimum of 3000RPM.

 

[Mech_Engineer]

Yikes sounds like a pretty dangerous system to me.

 

[Travis_King]

Just a note: You can increase the effective speed of the ball by moving it closer to the target.

I don't know what this is for, but if it is a pitching machine (for practicing cricket), then don't necessarily need the speed to be accurate, you want the reaction time. So if you want to simulate 160 kph at 17.5 meters, you only need to simulate the time you have to react before you would miss the ball. The required speed goes down nicely as you move the machine closer.

Obviously you want to find a happy medium, though. a ball going 5 kph 10 cm away from you is not really a useful tool...

 

[Danger]

From a designer's standpoint, I have to ask why you need to deform the ball. To me, it makes more sense to use something like silicone or rubber as the rims of the wheels, and let them deform instead of the ball. If you're worried about that causing random trajectories, then a guide tube could be implemented at the exit of the wheels.

 

[OffTheRecord]

Yeah I like that... deform the wheel. That way, you can pick the material that works best.

Hmm... so if my head-calcs are right, those wheels are going to be almost 2 meters in diameter, each. You're going to have to make 'em pretty light.

Anyways. The closer the wheels are together, the more force you get on the ball. The more force, the more friction. Friction is what you want, because it gives you traction. So you want the wheels to be as tight as possible. However, if they're too tight, the ball will break the wheels. Tighter still, and the ball won't fit at all.

The amount of "give", i.e. how far the ball can push the wheels inward, depends on the strain of the wheel. The force it can take will depend on the internal stress of the material, which in turn depends on that strain. My advice would be to use something light and inexpensive like aluminum. Make a wheel out of it, or at least a partial wheel for testing purposes. Anchor that wheel in place, then press on it with the ball, to simulate the force. Get a clamp or a vise for control. You want to figure out what the max force you can put on that wheel is, to where it won't lose its shape. Then, let off by about half that force for safety, and record the strain (how much it gives). Let's call that "give" distance 'x'. Let's say the diameter of the ball is "D". The distance between wheels is then D - 2x .

If you're not getting the pressure you need on the first try, then you'll have to change the wheel parameters. Try making it thicker. Too tight? Try making it thinner.

Something else you have to watch out for is the separation of the spokes. No matter how thin your wheel is, if the ball pushes on it at a spoke, it's going to act pretty rigid at that point. You may have to get creative with the spokes. If they don't give enough, try making them zig-zag on their way between the wheel and the axle.

 

[Danger]

Spokes?
Also, I don't see any need to alter the wheel thickness for adjustment. The spacing between them is the only thing that should need to be changed to maximize efficiency.