Help with flywheel / clutch calculations

[Mattuu]

Hey everyone,

I have a problem with sizing a clutch for my machine. My problem is, I don't know how to calculate the needed value (Nm) for the clutch to withstand the torque affected by the flywheel. I have a flywheel that weighs 90kg and is 600mm in diameter. It is rotating at 500rpm (52,36rad/s) via electric motor and 1:3 gear ratio. Torque transmitted to the flywheel constantly is around 60Nm and inertia of the flywheel is 4,05kgm^2. After the flywheel at its shaft is toothed clutch, that connects the shafts of the flywheel and the cutting tool. The flywheel rotates constantly and at desired time the clutch is activated and the cutting tool starts rotating with the flywheel.

Problem is, I don't know how to calculate the needed value (Nm) for the clutch. I know it usually is calculated with acceleration, but in this case I don't know it. The cutting tool rotates 180 degrees at a time, and will do the cut within 90-120 degrees from its starting point. Since the tool is rotating at 500rpm, it takes 0,12 seconds for the tool to rotate once. I'm not sure how to explain this better, so if I left out some important values, please let me know. If anyone could help me with my problem, I would be really grateful.

 

[jack action]

What's wrong with using the input torque (60 N.m)?

 

[Mattuu]

What's wrong with using the input torque (60 N.m)?

The flywheel has been spun for t (4s) amount of time and has reached its peak kinetic energy (Ke) of 11kJ. Do I not need to take this in account, when the clutch activates and forwards the energy from the flywheel to the 2nd shaft where the cutting tool is located? This is all just speculation since I don't really know yet, but I thought I would need to take in account the flywheels mass and angular speed?

 

[Twigg]

Why not just choose a clutch that can take the maximum torque of the motor after the 1:3 reduction? That way you don't have to worry about the clutch turning into an angle grinder (yikes?). Instead of the clutch failing, the motor will stall. Just make sure the motor has current limiting or it'll wind up real smokey in your shop.

 

[DaveE]

OK, I'm a bit confused about clutch specs. So this maybe more of a question than an answer.

Clutches are designed to be able to tolerate slipping (within some energy limit), so the torque number you are looking for (assuming Nm is torque not energy) isn't so much a limit as a description of when the clutch starts slipping, correct? Of course with zero slippage, the torque is infinite for zero time. In practice there will be some compliance in the system to buffer this, you never really get infinity. If the torque spec is too low the clutch will slip longer and the tool won't accelerate quickly enough, if it's too high there will be rapid acceleration along with lots of torque stress on the system. So I would choose a clutch that accelerates the tool as slowly as possible but still achieves the desired final speed, with some design margin, of course.

I would imaging that the maximum ratings for the clutch would be something like energy or power (i.e. temperature).

Note: I'm not a real mechanical engineer, I just play one on PF sometimes!

 

[Twigg]

@DaveE I think you're thinking of friction clutches. The OP mentions its a tooth clutch in their first reply. Tooth clutches do not slip. It's like two gears and a solenoid actuator. Solenoid fires and it locks up immediately.

Also, I'm no mechanical engineer either. Just someone with too many hobbies. OP, definitely take my advice with a grain of salt.

 

[jrmichler]

Does this schematic diagram correctly show your system?

Your description sounds like a mechanical punch press, where the motor spins up the flywheel, the operator engages the clutch, the driven shaft makes one revolution, then the clutch is pushed open by a cam.

We need to know if this is correct. If not, we need to know exactly what you are trying to do.

 

[DaveE]

@DaveE I think you're thinking of friction clutches. The OP mentions its a tooth clutch in their first reply. Tooth clutches do not slip. It's like two gears and a solenoid actuator. Solenoid fires and it locks up immediately.

Also, I'm no mechanical engineer either. Just someone with too many hobbies. OP, definitely take my advice with a grain of salt.

OK, if that's the case then he has to know what else in his system is buffering the impulse, that will determine the torque in the system. This is the "acceleration" the OP mentions. Without this sort of characterization there's no point speculating, IMO.

 

[Twigg]

Agreed, we definitely need more info.

 

[Mattuu]

Does this schematic diagram correctly show your system?
View attachment 272295
Your description sounds like a mechanical punch press, where the motor spins up the flywheel, the operator engages the clutch, the driven shaft makes one revolution, then the clutch is pushed open by a cam.

We need to know if this is correct. If not, we need to know exactly what you are trying to do.

Yes, this is on point. I started the whole design based on eccentric punch presses.

 

[jack action]

The flywheel has been spun for t (4s) amount of time and has reached its peak kinetic energy (Ke) of 11kJ. Do I not need to take this in account, when the clutch activates and forwards the energy from the flywheel to the 2nd shaft where the cutting tool is located? This is all just speculation since I don't really know yet, but I thought I would need to take in account the flywheels mass and angular speed?

First, the energy only get released/added when the there is a change in angular speed. So if your motor/flywheel turns freely at constant speed, without being connected to the clutch, it means that the motor torque is just enough to fight bearing friction. Nothing comes from, or get into, the flywheel.

Once you connect the clutch, you add a resistance to the shaft. A resistance that will tend to decelerate the shaft. The flywheel will make this harder to do; but the shaft will slow down if nothing changes. By design, the motor will try to keep its rpm by increasing its torque. The torque will increase to match the one coming from tool. This way, the shaft rpm should stay constant during the whole process. Therefore, the torque at the clutch should never go over the maximum torque that the motor can produce.

 

[Mattuu]

Thank you all for your answers. I haven't done calculations regarding this kind of machines before, so if there is some info that you need and I didn't provide, please let me know and I will do my best to provide it.

 

[DaveE]

If the flywheel is big, the motor is irrelevant in the time frame you care about, that's why you would put a flywheel in the machine. The issue is essentially the same problem as "how do you connect a large spinning flywheel to a smaller, initially stationary flywheel." This is roughly the rotational version of slamming an fast car into a slow car and asking how much force will the bumper feel.

 

[Twigg]

Thanks for the followup!

In the worst case scenario, let's say the workpiece brings the flywheel to a stop. As a first approximation, the torque of impact will be given by the change in angular momentum divided by the time of the cut. The actual torque can exceed this value, so I would throw a hefty safety factor on this. $$M = \frac{L_{flywheel} - 0}{t_{cut}} = \frac{I_{flywheel} \times \omega_{flywheel}}{t_{cut}}$$

The time of the cut you can approximate from the initial RPMs and the fact that the cut takes place over 90 degrees per your original post: $$ t_{cut} = \frac{\pi}{2} / (2\pi \times 500 RPM) = 30ms$$ This is an underestimate of the time (overestimate of the torque) because the cut slows from 500 RPM to 0 during the cut.

You know $I_{flywheel} = 4,05 kg \cdot m^2$ and $\omega_{flywheel} = 2\pi \times 500RPM = 52 rads/s$, so $M = 7,02 kN\cdot m$. Throw a big safety factor on there. Even if this won't cause a clutch failure on the first go, metal fatigue is a thing.

 

[jrmichler]

I started the whole design based on eccentric punch presses.

The toothed clutch is a dog clutch (search the term). Dog clutches are commonly used in mechanical punch presses and outboard motor lower units for forward - neutral - reverse shifting. They engage with a clank because the driven load goes from zero to full speed "instantly". "Instantly" is in quotes because every part in the driven system from the driven dog clutch member to the load is elastic. That elasticity is what allows the parts to survive repeated engagements. Dog clutches require low inertia driven loads.

The clutch must be strong enough to survive the shock of engagement. There are no good calculations for engagement force because it is entirely dependent on the inertia and elasticity of all of the parts being driven. I have seen attempts to compare the kinetic energy of the driven load to the maximum elastic strain energy in the dog clutch. In the real world, the best approach to designing a dog clutch seems to be to copy one that works in a similar application, and test it. If if breaks, make it stronger.

The next load is the force of the tool against the workpiece. That force could be greater than or less than the peak engagement force. The dog clutch needs to be strong enough for the work force, and that force can be calculated.

The last load is the crash load. Something goes wrong and the press jams to a dead stop. Real world punch presses have been destroyed by this. The remedy is to design a weak link that will fail first. The weak link could be the drive side of the dog clutch, the driven side of the dog clutch, the driven shaft, or a shear pin in the system. Good practice is to design a low cost weak link, such as using a bolt for a shear pin.

 

[Lnewqban]

How much energy or work each cut requires?

 

[jrmichler]

After sizing the driveline parts for the peak forces, the flywheel is sized for the peak work of each cycle. A normal NEMA design B induction motor is designed for full load at about 3% slip. This is 1750 RPM for a 4 pole 60 Hz motor or 1450 RPM for a 4 pole 50 Hz motor. If using such a motor, the flywheel should be sized for no more than a 3% RPM decrease at each cut. The motor should be sized to get the flywheel back up to full speed before the next cut.

Punch presses are usually driven by NEMA design D motors. These motors have higher starting torque, and run at higher slip. They are better for getting the flywheel initially up to speed, and allow the press to be designed with a smaller flywheel with its higher RPM drop in the cut. Good search terms to learn more about motors are induction motor slip vs torque. Here's one link: https://www.engineeringtoolbox.com/nema-a-b-c-d-design-d_650.html

 

[Mattuu]

The toothed clutch is a dog clutch (search the term). Dog clutches are commonly used in mechanical punch presses and outboard motor lower units for forward - neutral - reverse shifting. They engage with a clank because the driven load goes from zero to full speed "instantly". "Instantly" is in quotes because every part in the driven system from the driven dog clutch member to the load is elastic. That elasticity is what allows the parts to survive repeated engagements. Dog clutches require low inertia driven loads.

The clutch must be strong enough to survive the shock of engagement. There are no good calculations for engagement force because it is entirely dependent on the inertia and elasticity of all of the parts being driven. I have seen attempts to compare the kinetic energy of the driven load to the maximum elastic strain energy in the dog clutch. In the real world, the best approach to designing a dog clutch seems to be to copy one that works in a similar application, and test it. If if breaks, make it stronger.

The next load is the force of the tool against the workpiece. That force could be greater than or less than the peak engagement force. The dog clutch needs to be strong enough for the work force, and that force can be calculated.

The last load is the crash load. Something goes wrong and the press jams to a dead stop. Real world punch presses have been destroyed by this. The remedy is to design a weak link that will fail first. The weak link could be the drive side of the dog clutch, the driven side of the dog clutch, the driven shaft, or a shear pin in the system. Good practice is to design a low cost weak link, such as using a bolt for a shear pin.

Thanks for the tip about dog clutches. This was completely new term for me. I originally had an eye on these types of clutches (https://www.mwmfrenifrizioni.it/en/electromagnetic-toothed-clutches-positive/esb-z.html). I'm not sure if these work completely in the same way as dog clutches. Also would you happen to know what "build up time" and "decay time" means? I'm suspecting it's the time it take for the clutch to engage, but I am not sure and I have no idea about "decay time".

What would you consider to be a low inertia? I roughly calculated that the strongest materials to be cut could withstand max. 100kN impact and the tool should have no problem doing the cut, as long as the tools material can withstand the impact. I found a formula for rotational impact force and used that to calculate the force the impact would create.

 

[Mattuu]

How much energy or work each cut requires?

According to my rough calculations 4kJ should be enough, for the strongest materials.

 

[Mattuu]

After sizing the driveline parts for the peak forces, the flywheel is sized for the peak work of each cycle. A normal NEMA design B induction motor is designed for full load at about 3% slip. This is 1750 RPM for a 4 pole 60 Hz motor or 1450 RPM for a 4 pole 50 Hz motor. If using such a motor, the flywheel should be sized for no more than a 3% RPM decrease at each cut. The motor should be sized to get the flywheel back up to full speed before the next cut.

Punch presses are usually driven by NEMA design D motors. These motors have higher starting torque, and run at higher slip. They are better for getting the flywheel initially up to speed, and allow the press to be designed with a smaller flywheel with its higher RPM drop in the cut. Good search terms to learn more about motors are induction motor slip vs torque. Here's one link: https://www.engineeringtoolbox.com/nema-a-b-c-d-design-d_650.html

I calculated that the motor should get up to speed within 4 seconds, but this value is made up and to be honest it will be used only in very rare cases. The machine will mostly be used to continuously cut in every 10-20 second or so, so it shouldn't be a problem to get the flywheel back to full speed between cuts.