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I guess it depends on what kind of clutch you are talking about. What kind of clutch is of interest to you? Typical single surface clutches can be engaged at zero speed with no problem. The only clutches that "could" have a problem engaging at 0 rpm are some of the tooth clutches. That is because if lined up just the wrong way, the top landing of the teeth might contact in an awkward way. It would depend on the tooth profile.
When we talk about engaging a clutch or engaging a brake at some rotational speed, we are talking about that component absorbing the energy required to stop that inertia. Energy is related to inertia and the square of the rotational speed. So some inertia at 100rpm requires 10,000x energy to start/stop compared to the same inertia at 1rpm. That energy gets converted into some kind of heat, wear, noise, etc. So, generally speaking, a clutch or brake engaging at high speed will wear a lot faster than the same application/setup at low speed or zero speed.
One last thing, some clutches/brakes are specifically made to engage at speed, while others are just meant to engage at zero rpm. For "industrial" (higher precision, high cycle rate) products, this is usually done through some kind of friction material on the contact surfaces. It helps to limit wear. There are different type of materials for different types of applications.
Does torque vary with speed?
Oh boy, again it depends on what kind of clutch you are interested in. I would say the most susceptible clutches to speed are some of the slip clutches out there. Some of those have torque dependent upon speed, eddy current clutches definitely have torque that is speed dependent. Other slip clutches like the magnetic particle clutches have almost a flat curve when comparing torque to speed (they are "almost" consistent). With some types of slip clutches, there has been mention of some inconsistency when speed approaches zero. So, the design engineer should make high selection wisely when looking at slip clutches with very slow speed near zero. Different clutch designs offer different amounts of what they call cogging.
Again, I am not sure what type of products you are asking about, but in the clutch/brake world, we usually talk about static torque and dynamic torque. Different product types can have different ratings. For the most part, static torque ratings are going to be higher than the dynamic torque rating. Again, inertia and speed have a big impact on how a clutch is going to react and how much heat/wear is going to occur.
Does this effect the lifetime of the clutch?
You can look up wear rate formulas if you want, but basically the lifetime is about the formula below. I copied and pasted the info from this article https://www.machinedesign.com/motion-co ... ing-brakes
E = (1/2)mv2
Ee = (M*v2*td)/[182*(td+tl)]
where Ee = energy per engagement; M = inertia; v = speed; td = dynamic torque; and tl=load torque.
Then we use the energy per engagement and put that into the cycle formula:
L = v/Ee*w
where L = life in cycles; v = total engagement area; and w = wear rate.
How can we calculate this lifetime?
See above. Or just guess. Heat is probably a clutch or brake's worst enemy...so keep cool. Stay away from over-loading, over-cycling, over-speeding, over-everything-all-at-once.
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