Stepper motor selection 1

[htngwilliam]

Guys

Sorry to ask this stupid questions. When we size a stepper motor, we need to calculate the load inertia.

However, if I were to use bearings and my load is driven by a timing belt system, how do I go about calculating the inertia of the bearings and timing belt?

 

[tygerdawg]

If I recall correctly, the stepper sizing task was to roughly match rotor inertia with load inertia. The goal was to NOT have a huge mismatch in inertias. This affects acceleration response and oscillation in your system. Many of the modern stepper systems are "microstepping" and mostly eliminate this problem. In your case what I always did was roughly model the bearing as cylinders and then add a small percentage fudge factor to the total to account for timing belts/chains.

TygerDawg
Blue Technik LLC
Virtuoso Robotics Engineering

http://www.bluetechnik.com

 

[zekeman]

The inertia load felt at the motor shaft is the load inertia "reflected" to the output shaft of the stepper. You get it by equating the kinetic energy of the output inertia, Jo to a fictitious inertia , J1 sitting on the motor shaft having the same energy. For example if the output speed is N1 rad/sec while the stepper speed is No rad/sec , the energy equation is
1/2*Jo*No^2=!/2*J1*N1^2
and therefore
J1=Jo*(No/N1)^2
where
Jo is the load inertia
J1 is the reflected inertia
so it shows that the load inertia is multiplied by the square of the gear ratio, No/N1, to get the reflected inert1a at motor shaft.
The bearings and belt are usually negligible for these systems; however, if you must include them, you simply add their energies to the lefthand side of the the first equation.

 

[zekeman]

The equivalent inertia load at the motor shaft is the load inertia "reflected" to the motor shaft of the stepper. You get it by equating the kinetic energy of the output inertia, Jo to a fictitious inertia , J1 sitting on the motor shaft having the same energy. For example if the geared output speed is N1 rad/sec while the stepper speed is No rad/sec , the energy equation is
1/2*Jo*No^2=!/2*J1*N1^2
and therefore
J1=Jo*(No/N1)^2
where
Jo is the actual load inertia
J1 is the calculated reflected inertia
so it shows that the actual load inertia is multiplied by the square of the gear ratio, No/N1, to get the reflected inert1a at motor shaft giving the same dynamics as if the actual inertia were replaced by J1 at the motor shaft.
The bearings and belt are usually negligible for these systems; however, if you must include them, you simply add their energies to the left hand side of the the first equation written above.