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Moment of inertia

Marina Mrcela
Prodigy 20 points

Hi there,

I am working with TMS320C2000 Microcontroller, and my assignment is to do vector control of an iduction machine. Before I do that, I have to make a model in Matlab, for which I need some parameters of the machine. I have informations about resistances and inductances, but I don't have any info about the moment of inertia. The machine I am working with is Marathon Electric, CAT NO K111, ser.no. K11J140034.

So, if you by any chance know what the moment of inertia for the machine is, or if you have any idea how I could measure that, please let me know.

Best regards,

Marina

  • 0
    TI__Guru 61235 points

    Marina,

    Have you contacted the motor manufacturer about this?  They would know.

    Trying to measure the intertia would take some decent lab equipment.  The governing differential equation of the motor mechanicals is:

      Jw'(t) + Bw(t) = T(t),     w(0) = w0

      where   J = rotational inertia
                  B = rotational damping
                  T(t) = applied torque
                  w(t) = angular velocity (rad/s)
                  w'(t) = angular acceleration (i.e. time derivative of w) (rad/s^2)
                  w0 = initial angular velocity of the motor (rad/s)

    You need to find J and B.  To find B, apply a constant, known torque.  You'll need some sort of machine that can do this accurately.  At steady-state, the governing equation becomes:

      Bw = T

    Measure w at steady-state.  You can solve for B since T is known.  Best to do this for several different applied torques and see if B comes out consistent.

    Now to obtain J, we go back to the governing differential equation.  If there is no applied torque, you have:

      Jw'(t) + Bw(t) = 0,     w(0) = w0

    The solution to this equation is:

    w(t) = w0*e^[(-B/J)t]

    Spin the motor up to some known initial speed, and measure the speed decay.  This gives you data points for w(t) vs. t, and you know w0 and B.  You can do a curve fit to determine J in the solution equation.

    Personally, I'd just contact the motor manufacturer before going down the experimental route.

    Regards,

    David

  • 0 in reply to David M. Alter
    TI__Guru** 119380 points

    Dave Wilson has a series on tuning PI controllers, and part 8 just starts to get into inertia.  9 and 10 will be release shortly.

    http://e2e.ti.com/blogs_/b/motordrivecontrol/default.aspx

    I think all 10 are already included in the InstaSPIN-FOC & -MOTION user's guide in Chapter 11. Just search for Inertia and you'll find quite a few hits.

    Our InstaSPIN-MOTION solution includes inertia identification using SpinTAC Identify.  Here a torque is applied and time and acceleration is measured over a range of speed.

    This is from page 588 of the UG

    Background

    Inertia is the resistance of an object to rotational acceleration around an axis. This value is typically calculated as

    the ratio between the torque applied to the motor and the acceleration of the mass ridigly coupled with that motor.

    This test needs to be done under negligible friction and load.

    There is a common misunderstanding that inertia is equivalent to load. Load usually consists of two components,

    load inertia and load torque. Load inertia is the mass that will spin simultaneously with the motor rotor, while the

    load torque appears as an external torque applied on the motor rotor shaft. An easy way to differentiate the load

    inertia from load torque is to consider whether the load will spin together with the rotor shaft if the rotor shaft

    changes spinning direction. Direct couplers and belt pulleys with the mass rigidly mounted to the load shaft are

    examples of load inertia. Load inertia and motor rotor inertia contribute to the system inertia. Example of load

    torque include: gravity of a mass applied to one side of the motor rotor shaft, distributed clothes in a washing

    machine drum during the spin cycle, and the fluid viscosity of a pump. SpinTAC Velocity Identify estimates the

    load inertia and the friction of the system; Eliminate or minimize the load torque before running SpinTAC Velocity

    Identify.

  • 0 in reply to ChrisClearman
    Prodigy 20 points

    Thank you David and Chris for your help. I don't have much equipment that I could use for the measurement, so I'll ask the manufacturer for the info. If I found out an answer, I'll post it here. Thank you once again.