I would like to build a system that represents a rotational double mass spring damper system with one set of spring and damper being represented by an electrical system. See image.

The first mass (J1) is connected to earth via a rotational spring (K1) and damper (B1) with constant stiffness and damping values. De first mass is connected to a second mass (J2) via a another rotational second spring (K2) and damper (B2) of which the stiffness and damping should be adjustable.

The driving force of the system is an oscillating moment around the first mass (J1). The frequency of this moment can vary.

Now I would like to represent the second spring and damper by an electrical motor/generator and a planetary gearbox. The electrical motor/generator should be controlled and operate such that maximum power is extracted from the relative oscillating motion between mass 1 and mass 2.

Typical amplitude of relative angular position between mass1 and mass2 is 30 degrees. Typical amplitude of relative angular velocity between mass 1 and mass 1 is 10 deg /s. Gearbox ratio would be around 1:200.

Question is which electrical motor would be best for say a 250W system. The motor/generator torque should be adjusted based on the relative angular velocity and displacement between the two bodies, equivalent to a spring damper system.

Should I use an induction motor with variable frequency drive or maybe a servo motor with some sort of feedback control system. Any thoughts?


Double mass spring system


1 Answer 1


If I understand your idea correctly, you wish to actually extract 250 W from the relative rotation between J1 and J2.

10 degrees per second is a very low speed; it would take 36 seconds for a single revolution. To generate 250 watts at this speed in a lossless system, you would require > 1400 Nm of torque. A gearbox with four stages won't be more than 80% efficient, and if you want to average 250 watts, well, you can see the problems with scale. Your masses would have to be very large to generate this kind of torque. So I would suggest you either speed up your rotational velocity or scale down your power output.

If this is for demonstration purposes, I might suggest that you try smaller masses, and make use of a pendulum instead of the disk you have shown to give you more torque with less mass. I would not suggest a motor. By using an arrangement of a coil and magnet, something like a voice coil, you can generate (admittedly small) amounts of power and vary the load on the output of your "generator" to increase or decrease the damping factor.

Sounds like a fun project. Good luck!

  • \$\begingroup\$ Thanks for the answer. The masses are in fact large. The first mass would be a floating platform on the sea. The second mass can be chosen. This can indeed be a pendulum. So in this case where the masses are indeed large and the 'the generator' should act both as damper and spring (so part regenerative power), what electrical motor / generator could do this (in combination with a gearbox) \$\endgroup\$ Apr 28, 2023 at 9:15
  • \$\begingroup\$ I would look at wind turbine generators - they have gearboxes designed as speed increasers. You will still be going to slow for best efficiency, but you should be able to get to 250W if you go with an oversized one. \$\endgroup\$ Apr 28, 2023 at 14:14
  • \$\begingroup\$ Thanks for the answer. Will look into it. \$\endgroup\$ May 6, 2023 at 11:40

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