RigTest
Automotive
- Jan 19, 2007
- 19
Hello everyone,
I have been struggling to properly calculate energy ratios (energy dissipated/energy input) in servo-hydraulic test systems. Specifically, the test specimens are quarter-car (2DoF) suspensions, which include tire compliances. The rig is capable of many excitation waveforms, but I typically use a constant peak velocity swept-sine. The rig has a load-cell under the tire pad and there are accelerometers at the pad (input), the hub, and the body, which are integrated to give relative displacements. I am hoping to get some feedback on what I'm trying, as currently my system is breaking energy conservation(!).
Initially I performed the calculations in the time domain:
Input Energy(t) = int(Force(t)*dx(t),x) where t is time
A swept-sine allows the time history to be broken up into cycles, and for each cycle I would determine the contained area within the Force vs. Displacement curve: one area for 1 cycle (frequency), so I manually constructing a spectral energy signal (I'm not sure this is valid). The calculation is performed using Pad Force and 3 displacements:
-Actuator displacement (to get input energy)
-Pad to Hub displacement (to get energy dissipated by tire)
-Hub to Body displacement (to get energy dissipated by dampers)
At the body resonance, the energy dissipated by the Hub - Body is greater than the input energy (not good). I repeated the calc using Pad - Body and it was also much greater than input near resonance.
I switched to the frequency domain and calculate a cross-spectral density with the displacement signal as input and force as output.
Energy(jw) = cross-spectral-density(Displacement(t),Force(t))
using the same 3 displacements. I actually receive something similar to the time domain calculation though it matches my predictions better. More importantly, the energy dissipated by the dampers is larger than the input energy(!).
So I realize that I have an issue with my calculations. Can someone offer their opinion on the validity of calculating input energy and dissipated energy in this manner?
I appreciate any feedback.
Chris
I have been struggling to properly calculate energy ratios (energy dissipated/energy input) in servo-hydraulic test systems. Specifically, the test specimens are quarter-car (2DoF) suspensions, which include tire compliances. The rig is capable of many excitation waveforms, but I typically use a constant peak velocity swept-sine. The rig has a load-cell under the tire pad and there are accelerometers at the pad (input), the hub, and the body, which are integrated to give relative displacements. I am hoping to get some feedback on what I'm trying, as currently my system is breaking energy conservation(!).
Initially I performed the calculations in the time domain:
Input Energy(t) = int(Force(t)*dx(t),x) where t is time
A swept-sine allows the time history to be broken up into cycles, and for each cycle I would determine the contained area within the Force vs. Displacement curve: one area for 1 cycle (frequency), so I manually constructing a spectral energy signal (I'm not sure this is valid). The calculation is performed using Pad Force and 3 displacements:
-Actuator displacement (to get input energy)
-Pad to Hub displacement (to get energy dissipated by tire)
-Hub to Body displacement (to get energy dissipated by dampers)
At the body resonance, the energy dissipated by the Hub - Body is greater than the input energy (not good). I repeated the calc using Pad - Body and it was also much greater than input near resonance.
I switched to the frequency domain and calculate a cross-spectral density with the displacement signal as input and force as output.
Energy(jw) = cross-spectral-density(Displacement(t),Force(t))
using the same 3 displacements. I actually receive something similar to the time domain calculation though it matches my predictions better. More importantly, the energy dissipated by the dampers is larger than the input energy(!).
So I realize that I have an issue with my calculations. Can someone offer their opinion on the validity of calculating input energy and dissipated energy in this manner?
I appreciate any feedback.
Chris
