Dyno torque calibration

[Bribyk]

I'm trying to determine the statistical uncertainty of an engine dynamometer's torque reading (load cells). I've taken 120 randomized (target load value and order) data points (well normally distributed) over three separate time intervals to compare the "known" torque to the measured. The current calibration is a two-point (zero and 17850 ft-lbs) and, thus is assuming linearity.

My numbers show the linearity assumption to be good (slope 0.996, intercept may be zero) but my residuals of the linear regression show issues. My residuals vs torque (both predicted and measured) show a sinusoidal pattern (like 1.5 periods of increasing harmonic motion) and the variance increases with torque. The increase in variance is expected to be due to increased friction in the bearings/linkages as the load increases. The waveform I can't explain.

The worst part is my cumulative probability diagram of the residuals shows a "knee" at about 25%. This is supposed to indicate two distributions(?!) The residuals in the knee region are made up of about 5 points near 10% of the torque range and the other 13 or so are from about 60% to 85% of the range. I can't predict uncertainty from the regression unless the distribution is normal (and, thus, due to random error(s)).

Any clue as to what's going on? Do I have some systematic error? I've randomized everything to remove any drift, temp/time effects and hysteresis I can think of.

I can post the charts tomorrow.

 

[Bribyk]

Oh yeah, and the chronological and lag plots of the residuals look good (scattered randomly).

 

[roydm]

I think you are confusing yourself with the math.
Load cells are very reliable, linear and repeatable.
If for some reason they are not it's usually a mechanical issue, not a mathmatical error.
Roy

 

[Bribyk]

I need to be able to quote a proper accuracy for this as in +/- 1% of measured value with 95% confidence;which, I think, wouldn't use a confidence interval, it would be a predication interval, because I haven't calibrated at exactly every possible torque value.

I also need to ensure my total uncertainty, including the uncertainty of the calibration equipment, is less than +/- 2% of measured to be able to test the engines according to the manufacturer's standards, ISO 3046/1.

The math is very confusing though. It seems like the more statistics I use, the more confusing and wrong the data seems.