Tim.Wright wrote:Typically acceleration (so second derivative of displacement) is used to measure ride comfort.
You are correct, Tim, but there is a little more to it than that.
Take Greg's SiL car as an example, and concentrate on the rear axle. The
transfer function of the rear axle body acceleration (mounted on the top of the suspension towers) for a unit input road acceleration (both averaged left & right) would represent the transmissibility of the rear suspension if the PSD of the input to the wheel was "white" (independent of frequency).
In reality, a typical road input would have a PSD whose
velocity is (close to) "white". For that reason the transfer function is differentiated, so that the Magnitude goes from acceleration (output) per unit acceleration (input) to acceleration (output) per unit velocity (input) or, as the industry seems to prefer, jerk (output) per unit acceleration (input) - no matter, the two are the same.
Now it is required to scale the differentiated transfer function, and it is helpful (arguably) to filter the transfer function. The reason for the last is to weight responses to take account of the human body's selective response to different excitation frequencies. Fortunately, perhaps, the the International Organization for Standardization (ISO) has sponsored standards for the effect (we may disagree in detail, but it is an easy solution).
Here is the same plot (shown as a continuous line) after it has been differentiated and scaled (by 0.010), and also after it has been filtered by the (an) ISO standard representing a seated human response to vertical acceleration. The scale factor is fairly arbitrary, but it happens to deliver an integral value of unity for a "high end" Mercedes road vehicle. The legend contains some statistics for the filtered results. "Int" is the magic number. The observant will note that its value is higher than the number I quoted earlier. This is because the Comfort Rating is computed as the average of the front & rear axle response, see
here.
The processed results show clearly why Greg was so dismissive of the vehicle. The large peak in the transfer function centered on 17 Hz. is indicative of a large dynamic response of the vehicle, which would be disliked by most "expert" drivers.
More can be discovered about the dynamic response by exploring the test results in an alternative way. A frequency response plot of estimated suspension load per unit body acceleration is shown
here. Again the solid line represents the measurements, which have the units N/gn (i.e. effective mass*go). Here, however, I have identified a second order filter from the data, and over-plotted the results as the crosses. The legend contains model parameters.
Arguably, the measurements represent a second order system fairly closely, and experience would suggest that the power unit of the vehicle is around (look at the numbers) (1340.27*2/9.81) = 270 kg mounted in a chassis of (1542.79*2/9.81) = 314.5 kg. The natural frequency of the mounted engine is 12.16 Hz, with a damping ratio of 0.116. Interestingly, perhaps, the engine acts as a "tuned mass damper" at lower frequencies, but turns around at frequencies higher the natural frequency to reduce the effective sprung mass. It is the latter that grabbed the attention of Greg.
Possible solutions are:
1. Reduce the power train mass.
2. Increase the chassis mass (there is no substitute for mass).
3. Decrease the stiffness of the engine mounts (if packaging allows).
4. Use damped mounts (the preferred solution).
It is a fairly trivial task to re-plot the
identified model in Excel, and then to play with parameters. This suggests that increasing the damping ratio from 0.116 to 0.300 (not unrealistic, I think) would increase the minimum effective mass by a factor of 2...
Edit: This is a case of a subjectively poor ride that has little to do with suspension set-up. I would suggest that no (sensible) changes to suspension springs &/or dampers would solve the issue, although suspension changes might be required once it has been "fixed". It is unfortunate that, in production, items like engine mounts are often "signed off" before subjective data is available, so that issues like the one discussed above cannot be addressed properly.