CALIBRATING THE DAMPER POSITION SENSORS TO MEASURE ACTIVE AXLE LOADS
Knowing the static axle loads I now want to measure the “active” axle loads using the damper position sensors. To do this, I have calibrated the sensors by recording their average positions for each axle at two different known weight conditions.
CALIBRATION
I performed a two-point calibration with the two points being 1) full fuel with driver (unladen condition), and 2) full fuel with driver plus 300 lbs of ballast (laden condition). The ballast was carefully distributed in the trunk and passenger footwell so that it increased the static weight of each axle by 150 lbs. Setting these conditions was done on a set of platform scales.
1 Laden and Unladen Test Configurations
The vehicle was then driven slowly (approximately 15 km/h based on GPS speed) over a flat, straight, smooth test road and damper positions were logged. This was repeated in the Laden and Unladen conditions. Fuel levels were monitored, and they remained between 96% and 94% so that the weight of fuel consumed during the test was small enough so as to be negligible. Winds were low enough that the magnitude of any aerodynamic forces acting on the vehicle could be neglected. On a good smooth road the damper fluctuation is less than ±1 mm at this speed.
Stable test data was recorded for approximately 30 seconds. From this log, a section of data at least 3 seconds long was selected based on the GPS speed being stable, the road being smooth, and the recorded wind being low and stable. Two runs were made in the Laden condition to confirm that consistent data could be collected using this method, and then one run was made in the Unladen condition. The damper positions were averaged for each wheel position, and then the front and rear pairs were then averaged for an average damper position for each axle. These axle averages were then plotted against the calculated axle loads for each operating condition. A regression line between these points then provides the equation for axle load as a function of damper position.
DATA
The average damper positions for each axle were recorded for each run, and we note the very good consistency between the two Laden test runs.
2 Average Damper Positions
For simplicity the axle weight is assumed to be shared equally by the left and right wheels
3 Axle Weights and Average Damper Positions
4 Axle Loads vs. Damper Position
We can use these equations to measure the live load on the axles based on logged damper positions. The range of wheel loads covered in this graph covers the area of primary interest when measuring downforce. Non-linearities likely exist at the over a wider range of damper positions. They certainly exist once the bump stops are engaged. The rear bump stop begins to engage at 84 mm and the front at 88 mm, so well outside the operating conditions noted above.
This data also provides an opportunity for a sanity check of wheel rates and motion ratios. I have previously determined the correlation between damper positions and wheel center heights (ride heights measured from wheel center to fender lip):
5 Equations
Converting the axle loads to Newtons and dividing by two to get wheel loads is convenient for what I have in mind, as is plotting this against wheel centre heights:
6 Wheel Loads vs. Ride Height
The slope of the lines represents the wheel rates in N/mm. Given that my spring rates are 60 N/mm front and 140 N/mm rear, we can calculate the motion ratios as follows:
Front MR = SQRT(56.7/60) = 0.975 (inverse is 1.03)
Rear MR = SQRT(51.1/140) = 0.604 (inverse is 1.66)
I have included the inverse because some people (including the OptimumG Magic Number spreadsheet) calculate MR that way. For that purpose I have used values of 1.04 front and 1.76 rear in the past. Because of the articulation of the rear spring geometric calculation of the rear MR is a bit dubious. I am happy to revise my assumptions to these new values.
LIMITATIONS
The purpose of making these measurements is to estimate aero downforce. For that purpose, the method described does have some limitations.
1) Steady state conditions must prevail over the sampling period.
2) Damping forces are assumed to average to zero over the sampling period. Very smooth road surfaces are required to minimize damper movements, and the sampling period should exclude any intervals with large damper movement. This becomes more critical as test speeds increase.
3) Damping coefficients must be significantly sub-critical to allow the suspension positions to achieve a valid average value. In particular, rebound damping must not be excessive to prevent the vehicle from jacking down over bumps. (Damper settings were 4 front and 5 rear for the calibration testing).
4) Any significant lateral, longitudinal or vertical load factors will result in weight transfers which negate the steady state assumption. Thus, test surfaces must be straight, flat, level and smooth.
5) Any significant wind gusts (i.e. variations in dynamic pressure) over the sampling period will negate the steady state assumption. Thus, the sampling period should eliminate any intervals with significant observed gust activity. Likewise significant crosswinds will affect the results.
6) The accuracy of this method for average damper positions significantly outside the range used for calibration is not known, but some extrapolations should be ok.