Transient Roll Response Calculator: Optimizing Spring and Damper Rates for Minimized Load Transfer
Written by Ivan Pandev, August 2020
In a Word
A calculator is developed which approximates the roll motion of Project Battle Bimmer as a 1-dimensional, underdamped 2nd order harmonic system. Outputs of the calculator include (all time-dependent) lateral load transfer, tire loads, damper velocity, and many more, in response to either a lateral-G step-input or sin input. Its purpose is to be a detailed performance benchmark (moreso than a simple one-wheel model) for current and future suspension configurations as we evaluate changes to spring and damper rates, roll geometry, corner weights, etc.
The main goal of this study is to reduce the lateral load transfer (LLT) and settling time of rapid step-change maneuvers, using reasonable rates for our Koni Yellow twin-tube dampers. Our winning configuration can reduce peak LLT by 5.6%, LLT overshoot by 47%, and settling time by 45% in 1.4G step-input, using only 30% increase in high- and low-speed bump damping rates, and a 15F/10R% increase in high- and low-speed rebound damping rates. In the context of a high-speed kink or chicane in autocrossing, this means the chassis increases its minimum grip capacity during the maneuver, has more consistent grip during the whole response, and settles more quickly in anticipation for the next input. Further LLT reductions were possible, but with less favorable compromises (see Results and Analysis section).
See the full Suspension Spec Sheet and Test Results comapring the baseline and optimized roll performance.
Model Development and Assumptions
To model the rolling motion of any vehcile, the polar inertia, roll couple length, corner weights, various motion ratios, and of course spring and damper rates must be known. Damper curves are estimated from the Q.C. values of the Koni twin-tube dampers used on the car. The calculator accounts for both low- and high-speed damper domains. The program Racing Aspirations is used to find the roll center. A primitive Solidworks model of the Battle Bimmer estimates the polar moment and C.G. location. The roll couple length is found from combining this information. The vertical component of the roll couple, which is the “leverage” of lateral forces on the vehcile body, is assumed to be constant up to 2 degrees of roll. (Racing aspirations shows that it actually increases 0.5″ across this motion, about 3%, see Fig 1).
Modelling the OE anti-roll bars is a challenege as their wall thickness is unknown, and the OE bushings are likely compliant enough to reduce their rate by some other unknown amount. (The OE anti-roll bars are kept like this intentionally; I generally try to produce as much body control as possible with springs and dampers instead of anti-roll bars, keeping LLT as low as possible). Rather than using emperical motion ratios and bar stiffness, this model uses an estimation of the anti-roll bar’s contribution to the wheel rate in symmetric roll, namely 50F/20R lb/in.
All motion ratios are assumed constant across the range of roll angles (Generally less than 1 degree in steady state cornering).
Test Plan and Performance Goals
The main focus of this test is improving transient roll behavior with damper rates appropriate (low enough to prevent excessive foaming and hysteresis) for twin-tube Koni Yellows. Maximizing the minimum grip (or reducing peak LLT) is the primary goal, but minimizing settling time is crucial too. In autocrossing, slow roll response through irregular slaloms and tight chicanes could be the limiting factor to speed, as the driver could be forced to take extra time to slow down and settle the chassis, or chose a sub-optimal racing line to keep the transitions smooth. Reviewing footage from previous races, rapid driver inputs can be as quick as 400ms apart, so the settling time for the chassis should be approximately half that.
Iterations 1 and 2 are attempts at these goals. Bonus configurations 1-4 are included to further explore the problem space and demonstrate the capability of the calculator. All tested configurations are detailed below.
The response of each suspension config is looked at in 1.4G step input and 1.4G sin response. Real-world inputs are of course never true step-inputs, but chicanes in autocrossing sometimes require steering input rapid enough to make the comparison make sense. Measuring the system response to sin inputs simulates slaloms in autocrossing.
Results
Key results are tabulated below. Both Iteration 1 and 2 perform much better than the current suspension configuration, both reducing settling time by about 45%, and eliminating any resonnance in sin input. Iteration 1 is about 80% as effective as Iteration 2 at reducing LLT overshoot. Iteration 1 has marginally lower lag in sin input as well. “Bonus 2,” which is built by disconnecting the sway bars from Iteration 2, predicts the lowest steady-state and peak LLT, but with a greater roll gradient.
Iteration 1 seems like the winning option since it achives most of the performance benefits of Iteration 2, but at lower total damper forces, reducing foaming and hysteresis in the damper itself. We’ll need to consult with a damper builder to fully understand how bad hysteresis and foaming are in our particular case with the proposed changes; remember its a low-pressure twin-tube design. Bonus 2 looks especially promising from a LLT minimization (maximum grip) perspective, but we’re nervous about the increased body roll worsening the already-poor camber control of the front McPherson suspension. Luckily, Bonus 2 simply suggests disconnecting the sway bars, so this can be tested easily at our next test-n-tune day with the new damper specs.
Graphics and Analysis
Let’s take a deeper dive into the differences between the current suspension configuration and our winning option, Iteration 1, starting with the modified damper curves. Figs 3 and 4 (left and right) below graphically represent the increase of 30%F/R compression damping, and 15%/10% F/R rebound damping. The knee speed is always above 0.13 m/s, meaning no configuration tested above enters the high speed damping domain.
This affects the damper forces in step response as show in Figs 5 and 6 (top and bottom) below. Peak compression damping increases from 356 to 420N, about 18% more damping force despite the 30% increase in damping rate. This is explained by the reduced damper velocity. With these competing effects, rebound damping in step response has barely changed.
These new damper properties have affected weight transfer and tire load as in Figs 7 and 8 (top and bottom) below. As the results table shows, the steady state weight transfer remains the same. During the response, however, there is less overshoot and quicker settling time. In the context of taking a high-speed kink or chicane in autocrossing, this means the chassis will retain more grip during the maneuver, have more consistent grip after the overshoot, and settle more quickly to its new steady state in anticipation for the next input. In fact, a step-change input can be given to the chassis roughly every 300ms, and the chassis will nearly settle into its steady state before the next input.
Finally, let’s consider the two suspension configurations in 1.4G Sin input. Figure 9 relates the suspension travel amplitude ratio (maximum during sin input/ steady state) to the frequency of the sin input, which might approximate a slalom. The increased damper rates eliminate the resonance seen in the baseline, meaning total suspension travel is reduced.
Design Change and Conclusion
Iterations 1 and 2 both outperform the current suspension configuration with very little drawbacks. Iteration 1 is nearly as great of an improvement as It.2, but does so at lower damper rates, likely meaning more consistent performance (less foaming, hysteresis) over multiple runs. Iteration 1 will be the starting point when considering our next damper revalving.
MIL-Spec Ball Joint Stud Fatigue Inspection
Written by Ivan Pandev, March 2020
Project Battle Bimmer uses Ground Control Roll Center Correction (RCC) and Bump Steer Correction (BSC) kits on the front uprights, which feature extended ball joint studs under greatly increased bending moments than standard. During the Spring 2020 Front Suspension Overhaul (more here), the ball joint studs were inspected for signs of fatiguing or cracking using Dynaflux penatrating dye and developer. It was concluded that the RCC ball joint studs had cracks from fretting fatigue, and replacements were ordered. Below is the process.
During disassembly from the front suspension, 3 of the 4 castle nuts had clearly loosened over time and were held in place by the cotter pins. Only one steering rod ball joint was still properly torqued, so the other 3 might have had accelerated wear as a result. Further, the height adjustment rings on the BSC studs all had indications of wearing against the rod end, indicating the suspension might have been binding at extreme travel, such as when lifted on jack stands. Finally, the 1 of the 2 RCC sperical bearings seemed worn as well. As much corrosion as possible is removed from the studs using a brillo pad. Once cleaned, the studs are degreased, dyed, wiped, and developed as per DynaFlux’s instructions.
Both RCC studs from the control arms showed narrow, distinctive lines of penetrant leaking out into the developer. The sharp boundaries and high color contrast of these lines mean they possibly indicate a crack, as opposed to the light-pink splotches elsewhere on the stud, which mostly identify light corrosion or pitting. The BSC studs from the steering rods had no such crack lines.
The three biggest crack lines were identified, all on the two RCC control arm studs. The developer is removed with degreaser. Those areas of the ball joints are then inspected under a microscope to find surface wear that might indicate fatigue damage. In all 3 cases, wear marks are clearly visible against the otherwise machined finish of the taper. These marks are most likely a result of fretting, or surface abrasion from microslipping between two parts (the stud and suspension kingpin) which are nominally fixed (bolted) together. Fretting fatigue is the combination of fretting accelerating initial crack growth at the fretting site, and frictionless (single-part, no contact) fatigue driving the remainer of the crack growth. Given that the RCC control arm studs were both found with slightly loosened nuts, its likely that the reduced friction between the taper and the kingpin further accelerated the fretting fatigue.
These RCC and BSC studs have been installed on the battle bimmer for about 5 years, and have endured many autocross runs, a track day, and lots of street miles as well. For race-only part most teams would consider consumables, that’s a fine service life.
Ground Control courteously sent replacement studs independent of the kit they are sold with, and the front suspension overhaul marches on!
How to Achieve Mission 2019: Modeling Time Loss per Power and Weight Improvement
Written by Ivan Pandev, November 2018
To achieve the 2019 mission of winning a trophy position at the 2019 SCCA Solo Nationals, significant modifications to the Battle Bimmer are necessary. In 2017, our time was 109.5% of the lowest-awarded trophy position, with the greatest factor in the disparity being power; our 190hp is well off the 350-400hp seen at the top of the sheets in XP. This study quantifies how much increased power and lost mass would be necessary to close the gap.
The results below are from simulated laps from an E46 simulade on autocross-like courses in Forza Motorsport 7, where power and mass were independently varied.
Based on results in Figs 1-2, a power increase to about 270hp and accomapnying weight loss to around 2260 lbs (from 180hp, 2380 lbs at Nationals 2017), could net a 7.0% time reduction above the 2017 performance. Table 1 lists combinations of engine modifications which can achieve that power (2.5L or 2.8L M52tu, naturally aspirated or supercharged, various “bolt-ons”). As of April 2019, the Battle Bimmer weighs 2283 lbs.
Table 1. Options to increase engine power tabulated, with transmission FOS based on a ZF S5D-320Z.
With a reasonable expectation that the remaining 1.8% can be found with “fudge factors” like increased experience with Hoosier A7s, various chassis upgrades, and not missing my first run (!), the 2019 mission looks achievable.