TL;DR:
This article presents a method to quantify loadcell signal fluctuations during dynamic pedal movement in a DIY force-feedback sim racing pedal. It evaluates the effects of mechanical play and flexible (TPU) adapter materials on signal stability. Results show that eliminating mechanical play had minimal effect, while using damping material (TPU) significantly reduced loadcell noise during pedal activation, potentially improving control loop stability and reducing oscillations.

Introduction

In a previous wiki entry, loadcell reading accuracy and precision have been analyzed. Software and hardware improvements were identified to enhance the loadcell readings. In this wiki entry, we'll focus on analyzing the loadcell precision further in dynamic situations, namely when the pedal is being pressed. Three topics will be analyzed in detail.

1. Establish a method to quantify loadcell reading fluctuations in dynamic situations.
2. Analyze the influence of mechanical play in the loadcell linkage system, in particular the upper and lower joints; see below. ,
3. Use the method to analyze the influence of using damping material (TPU) in the loadcell linkage system, like 3D printed loadcell adapters as shown below .

1. Estimating force fluctuations

In stationary situations (no external force applied to pedal, e.g., pedal not pressed)

In the referenced wiki entry, only static loadcell fluctuations were measured by keeping the pedal untouched, taking multiple loadcell measurements over time, and plotting the resulting sample distribution as a histogram, as depicted below. .

The left plot shows the raw loadcell measurements over time. The right plot shows the resulting histogram. The noise figure looks normally distributed. The resulting mean and standard deviation are shown in the title of the right-hand subplot. The mean provides little useful information, and its main purpose is to compute the standard deviation. The standard deviation $\sigma$ on the other hand, describes the fluctuation of the samples. Assuming normal distribution, ca. 68%, 95% and 99.7% of the samples will be covered by an interval of $\pm \sigma$, $\pm 2\sigma$ and $\pm 3\sigma$, see. Thus, a smaller computed standard deviation indicates lower loadcell reading fluctuations.

Assuming normal distribution, the mathematical formulas and unbiased estimate of the mean and standard deviation are computed as $\hat\mu = \frac{1}{N}\sum_{n=1}^N x_k$ and $\hat\sigma = \sqrt{ \frac{1}{N-1}\sum_{n=1}^N (x_k - \hat\mu)^2 }$, where $x_k$ is the k-th raw loadcell measurement.

In dynamic situations (when the pedal is pressed)

Estimating the standard deviation in dynamic situations is more challenging, since the mean is not constant anymore but now changes over time $\mu_k$. To estimate that mean, we take the raw measurements of the loadcell and apply non-causal, forward-backward filtering (4th order Butterworth, 30 Hz cut-off frequency); see below. . This non-causal filter doesn't induce any lag. The formula is non-trivial and will be omitted for brevity and just call the output $\hat\mu_k$. The following plot shows the raw measurement in blue and $\hat\mu_k$ in red. The red curve essentially represents a smoother version of the blue curve without the high frequency noise.

In the static situation, the standard deviation was estimated taking into account all samples. We'll take a smaller portion of the samples by windowing (0.2 s was selected as a window). Only samples within that time window are used to compute the standard deviation now; see the formula below: $\hat\sigma_k = \sqrt{ \frac{1}{N-1}\sum_{n=k-M/2}^{k+M/2} (x_k - \hat\mu_k)^2 }$.

2. Analysis of the influence of mechanical play on loadcell fluctuations

Let's examine how mechanical play in the linkage system can deteriorate the loadcell reading and increase the estimated standard deviation in dynamic situations.

With mechanical play

For completeness, the mechanical play in the linkage system was measured to be approximately 0.5 mm, as shown below .

The following plot represents a trace where the pedal was left untouched at the beginning and then pressed a few times. The raw loadcell measurement is plotted in blue, and the non-causal filter mean estimate is plotted in red. Their values are given on the left y-axis. The fluctuations $x_k - \hat\mu_k$ are plotted in purple. The $\hat\sigma_k$ is plotted in orange. Both values are shown on the right-hand-side y-axis.

One can see that the estimated standard deviation $\hat\sigma_k$ isn't constant over time (orange lines increase in height) and changes significantly when the pedal is being activated.

Reducing mechanical play

First try

To reduce the play in the linkage system, at first, I tried using a precision 8mm steel shaft. The measurement from the shaft is depicted below .

Despite the 608Z bearings being rated ABEC-7, there was noticeable play between the shaft and the bearing, visible by observing the light pass-through test. .

Second try

As a pragmatic workaround, the M8 threaded rods were wrapped with white Teflon tape until no play was felt anymore; see .

Observation

A similar trace was captured, and the data was processed. The resulting graph can be seen below. .

It can be seen that the $\hat\sigma_k$ still increases when the pedal moves. No significant improvement in standard deviation was observed.

3. Analysis of the influence of damping material on loadcell fluctuations

Loadcell reading fluctuations may be caused by high-frequency or nonlinear disturbances, e.g. motor detent, rail roughness. To attenuate higher frequency components, adding flexible material into the linkage system has been analyzed. In particular, the loadcell linkage adapters have been printed from flexible 95A TPU. To make the block even softer, additional cutouts have been added. The CAD models of the modified blocks are depicted below. .

A GIF demonstrating the flexibility of the printed adapter is depicted below .

A pedal trace has been collected and its plot is shown below. .

In contrast to the previous plots, a significantly reduced increase in the standard deviation when the pedal is being pressed can be observed. While the rolling standard deviation previously reached up to 0.05 kg with rigid plastic adapter blocks, it now typically only reaches up to 0.025kg. That is a substantial improvement. However, in steady state the standard deviation typically was 0.011kg, which was exceeded by a factor of 2 in dynamic situations.

Subjectively, the pedal felt smoother, quieter and closed-loop stability seems to be improved as well, since pedal oscillations were harder to trigger. I haven't felt any added cushion when pressing the pedal compared to the metal/hard plastic adapters. From that perspective, even softer TPU adapters could have been used for the purpose of this test. What hasn't been checked so far is the long-life resilience of the TPU parts. This is an ongoing topic.

Conclusion

This document proposed an algorithm for estimating loadcell reading fluctuations even in dynamic situations. Data was captured from a pedal with mechanical play in the loadcell linkage system and from a pedal (actually the same pedal but with a modified linkage) with zero mechanical play in the loadcell linkage system. The data does not indicate a significant difference in loadcell reading fluctuations.

In the previous section, the influence of using flexible material in the linkage system has been analyzed. The loadcell arm adapters have been 3D printed out of TPU. A similar data trace was collected. The data shows a significant reduction in loadcell reading fluctuations, potentially improving closed-loop pedal behavior and reducing the risk of oscillations.