Identification and Modeling of a Mountain Bike Front Suspension Subsystem Equipped with a Telescopic Fork and Tire Damping

Type of the Paper: Extended Abstract

Identification and Modeling of a Mountain Bike Front Suspension Subsystem Equipped with a Telescopic Fork and Tire Damping

Noah Schoeneck^1*, James Sadauckas², and Mark Nagurka³

¹Vehicle Measurements Group, Harley-Davidson Motor Company, Yucca AZ 86438, USA; noah.schoeneck@harley-davidson.com
²Trek Performance Research, Trek Bicycle Corporation, Waterloo, WI, 53594, USA; jim_sadauckas@trekbikes.com; ORCID 0000-0002-6055-9047;
³Professor Emeritus, Department of Mechanical Engineering, Marquette University, Milwaukee, WI 53233, USA; mark.nagurka@marquette.edu
*corresponding author.

Name of Editor: Jason Moore

Submitted: 26/04/2023

Accepted: 13/04/2023

Published: 26/04/2023

Citation: Schoeneck, N., Sadauckas, J. & Nagurka, M. (2023). Identification and Modeling of a Mountain Bike Front Suspension Subsystem Equipped with a Telescopic Fork and Tire Damping. The Evolving Scholar - BMD 2023, 5th Edition.
This work is licensed under a Creative Commons Attribution License (CC-BY).

Abstract:

A key component in the mountain bike industry is the telescopic front suspension, which offers the advantage of improved performance when traversing obstacles and rough terrain and during high impact landings. Over the last three decades these suspensions have become more widely adopted and more complex in design. Despite their popularity, there has been limited reported literature focused on the behavior of the telescopic front suspension as a dynamic subsystem in models commonly used in both the motorcycle and automotive industries, e.g., half moto and quarter car models. This paper presents a system identification and modeling approach that promises a deeper understanding of the dynamic behavior of vehicles with telescopic front suspensions.

The quarter car model suspension consists of a set of springs and dampers that act between the body and the wheel as well as another set that acts between the wheel and ground. To reflect the common airborne event that occurs with a mountain bike front suspension subsystem, the half moto model has been modified to explore post-impact behavior. This approach is distinct from the more traditional approach in the literature with the tire starting at rest on the ground.

Figure 1. Half moto free body diagram

Figure 1 shows the free body diagram for a half moto impact model, where m_b is the mass of the body, m_w is the mass of the wheel assembly, k_s and b_s are the stiffness and damping coefficients of the suspension, k_t and b_t are the stiffness and damping coefficients of the tire, z_w is wheel displacement, z_b is the body displacement, and h₀ is the initial height for impact. This height is used to calculate the velocity at impact, v_i, an initial velocity condition for z_b and z_w of the model.

The equations of motion for the model of Figure 1 are

To capture the flight, impact, and landing event routinely seen by a mountain bike front-end, a vertical drop test was utilized. The tire starts the test airborne, i.e., above the ground by an appreciable amount (roughly pedestrian curb height). This leads to relatively higher initial impact than the small perturbations, often forced sinusoids, more commonly seen in quarter car literature. Subsequently, depending on the system parameters, the system may actually bounce and leave the ground again before eventually settling into damped oscillation and decay. A vertical drop test sled fixture was developed and fitted with a telescopic mountain bike front suspension and mountain bike tire. Additional weight was added to the fixture sled to approximate the loading of a mountain bike front end with a rider seated on the vehicle.

Measuring and quantifying individual component parameters is a necessary step before a subsystem model can be developed. A mountain bike front end consists primarily of two components – the tire and the front suspension. Measuring tire parameters can be difficult. Because of that, this work builds on previous work by the authors to quantify the tire parameters obtained by a coefficient of restitution approach. The telescopic front suspension stiffness and damping parameters were found utilizing a shock dynamometer.

Eleven simulations were performed to gain a deeper understanding of each parameter’s contribution to the overall system. The parameters were varied between linear, bi-linear, non-linear or the parameter was eliminated completely from the model to quantify its effects. The peak sled, suspension, and tire displacements from the simulation were compared to the results obtained from the test fixture. The results show that a purely linear model of the front subsystem can lead to suspension displacement errors on the first peak following impact of 13.1 mm (14%) and 14.2 mm (21%) error on the second peak when compared to the measured data on the test fixture. In addition to large peak displacement errors, the linear system does not accurately predict that the subsystem will come to rest but exhibits an underdamped behavior. A bi-linear simulation produces clear improvements of the signature shape of the curve and no longer acts as an underdamped system. Suspension displacement error of the first impact event matches the error seen in the linear model, but the second peak has an improvement seeing 6.6 mm (10%) of error. Tire displacement has very little error on the first impact event, but under predicts the last two peaks. The non-linear model produces suspension and sled displacements that closely match the test data for the first two peaks. The suspension displacement error of the first peak is 2.5 mm (3%) and 1.5 mm (2%) for the second peak. However, the nonlinear simulation exhibits comparable error to the final valley and peaks in the bi-linear system.

A set of simulations was created to explore the effects of tire damping. There is a differing opinion in the literature if it is appropriate to exclude tire damping in the half moto model because the influence of tire damping on the subsystem is presumed small compared to the suspension. Tire damping provided a modest improvement in peak displacement for both the sled and suspension displacements. The quality of the results and stability of the simulation were improved with the incorporation of tire damping. Suspension velocity and tire displacement both displayed unrealistic ringing if tire damping was excluded from the model.

Comparison of the results from the test fixture and modified half moto model provides a systematic process of testing and validating a mountain bike front subsystem equipped with a telescopic front suspension and damped tire. The drop test used here with an appreciable (curb) drop height has added benefits to other small displacement and/or forced perturbation test fixtures often used in aerospace and agriculture applications in that it has the ability to capture impact routinely encountered in mountain bike riding conditions. The fixture under the test conditions described is able to stroke the suspension to 90% of available fork travel and achieve stroking velocities in excess of 1.5 m/s, which captures fork damping dynamics beyond common dynamometer limits.

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Sadauckas, J., Schoeneck, N., & Nagurka, M. (2023) Radial Stiffness and Damping of Mountain Bike Tires Subject to Impact Determined Using the Coefficient of Restitution. Manuscript submitted for publication.