MTB Suspension Load Simulation

Engineering Question

How do you determine realistic design loads for a component as stressed as a mountain bike rear hub? Lab testing and field measurements remain the primary tools, but numerical simulation plays a complementary role: it allows rapid exploration of terrain types, rider weights, and suspension configurations that would be impractical to test experimentally.

Model and Assumptions

The simulation extends the classical 4-DOF half-car model with several MTB-specific features. Tyre contact is unilateral: the wheels can leave the ground, allowing the bicycle to become airborne over obstacles. Rather than prescribing a road profile as a function of time, the model introduces an additional degree of freedom for position along the course and runs as a forward dynamic simulation with terrain contact detection.

High pitch angles on steep terrain mean that tyre-road interactions can occur anywhere around the tyre's circumference, not only at the bottom. Contact detection is therefore circle-to-curve rather than point-to-curve. Both the front and rear suspension forces are two-dimensional because the front fork is inclined relative to the chassis and the rear suspension uses a pivoting linkage.

Treated as a rigid multibody system, the bicycle is three rigid bodies connected by a revolute joint at the rear suspension pivot and a telescopic slider at the front fork — 9 generalized coordinates and 4 constraint equations, giving a system of 13 differential-algebraic equations integrated forward in time with a BDF integrator. A simplified 5-DOF version of the model is available on GitHub in both Python and MATLAB, including visualization, for experimenting with suspension parameter variations such as stiffness, damping and geometry and observing their effect on comfort, dynamic load factors and airborne phases.

Outputs

The model produces the time history of forces at key attachment points — the rear axle and suspension linkage — alongside suspension-travel history, wheel-lift events and chassis-pitch dynamics. The attachment-point force histories are the payoff: they feed directly into the component fatigue and durability assessments that motivated the model in the first place, turning terrain type, rider weight and suspension configuration into quantified design loads for the most stressed parts of the bike.