Suspension & Sway

Suspension & Sway (suspension)

Purpose

Screen vehicle roll response and lateral load transfer under cornering acceleration. Computes roll angle, roll moment, and wheel load transfer for sprung-mass suspension geometry screening.

Physics & theory

Lateral acceleration $a_y$ on sprung mass $m_s$ creates inertial force $F_y=m_s{a}_y$ at the center of gravity (CG). This force times CG height $h$ produces roll moment about the roll axis: $M_{\mathrm{roll}}=F_y\cdot (t/2)$ referenced to track width $t$ and wheelbase geometry in simplified models.

Roll angle $\varphi =M_{\mathrm{roll}}/k_{\varphi }$ depends on roll stiffness $k_{\varphi }$ (spring, anti-roll bar, and tire vertical rates combined). Load transfer across track: $\Delta W=F_{y}h/t$ increases outer wheel load and reduces inner — affects tire grip limits.

Dynamic analysis requires careful identification of mass, stiffness, and damping distribution. Natural frequencies depend on boundary conditions — a cantilever beam has fundamentally different modes than a simply supported beam of the same dimensions.

Damping limits resonant amplification; lightly damped structures (( zeta < 0.05 )) can see transmissibility peaks exceeding 10 near resonance. Separation margin between operating excitation and natural frequency should typically exceed 15–20% for rotating machinery.

Governing equations

Numerical method

Closed-form roll and load transfer (engine). Roll angle in degrees compared to stability thresholds (≤ 2° stable, ≤ 5° moderate, > 5° high roll).

Inputs

Outputs

• Lateral force, roll moment, roll angle (degrees), load transfer, design status.

Design codes & checks

• Indicative: Roll angle and load transfer screening

Assumptions & limitations

• Steady-state cornering; no transient roll dynamics or damping.
• Rigid body sprung mass; no compliance frequency analysis.
• Does not compute understeer gradient or tire friction ellipse.
• Anti-roll bar tuning requires detailed suspension model beyond this screen.

Verification

• CI: suspension-indicative-01.json
• Engineer sign-off: validation-master-checklist.md

References

1. Gillespie, T. D. Fundamentals of Vehicle Dynamics. SAE International.
2. Milliken, W. F., & Milliken, D. L. Race Car Vehicle Dynamics. SAE.
3. Reimpell, J., et al. The Automotive Chassis, 2nd ed. SAE.
4. ISO 4138:2012. Passenger cars — Steady-state circular driving behaviour.
5. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.