MSc Coursework
Quarter-Car Suspension Analysis
A passive suspension study linking force balance, coupled vibration modes and road-input response. The analysis examines how spring stiffness and damping influence body displacement, acceleration, suspension travel and tyre loading.
Project at a Glance
- Approach
- Linear two-degree-of-freedom suspension model with a constrained 144-point spring/damper comparison.
- Key Finding
- 21.4% lower body displacement RMS for the nominal bump, with 9.3% higher peak dynamic tyre load.
- Tools
- Python reference · MATLAB implementation · Numerical dynamics
- Evidence
- Executed Python reference, inputs, code and numerical outputs; MATLAB execution remains unverified.
Objective
Derive a two-degree-of-freedom quarter-car model and assess changes that reduce body motion while accounting for acceleration, available suspension travel and dynamic tyre load.
Model and Method
The model represents a 303.3 kg sprung mass and a 43.7 kg unsprung mass connected by a spring and damper, with tyre stiffness and damping linking the wheel to the road. It uses linear elements and vertical motion about static equilibrium. Free vibration is evaluated from prescribed offsets. Road excitation is a 30 mm smooth bump with an assumed 0.5-second duration.
Vibration Modes
The coupled undamped natural frequencies are 1.157 Hz for the body-dominated mode and 10.680 Hz for wheel hop. Both masses participate in each mode. The free-response energy decays as the dampers dissipate the initial vibration.
Design Comparison
A 144-point constrained grid compares spring and damper settings under identical road input and zero initial motion. Reducing suspension stiffness by 30% and doubling damping reduces body RMS displacement from 7.148 to 5.618 mm, a 21.4% reduction. Unweighted acceleration RMS decreases by 10.8%, while peak absolute dynamic tyre load increases by 9.3%. These are numerical results for the stated bump, not measured vehicle performance.
Trade-offs and Limitations
The modified design increases direct static suspension sag from 168.78 to 241.12 mm. For a shorter 0.25-second bump, acceleration RMS increases by 39.3%, despite lower displacement RMS. This prevents a general comfort-improvement claim. The model excludes suspension geometry, nonlinear elements, bump stops, pitch and roll; no experimental validation or ISO comfort classification is claimed.
Reproducible Reference
The downloadable package includes SI-unit inputs, a Python implementation, run instructions, metric tables and time-series output. A fresh run reproduced the reported modal frequencies and nominal design comparison. Numerical checks confirmed stable poles, decreasing free-response energy and agreement with tighter solver tolerances. These checks establish numerical consistency, not experimental validation.
Engineering Implications
A suspension change that reduces body movement under one road input can worsen acceleration or tyre loading under another. I would assess a wider set of road conditions and physical suspension constraints before selecting a practical design.
MATLAB Status
The MATLAB implementation is available alongside the checked Python reference. It has not been executed in MATLAB. The package explains how to run it and compare its outputs with the reference results.
Checked Nominal-Bump Comparison
| Metric | Baseline | Modified |
|---|---|---|
| Body displacement RMS (mm) | 7.148 | 5.618 |
| Body acceleration RMS (m/s²) | 0.3802 | 0.3390 |
| Peak dynamic tyre load (N) | 610.1 | 666.6 |
| Direct static sag (mm) | 168.78 | 241.12 |
Sensitivity to Bump Duration
| Duration (s) | Body RMS: baseline → modified (mm) | Acceleration RMS: baseline → modified (m/s²) |
|---|---|---|
| 0.25 | 4.152 → 3.346 | 0.3657 → 0.5093 |
| 0.50 | 7.148 → 5.618 | 0.3802 → 0.3390 |
| 1.00 | 9.423 → 8.138 | 0.2809 → 0.1871 |
Report and Simulation Code
Source: Passive Quarter Car Suspension Analysis report prepared 7 October 2026, using the individual parameters in the supplied University of Hertfordshire class list. Road timing, duration and initial velocities are explicitly stated modelling assumptions.