Modal Analysis of a Chassis to Avoid Motor and Road Resonances

The problem

Electric motors and gearboxes excite the chassis at frequencies that rise with speed, and road inputs excite low-frequency body modes. If a chassis mode sits on one of these, the result is noise, vibration and fatigue. Without an engine to mask noise, EV structural resonance is more noticeable to occupants.

Objectives

• Run free-free and mounted frequency studies on a chassis with battery and motor masses.
• Build a Campbell-style chart of excitation orders against chassis modes.
• Change stiffness and mass distribution to separate modes from excitation.
• Validate the first modes with an impact-hammer test.

What you need

Key concepts

Natural frequency and mode shape

Frequencies at which a structure vibrates freely, each with a characteristic deformed shape such as bending or torsion.

Excitation order

A frequency that is a multiple of rotating speed, such as once per motor revolution or gear mesh frequency. Orders sweep through frequency as speed changes.

Campbell diagram

A plot of frequency against speed showing excitation orders as lines and natural frequencies as horizontal bands. Crossings show potential resonance.

Mass participation

How much of the structure's mass moves in a mode in each direction. Modes with high participation are easier to excite by base motion.

Step-by-step guide

1. 1

   Define the chassis and excitations

   Take an example electric three-wheeler or small car chassis and list the main masses: battery, motor and gearbox, body and payload. List excitations: motor rotational order, a stated multiple for electromagnetic orders based on pole and slot counts, gear mesh frequency from tooth count and ratio, wheel rotation and road inputs, typically low frequency. Calculate their frequencies across the vehicle speed range.

   Checkpoint: An excitation table with each source's frequency as a function of vehicle speed, and assumptions stated.

2. 2

   Build the analysis model

   Model the chassis with Weldments and simplify brackets. Represent the battery, motor and body masses with Remote Mass features at their centres of mass connected to the mounting faces, with stated mass and inertia, or with simple solid bodies of the right mass. Assign materials. Create a free-free configuration and a mounted configuration with springs at the suspension points. Check the remote mass connections are not too stiff, since rigid connections can add false stiffness.

   Checkpoint: A model whose total mass from Mass Properties and remote masses matches the vehicle's example mass.

3. 3

   Run the free-free study

   Run a frequency study with no fixtures and ask for the first 12 modes. The first six should be near-zero rigid body modes; if not, check connections. Note the first elastic modes: usually global torsion and bending. Animate each mode and record its frequency and mass participation. Check convergence by refining the mesh until the first elastic frequencies change by less than about 2 per cent.

   Checkpoint: Six near-zero rigid body modes, a converged list of elastic modes with shapes described and mass participation recorded.

4. 4

   Run the mounted study

   Add elastic supports or spring connectors at the suspension mounts with stiffness from the example suspension and tyre, or fix them for a bounding case. Run the frequency study again. Compare the mounted modes with free-free and identify low-frequency body modes such as bounce and pitch, and higher structural modes. Explain which case matches which real situation. Record which suspension stiffness values you used and their source, since they control the low-frequency body modes.

   Checkpoint: A mounted mode table compared with the free-free table, with each mode's shape and frequency.

5. 5

   Build the Campbell chart

   In MATLAB or Excel, plot each excitation order as a line of frequency against vehicle speed, and each chassis mode as a horizontal line. Mark crossings within the normal speed range. Add a margin band, for example ±10 per cent of each natural frequency, and highlight orders that enter it. Prioritise crossings at common cruising speeds and high-participation modes. Export the chart as an image for the report with crossings labelled by mode number.

   Checkpoint: A Campbell chart with crossings highlighted and ranked by speed and mode importance.

6. 6

   Change the design

   For each important crossing, decide whether to raise or lower the mode. Increase torsional stiffness with a cross member or closed section, add a bracket stiffener near the motor mount, or change motor mount isolator stiffness. Use a Design Study to sweep a member size or wall thickness and track the frequency of the targeted mode and frame mass. Choose a change that clears the margin band with least mass.

   Checkpoint: A design change that moves the targeted mode out of the margin band, with mass change recorded.

7. 7

   Check mode shape locations

   Look at where the target modes have large motion: battery tray, motor mount or floor panel. Mounting the motor at a node of a mode reduces excitation. Plot displacement for each mode and record motion at the motor and battery mounts. Use this to adjust mount positions as well as stiffness. Moving a mount closer to a node can be cheaper than adding stiffness. Check that any new mount position still fits the packaging and keeps the drive alignment.

   Checkpoint: A table of relative motion at the motor and battery mounts for each key mode.

8. 8

   Validate with a hammer test

   Hang the chassis or a scaled frame on soft bungee supports for free-free conditions. Fix an accelerometer at a chosen point and tap with an impact hammer at several points. Compute frequency response functions and pick peaks for the first modes. Compare with the free-free model and explain differences, such as welds, joints and mass representation. Repeat each tap several times and average to reduce noise, and check coherence to confirm good data.

   Checkpoint: Measured first elastic frequencies compared with the model, with the difference stated for each mode.

9. 9

   Update the model

   If measured and predicted frequencies differ by more than a stated amount, adjust uncertain parameters such as joint stiffness or remote mass inertia within physical limits, and rerun. Do not tune beyond what you can justify. Check that the updated model still matches the static stiffness if measured. Recheck the Campbell chart with the updated model. Record each parameter change and its justification in a table so the update can be reviewed.

   Checkpoint: An updated model within the stated difference of measured frequencies and a revised Campbell chart.

10. 10

    Report

    Report excitation sources, model setup, free-free and mounted results, Campbell chart, design changes, hammer test and model updating. State limits, such as linear analysis without damping and simplified masses. Recommend a forced-response or harmonic study as a next step if your licence allows, to estimate vibration amplitudes. Include mode shape images and the measured frequency response functions. Explain which crossings remain and why they are acceptable, such as being outside normal speeds or at low-participation modes.

    Checkpoint: A report linking excitations, modes, design changes and test results.

Testing & validation

• Six rigid body modes near zero in the free-free study.
• Mesh convergence of key frequencies.
• Hammer test frequencies compared with the model.
• Campbell chart crossings cleared after design changes.

Expected results

A modal analysis of an EV chassis with a Campbell chart of motor, gear and road excitation, design changes that move critical modes away from excitation, and validation against impact-hammer measurements.

Take it further

• Run a harmonic or random vibration study (Simulation Premium) for forced response.
• Optimise motor mount isolators for vibration isolation.
• Add a battery pack internal model and study its modes.

Viva and review questions

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