Battery Pack Vibration Analysis Against a Road-Load Profile

The problem

Battery packs are shaken constantly by road input, especially on rough Indian roads. Resonance of modules, busbars or the enclosure can loosen fasteners, crack welds and fatigue busbars. Packs must pass vibration tests in standards, and simulation is used to design out resonances before testing.

Objectives

• Build a pack model suitable for frequency and random vibration analysis.
• Find natural frequencies, mode shapes and mass participation.
• Apply a base-excitation PSD profile and compute RMS and 3-sigma responses.
• Estimate fatigue risk at mounts and busbars.
• Redesign to shift critical modes and reduce response.

What you need

Key concepts

Mass participation

The share of total mass that moves in each mode for each direction. Including enough modes to reach about 80 per cent participation captures most of the dynamic response.

Power spectral density

A random vibration input described as acceleration squared per hertz over a frequency range. Its area gives the mean square acceleration.

RMS and 3-sigma stress

Random vibration gives statistical results. RMS is 1-sigma; peaks are often taken as 3-sigma, exceeded only a small fraction of the time.

Miles' equation

A hand estimate of RMS acceleration of a single-degree-of-freedom system on a flat PSD, using natural frequency, damping and PSD level. It is a useful check on simulation.

Step-by-step guide

1. 1

   Define the vibration environment

   Choose the vibration input: a PSD from the applicable standard, such as those used in AIS-038 Rev 2 or AIS-156 for traction batteries, or measured data from an accelerometer on a vehicle's battery mount. Check the current standard for profile, duration and axes. Note the frequency range and whether excitation is applied in each axis separately. Record the source of every number.

   Checkpoint: A PSD table with frequency range, levels, axes and a stated source.

2. 2

   Prepare the dynamic model

   Defeature the pack, keeping housing, ribs, module mounts, busbars and fasteners. Represent modules as blocks with correct mass and equivalent stiffness, or as Remote Mass with distributed coupling where module flexibility is not important. Use Bolt connectors with preload at mounts. Check model mass and centre of gravity against the detailed design. Model busbars as beams or shells, since their spans often give the lowest local modes.

   Checkpoint: Model mass and centre of gravity within about 2 per cent of the detailed pack.

3. 3

   Run the Frequency study

   Fix the pack at its vehicle mounting points as the base. Request enough modes to cover the PSD range and to reach about 80 per cent mass participation in each axis. Run a mesh refinement until the first few frequencies change by less than about 2 per cent. List frequencies, mode shapes and participation for each direction. Note any modes with very low participation that still matter locally, such as busbar modes.

   Checkpoint: A table of modes with frequencies, participation and a mesh convergence check.

4. 4

   Identify critical modes

   Animate each mode and name what moves: lid panel, module on its mounts, busbar span or whole pack on its brackets. Compare frequencies with the PSD peaks and with known excitation, such as wheel hop and motor orders. Flag modes with high participation inside high PSD bands as critical. Hand-check one mode, such as a busbar span as a beam, against Simulation.

   Checkpoint: A list of critical modes with a hand check of one frequency within about 15 per cent.

5. 5

   Set up the random vibration study

   Create a Random Vibration study using the frequency results, apply base excitation with the PSD curve in one axis, and set modal damping, for example an example 2–5 per cent of critical, stating that it is assumed unless measured. Request RMS results for stress, acceleration and displacement. Repeat for each axis. Check that the requested frequency range covers the full PSD and that the number of modes includes all frequencies up to well above the top of the PSD.

   Checkpoint: Random vibration studies solve for each axis with RMS results available.

6. 6

   Evaluate responses

   Plot RMS von Mises stress and take 3-sigma values at module mounts, bracket welds and busbar joints. Plot RMS acceleration at module centres. Compare 3-sigma stress with yield and with the fatigue limit or S–N data. Use Miles' equation on the dominant mode to check RMS acceleration at one point by hand. Note which mode dominates each critical location by checking the modal contribution, which guides the redesign.

   Checkpoint: 3-sigma stresses tabulated per axis and a Miles' check within a reasonable band of Simulation.

7. 7

   Estimate fatigue risk

   Use Simulation Premium's fatigue from random vibration if available, or apply Steinberg's three-band method by hand with the RMS stress, natural frequency and test duration to estimate cycles at 1, 2 and 3 sigma. Use S–N data for the actual material and, for welded or riveted joints, appropriate joint data. Report damage or life for critical locations. Note that this method is approximate.

   Checkpoint: A fatigue estimate for each critical location, with the method and data source stated.

8. 8

   Redesign

   Shift critical modes above the high-energy band or out of resonance with known excitations: add ribs to the lid, add a mid-span support to long busbars, stiffen brackets or add a cross member under modules. Rerun Frequency and Random Vibration studies. Track frequency change, 3-sigma stress reduction and mass added for each change. Keep mass added small, because extra mass lowers natural frequencies and can work against the change. Check that a new support does not create a new resonance elsewhere.

   Checkpoint: Redesign raises critical modes and reduces 3-sigma stress at the worst location.

9. 9

   Compare with a simple g-load method

   Run a Static study with an equivalent g-load in each axis, such as the 3-sigma acceleration at the module, and compare stresses with the random vibration result. This shows when a simpler method is adequate and when dynamic amplification makes it unsafe, which is useful when Simulation Premium is not available. Show the ratio of random vibration to static stress at each critical location as a dynamic amplification factor.

   Checkpoint: A comparison table between random vibration and equivalent static results.

10. 10

    Report and test plan

    Report the environment, model, frequencies and mode shapes, random vibration results, fatigue estimates, redesign and the static comparison. Write a test plan for a shaker test with accelerometers at module centres and busbars, with resonance search before and after the profile. State that damping is assumed until measured. Include mode shape images for the critical modes and a table linking each to its redesign. Note the resonance search frequencies so the test can be compared with Simulation directly.

    Checkpoint: A report with mode tables, 3-sigma results, redesign and a shaker test plan.

Testing & validation

• Mass and centre of gravity match the detailed model.
• Frequency mesh convergence and 80 per cent mass participation.
• Hand check of one mode frequency.
• Miles' equation check of RMS acceleration.
• Sources stated for PSD, damping and S–N data.

Expected results

A vibration analysis of an example battery pack with mode tables, random vibration RMS and 3-sigma stresses per axis, fatigue estimates, a redesign that moves critical modes and a comparison with a static g-load method.

Take it further

• Measure modes with a hammer test on a prototype and correlate with Simulation.
• Model bolt loosening risk with preload loss under vibration.
• Add a sine sweep (harmonic) study for the resonance search part of a test.

Viva and review questions

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