Powertrain Mount Design for Vibration Isolation

The problem

Electric drive units have no engine firing pulses, but they produce high-frequency gear whine and motor torque ripple, and large step torques at launch and regeneration. Mounts must be soft enough to isolate vibration yet stiff enough to limit motion under torque. Placing the six rigid-body modes of the unit on its mounts is a classic NVH packaging task that a student can do with modal analysis and careful modelling of rubber stiffness.

Objectives

• Identify excitation sources and frequency bands for an example drive unit.
• Model the unit as a rigid mass with correct inertia on three or four mounts.
• Represent mounts as springs or bushing connectors with stiffness from an elastomer estimate.
• Run frequency studies, place modes and decouple key directions by mount position and stiffness.
• Estimate transmissibility and check static motion under peak torque.

What you need

Key concepts

Rigid-body modes

A heavy unit on soft mounts has six low-frequency modes (three translations, three rotations). Their frequencies and coupling set how vibration passes to the body.

Transmissibility

Ratio of transmitted to input vibration. Isolation starts above about 1.4 times the mount natural frequency, so mounts are tuned below the main excitation.

Torque roll axis

The axis about which a free rigid body rotates under an applied torque. Placing mounts so the unit rolls about this axis decouples torque-induced motion.

Dynamic stiffening

Rubber is stiffer at higher frequency than in static tests, so a dynamic-to-static stiffness ratio is applied in NVH estimates.

Step-by-step guide

1. 1

   List excitations

   For an example drive unit with 12000 rpm maximum motor speed and an 8-pole motor, list excitation sources: road input up to about 20 Hz, wheel hop near 10 to 15 Hz, body modes, motor torque ripple orders and gear mesh frequency. Compute order frequencies at several motor speeds in a spreadsheet. Set a target band for the rigid-body modes, for example 8 to 20 Hz, avoiding wheel hop and the body's first bending mode.

   Checkpoint: A frequency chart showing excitation bands and the chosen target band for the mounted unit.

2. 2

   Get mass and inertia

   Assemble a drive unit model with housings, motor, gears and inverter, using mass overrides for bought-in parts whose internals you have not modelled. Use Mass Properties to get mass, centre of gravity and the inertia tensor about the CG. Compute the principal axes and the torque roll axis direction from the inertia tensor and the torque direction, and insert it as a reference axis in the assembly.

   Checkpoint: A mass, CG and inertia table and the torque roll axis plotted as a reference axis in the assembly.

3. 3

   Estimate mount stiffness

   For a simple cylindrical or sandwich rubber mount, estimate compression and shear stiffness from the shear modulus, shape factor and geometry using textbook formulas. Apply a dynamic-to-static stiffness ratio, labelled as an assumption, such as 1.3 to 2. Record stiffness in three directions for each mount and compare with supplier data if you have it, because rubber behaviour varies widely between compounds.

   Checkpoint: A stiffness table per mount and direction with formulas and assumptions stated.

4. 4

   Build the frequency model

   In a Frequency study, make the drive unit housing rigid or give it a coarse mesh, and connect each mount point to ground through spring connectors or a bushing connector carrying the three translational stiffnesses in the mount's local axes. Apply fixtures only on the ground side. Check that the mass reported in the study matches Mass Properties, including overridden masses, before trusting the frequencies.

   Checkpoint: The study solves and returns six low modes whose shapes are rigid-body motions of the unit.

5. 5

   Check with a hand model

   Write a six-degree-of-freedom rigid-body model in MATLAB or Excel with the same mass, inertia tensor, mount positions and stiffnesses, assemble the stiffness and mass matrices and solve the eigenvalue problem. Compare the six frequencies and mode shapes with SOLIDWORKS. This independent check catches unit errors and wrongly oriented connectors before you spend time tuning mount positions. Keep the script so every later mount change can be rechecked in seconds.

   Checkpoint: Hand and SOLIDWORKS rigid-body frequencies agree within about 5 per cent.

6. 6

   Place and decouple modes

   Adjust mount positions and stiffness ratios to move all six modes into the target band and to align the roll mode with the torque roll axis. Use modal participation factors or the hand model's mode shapes to see coupling between directions, for example bounce mixing with pitch. Record each iteration in a table and keep the version that best separates the modes from the listed excitations.

   Checkpoint: All six modes inside the target band and the roll mode dominated by rotation about the torque roll axis.

7. 7

   Check torque motion

   Run a Static study with peak drive torque and, separately, peak regenerative torque applied to the housing, with the mounts as springs. Record maximum mount deflection and unit rotation. Check clearance from the unit to the body and subframe, and that deflection stays inside a safe range for the rubber, for example a stated percentage of rubber height, otherwise snubbers are needed.

   Checkpoint: Unit motion under peak torque within an example limit, such as 5 mm at the farthest point, with clearances maintained.

8. 8

   Estimate isolation

   With Simulation Premium, run a harmonic study with a unit force at the housing and plot the force transmitted at the mount ground points against frequency. Without Premium, compute single-degree-of-freedom transmissibility curves for each mode with an assumed damping ratio in Excel or MATLAB. Mark gear mesh and motor torque ripple orders on the plot so isolation at each can be read directly.

   Checkpoint: Transmissibility below 1 at the main motor and gear orders, shown on a frequency plot.

9. 9

   Design mount hardware

   Model one mount in detail with rubber, inner and outer metal parts and a snubber that limits travel under abuse loads. Check the bracket's strength under the worst static case with a converged mesh. Run a Frequency study on the bracket alone and confirm its first natural frequency sits well above the rigid-body band, so it does not amplify vibration at motor or gear orders.

   Checkpoint: Bracket first mode well above the target band, for example above 200 Hz, and bracket factor of safety above 2.

10. 10

    Report

    Report excitations, mass and inertia, stiffness derivation, mode tables before and after tuning, torque motion, transmissibility and mount hardware. State the limits clearly: linear springs, an assumed dynamic stiffness ratio, no body or subframe flexibility and no frequency-dependent damping. Recommend a mount stiffness test on a rig and an in-vehicle vibration measurement to close the loop. Include the hand-model script and the stiffness spreadsheet as appendices.

    Checkpoint: A report whose mode table, motion check and isolation plot can each be traced back to their inputs.

Testing & validation

• SOLIDWORKS and hand rigid-body frequencies agree within about 5 per cent.
• Final modes sit inside the target band away from listed excitations.
• Static motion under peak torque meets the clearance limit.
• Mount bracket modes are well separated from rigid-body modes.

Expected results

A tuned three- or four-mount system for an example drive unit with rigid-body modes placed in a target band, decoupled roll about the torque roll axis, torque-motion limits checked and an isolation estimate at motor and gear orders.

Take it further

• Add hydraulic or frequency-dependent mount models.
• Include subframe flexibility with a shell-meshed subframe.
• Measure a real mount's stiffness on a test rig and update the model.
• Optimise mount positions automatically with a script around the hand model.

Viva and review questions

Learn it at DIYguru

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