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Elastomeric Engine Mount

Shape Design Optimization

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Agenda Overview

Bushing-style Elastomeric Engine Mounts

Data Matching Optimization Problem Statement

Problem Setup

Results

Summary

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Bushing-style Elastomeric Engine Mounts

The powerplant is the largest concentrated

mass in the vehicle and if not properly constrained will

cause vibration and shocks to be transmitted into the

vehicle.

The proper design of the rubber

mounts may be the most

effective engineering approach

to improve the ride.

Background

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Bushing-style Elastomeric Engine Mounts

Engine mount (bushing) is made of rubber.

This bushing is encased in a steel sleeve, attached to

the frame of the car.

The steel center cylinder is attached to the engine.

Basic Geometry

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Bushing-style Elastomeric Engine Mounts

Different stiffnesses desired in each principal direction. Compromise between isolation (i.e. soft rates) and gross motion control

(i.e. stiff rates) characteristics

Desired Response

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Bushing-style Elastomeric Engine Mounts

Analysis is achieved in following stages: Thermal shrinkage/cool-down of the molded rubber journal

Diametrical radial swage of outer metal

Displacement of inner tube to determine tangential static rates in principal

directions

Typical Analysis Objectives: Model key aspects of physical manufacturing process

Predict static rates in key principal directions

Prevent detrimental residual stresses (strains)

Predict dynamic rates

Typical Analysis Goals

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Elastomeric Engine Mount Loadings

Cool-down: Mount is cooled from 160 C to 20 C to

simulate mold injection and cool-down

As the mold-bonded bushing cools residual stresses due to

thermal shrinkage puts the rubber in tension, which greatly

reduces durability

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Elastomeric Engine Mount Loadings

Swaging: Reduction of the outer sleeve diameter

The effect of proper swage is to convert the negative-valued

pressures to positive compressive stresses. This improves

durability.

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Elastomeric Engine Mount Loadings

Vertical Compression: Determine Primary Direction

Static Stiffness

Displace inner cylinder in large-void direction

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Elastomeric Engine Mount Loadings

Vertical Tension: Determine Secondary Direction

Static Stiffness

Displace inner cylinder in small-void direction

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Elastomeric Engine Mount Loadings

Lateral/Radial: Determine Third In-Plane Direction

Static Stiffness

Displace inner cylinder in no-void direction

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Elastomeric Engine Mount Optimization

The original rubber bushing was designed with a Shore A

hardness value of 60.

The Purchasing department has acquired a rubber with a

Shore A hardness value of 70. The initial Elastic Modulus difference is ~40%!

You have been requested to re-design the rubber

bushing geometry such that the principal-direction static

bushing stiffness rates are equivalent while maintaining

the peak maximum principal strains to be less than 45%.

Problem Statement

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Elastomeric Engine Mount Optimization

Isight Simflow

Problem Setup

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Elastomeric Engine Mount Optimization

Problem Setup - Abaqus

Geometry – 14 independent, parameterized geometry variables

OD: 101.6 mm

ID: 25.4 mm

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Elastomeric Engine Mount Optimization

Problem Setup - Abaqus

Mesh

Hybrid, reduced-Integration, first-order plane strain

elements (CPE4RH)

Local refinement seeds along radii of voids

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Elastomeric Engine Mount Optimization

Problem Setup - Abaqus

Material

Mooney-Rivlin material model for a 70 Shore A rubber with an effective Poisson’s ratio of 0.4995

Solver

Abaqus/Standard run in a quasi-static fashion

Contact

Self-Contact Pairs with a Coulomb friction coefficient of 0.2

Procedure

Seven analysis stages (steps) to represent manufacturing and desired load-unloading sequences

Computational Resources

Using 4-cores on a 3.0 GHz Quad-Core 64-bit Windows machine, each Abaqus analysis completes in ~ 6 minutes.

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Elastomeric Engine Mount Optimization

Problem Setup – Data Matching

Data Match components are used to compare Simulation and Target curves based on

Absolute area difference between simulation and experiment load-deflection curves

Minimizing the “absolute area difference” objective function brings all the simulation data points in proximity to the experimental data points

Maximum difference between the simulation and experiment curves.

Focuses on reducing the local maximum differences between the two data sets.

When used in combination, these objective functions provide a robust solution to the data matching problem.

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Elastomeric Engine Mount Optimization

Problem Setup – Optimization

Optimization Technique

Hooke-Jeeves with a max of 100 evaluations

H-J is well suited for non-linear design spaces and does not require the calculation of gradients

100 evaluations completes in ~10 wall clock hours

Design Variables

14 geometrical variables

Constraints

Peak Max Principal Strain cannot exceed 45%

Objectives

Minimize Data Match parameters for each loading

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Elastomeric Engine Mount Optimization

Results

A quality fit is found within 50 evaluations

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Elastomeric Engine Mount Optimization

Does the Preload affect the Final Optimal Shape?

Data Match to Target with No Preloading

Cooldown and Swaging not included

A significant shape change is observed as compared

to preloaded optimal shape.

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Elastomeric Engine Mount Optimization

Does the Preload affect the Final Optimal Shape?

“No Preloading” Optimal Geometry Utilized with Preloading

A stiffer-than-expected response would be found for this geometry.

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A significant shape change is

observed between the analyses

A stiffer-than-expected response

would be found for the “No-Preload”

optimal geometry.

Bottom-line:

Include preload effects in

shape optimization analyses

The importance of including preloading effects

Elastomeric Engine Mount Optimization

Preload Excluded

Preload Included

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Elastomeric Engine Mount Optimization

Abaqus Token Reduction Scheme with Isight

Abaqus jobs “launched” via Isight sim-flows use progressively fewer Abaqus

tokens than nominal stand-alone Abaqus job execution

Depends on total number of analyses, number of cores per analysis and

the number of simultaneous jobs

For typical Isight studies up to 60% fewer Abaqus tokens consumed per job

vs. nominal stand-alone execution

Implementation subject to several limitations affecting availability of token

reduction

For this 100-analysis problem, we used 4-cores with one simultaneous job.

The token usage is as follows:Job Number 1 2 .. 6 .. 16 .. 41 .. 100

Abaqus Tokens 8 6 5 4 3 3

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Elastomeric Engine Mount Optimization

Summary

We have learned the following in this study:

Bushing-style elastomeric engine mounts require complex and

competing structural requirements.

Abaqus is able to analyze this class of problem that includes

nonlinear geometry, nonlinear materials and contact.

Preloading effects should be included in this class of problem such

that the optimized shape can meet the design requirements.

Isight automates the steps of a single analysis workflow and then

can systematically evaluate the design based on the input variable

ranges, objectives and constraints.

Abaqus Token Reduction Scheme with Isight can greatly reduce the

cost of Design Exploration studies.