The Altair Bushing Model for Multibody Simulation

The Altair Bushing Model for

Multibody Simulation

Ingo Nolden

June 25, 2014

Copyright © 2012 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.

Development Partners

• Detailed Specifications

• Bushing Testrig Data

• Testing

• Real-World Full-Vehicle and Suspension-Models for thorough testing

(USA)


Applications for Bushings

• Function

• Absorb shock

• Reduce vibration

• Transmit power

• Eliminate metal-to-metal contact

• Tolerate misalignment

• Industry

• Automotive (cars, trucks, buses & other variants)

• Farm equipment (harvesters, combines, etc.)

• Industrial machines

• Construction machinery

• Marine Industry (boats, ships, etc.)

• Helicopters, etc.


Rubber Bushings In a Car

Rear knuckle

bushing

Disc brake

caliper bushings

Control arm

bushing


Spherical Joint can be modeled as a bushing


How do Bushings/Joints behave?

• Bushing:

• Stiffness is nonlinear

• Damping changes with amplitude and preload, but only little with frequency

• Isotropic bushings don‘t change stiffness at different angles (coupling )

• Memory Effect

• Hydromount:

• Have large damping in a specific frequency range

• Inherit most of the rubber bushing properties due to rubber shell

• Spherical Joint:

• Is isotropic (coupling)

• Has friction on the sphere surface

• Assembly behaviour:

• Attached components are flexible

• Attached components can collide


Ho do rubber bushings and hydromounts behave

• Rubber Bushings behavior are complex

Displacement

Fo

rce


Ho do rubber bushings and hydromounts behave

• Separate the static stiffness from the damping

+ =

= +

• And solve with static and dynamic models

𝐹(𝑥, 𝑥 ) 𝐹𝑠(𝑥) 𝐹𝑑(𝑥 )


One frequency/amplitude/preload

• Consider different preloads/operating points

Displacement

Fo

rce

Point of

Dynamic

Stiffness

Point of

Static

Stiffness


Why an “Altair Bushing”

• Bushings are complex – Forces lag Displacements at steady state

DX +X

-X

DF +F

-F

DynamicStiffness=

DF

DX

∆𝑡



• Dynamic Stiffness and Loss Angle for different Amplitudes at the same

preload as function of the frequency

Dyn

am

ic S

tiff

ness

Frequency (Hz) 0 300

500

1100

1.0 mm

0.5 mm

0.3 mm

0.1 mm

Lo

ss A

ng

le

Frequency (Hz) 0 300

500

20°

1.0 mm

0.5 mm

0.3 mm

0.1 mm



• Bushings are complicated: “Operating Point” Dependence

0 100 200 300 400 500 600 -100 -200

400

600

800

Dyn

am

ic S

tiff

ness

Operating Point

10 Hz

20 Hz

40 Hz

60 Hz


Altair Bushing Model Design Decisions

• The bushing is described by a bushing property file

• The property file defines the Bushing as „lying on the table“

• Mount conditions, DOE adjustments are NOT part of the Bushing (file)

• The software will make sure, that the above rules can be observed in

practice


Implementation Architecture

• Solver Support:

• Available for Windows & Linux

AltairBushingCore

(.dll/.so)

Matlab/Simulink (S-Function)

MotionSolve (GSE+GFORCE)

Simpack (UFORCE)

ADAMS/Solver (GSE+GFORCE)

UserForceMethodB UserForceMethodA


Implementation Scenarios

• Preprocessing Support

Matlab/Simulink MotionView

Simpack ADAMS/Car

• S-Function Subblock

• Combined Subblocks for

Friction + Mount Stiffness

• Full GUI support equivalent to

other modeling entities

• Substructure with Bushing

capabilities inside

• Full GUI support equivalent to

other modeling entities and for

all capabilities

• ac_bushing derived UDE


Workflow

Fitting Tool

Test

Data

Bushing

Property

File MBD Solver

Bushing

Simulation

Model

Solver

Results

Solver

Input


Stiffness

• Constant Stiffness (concept phase)

• The property file defines a stiffness coefficient for the direction

• Cubic Stiffness (concept phase)

• The property file defines two slopes and two force values for specific

displacements

• Spline-Stiffness (measured data)

• The property file defines a table of displacement and forces Spline

Stiffness

Cubic

Stiffness

Constant

Stiffness


Damping

• Constant Damping (concept phase)

• The property file defines a viscous damping

coefficient for the direction

• Rubber Damping (measured data)

• The property file defines coefficient gained from a

fitting process

• Hydromount-Damping (measured data)

• The property file defines more coefficients gained

from a fitting process

Rubber Damping

Hydromount Damping

Constant

Damping


Coupling


• Asymmetric, Anisotropic Example: Fy vs Y

The Altair Bushing Model: Coupling

Existing Coupling Modified Coupling


External Friction

• The external frictions intent is to be used with ball joints

• The external behaviour is a friction torque as a result of rotations

in the joint

• It can be used with any combination of rubber or hydromount

force methods

• The friction is using the LuGre friction model

and is defined in an on-surface translational

model (e.g. bristle stiffness and damping is

translational)

• Instead of LuGre, the Dahl model can be used

by simply setting a few parameters to zero


Mount Stiffness

• For each of the connected bodies, one can define the local stiffness and

damping, so that flexible behaviour of those can be approximated when

flex bodies are not available or even geometry has not been designed

• This is also useful in the conceptual phase, when hardpoints are still

subject to change

• The stiffness can only be defined in the bushing local coordinate

system


Mount Limits

• For each translational or rotational modes and for both positive and

negative direction of deflection, the motion of the bushing can be

further limited by bumpstop like forces

• The forces use an IMPACT function

• Can be used to model clash between the connected bodies of the

bushing at large deflections


DOE

• Since all the bushing properties are defined in a file and the files is

expected to represent a real bushing, a method for changing those

properties for a single simulation must be invented

• The Bushing Simulation Model will read a special „DOE-File“, which

contains parameter updates for the property file

• Preprocessors can provide methods to generate those file in an

automated way and interface with DOE methods in those programs


How does it all work together?

𝐹𝑥 = 𝐹𝑠𝑡𝑎𝑡 𝑥 + 𝐹𝑑𝑦𝑛(𝑥, 𝑥)

𝐹𝑦 = 𝐹𝑠𝑡𝑎𝑡 𝑦 + 𝐹𝑑𝑦𝑛(𝑦, 𝑦)

𝐹𝑧 = 𝐹𝑠𝑡𝑎𝑡 𝑧 + 𝐹𝑑𝑦𝑛(𝑧, 𝑧)

𝑇𝑥 = 𝑇𝑠𝑡𝑎𝑡 𝑟𝑥 + 𝑇𝑑𝑦𝑛(𝑟𝑥, 𝑟𝑥)

𝑇𝑦 = 𝑇𝑠𝑡𝑎𝑡 𝑟𝑦 + 𝑇𝑑𝑦𝑛(𝑟𝑦, 𝑟𝑦)

𝑇𝑧 = 𝑇𝑠𝑡𝑎𝑡 𝑟𝑧 + 𝑇𝑑𝑦𝑛(𝑟𝑧, 𝑟𝑧)

Couplin

g

Couplin

g

𝑥, 𝑥

𝑦, 𝑦

𝑧, 𝑧

𝑟𝑥, 𝑟𝑥

𝑟𝑦, 𝑟𝑦

𝑟𝑧, 𝑟𝑧

𝑥, 𝑥 𝐹𝑥 = 𝐹𝑙𝑖𝑚𝑖𝑡(𝑥, 𝑥) 𝐹𝑥

𝑦, 𝑦 𝐹𝑦 = 𝐹𝑙𝑖𝑚𝑖𝑡(𝑦, 𝑦) 𝐹𝑦

𝑧, 𝑧 𝐹𝑧 = 𝐹𝑙𝑖𝑚𝑖𝑡(𝑧, 𝑧) 𝐹𝑧

𝑟𝑥, 𝑟𝑥 𝑇𝑥 = 𝑇𝑙𝑖𝑚𝑖𝑡(𝑟𝑥, 𝑟𝑥) 𝑇𝑥

𝑟𝑦, 𝑟𝑦 𝑇𝑦 = 𝑇𝑙𝑖𝑚𝑖𝑡(𝑟𝑦, 𝑟𝑦) 𝑇𝑦

𝑟𝑧, 𝑟𝑧 𝑇𝑧 = 𝑇𝑙𝑖𝑚𝑖𝑡(𝑟𝑧, 𝑟𝑧) 𝑇𝑧

general_state_equation

(GSE)

Bushing &

Mount Limits


How does it all work together?


The Altair Bushing Model

• Thank You!