An Introduction to Tire Modelling for Multibody Dynamics Simulation
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Transcript of An Introduction to Tire Modelling for Multibody Dynamics Simulation
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An Introduction to Tire Modelling for Multibody Dynamics Simulation
SD 652Professor John McPheeUniversity of Waterloo
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Acknowledgement:
Kevin Morency, Automatic Generation of Real-Time Simulation Code for Vehicle Dynamics using Linear Graph Theory and Symbolic Computing, MASc Thesis, University of Waterloo, 2007
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SAE Axis System
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ISO Axis System
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Rolling Resistance (My)
Produced by hysteresis in tire tread and sidewall rubber
My = (Fz)(x)
Normal force Fz is integral of the distributed load
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Braking Force (Fx)
S = (V – wR) / V
0 < S < 1
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Braking Force (Fx)
S = (V – wR) / V
0 < S < 1
Longitudinal Stiffness, CS, is the slope of the Fx vs. S curve at S=0
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Driving Force (Fx)
S = (wR-V) / wR
0 < S < 1
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Lateral Force (Fy) and Aligning Moment (Mz)
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Lateral Force (Fy) and Aligning Moment (Mz)
Cornering Stiffness, C, is the slope of the Fy vs. curve at =0
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Effect of Camber Angle () on Lateral Force (Fy)
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Combined Slip (Fx AND Fy)
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Overturning Moment (Mx)
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Characterizing a Pneumatic Tire:Physical Testing
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Characterizing a Pneumatic Tire:Physical Testing
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Consider how Fx varies with S: 20 data points
Data From Physical Tests
Consider how Fx varies with Fz and S: 202 =
400 data points
Consider how Fx varies with Fz, S,, : 204 =
160 000 data points x5 = 800 000 data points
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Tire Models:Mathematical Functions to Fit Measured Data
Fiala: 6 parameters needed to describe a tire
•Easy to understand the physical significance of all parameters•Simple force and moment equations.•Does not handle combined slip•Effects of normal force and camber are largely ignored.
Pacejka 2002 : 117 parameters needed•Very good fit to experimental data•More complicated force and moment equations
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1. Define a point where tire forces and moments will act on the multibody model
How Tire Forces are Included In Multibody Vehicle Model
P2
P1
C2
C1
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2. Determine an expression for the vertical tire force, Fz, which is required as an input to the tire model.
How Tire Forces are Included In Multibody Vehicle Model
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3. Establish vector directions for longitudinal and lateral components of tire force.
How Tire Forces are Included In Multibody Vehicle Model
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4. Determine kinematic inputs to tire model (S, , )
5. Use a tire model to calculate Fx, Fy, Mx, My, Mz
How Tire Forces are Included In Multibody Vehicle Model
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MapleSim Demo
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The Fiala Tire ModelThe original tire model in MSC.ADAMS
Inputs:
1. Multibody model (mass, rotational inertia)
2. Tire parameters (Cs, C, etc.)
3. The current kinematic state (S, ,, etc.)
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Effect of Normal Force (Fz) on Lateral Force (Fy)