The Inclusion of Thermal
Deformations in
Flexible Body Models Through
the Use of Modal Forces
Presentation 2003-01
Richard A. Swift, Ph.D., P.E.
Bosch Automotive Corporation, South Bend, IN
Introduction/Overview
ƒ Description of the problem
ƒ Modal forces for thermal deformations
ƒ Examples
ƒ Beam undergoing constrained expansion
ƒ Automotive disc brake rotor coning
ƒ Conclusions
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Problem Definition
ƒ Thermal expansion affects system response
ƒ Thermal Strains
ƒ Altered load distributions
ƒ Modified dynamic response
ƒ Modal Forces for thermal deformations
ƒ Flexible temperature distribution definition
ƒ Scalable in run-time and design-time
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Modal Forces for Thermal Deformation
ƒ Solution 103 in MSC NASTRAN
ƒ INCLUDE ‘mnfx.alt’ in NASTRAN V2001
ƒ Define a temperature distribution (TEMP)
ƒ Use TEMPERATURE(LOAD)= # subcase
ƒ SPOINT number reflects modal force(s)
ƒ Total Modes reflect:
ƒ normal modes
ƒ static correction modes
ƒ residual load modal vectors
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Example - Isothermal Expansion
ƒ Square cross-section beam
4182 GRID, 2235 CTETRA
ƒ 1 m total length
ƒ 0.1 m sides
ƒ MPC end constraints (2-6 DOF nodes)
ƒ Uniform temperature of 1oC
ƒ Steel (E =207 GPa, ν = 0.29, ρ =7820.00 kg/m3, α =11.7E-6 /oC)
ƒ $ MNF Transfer Summary:
ƒ$
64 normal modes
ƒ$
12 static correction modes
ƒ$
1 residual load modal vectors
ƒ$
Total: 77 modes
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Example - Isothermal Expansion
Modal Force Scale Function = 100*time (100oC/second)
Theory: Load = AEα(∆T) = 12.110 MN
ADAMS: Load = 12.450 MN (2.7% error)
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Example - Disc Brake Rotor Coning
ƒ Local stick-slip drives force oscillation
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Example - Disc Brake Rotor Coning
ƒ Two temperature regions - disc and hub
ƒ Uniform disc temperature of 200oC
ƒ Uniform hub region of 100oC
ƒ Iron E = 134 GPa, ν = 0.21,
ρ = 7200 kg/m3, α =12.1E-6 /oC
ƒ MNF Transfer Summary:
ƒ 61 normal modes
ƒ 120 static modes
ƒ 2 residual load vectors
ƒ Total: 183 modes
247mm OD
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Example - Disc Brake Rotor Coning
ƒ Constrained thermal expansion leads to outof-plane deformation (i.e., “coning”)
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Pad Loading with Coning Effects
OD
120
ID
80
OD
60
OD
40
ID
Contact Force (N)
100
Coned Rotor
W/O Coning
20
OB Pad
0
-60
-40
-20
0
20
40
ID
60
IB Pad Contact Point Location WRT Centerline (mm)
120
Coned Rotor
100
W/O Coning
characteristics
Contact Force (N)
80
60
40
20
0
-60
-40
-20
-20
0
20
40
OB Pad Contact Point Location WRT Centerline (m m )
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ƒ Perimeter contact point forces shown
ƒ Coning dramatically alters load
60
ƒ IB pad loads “invert”
ƒ OB pad load uniformity reduced
ƒ System dynamics also strongly
influenced
Conclusions
ƒ Thermal deformations can readily be
included through modal force definitions
ƒ Accurate component response
ƒ Significant system influences can be noted
ƒ MFORCE Approach is flexible
ƒ Modal forces are scalable
ƒ Multiple modal forces may be employed
simultaneously
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