Simulation Study of Brake System Performance

The Conference on Advancing Analysis & Simulation in Engineering | CAASE20nafems.org/caase20 June 16th – 18th | Indianapolis
Simulation Study of Brake System
Performance
Wear Modelling of Brake Pad Due to Friction & Heat Generation
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Virtual Integrated Analytics Solutions, 1400 Broadfield Blvd., Suite
325, Houston,TX 77084
Subhadip Maiti, Senior Simulation Consultant

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June 5th-7th | Cleveland, OH
Industry Process Experience: Technical Capabilities
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Component Design and
Validation using Simulation
FEA based Fracture /
Damage Mechanics / ECA
Design Optimization and
Reliability
Structural Analysis /
Vibration Assessment
Electromagnetic Systems
(Design, Simulation, and
Optimization)
Multi-physics Simulations
(CFD, Flow Analysis, Thermal
Analysis)
S-N and e-N based Fatigue
Analysis (varying
temperatures)
Composites Modelling and
Analysis
Simulation Automation
Digital Mock – Up
Development and Systems
Engineering (Electrical
Cabling / Piping / Ducting)

Contents
• Introduction
• Challenges of Braking System
• Primary Workflow
• Advanced Workflow
• Scope of Optimization
• Conclusion
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T&M Industry Is Evolving Rapidly!
Higher efficiency standards drives more innovation Time to market drives adoption of new methods
Occupant comfort and safety drives more complexity Model proliferation drives more brake customization
Brake System Engineering

Overview: Classification of Brakes
• Frictional brakes works on the principal of friction between contacting surfaces to resist
the motion.
– Other types of brakes include Magnetic brakes or Electrical Brakes.
• The Simulation Study would focus primarily on disc brakes
Frictional Brakes
Disc BrakesDrum Brakes
Fixed Calipers
Floating Calipers
Images Courtesy: GrabCAD

Disc (or Caliper) Brakes
• Disc brakes are today common in passenger vehicles, including motorcycles
– For rear wheels in some vehicles, drum brakes are used for cost and weight
reasons
• Disc brakes are preferred over drum brakes because they offer:
– Better stopping performance
– Quicker heat dissipation capacity
Images Courtesy: Paper published by PSA et al in SCC 2015; Wikimedia Commons
An exploded view of disc brake assembly components
An animation showing the hydraulic
operation for a disc brake

Challenges of Braking System
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Challenges: Brake Performance Varies
Overheated brakes can fail
Cool Brakes
Overheated Brakes
Repeated braking increases stopping distance
Example
Test Track

Challenges: Brakes Can Cause Annoyances
❑ Brake Dust
❑ Noises
❖ Squeal
❖ Groan
❑ Big customer complaints
❖ Trips to dealer and warranty
❖ Poor quality ratings
❖ Recalls
Example of brake squeal
Brake Dust on
Body

❑ Brake cooling affects vehicle drag and lift
❑ Brake pad drag on the rotor reduces range and fuel economy
❑ Excess brake mass increases to energy consumption and decreases ride quality
Excess friction
when driving
Challenges: Brake Systems Affect Range and Efficiency
Excess mass in
rotors

❑ Vehicle testing can not be done until prototypes are available
❑ Bench testing is different than installed conditions
❑ Only limited data can be collected
Challenges: Physical Testing Is Limited
Few ways to measure what
happens in a test
Cooling on a bench is different than on a
vehicle

Primary Workflow
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Image Courtesy: Wikimedia Commons with link here and here

Fully Coupled Thermal-stress Analysis
❑ This procedure is intended for situations where the stress analysis depends on the
temperature field and the temperature solution depends on the stress solution:
there is full coupling between stress and temperature fields
❑ Only one analysis job is required: since temperature and displacement depend on
each other they must be solved for at the same time!
❑ Example: Thermal-stress analysis of a disc brake
– Temperature changes of the brake cause axial and radial deformation; this change in shape
which in turn affects the contact between the pads and the disc (and therefore, the
frictional heat generation)

Performance Evaluation Tests
❑ At a component level, some common tests for a disc brake assembly include:
– Durability analysis of caliper bracket & housing
– Caliper seal analysis
– Contact pressure distribution (disc and pad) during brake application

Durability of Caliper Bracket (1 of 2)
❑ The caliper bracket is critical as it takes frictional forces during braking
– The caliper bracket should not yield or overly deflect during braking
❑ The objective, therefore, is to determine stress and deformation due to braking
– The analysis typically also includes thermal effects due to friction-induced heat
Image and Details: http://www.simulia.com/download/academics/Caliper_Bracket_Paper.pdf
Bracket positioned in the assembly (extreme left), bracket with the location of applied force (left), and 3D model of the bracket (right)

Durability of Caliper Bracket (2 of 2)
❑ Results of Interest
– Stress distribution, especially hotspots (regions of high stress concentration)
which affect the durability of the caliper, and
– Deformation, to be compared with some benchmark value for compliance
❑ The results can be further used for fatigue life estimation
Image and Details: http://www.simulia.com/download/academics/Caliper_Bracket_Paper.pdf
Contours of von Mises stress on the caliper bracket to
observe regions of high stresses

Caliper Seal Analysis
❑ Caliper seal, besides preventing leakage of brake fluid,
also retracts caliper piston after braking
– Piston retraction depends on the profile of the
rubber seal and the groove
❑ Analysis of seal groove geometry requires accurate
material and contact modeling
– Abaqus provides hyperelastic material models and
contact algorithms for such challenging nonlinear
problems
A schematic explaining how the square seal helps with
piston retraction (top), and an axisymmetric Abaqus
model of seal and groove (bottom)
Images Courtesy: www.mustangandfords.com/parts/mump-0209-ford-mustang-brakes/photo-12.html ; Based on paper by Delphi at AUC 2003

Contact Pressure Distribution (1 of 3)
❑ Provide more accurate insights into brake performance
❑ The same model used for:
– evaluating brake squeal modes
– studying the effects of wear
– and other workflows
❑ Brake assembly analysis involves:
– Step 1: Bolt pretension and interference fit resolution
– Step 2: Establish contact between pad(s) and stationary disc
– Step 3: Establish steady state rotational motion
A detailed 3D model of the brake assembly (top). Assembly of springs that secure the brake
pads (center). Caliper and piston, with pressure-loaded surfaces shown (bottom).

❑ Specialized technique to model steady state frictional sliding
– The motion of the rotor is treated as a predefined field
instead of a boundary condition
– The technique saves computational time
– Selective refined mesh is at the initial contact region
– No need of matched mesh between the contacting
surfaces
A meshed model of the disc, with the
close-up of the initial contact region
showing local mesh refinement.

– Step-1: Stress distribution after assembly (bolt) loading and interference resolution
– Step 2: Contact pressure distribution for stationary rotor
– Step 3: Contact pressure distribution when the disc is rotating at a steady velocity
Stress distribution after assembly loads (left). Contact pressure distribution on the outboard
lining for stationary (center) and rotating disc (right).

Advanced Workflow
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Image Courtesy: Wikimedia Commons

Thermo-mechanical Analysis of Brakes (1 of 2)
❑ Friction-induced heat leads to brake fade (reduced stopping performance)
– Along with wear, this may lead to noise and vibration issues (“rumble”)
❑ Uneven thermal bands in disc leads to variations in thickness and brake torque
❑ A fully-coupled thermo-mechanical analysis is required for accuracy
– Friction induces heat, which may affect parameters such as friction coefficient, gap
conductance (across contacting surfaces), and material properties
Based on paper by Jaguar Land Rover at SCC 2015
A detailed finite element model of the
brake assembly for thermal simulation,
with a cross-section to show details

Thermo-mechanical Analysis of Brakes (2 of 2)
– Temperature profiles, thermal bands, thickness variations
❑ A “design of experiments” study can be done to minimize distortion, and study
the sensitivity of braking performance on different disc and pad designs
Temperature contours for two different designs (left). Temperature contours across the disc for the two designs
(center). Disc thickness variation for the two designs (right).

Brake Squeal Analysis
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Brake Squeal Analysis (1 of 3)
❑ “Brake Squeal” is the noise that results from dynamic instability
due to friction between the lining and the disc
– Friction can induce coupling of two neighboring vibration
modes at high frequencies (>1 kHz), with one of the modes
becoming unstable
• Squeal modes, therefore, depend on friction coefficient, besides
other parameters such as caliper pressure and liner wear
– Brake squeal analysis requires complex eigenvalue extraction
• A mode is considered unstable if its real part is positive (> 0)
❑ The initial part of the methodology for brake squeal analysis is
the same as that described for contact pressure distribution
Brake squeal analysis relies on the same brake assembly
model used to estimate contact pressure distribution

❑ After defining the steady state rotational motion (described earlier), the next steps for
brake squeal analysis are:
– Step 4: Extracting natural frequencies (real eigenvalues and modes)
• Natural frequencies are extracted considering the updated stiffness due to
assembly loads, contact interaction, and steady state rotational motion
– Step 5: Extracting complex frequencies (complex eigenvalues and modes)
• Friction-induced damping effects can be optionally considered during this step
❑ Complex eigenvalue extraction can take advantage of the SIM architecture
– SIM allows advantages such as the use of AMS eigensolver (for faster runs), use of
unsymmetric matrices, and accounting for structural and modal damping

❑ Plug-in to compute CCF and CMCF
– Abaqus/CAE provides a built-in plug-in to view CCF (component contribution
factors) and CMCF (component mode contribution factors)
– CCF and CMCF provide a simple way of identifying components contributing
to the unstable mode
The CCF/CMCF plug-in can be accessed from the Plug-ins menu in Abaqus/CAE (left). A dialog box showing
components and a list of unstable modes (center). Contribution of selected components to an unstable mode (right).

Friction Induced Wear Analysis
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Effect of Friction Induced Wear (1 of 4)
❑ Lining wear can have a significant impact on brake performance and operational noise.
Contact pressure in the outboard (left) and inboard
(right) pads before (top) and after (bottom) wear.
* User subroutines require a compatible Fortran compiler to be installed
❑ Effects of wear using “adaptive meshing” in
Abaqus/Standard
– Models arbitrary amount of material “ablation”
or “wear” in a given domain
❑ The “wear law” is usually defined through the user
subroutine, UMESHMOTION*
– A “wear law” defines how the rate of wear
should be calculated from given quantities such
as frictional sliding and pressure

Effect of Friction Induced Wear(2 of 4)
❑ Brake performance depends on factors such as friction coefficient, lining wear, lining
material, and contact pressure distribution
❑ Isight provides deeper insights on sensitivity of brake performances to changes in the
above parameters
– Isight can also be used to optimize brake performance by containing squeal modes
An Isight sim-flow to study sensitivity of brake squeal to design parameters, including correlation at part and system
level with available results (left). Graph in Isight showing results of complex eigenvalue extraction from Abaqus (right).

Optimization
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Conceptual lightweight design
Topology Optimization
- Tosca Structure
Insured reliability
Durability Analysis
- fe-safe
Understand physical behavior
Structural & Thermal Analysis
- Abaqus
Exploration of design alternatives
Parametric Optimization
- Isight
Improved structural integrity
Shape Optimization
- Tosca Structure

Optimization and Durability for Brakes (1 of 4)
❑ Structural and thermal analysis to understand physical behavior
– Detailed geometry creation, meshing, scenario definition using Abaqus/CAE
– The analysis includes bolt loads, and subsequently, moving loads to mimic
loading of the brake disc
Abaqus/CAE is used for complete finite element modelling of the brake assembly (left). Contact pressure developing due to the
applied bolt loads (center). Stresses in the brake disc due to “moving” brake load (right).

❑ Parametric optimization to explore design alternatives
– Brake fade is caused by accumulation of friction-induced heat due to excessive
braking
• Vent holes aid cooling, but should be designed without affecting strength and
performance
– Using Isight, a parametric optimization can be performed to maximize cooling
• Brake area is provided as a constraint (≥ 95% of the disc surface)
Number Position Size
Design parameters used to change vent hole distribution (left). An Isight simflow for getting the optimal design based on specified objectives and
constraints (right).

❑ Results of topology optimization
– Tosca helps reduce the weight by 30% while at the same time, doubling
stiffness
Optimization results
Reference Optimum
Weight
(carrier only)
292g 205g
Max
displacement
1.1mm 0.6mm
Evolution of material distribution in Tosca with each
successive iteration (top). Comparison of results (right).

❑ Durability analysis for fatigue life estimation
– Usually, components are designed for a target fatigue life based on standard usage
– fe-safe provides advanced fatigue algorithms to calculate fatigue life accurately
– fe-safe comes with a built-in material database with fatigue parameters
❑ In this case, we assume 200,000-300,000 braking instances
– Translates to 5-7.5 million cycles
❑ The source for fatigue analysis would be the same FEA model
– Includes bolt loads, centrifugal loads, moving load on disc
𝟐𝑭 𝒓𝒐𝒕𝒐𝒓
𝑭 𝒕𝒊𝒓𝒆
𝑵
Factor of safety (left) and log(life) contours (right)
FOS = 0.7
For infinite life
Fatigue life
340000 cycles
Comparison of life contours for original design (left) and
fine-tuned with shape optimization (right)

Models & References
❑ Paper: Brake Squeal Analysis using a Complex Modes Approach
❑ Paper: High Fidelity Anti-lock Brake System Simulation using Abaqus and Dymola
❑ Dassault Systemes Power of Portfolio
❑ Abaqus Example Problems Manual
❑ FEA Analysis of a Caliper Abutment Bracket
❑ Image and CAD model Courtesy: Wikimedia common & GrabCAD

Thank You!
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