Rotor Contact

Braking Fundamentals a Study of the Dynamics of Disc Brakes and Pad/Rotor Contact by Jared Feist An Engineering Project Submitted to the Graduate Facu...
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Braking Fundamentals a Study of the Dynamics of Disc Brakes and Pad/Rotor Contact by Jared Feist An Engineering Project Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the degree of Master of Engineering Major Subject: Mechanical Engineering

Approved: _________________________________________ Ernesto Gutierrez-Miraete, Thesis Adviser

Rensselaer Polytechnic Institute Troy, New York December, 2014

CONTENTS Braking Fundamentals a Study of the Dynamics of Disc Brakes and Pad/Rotor Contact . i LIST OF TABLES ............................................................................................................ iv LIST OF FIGURES ........................................................................................................... v LIST OF SYMBOLS ........................................................................................................ vi ACRONYMS AND DEFINITIONS ............................................................................... vii KEYWORDS .................................................................................................................. viii ACKNOWLEDGMENT .................................................................................................. ix 1. Introduction.................................................................................................................. 1 1.1

Background ........................................................................................................ 1 1.1.1

1.2

Principle of Disc Brakes......................................................................... 1

Problem Description........................................................................................... 2

2. Theory and Methodology ............................................................................................ 4 2.1

Theoretical Background ..................................................................................... 4

2.2

Finite Element Model Definition ....................................................................... 6 2.2.1

Part Geometry and Mesh........................................................................ 6

2.2.2

Materials ................................................................................................. 8

2.2.3

Assembly, Interaction ............................................................................ 8

2.2.4

Loads and Boundary Conditions .......................................................... 10

3. Results........................................................................................................................ 11 3.1

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4. Conclusion ................................................................................................................. 12 4.1

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5. References.................................................................................................................. 13 6. Appendices ................................................................................................................ 15 6.1

Vehicle Dynamics ............................................................................................ 15 6.1.1

Aerodynamic Drag ............................................................................... 15 ii

6.1.2

Driveline Drag...................................................................................... 15

6.1.3

Grade .................................................................................................... 15

6.1.4

Brake Proportioning ............................................................................. 15

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LIST OF TABLES

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LIST OF FIGURES Figure 1 – Brake Rotor ...................................................................................................... 1 Figure 2 – Brake Pads ........................................................................................................ 2 Figure 4 – 3D Disc Geometry............................................................................................ 7 Figure 5 – 3D Pad Geometry ............................................................................................. 7 Figure 6 – Disc Mesh ......................................................................................................... 8 Figure 7 – Pad Mesh .......................................................................................................... 8 Figure 8 – Brake FEM Assembly ...................................................................................... 9 Figure 9 – Initial Gap ......................................................................................................... 9 Figure 10 – Tie Constraint ............................................................................................... 10 Figure 3 – Simple Disk Brake Schematic [2] .................................................................. 11

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LIST OF SYMBOLS

vi

ACRONYMS AND DEFINITIONS

vii

KEYWORDS

viii

ACKNOWLEDGMENT Type the text of your acknowledgment here.

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1. Introduction 1.1 Background A moving vehicle possesses kinetic energy whose value depends on the weight and speed of the vehicle. This energy must be partially or completely dissipated when the vehicle is slowed down or brought to a stop. The function of automotive brakes is to convert a vehicles kinetic energy at any time into heat energy by means of friction. Sentence explaining how this study will focus on the friction aspect. 1.1.1

Principle of Disc Brakes When a vehicle is in motion, it has kinetic energy based on its mass and velocity.

To completely stop a car, the braking system will use friction force to oppose the rotational forces of the wheels. An automotive brake system is a hydro-mechanical system used by the operator to control speed. This system can be broken down into many different hydraulic and mechanical components; this project will focus on the primary friction components a disc brake system. 1.1.1.1 Brake Disc The brake disc, also called the rotor, is connected to the wheel hub which makes up the rotating component within the brake system. The rotor also provides the friction surface for the pads, which generates braking torque. Rotors usually are vented or cross drilled to aid in the dissipation of heat. A typical rotor can be seen in Figure 1.

Figure 1 – Brake Rotor 1.1.1.2 Brake Pads The brake pads consist of a stamped steel baking plate to which the friction material is attached. Brake pads are housed within a brake caliper, make up the non-rotating 1

component, and provide the interface to the rest of the brake system. The material, also called lining is what actually engages the rotor surface creating friction to generate braking torque. Typical pads can be seen in Figure 2.

Figure 2 – Brake Pads

1.2 Problem Description This project will analyze a typical domestic passenger car with a mass (m) of 1650 kg, a tire radius (R) of 660.4 mm, and a brake pad surface area (Ap) of 10,700 mm2. Assuming the vehicle has an initial linear velocity (v1) of 40 km/h and has to come to complete stop (v2) 0 km/m. The Society of Automotive Engineers (SAE) Handbook contains requirements and testing procedures for automotive braking systems. Without going in the details of every test, the deceleration requirements for in-service brake performance of passenger car and light duty trucks up to 4500 kg is between 2.4 m/s2 and 5 m/s2 not to exceed 6 m/s2. A simplified finite element disc brake system will be modeled using the physical characteristics outline above. Explicit finite element analysis (FEA) will be performed to determine the inputs of the independent system variables needed to meet the SAE requirements for passenger vehicle braking performance. These results will also be compared to the theoretical background typically used in the commercial automotive industry to design passenger vehicle brake systems. The contact pressure will depend on the size and style of brake pad used in application. Load variation is known to affect coefficients of friction; studies show typical coefficients of friction fluctuate between 0.3 and 0.5 through a pressure range of 1 to 2 MPa. In general the interaction between brake pads and rotors involve dry sliding contact at varying speeds and contact forces. Dry friction is the resistance of relative motion between two solid surfaces in contact at rest or in motion. Friction is often

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quantified as a ratio of normal force (FN) to lateral or tangential force (Ft), by the friction coefficient (μ). Typical clamping forces (FN) for normal braking are between 6kN and 10kN. These variables will be manipulated within the finite element model (FEM) to accurately represent and study the braking scenario.

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2. Theory and Methodology 2.1 Theoretical Background For simplicity it will be assumed that stopping is be completely attributed to the brakes on a level grade and will ignore all other forces associates with vehicle deceleration, such as aerodynamic drag, rolling resistance and any driveline drag that may be associated a vehicle’s powertrain. The total kinetic energy of a vehicle may be given by Equation [1]. =

1 2 [1]

Assuming the average braking force (FAvg) times distance traveled (x) is equal to kinetic energy FAvg can be determined by Equation [2]. =

2 [2]

The average power (PAvg) absorbed by the brakes is given by Equation [3]. =

2 [3]

When braking a moving vehicle to a standstill, the work done by the brakes must be equal to the initial kinetic energy possessed by a vehicle and combining above two equations and solving for average braking force can be determined. Braking power (Pbrakes) necessary to stop this kinetic energy is the product of the force and initial velocity of the vehicle, Equation [4]. =

∙ [4]

By substituting the momentum equation and converting linear motion to rotational speed (ω) and acceleration (α), where R is the vehicles tire outer radius, results in Equation [5]. =

( )

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[5] Braking is accomplished through friction force (ff) between the pad and rotor. It is important to note that a vehicle’s disc brake system as a whole is typically comprised of one rotor per wheel (four) and at least two pads per rotor (eight). Therefore, when discussing the friction force per unit area the sum total of pad areas needs to be considered when calculating the work done during braking. This friction force per unit area is assumed to be constant over the surface and is directed in the opposite direction of the disc’s rotational velocity. Braking power can calculated as the integral over the contact surface of a single pad times the total number of brake pads in the system as shown by Equation [6]. =8 ( ) ( ) [6] The integral in Equation [6] will be approximated as the pad surface area (Ap) times the distance from the center of rotation to the pad’s center of mass (rm) as shown in Equation [7]. =

∙ [7]

By combining Equations [5], [6], and [7] solving for friction force as shown in Equation [8] results in an idealized braking scenario to which the later finite element model can be validated against. =

8 [8]

The analysis of the torque capacity of a disc brake can be done by assuming uniform pressure over the pad in general Equation xx = [] Looking at the differential area on the pad surface, this becomes Equation xx. 5

= [] The total force on the pad face may be obtained by integrating Equation xx over the face of the friction material making sure θ is in radians. = [] =

∆ 4

( − ) []

The frictional force on the face of the pad is simply the normal force (FN) times the friction coefficient (μ) for the pad rotor combination. The braking torque can be found by integrating the product of the frictional force and the radius. =

=

∆ 16

(



) []

2.2 Finite Element Model Definition There are two distinct methods to solve finite element problems, implicit and explicit. The implicit method solves for a static or dynamic equilibrium, while the explicit method solves transient dynamic response problems using an explicit direct-integration procedure. The finite element code used to model the brake pad rotor system herein will utilize ABAQUS/Explicit, Abaqus 6.13-EF2 to solve a dynamic simulation of brake pad to rotor contact and ABAQUS/CAE, Abaqus 6.13-EF2, for modeling the brake system. 2.2.1

Part Geometry and Mesh The brake FEM used is a simplified version of a typical disc brake system used

in domestic passenger vehicles. Figure 3 shows a simplified 3D solid disc, which allows the model to use coarser meshes than would be required to model the details of a typical

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brake disc with complicated geometrical features such as cooling ducts and bolt holes.

Figure 4 shows simplified 3D pad geometry and is modeled such that it can only contact part of the circumference of the disc.

Figure 4 – 3D Pad Geometry

Figure 3 – 3D Disc Geometry

The rotor has an outside diameter of 355.6 mm, an inside diameter of 203.2 mm, and a thickness of 31.75 mm. The pad surface area is 10,700 mm2. The FEM is further simplified by making it symmetrical about a plane normal to the z-axis. Therefore, only half of the disc thickness and one pad is modeled, and symmetric boundary conditions are applied. Each model was meshed dependently on the part. Figure 5 shows the disc mesh with a global seed size of 0.01 and an edge seed of five to obtain an acceptable number of elements through the thickness. Figure 6 shows the pad mesh with a global seed size of 0.0055 and a similar edge seed of five to get an acceptable number of elements though the thickness. 7

Figure 6 – Pad Mesh

Figure 5 – Disc Mesh

Both pad and rotor utilize eight-node linear brick (C3D8) fully integrated elements in order to give more resolution at the surface than reduced integration (C3D8R). Artificial incompressible bending or locking is not a concern in this analysis. Since the FEM was simplified by using symmetric boundary conditions bending of the disc is not an issue. Both pad and rotor contact surfaces were modeled as flat, so a quadratic or curved surface definition is not necessary. The C3D8 element used throughout the analysis is the most computational efficient and will provide accurate analysis results. 2.2.2

Materials Elastic material properties were used for the analysis; the values are summarized

below. 2.2.3

Assembly, Interaction A reference point was established as the center of rotation at the global origin (0,

0, 0). The FEM assembly was created based on the pad and rotor simplifications outlined in section 2.2.1 and the center of the rotor was arranged coincident to the center of rotation as seen in Figure 7.

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Figure 7 – Brake FEM Assembly

Figure 8 – Initial Gap Figure 8 shows the Pad is initially spaced 1.5mm away from the disc to assure the disc can properly rotate and no friction forces are present prior to prior to pad-disc contact. Define and explain why General contact was used between the pad and rotor will be used. Figure xx shows the general contact interactions applied between the pad and rotor. General contact was used to simulate braking and so the proper contact interactions can be applied. 9

The center of rotation reference point was connected to the interior surface of the disc using a rigid body tie constraint. A tie constraint was chosen over a coupling because the rigid body tie is transmitted directly to the solid elements and they are computational more efficient in this application.

Figure 9 – Tie Constraint Define and explain why predetermined rotation was applied to center of rotation. Expand on how it represents vehicle linear velocity of xx. 2.2.4

Loads and Boundary Conditions Two boundary conditions were used. The first being at the center of rotation all

the pad rotor assembly to only rotate in about the z axis. The second BC was applied to the entire surface of the disc to represent the symmetry about the z-axis as described in section 2.2.1 above.

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3. Results 3.1 Disc brakes slow the rotational motion of automobile wheels with friction caused by brake pads pushing against the rotors. This force is typically applied by a piston and cylinder which is hydraulically powered and controlled by the vehicle operator. This system is mechanically linked to the wheel or drive train and used to stop the vehicle; friction causes the rotor and attached wheel to slow and/or stop.

Figure 10 – Simple Disk Brake Schematic [2]

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4. Conclusion 4.1

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5. References [1] Deaton, Jamie P. "How Brake Rotors Work." howstuffworks, n.d. Web. 25 Oct. 2012. [2] N.M. Kinkaid, O.M. O'Reilly, P. Papadopoulos, Automotive disc brake squeal, Journal of Sound and Vibration, Volume 267, Issue 1, 9 October 2003, Pages 105166, ISSN 0022-460X, 10.1016/S0022-460X(02)01573-0. [3] SAE International J843, Brake System Road Test Code – Passenger Car and Light – Duty Truck, Surface Vehicle Recommended Practice, dated March 2013 [4] Shigley’s, Mechanical Engineering Design, Eigth Edition, 2008 [5] Wear and Contact Conditions of Brake Pads, M. Eriksson, J. Lord, and S. Jacobson. s.1: VTT, 2000, Vol 2. [6] Two Body Abrasive Behavior of Brake Pad Dry Sliding Against Interpenetrating Network Ceramics. SY. Zhang, SG. Qu, and YY. Li. Guangzhou, China: Wear, 2009, Vol. 268. [7] On the Dry and Wet Sliding Performance of Potentially New Frictional Brake Pad Material for the Automotive Industry. EL-Tayeb, NSM and KW. Liew. s.1.: Wear, 2009, Vol. 266. [8] The Effect of Metal Fibers in Friction Performance of Automobile Brake Friction Materials. H. Jang. et al. s.1.: Wear, 2004, Vol. 259. [9] Load, Speed, and Temperature Sensitivities of a Carbon Fiber Reinforced Phenolic Friction Material. P. Gopal, LR. Dharani, and D. Frank. S.1.: Wear, 1995, Vol. 181. [10]

Dry Sliding Wear of AL-alloy. M. Narayan, MK. Surappa, and PK. Pramilla Bai.

s.1.: Wear, 1995, Vol. 181. [11]

Tribological Properties of Automotive Disc Brakes with Solid Lubricants. L.

Gudmand-Hoyer and A. Bach. s.1.: Wear, 1999, Vol. 232.

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[12]

The Effects of Antimony Trisulfide Sb S and Zirconium Silicate in the Automo-

tive Brake Friction Material on Friction. H. Jang and S. Kim. s.1.: Wear, 2000, Vol. 239. [13]

Principles of Automotive Vehicles, Technical Manual TM 9-8000, Department

of the Army, dated 25 October 1985 [14]

Antimony in Brake Pads a Carcinogenic Component? O. Uexkull, et al. 1, s.1.:

Journal of Cleaner Production, 2005, Vol. 13.

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6. Appendices 6.1 Vehicle Dynamics This project makes a few assumptions to simplify disc braking anlsysis of a passenger vehicle, however, the following sections will outline why it is important to consider all aspects of vehicle dynamics when designing a brake system which is really a subsystem of the overall automotive system. 6.1.1

Aerodynamic Drag Aerodynamic drag will aid deceleration due to wind resistance. Aerodynamic

drag force is dependent on the vehicles drag factor and velocity squared. These forces can be ignored at normal passenger vehicle operating speeds because they are small compared to braking force. 6.1.2

Driveline Drag The engine, transmission, and final drive components contribute to both drag and

inertia effect during braking. The inertia of these comments adds to the effective mass of the vehicle, and warrants consideration in braking. 6.1.3

Grade Road grade contributes directly to the braking efforts in a positive sense when

going uphill and negatively when traveling downhill. The additional force acting the vehicle due to grade is given by Equation xx. For small angles θ typical for most grades small angle theory can be applied. 6.1.4

Brake Proportioning Balancing the brake efforts on both the front and rear axles is achieved by pro-

portioning the application pressure on the front and rear brakes and in accordance with their loads. Additionally, brake systems typically have physically larger brake pads and rotors on the front axle in comparison to the real axle. During braking load transfers dynamically from the real to the front axle of a vehicle; the maximum brake force is dependent on the deceleration, varying differently at

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each axle. The maximum braking force of on an axle is dependent on that present on the other because deceleration affects transfer load. An attempt to brake the front axle to a level above the front brake force boundary will cause front wheel lockup to occur in which steering control will be lost. Braking the real axle beyond its boundary will cause real axle lockup, which places a vehicle in an unstable condition. The challenge in brake system design is selecting a proportioning ratio that will satisfy all design goals despite the variability in: road conditions, vehicle weight distribution and center of gravity, and braking conditions. Anti-lock Brake systems (ABS) consist of an electronic control unit to effectively proportion brakes by releasing individual wheel brakes momentarily when it senses wheel lockup. ABS systems are not designed to control poorly designed brake systems, they can only assist a vehicle’s operator in braking when being it is outside the limits of proportional braking.

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