WESTERN MICHIGAN UNIVERSITY

STRUCTURAL VIBRATION

ME 6630

MODAL AND VIBRATION ANALYSIS OF DISC BRAKES

Ashwin Kumar Chikkabalapur Nagaraj

ABSTRACT

The project deals with the explanation of the working principle of Disc brakes and the problems associated with disc brakes. Understanding the causes of failure. Analyze the effects like squeal by complex eigenvalue method and model a disc brake for modal and frequency analysis. The analysis determines the mode shapes of the disc brake and respective frequency for mode shapes

INTRODUCTION

A vehicle requires a brake system to stop or adjust its speed with changing road and traffic conditions. The basic principle used in breaking system is to convert the kinetic energy of a vehicle into some other form of energy. In friction braking, it is converted into heat, and in regenerative breaking, it is converted to electricity or compressed air. During braking, all the kinetic energy is converted to into the desired form, in friction braking the energy is dissipated in form of vibrations.

The braking system is one of the most important unit in any vehicle. The safety of the vehicle is completely dependent on the effectiveness of the brakes. Road traffic injuries and deaths are a growing public health concern worldwide. one of the reasons for these kinds of accidents is brake failure. There are many causes for a brake system failure like brake fade, friction fade, mechanical fade and so on.

Noise in disc brakes is a major problem in automotive industries. Brake noise is very annoying and an indication of a problem with the brake system. in most systems, this noise has no effect on the performance of the brake system. however its perception affects the satisfaction of the customer.

The modal analysis gives the effect of vibration that is observed during braking. The modal analysis also gives the mode shapes of the disc brakes for different nodes.

WORKING PRINCIPLE

We all know that pushing down on the brakes slows a car to a stop. But how does this happen? How does a car transmit the force from a press on the brake pedal to its wheels?

When the brake pedal is pressed, the force from the foot is transmitted its brakes through a fluid. Since actual brake requires much higher force to bring the car to a halt. The mechanics mainly deals with mechanics, hydraulics and friction.

This simplified system explains the basic working of a disc brake.

The basic concept that is used for this system depends on Bernoulli’s principle of fluids and leverage about a pivoted point.

From the above illustration firstly, we can see that the distance of the pedal is four times the distance of the primary piston lever. If the pedal is pushed the force transmitted will be amplified by four-time when it is input to the piston. If we observe, we can notice two pistons of varying size are used. The diameter ratio is 1:3. The primary piston is connected to the secondary by a fluid line that is at a specific pressure. When the input force from the primary cylinder is transmitted to the secondary cylinder. Due to the difference in cylinder diameter and presence of a pressurized fluid link the force transmitted is amplified by nine times. So, the net amplification of force from the pedal end to the secondary piston end is by a factor of thirty-six.

Even a small amount of force applied on the brake pedal leads to a huge application of force on the secondary piston. The secondary piston is attached to a brake pad. It has high friction coefficient. When such a material is pushed against the disc part of the brake and due to the friction between the pad and the disc results in reducing the speed of the vehicle.

PROBLEMS ASSOCIATED WITH BRAKES

Brakes are the most important system in any vehicle. The safety of any vehicle is determined by the effective working of the braking system. There are some limitations also. Disc brakes are usually made of cast iron. The major issue faced with cast iron is rusting, uneven erosion, scarring, fade and cracking. Apart from this, there are issues like low brake pedal, excessive pedal travel, pedal pulsation, scraping noise, squeals, chatters, grabby and dragging brakes and brake fluid problems.

Friction Fade

Friction is the method by which kinetic energy is converted into heat in a brake system. resistance of motion between two surfaces is friction. If friction at contact surface is reduced to a very low level, there is no effective conversion of kinetic energy into heat. When there is a reduced friction at the friction surface result of heat it is called Friction Fade. When fade occurs in hydraulic systems the rider can feel the brake, but in pneumatic system the is no effect of braking.

The braking is affected by the temperature at the surface of friction. The heat/friction profile is different for every lining and can be linear, curvilinear. when the temperature of the friction material goes beyond a certain limit, it melts and the co efficient of friction is reduced.

If the friction contact surface is partially in contact, there is friction fade. The brake surface get hotter due to partial contact, this leads to overheating of the brake pads. Brakes in this condition are easily heated up to the point of failure. The discolouration on the disc surface is the evidence that there is incomplete surface contact that is causing friction fade

Incomplete friction surface contact is very common. It can be caused by the following:

· Spiders, Brake backing plates are bent

· When brake shoes are twisted or bent.

· When brake drums and rotors are reused without resurfacing.

· Common when on cheaply imported linings, it causes uneven pressure distribution.

Brake rotor and drum thickness is also an element of friction fade. When the drum thickness of the rotor is excessively thin it does not have capacity to withstand heat. This also can cause the friction surfaces to get hotter compared to normal circumstances. Due to this the rotor is heated faster than the normal rates leading to friction fade. Moreover, lesser drum thickness can cause heat expansion of the drum to be greater.

Mechanical Fade

Mechanical Fade is most commonly found with drum brakes and not disc brakes. In a drum brake, the lining for a drum break is toward the drum’s contact surface. The expansion will increase the drum’s diameter, moving it away from the lining and the brake drum heats up resulting in outward expansion. If expansion is greater than a certain it will result in failure of the brake. A disc brake lining application is at a right angle to the rotating disc and has no such constraints. For this reason, disc brakes have better fade resistance.

SQUEAL

Cars generate unwanted sound and vibrations under brake application. The disc brake squeal is a high- frequency noise. It is very annoying and difficult to correct. Brake squeal usually occurs in the frequency range of 1 to 16 kHz. The Understanding the mechanism for squeal generation is crucial for designing quiet brakes and for treating the noise effect. There are typically two methods available to study the squeal, namely complex eigenvalue analysis and dynamic transient analysis.

COMPLEX EIGENVALUE ANALYSIS

Frictional sliding contact between disc and pad is the source of nonlinearity for solving brake squeal analysis. Ansys has a method for complex eigenvalue analysis to simulate the disc brake squeal. It begins from preloading the brake, rotating the disc, and then extracting natural frequencies and complex eigenvalues, this method combines all steps in one continuous run. The eigenvalue is computed by subspace projection method. To find the subspace project the natural frequencies must be computed beforehand. The equation of the system is

M? +C? +Kx=0

where M is the mass matrix, C is the damping matrix, which includes friction-induced contributions, and K is the stiffness matrix, which is unsymmetric due to friction. The equation is

(?2M + ?C +K) ? =0

? is the eigenvalue, ? is the corresponding eigenvector, and they both can be complex. To solve the complex eigenproblem, this system is symmetrized by not considering damping matrix C and the unsymmetric contributions to the matrix K. Then this problem is solved for the projection subspace. The N eigenvectors from the symmetric eigenvalues are expressed in a matrix as ?1,………. ?N. The actual matrices are projected onto the subspace of N eigenvectors

M* = ?1, …………., ?NT M ?1, ………. ?N

C* = ?1, ……… ?NT C?1, ………. ?N

and

K* = ?1,………… ?NTK?1,……… ?N

Then the complex eigenproblem becomes

(?2M* + ?C* +K*) ?* =0

The complex eigenvectors of the original system can be obtained by

?= ?1,……….. ?NT ?*

The complex eigenvalue ?, can be expressed as ? = ? ± i? where ? is the real part of ?, Re(?), indicating the stability of the system, and ? is the imaginary part of ?, Im(?), indicating the mode frequency. The generalized displacement of the disc system, x, can then be expressed as

x = Aet? = e?t (A1 cos?t +A2 sin?t)

This analysis determines the stability of the system. When the system is unstable, ? becomes positive and squeal noise occurs. The damping ratio is defined as -?/(?|?|). The system is unstable when the damping ration is negative.

MODAL ANALYSIS OF DISC BRAKES

Date: Wednesday, December 6, 2017Designer: Solidworks

Study name: Modal analysis

Analysis type: Frequency

Table of Contents

Description. 1

Model Information. 2

Units. 2

Study Properties. 3

Material Properties. 3

Loads and Fixtures. 4

Mesh information. 5

Study Results. 6

Description

The disc brake will be analyzed for its natural frequencies. The mode shapes and the resonant frequency for the same will be analyzed.

Model Information

Model name: DISC BRAKES FREQUENCY SIM

Current Configuration: Default

Solid Bodies

Document Name and Reference

Treated As

Volumetric Properties

Document Path/Date Modified

Fillet3

Solid Body

Mass:8.52815 kg

Volume:0.00118447 m^3

Density:7200 kg/m^3

Weight:83.5759 N

C:PARTsolutions PartspoolsolidworksDISC BRAKES FREQUENCY SIM.SLDPRT

Dec 06 19:43:50 2017

Units

Unit system:

SI (MKS)

Length/Displacement

mm

Temperature

Kelvin

Angular velocity

Rad/sec

Pressure/Stress

N/m^2

Study Properties

Study Name

Modal analysis

Analysis type

Frequency

Mesh type

Solid Mesh

Number of frequencies

8

Solver type

FFE Plus

Soft Spring:

On

Incompatible bonding options

Automatic

Thermal option

Include temperature loads

Zero strain temperature

298 Kelvin

Include fluid pressure effects from SOLIDWORKS Flow Simulation

Off

Result folder

SOLIDWORKS document (C:PARTsolutions Partspoolsolidworks)

Material Properties

Model Reference

Properties

Components

Name:

Gray Cast Iron

Model type:

Linear Elastic Isotropic

Default failure criterion:

Mohr-Coulomb Stress

Tensile strength:

1.51658e+008 N/m^2

Mass density:

7200 kg/m^3

Elastic modulus:

6.61781e+010 N/m^2

Poisson’s ratio:

0.27

Thermal expansion coefficient:

1.2e-005 /Kelvin

SolidBody 1(Fillet3)(DISC 2)

Load and fixtures

Fixture name

Fixture Image

Fixture Details

Fixed-1

Entities:

5 face(s)

Type:

Fixed Geometry

Mesh information

Mesh type

Solid Mesh

Mesher Used:

Curvature-based mesh

Jacobian points

4 Points

Maximum element size

0.8333 in

Minimum element size

0.16666 in

Mesh Quality Plot

High

Mesh information – Details

Total Nodes

227563

Total Elements

146351

Maximum Aspect Ratio

38.116

% of elements with Aspect Ratio < 3 91.6 % of elements with Aspect Ratio > 10

0.474

% of distorted elements(Jacobian)

0

Time to complete mesh(hh;mm;ss):

00:00:09

Computer name:

CAE-A13

Name

Type

Min

Max

Amplitude1

AMPRES: Resultant Amplitude Plot for Mode Shape: 1(Value = 630.132 Hz)

0.000e+000

Node: 3902

7.955e-001

Node: 771

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude1

Study Results

Name

Type

Min

Max

Amplitude2

AMPRES: Resultant Amplitude Plot for Mode Shape: 2(Value = 630.701 Hz)

0.000e+000

Node: 3902

7.996e-001

Node: 32919

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude2

Name

Type

Min

Max

Amplitude3

AMPRES: Resultant Amplitude Plot for Mode Shape: 3(Value = 721.367 Hz)

0.000e+000

Node: 3902

5.771e-001

Node: 80026

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude3

Name

Type

Min

Max

Amplitude4

AMPRES: Resultant Amplitude Plot for Mode Shape: 4(Value = 912.844 Hz)

0.000e+000

Node: 3902

8.286e-001

Node: 946

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude4

Name

Type

Min

Max

Amplitude5

AMPRES: Resultant Amplitude Plot for Mode Shape: 5(Value = 913.171 Hz)

0.000e+000

Node: 3902

8.279e-001

Node: 766

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude5

Name

Type

Min

Max

Amplitude6

AMPRES: Resultant Amplitude Plot for Mode Shape: 6(Value = 1303.36 Hz)

0.000e+000

Node: 3902

4.784e-001

Node: 1516

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude6

Name

Type

Min

Max

Amplitude7

AMPRES: Resultant Amplitude Plot for Mode Shape: 7(Value = 1362.31 Hz)

0.000e+000

Node: 3902

4.630e-001

Node: 80180

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude7

Name

Type

Min

Max

Amplitude8

AMPRES: Resultant Amplitude Plot for Mode Shape: 8(Value = 1362.73 Hz)

0.000e+000

Node: 3902

4.623e-001

Node: 79915

DISC BRAKES FREQUENCY SIM-Frequency 1-Amplitude-Amplitude8

Mode List

Frequency Number

Rad/sec

Hertz

Seconds

1

3959.2

630.13

0.001587

2

3962.8

630.7

0.0015855

3

4532.5

721.37

0.0013863

4

5735.6

912.84

0.0010955

5

5737.6

913.17

0.0010951

6

8189.2

1303.4

0.00076725

7

8559.6

1362.3

0.00073405

8

8562.3

1362.7

0.00073382

Mode Number

Frequency(Hertz)

X direction

Y direction

Z direction

1

630.13

0.014218

0.0026238

2.871e-006

2

630.7

0.0025848

0.01419

1.4622e-005

3

721.37

6.2963e-009

7.3564e-007

0.73324

4

912.84

2.0046e-007

1.1033e-007

2.0828e-008

5

913.17

7.5457e-008

2.3038e-008

8.0298e-007

6

1303.4

2.3626e-006

1.4878e-005

6.657e-009

7

1362.3

0.68263

0.1844

2.8602e-008

8

1362.7

0.1845

0.68276

5.6016e-008

Sum X = 0.88394

Sum Y = 0.88399

Sum Z = 0.73326

Mass Participation (Normalized)

COMAPRISION OF MODE SHAPES

CONCLUSION

· The basic working of brakes was understood.

· The cause for the failure of disc brakes was explained.

· the CEA for squeal was theoretical analyzed

· Based on the simulation the 8 mode shapes for the disc was determined and the frequency associated with each mode shape was determined

RECOMMENDATIONS

· The thermal analysis of the mode shapes can be analyzed.

· The effect of increased convection for the disc can be compared and the performance can be compared

· The effect of squeal can observed and analyzed by the experimental method.

REFERENCES

1 Analysis of disc brake squeal, P. Liu a,*, H. Zheng a , C. Cai a , Y.Y. Wang a, C. Lu a, K.H. Ang b, G.R. Liu c.

2 www.crashforensics.com/brakefailure.cfm

3 Design and Analysis of Disc Brake, Swapnil R. Abhang#1, D.P.Bhaskar*2, Pune University, Kopargaon, India

4 squeal analysis of disc brake system, Hao Xing

Beijing FEMA online Engineering Co., Ltd. Beijing, China.