Design and Analysis of Friction Brakes
2.4 Disc Brakes
2.4.5 Lining/Pad Friction and Classification
All linings begin to disintegrate at the friction surface due to high temperatures developed from the heat-generation process. Due to non-uniform pressure distributions between lining and drum or pad and rotor, and other surface irregularities, pad friction surface temperatures will not be uniform over the pad contact area. Areas of higher temperature will have lower friction levels than those with lower temperatures. An exact analytical prediction of the pad/rotor friction coefficient is not possible at the present time. However, close estimates based on test data can be made.
The basic brake system design layout is based on the brake torque
performance achieved with “cold” brakes. A brake is considered cold when its temperature is less than 366 K (200°F). Most lining friction coefficients will increase as brake temperatures rise to approximately 423 to 473 K (300 to 400°F). At elevated temperatures near 523 to 588 K (500 to 600°F) and above, linings tend to exhibit fade; i.e., their friction coefficient decreases below its cold value. Good linings will recover to their intended design levels after cooling. At extremely low temperatures, friction coefficients tend to decrease below the cold value. Because brake systems have to perform safely under all
foreseeable operating conditions, the proper selection of a lining material can be a challenge, particularly for drum brakes, and even more so for duo-servo brake designs.
Test procedures have been developed to measure lining friction at different temperatures and to classify ranges. SAE J661 procedure is used to determine the cold (366 K or 200°F) and hot (588 K or 600°F) friction levels of lining material samples, one inch square in size, when used with a drum made of a particular material to a particular set of dimensions. Two letters are used to mark cold and hot friction coefficients. The first letter represents an average value of the normal (cold) friction, the second hot friction. The higher the letter, the higher the coefficient of friction, so that
C refers to friction coefficients less than 0.15 D 0.15 to 0.25
E 0.25 to 0.35 F 0.35 to 0.45 G 0.45 to 0.55 H over 0.55 Z unclassified
For example, a lining edge code FE indicates that the normal (cold) coefficient of friction is between 0.35 and 0.45, say, 0.38, and when heated to 588 K (600°F) between 0.25 and 0.35, say, 0.34.
It is important to recognize that the SAE J661 lining classifications using fairly broad ranges of friction coefficients may cause errors when used in the design analysis of an existing braking system. Calculations determining brake lockup sequence require reasonably accurate brake factor computations and, hence, lining friction coefficients. Simply using any value within the specified letter range will not be acceptable. As a minimum, the actually measured average friction coefficients used to establish the friction range should be considered in the design analysis. Because only a lining sample area of 25.4 by 25.4 mm (one inch by one inch) is actually tested, additional differences may exist between the classification friction coefficient and the effective lining friction coefficient actually experienced by the drum brake.
Albin Burkman of General Motors used a laboratory test method to determine that moisture may have a significant effect on lining friction coefficient (Ref.
2.15). He concluded that the friction coefficients are higher during periods of high humidity than under dry operating conditions, and lower when the brakes are flooded by water.
Brake torque and brake factor can be measured directly with special torque hubs, or indirectly from vehicle deceleration tests. If such data are available, they should be used as a basis for the brake system design analysis.
2.4.6 Self-Energizing Disc Brake
Self-energizing disc brakes are not used in typical automotive applications.
Their basic operational principles involve a wedge effect provided by a ball-and-ramp type design, as illustrated in Fig. 2-26 for a fully covered disc brake design. The actuating force is the force directly pressing against the disc. This force is increased by the friction force, which causes an additional relative rotation. This leads to pushing the circular brake pads apart and increased normal force by means of the ball-and-ramp mechanism, thus introducing self-energizing.
With the notation shown in Fig. 2-26, the friction force of one circular brake pad is given by the relationship (Ref. 2.4):
or solved for the plate brake factor as
(2-28)
where rk = disc brake dimension, mm (in.) rm = disc brake dimension, mm (in.)
δ = disc brake ramp angle, deg μL = pad friction coefficient
Because two friction surfaces are involved, the total brake factor is
(2-29)
where µL∞ = self-locking pad friction coefficient
and the self-locking limits (see Section 2.3.3 for self-locking limit details) for the pad friction coefficient are given by
Fd=µL a[F F r r+ d m( / )]cot , ( )k δ N lb
Figure 2-26. Schematic of self-energizing fully covered disc brake.
Rotor
Circular brake Pad
rk a
rm
a
Released Position Plates Pushed apart Due to Wedge action
ballRamp
d
d
Normal Force Fd
Fa
Fd Fa
rk rm
applied Position
View of Section a-a
The sensitivity of the brake SB is expressed by
(2-30)SB
L L
= − ∞
2
1 2
cot
( / )
δ µ µ
Chapter 2 References
2.1 Breuer, Bert and Bill, and H. Karlheinz, Brake Technology Handbook, SAE International, Warrendale, PA, 2008.
2.2 Ostermeyer, George P. and M. Mueller, “New Insights into the
Tribology of Brake Systems,” Proc. IMechE. Vol. 222, Part D: Journal of Automobile Engineering.
2.3 Chao, Min Hyung, et al., “The Role of Raw Material Ingredients of Brake Linings on the Formation of Transfer Film and Friction Characteristics,” SAE Paper No. 2001-01-3130, SAE International, Warrendale, PA, 2001.
2.4 Dr. Strien, Hans, “Calculation and Testing of Automotive Friction Brakes,” Ph.D. Dissertation, Technical University, Braunschweig, 1949.
2.5 Shih, Shan, et al., “Improved Drum Brake Shoe Factor Prediction with the Consideration of System Compliance,” SAE Paper No. 2000-01-3417, SAE International, Warrendale, PA, 2000.
2.6 PCBRAKE FACTOR at www.pcbrakeinc.com.
2.7 Limpert, Rudy, et al., “Brake System Analysis in Pre-Crash Accident Reconstruction,” Short Paper PCB 9-2006, e-Publishing, www.
pcbrakeinc.com, 2006.
2.8 Elvenkemper, Andreas, “Investigation of Torque Output Variation in a Duo-Servo Park Brake System Using Six Sigma Tools and FE-Analysis,”
SAE Paper No. 2006-01-3199, SAE International, Warrendale, PA, 2006.
2.9 Raajha, M.P. and V. Lakshmi Narayanan, “High Performance Drum Brake Assembly for Automotive Braking Applications,” SAE Paper No.
2003-01-3306, SAE International, Warrendale, PA, 2003.
2.10 Automotive Handbook, Robert Bosch, 7th edition, SAE International, Warrendale, PA, 2007.
2.11 Agudelo, Carlos E. and Eduard Ferro, “Technical Overview of Brake Performance Testing for Original Equipment and Aftermarket Industries in the US and European Markets,” Link Technical Report FEV205-01.
2.12 LINK Engineering, Brake Dynamometer Test Report, 16.5´7 inches S-Cam Drum Brake.
2.13 Buckman, Leonard, Commercial Vehicle Braking System, Volume 1, Seminars, SAE International, Warrendale, PA.
2.14 MacAdams, C. and T. Gillespie, Determining the Sensitivity of S-Cam Brakes, Report No. UMTRI-98-6, February 1998.
2.15 Burkman, Albin J., “A Laboratory Method for Testing Moisture Sensitivity of Brake Lining Materials,” SAE Paper No. 620128, SAE International, Warrendale, PA, 1962.
2.16 Mueller, W., “Contribution to the Analysis and Testing of Motor Vehicle Drum Brakes,” Deutsche Kraftfahrtforschung und Strassenverkehrstechnik, No. 207, 1971.
2.17 Zhang, Shaoyang, Weiping Chen, and Yuanyyuan Li, “ Wear of Friction Materials during Vehicle Braking,” SAE Paper No. 2009-011032, SAE International, Warrendale, PA, 2009.
2.18 Tumbrink, H.J., “Measurement of Load Distribution on Disc Brake Pads and Optimizing of Disc Brakes Using the Ball Pressure Methods,”
SAE Paper No. 890863, SAE International, Warrendale, PA, 1989.
2.19 Wang, Nui, “The Evolution of the Pad Guided Disc Brake Caliper,” SAE Paper No. 940332, SAE International, Warrendale, PA, 1994.
2.20 Gohring, Ernst and Egon-Christian von Glasner, “Performance Comparison of Drum and Disc Brakes for Heavy Duty Commercial Vehicles,” SAE Paper No. 902206, SAE International, Warrendale, PA, 1990.