Hot Spotting and Judder Phenomena in Aluminum Drum Brakes

2002 ◽  
Vol 125 (1) ◽  
pp. 44-51 ◽  
Author(s):  
Kwangjin Lee ◽  
Frank W. Brooks,
Keyword(s):  
Surface Finish ◽  
Material Properties ◽  
Hot Spots ◽  
Critical Speed ◽  
Concave Surface ◽  
Thermoelastic Instability ◽  
Critical Speeds ◽  
Circumferential Groove ◽  
Drum Brakes ◽  
Test Schedule

Hot spotting and judder phenomena were observed in automotive aluminum drum brakes. A vehicle judder test schedule was developed to determine the critical speed for thermoelastic instability (TEI). The brake material properties relevant to the TEI analysis were measured as a function of temperature. The critical speeds for the brake systems with different drum materials were determined by the judder schedule and they are compared with the analytical predictions of Lee (2000). The brake drums and linings were then modified and tested in order to investigate its effects on the hot spotting and judder propensity. The design modifications include brake linings with a different compound, stress-relieved drums, linings with a convex or concave surface finish, three-segmented linings, and linings with a circumferential groove. The linings with a circumferencial groove effectively reduce the size of hot spots and the best judder rating was achieved.

Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes

1999 ◽  
Vol 122 (4) ◽  
pp. 849-855 ◽  
Author(s):  
Kwangjin Lee
Keyword(s):  
Coefficient Of Friction ◽  
Material Properties ◽  
Critical Speed ◽  
Hot Spot ◽  
Frictional Heating ◽  
Friction Material ◽  
Thermoelastic Instability ◽  
Critical Speeds ◽  
Drum Brake ◽  
The Coefficient Of Friction

Thermoelastic instability in automotive drum brake systems is investigated using a finite layer model with one-sided frictional heating. With realistic material properties of automotive brakes, the stability behavior of the one-sided heating mode is similar to that of the antisymmetric mode of two-sided heating but the critical speed of the former is higher than that of the latter. The effects of the friction coefficient and brake material properties on the critical speeds are examined and the most influential properties are found to be the coefficient of friction and the thermal expansion coefficient of drum materials. Vehicle tests were performed to observe the critical speeds of the drum brake systems with aluminum drum materials. Direct comparisons are made between the calculation and measurement for the critical speed and hot spot spacing. Good agreement is achieved when the critical speeds are calculated using the temperature-dependent friction material properties and the reduced coefficient of friction to account for the effect of intermittent contact. [S0742-4787(00)01503-4]

Thermoelastic Instability of Two-Conductor Friction System Including Surface Roughness

2004 ◽  
Vol 71 (1) ◽  
pp. 57-68 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Material Properties ◽  
Critical Speed ◽  
Thermal Contact ◽  
The Body ◽  
Thermal Contact Conductance ◽  
Contact Conductance ◽  
Thermoelastic Instability ◽  
Special Cases ◽  
Conducting Bodies

A model is developed to investigate the mechanism of thermoelastic instability (TEI) in tribological components. The model consists of two thermally conducting bodies of finite thickness undergoing sliding contact. Appropriate governing equations are derived to predict the critical speed beyond which the TEI is likely to occur. This model takes into account the surface roughness characteristics of the contacting bodies as well as the thermal contact conductance at the interface. Analytical expressions are provided for the special cases neglecting the disk thickness and the thermal contact conductance. An extensive series of parametric simulations and discussion of the implication of the results are also presented. The simulations show that the difference in material properties and geometry of the two conducting bodies has a pronounced influence on the critical speed. A special case of the model shows that the threshold of TEI critical speed is pushed to a much higher level when the conducting bodies have identical material properties and are geometrically symmetric. It is also shown that the perturbed wave generally tends to move with the body with higher thermal conductivity.

Thermoelastic Instability With Consideration of Surface Roughness and Hydrodynamic Lubrication

1999 ◽  
Vol 122 (4) ◽  
pp. 725-732 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Thermal Conductivity ◽  
Surface Roughness ◽  
Film Thickness ◽  
Hot Spots ◽  
Critical Speed ◽  
Hydrodynamic Lubrication ◽  
Lubricant Film Thickness ◽  
Governing Equations ◽  
Thermoelastic Instability ◽  
Liquid Lubricant

An idealized model consisting of a surface with high thermal conductivity separated by a film of liquid lubricant from a rough surface with low thermal conductivity is developed to study thermoelastic instability. The governing equations are derived and solved for the critical speed beyond which thermoelastic instability leading to the formation of hot spots is likely to occur. A series of dimensionless parameters is introduced which characterizes the thermoelastic behavior of the system. It is shown the surface roughness and the lubricant film thickness both play an important role on the threshold of instability. [S0742-4787(00)00104-1]

Effect of Pad/Caliper Stiffness, Pad Thickness, and Pad Length on Thermoelastic Instability in Disk Brakes

1999 ◽  
Vol 122 (3) ◽  
pp. 511-518 ◽  
Author(s):  
Dale L. Hartsock ◽  
James W. Fash
Keyword(s):  
Hot Spots ◽  
Critical Speed ◽  
Low Frequency ◽  
Friction Material ◽  
Original Model ◽  
Thickness Variation ◽  
Frequency Noise ◽  
Thermoelastic Instability ◽  
Disk Brake ◽  
Uneven Heating

Thermoelastic instability (TEI) results in uneven heating of the rotor and the development of hot spots in automotive disk brake systems. The hot spots cause rotor distortion and thickness variation which can cause torque variation resulting in brake roughness or low frequency noise. Lee and Barber (1993, ASME J. Tribol., 115, pp. 607–614) developed an analytical model to predict the critical speed above which TEI would occur. This paper describes enhancements to the model to include the effects of caliper/pad stiffness, the pad friction material thickness, and the pad length. The effects of these changes on the predicted speed are calculated and compared to the original model. [S0742-4787(00)01402-8]

scholarly journals Effect of Geometry on Thermoelastic Instability in Disk Brakes and Clutches

1999 ◽  
Vol 121 (4) ◽  
pp. 661-666 ◽  
Author(s):  
Yun-Bo Yi ◽  
Shuqin Du ◽  
J. R. Barber ◽  
J. W. Fash
Keyword(s):  
Eigenvalue Problem ◽  
Dimensional Analysis ◽  
Critical Speed ◽  
Hot Spot ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Thermoelastic Instability ◽  
Fourier Decomposition ◽  
Critical Speeds

The finite element method is used to reduce the problem of thermoelastic instability (TEI) for a brake disk to an eigenvalue problem for the critical speed. Conditioning of the eigenvalue problem is improved by performing a preliminary Fourier decomposition of the resulting matrices. Results are also obtained for two-dimensional layer and three-dimensional strip geometries, to explore the effects of increasing geometric complexity on the critical speeds and the associated mode shapes. The hot spots are generally focal in shape for the three-dimensional models, though modes with several reversals through the width start to become dominant at small axial wavenumbers n, including a “thermal banding” mode corresponding to n = 0. The dominant wavelength (hot spot spacing) and critical speed are not greatly affected by the three-dimensional effects, being well predicted by the two-dimensional analysis except for banding modes. Also, the most significant deviation from the two-dimensional analysis can be approximated as a monotonic interpolation between the two-dimensional critical speeds for plane stress and plane strain as the width of the sliding surface is increased. This suggests that adequate algorithms for design against TEI could be developed based on the simpler two-dimensional analysis.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

Taylor-vortex instability and annulus-length effects

1976 ◽  
Vol 75 (1) ◽  
pp. 1-15 ◽  
Author(s):  
J. A. Cole
Keyword(s):  
Critical Speed ◽  
Taylor Vortex ◽  
Vortex Instability ◽  
Critical Speeds ◽  
Taylor Vortices ◽  
Torque Measurements ◽  
Concentric Cylinders ◽  
Theoretical Predictions ◽  
Range Of Values ◽  
Visual Observations

Critical speeds for the onset of Taylor vortices and for the later development of wavy vortices have been determined from torque measurements and visual observations on concentric cylinders of radius ratios R1/R2 = 0·894–0·954 for a range of values of the clearance c and length L: c/R1 = 0·0478–0·119 and L/c = 1–107. Effectively zero variation of the Taylor critical speed with annulus length was observed. The speed at the onset of wavy vortices was found to increase considerably as the annulus length was reduced and theoretical predictions are realistic only for L/c values exceeding say 40. The results were similar for all four clearance ratios examined. Preliminary measurements on eccentrically positioned cylinders with c/R1 = 0·119 showed corresponding effects.

Estimating Critical Speeds of Stepped Shafts with Flexible Bearings

1971 ◽  
Vol 8 (03) ◽  
pp. 327-333
Author(s):  
R. H. Salzman
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Design Stage ◽  
Normal Range ◽  
Critical Speeds ◽  
Stepped Shaft ◽  
Bearing Stiffness ◽  
Variable Support ◽  
Method Show ◽  
Good Agreement

This paper presents a semi-graphical approach for finding the first critical speed of a stepped shaft with finite bearing stiffness. The method is particularly applicable to high-speed turbine rotors with journal bearings. Using Rayleigh's Method and the exact solution for whirling of a uniform shaft with variable support stiffness, estimates of the lowest critical speed are easily obtained which are useful in the design stage. First critical speeds determined by this method show good agreement with values computed by the Prohl Method for the normal range of bearing stiffness. A criterion is also established for determining if the criticals are "bearing critical speeds" or "bending critical speeds," which is of importance in design. Discusser E. G. Baker

scholarly journals Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

2020 ◽  
pp. 146134842094828
Author(s):  
Yang Yongfeng ◽  
Wang Jianjun ◽  
Wang Yanlin ◽  
Fu Chao ◽  
Zheng Qingyang ◽  
...  
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Circular Crack ◽  
Rotor System ◽  
Resonance Phenomenon ◽  
Dynamical Analysis ◽  
Dynamical Response ◽  
Critical Speeds ◽  
Hollow Shaft

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

On the Formation of Hot Spots in Wet Clutch Systems

2001 ◽  
Vol 124 (2) ◽  
pp. 336-345 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Hot Spots ◽  
Friction Material ◽  
Mechanical Seal ◽  
Comprehensive Model ◽  
Governing Equations ◽  
Thermoelastic Instability ◽  
Wet Clutch ◽  
Special Case

A comprehensive model is developed for analyzing the onset of thermoelastic instability in a wet clutch. For this purpose, appropriate governing equations are derived that take into account the porosity and deformability of the friction material. The effect of the thickness of the separator disk and that of the friction material are also included. The model is general and can be used to describe TEI in a variety of other systems such as in a mechanical seal, as a special case. A series of simulations are presented that predict the thermoelastic behavior of a wet clutch from an instability viewpoint.

Sign in / Sign up

Export Citation Format

Share Document