- Email: [email protected]
Effect of Material Properties On Disc Brake Squeal And Performance Using FEM and EMA Approach.
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 4986–4994
www.materialstoday.com/proceedings
ICMPC 2017
Effect of Material Properties On Disc Brake Squeal And Performance Using FEM and EMA Approach. N.K.Kharatea, Dr.S.S.Chaudharib a b
NDMVPSKBTCOE,Dept.Of Mechanical Engg,Gangapur Road,Nashik (M.S),422003,India YCCOE,Dept.Of Mechanical Engg,Hingna road,wanadongari,Nagpur (M.S),441110,India
Abstract This paper is concerned with the investigation of disc brake squeal with different materials for disc brake components.The objective of the present research is developing FE model of every component of the disc brake system for understanding the influence of material properties on the disc brake squeal and validated with experimental modal analysis. The aim of the research is to predict the squeal at the former phase of invention using a more realistic model. The results of FEM and EMA indicated that different material properties of disc brake components play a sustainable role in generating the brake squeal.
© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of 7th International Conference of Materials Processing and Characterization. Keywords: Brake squeal, Modal analysis, Natural frequency, Mode shapes, Frequency response function
1.
Introduction:
Squeal that generated in the disc brake of the automobile has been considered as a one of the major problem in the automotive industry due to the persistent complaints that reduces customer satisfaction.Most of the scientist and engineers have agreed that squeal noise in the disk brake is initiated by the instability due to friction forces, contributing to self-excited vibrations 1. With the help of industrial source,.
* Corresponding author. Tel.: +91 9822767671; fax: +91- 253- 2317016. E-mail address:[email protected]
2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of 7th International Conference of Materials Processing and Characterization.
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
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Nomenclature FFT Fast Fourier transforms FRF Frequency response function FEM Finite element method EMA Experimental modal analysis Akay 2 reviewed that warranty costs due to noise, vibration and harshness (NVH) including disc brake squeal, in the North America were up to one billion dollars. Similarly, Abendroth and Wernitz 3 noted that many friction material suppliers have to spend up to 50 percent of their engineering budget on the NVH issues. Therefore, the elimination of brake squeal noise is very significant as the problem leads to increases warranty costs as well as discomfort towards the vehicle occupants and walkers. There have been many related studies carried out on the behaviour of the disc brake through modal analysis. Finite element method has been used by the researcher to several conclusions. The most usual technique applied is to compute M and K matricesin the equation of motion + + + = 0 to determine the natural frequencies and mode shape of the brake system components4-6.In recent years, the finite element (FE) has reached wide acceptance to assist brake vibration and noise problem. Although substantial research and efforts with different theories and method ologiessuch as modifications in structure, material, and dimensions have been formulated and carried out since 1930’s in order to predict and eliminate the brake squeal, it is still difficult to predict its occurrence because of its interdisciplinary nature. For example, In 1975, G.M.L. Gladwell and D. K. Vijay7, uses a finite element modelling technique to find out the natural frequencies of a hollow cylinder5.Bae and Wickert, concentrated on the top-hat structure type of disc brake8. Finite element model of the brake rotor disc was developed to study the influence of the top hat structure on the modalities of the brake rotor disc.The result proves how the natural frequency of the structure relates to disc thickness and hat structure. Further research by Tuchinda et al 9, considered the same top hat structure type disc brake for their finite element analysis and indicated that the frequency of squealing are influenced by natural frequencies and modes of stationary rotors.Ibrahim10, in his literature, reviewed many theorems and mechanism such as stick-slip, sprag- slip, negative friction velocity slop and mode coupling of structures with several conclusions. Theoretically, it shows that the mechanism such as stick-slip, sprag- slip, and negative friction velocity slop can cause chaosand instability of the system. One of the earliest researches of Liles11 developed a finite element model of each brake component using solid elements and validated their accuracy using an experimental modal analysis. He showed that squeal propensity increases at higher friction coefficients. Lee et al.12reported that reducing the back plate thickness increases the squeal propensity with uneven contact pressure distribution. Abu Bakar et.al13 further elaborates the squeal phenomenon by considering surface topographies of two new and unworn pairs of brake pads. Both pairs of pads are tested under certain braking pressure by inserting pressure indicating film in between to investigate wear progress. He suggests that FE model is more practical and reliable method for simulating wear progress. According to Mario Triches Junior et al.14, disc brake squeal occurs when the system undergoes large amplitude vibration. In 2009, Noubyet al.15, in their research considered the complex eigenvalue analysis along with the design of experiments to find out the optimal design of the brake system.They reported that by increasing the Young’s modulus of the back plate and modifying the shape of friction material by adding chamfer and slots, brake squeal propensity can be reduced to a great extent.Recently in 2016, Belhocineali, NoubyM.Gazaly16concentrated on effect of young’s modulus on the stability of the disc brake system and squeal generation.They commented that increasing young’s modulus of the rotor, friction material, anchor bracket and back plate reduces the number of unstable frequencies and provides the better squeal performance. Although successful case studies and research with certain success have been conducted in the last few years but no real reliable brake noise prevention tool truly exists yet.In fact, research done on a special case of brake or on a fussy type of vehicle is not assignable to other types of brakes or vehicle.
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N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
2.Finite Element Method and Modeling A detailed three dimensional finite element model of a commercial ventilated disc brake system parts such as rotor, caliper, bracket and pad aremodeled considering the realistic dimensions for better correlation of the consequences with the experimental.Each component of the brake assembly is examined considering the free-free boundary conditions as it allows the structure to vibrate freely without interference of the other parts. It also facilitates better visualization of mode shapes associated with each natural frequency.For validation of FE model one must recognize the dynamic properties such as modulus of elasticity, density and Poisson’s ratio of the components. The dynamic properties of the structure are obtained by mode analysis or by its evaluation 4. The Block Lanczos method is applied to specify the frequencies with the help of FE software.Only linear behavior is viewed in a modal analysis while Non-linear properties are neglected. 2.1FE Modal Analysis of Brake Rotor: Modal analysis of brake rotor has been carried out for four different materials such as Gray C.I-1, Gray C.I2,carbonceramic and steel as it is one of the essential parts of the brake system which contributes more in the generation of noise. First ten modes are extracted for the rotor for predicting the natural frequencies. Solid 45-3D structural solid element is utilized for the three dimensional modelling of structure. The element is defined by eight nodes having three degrees of freedom at each node. Material properties of different rotor material are shown in table 1.Role of element shape and order of interpolation decides the element selection. Table1: Material properties of different rotor material Rotor Material
Density (kg/m3)
Young’s Modulus
Poisson’s ratio
Gray C.I-1
7200
66
0.28
Gray C.I-2
7100
125
0.28
Carbon Ceramic
2450
30
0.3
Steel
7840
210
0.3
2.2Modal analysis of pad, calliper and bracket: Finite element modal analysis is done on the various elements of the magnetic disk brake system such as brake pad, calliper and carrier. Material properties of different components of disc brake are shown in table 2.The same process is practiced for the analysis as that used for brake disc. Table 2: Material properties of disc brake components. Component Description Back Plate Friction material Brake Calliper Calliper Bracket
Young’s Modulus (Mpa) 220 ×103 03×103 110×103 130×103
Density (Kg/m3) 7800 2500 6100 7850
Poisson Ratio 0.3 0.3 0.3 0.3
3. Validation of FE model using experimental modal analysis (EMA) approach Each part of a disk brake assembly is tested through the EMA with free – free boundary conditions.The observational approach to investigate the way patterns and natural frequencies of the structure through impact hammer test consists of the following steps. • • • • • • •
Generation of model. Model test setting Divide the structure inadequate number of points with the appropriate special distribution. Excite the structure with impact hammer. Taking the measurements Analysis of measured output data. Establishment with the FEM data.
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
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The test equipment used for the experimentation is the Fast Fourier Transform (FFT) with sixteen channels along with data acquisition system made of Scadas Front End.The structure was excited using impact hammer (Dytran Make 5800B3) at all predefined locations as indicated in fig.1 and the response was collected using tri-axial accelerometer(PCB T356A02 & 356B21) at an identified driving point transfer function (DPTF) location. The type of EMA is known as the Frequency Response Function (FRF) method which evaluates the input excitation and output response simultaneously.The essence of all frequency response functions (FRF’s) are resolved to extract natural frequencies and mode shapes. Fig.1 shows the experimental modal analysis set up for rotor.
Figure1. Accelerometer localization for rotor
The same methodology has been used for obtaining the natural frequency of brake pad, calliper and bracket. The sum FRF was collected and worked out to discover out the natural frequency of the elements. The instrumentation for experimental modal analysis is shown in fig.2 (a) and (b)
(a)
(b)
Figure2. EMA set up fora) Calliper Bracket b) Brake Pa
4. Results and discussion Natural frequencies obtained for different disc material using FEM for first ten modes are presented in the table 4.While table 3 shows the values of deformation i.e. displacement of disc at particular mode From table 6, it is observed that amongst the four materials the gray cast iron-1has acceptable lower natural frequency for first ten modes with the help of FEA. In fact, as per the definition of squeal range prescribed by the various researchers and
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N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
experts found in the literature, GCI-1 does not much contribute to the generation of brake squeal. Finally, it is noted that gray cast iron-1 is considered as the best material composition for the disc rotor. It is also observed that the natural frequencies for the material carbon ceramic are less, but their shift at each modality is more as compared to rest of the materials as indicated in table 6.It is observed that for all types of materials, the oscillation (Vibrational) behaviour of the disc is same but with different values of natural frequencies and deformations. This is because of the two styles are differentiated by the fact that their in-plane displacements is different as shown in below Table 4. Table 3: Natural frequency for first ten modesofrotor. Gray Cast Iron 1
Gray Cast Iron 2
Carbon ceramic
Freq. (Hz)
Freq. (Hz)
Freq. (Hz)
Mode No.
Steel Freq. (Hz)
1
1093.9
1557.6
1264.3
1918.1
2
1098.1
1562.3
1269.2
1924.
3
1960.4
2930.6
2265.8
3630.
4
2239.4
3261.3
2588.3
4012.5
5
2239.6
3263.5
2588.5
4015.1
6
2331.9
3395.4
2695.2
4181.2
7
2365.4
3433.9
2733.8
4228.7
8
2475.6
3729.2
2861.2
4612.5
9
2478
3762.1
2864.
4653.4
10
2945
4649.3
3403.8
5742
Confirmation has also pulled in for the effects of natural frequencies of two different materials of the same model (Mode1) obtained in the FEA in terms of damping ratio coefficients which is the ratio of modulus of elasticity and compactness. For gray C.I 1modulus of elasticity (Ea) = 66Gpaand density (ρa) = 7200 Kg/m3.Similarly for, Gary C.I 2 modulus of elasticity (Eb) = 125Gpa and density (ρb) = 7100 Kg/m3.Thusthe ratio of natural frequencies and damping ratio coefficient of these two materials is equal to 0.7and are calculated by using the relation ⁄ and × × respectively.Likewise, for carbon ceramic and steel, natural frequency ratio and damping ratio coefficient is 0.67 for mode no 1.As the ratio between natural frequencies of two dissimilar types of materials are equal to the damping ratio coefficient, which is the ratio of modulus of elasticity and density, therefore it confirms the modes of frequencies obtained through Finite element modelling. Table 4: Minimum and Maximum Deformation of rotor for First 10 Modes in mm
Gray Cast Iron 1 Sr. No
Min.
Gray Cast Iron 2 Max.
Min.
Max.
Carbon ceramic Min.
Max.
Steel Min.
Max.
1
0.105
39.15
9.35
1230
5.73
2122.4
9.14
1171.9
2
0.036
39.13
11.09
1232
1.96
2121.3
10.93
1174.8
3
0.151
29.4
59.37
985.05
8.19
1593.8
55.86
936.17
4
0.044
44.26
3.42
1437
2.39
2399.6
3.17
1369.3
5
0.061
44.21
2.65
1417.7
3.32
2396.8
3.04
1351.4
6
1.736
31.34
58.56
1012.4
94.14
1699.3
56.88
962.04
7
1.745
32.19
52.23
1043.6
94.62
1745.1
49.62
991.3
8
0.134
36.64
31.15
1203.6
7.26
1986.6
32.65
1143.2
9
0.165
36.94
57.03
1230.1
8.95
2002.9
54.73
1168.7
10
0.189
99.27
1.50
3483.5
10.26
5381.6
1.44
3324.6
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
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Table 5.Natural frequencies for a Gray C. I- 2disc material
Mode
Natural Frequency
Deviatio
(Hz)
n
No
Mode Shapes
(%)
FEM
EMA
1
1557.6
1526
2
2
2930.6
3092 .7
3
3261.3
4
3263.5
Natural Mod
Frequency
Deviation
e No
(Hz)
( %)
FEM
EMA
5
3395. 4
3379
0
-5.24
6
3433. 9
3392. 8
1.21
3233 .2
0
7
3729. 2
3811. 6
-2.16
3266 .2
0
8
4649. 3
4659. 2
0
Mode shapes
As discussed earlier, a commercial disc was tested with the aid of experimental modal analysis. As a consequence, the natural frequencies and mode shapes obtained are really much nearer to the gray cast iron -2 materials. Therefore, it is reasoned that the rotor material examined in EMA is the gray cast iron-2.Table 5 shows the comparison of FEA and EMA results for a gray cast iron 2 material for the first eight modes. The FEM analysis deviation is considered acceptable as it fits within the scope.(Most of the deviation is zero) Small deviation is noted due to component production variability.(Geometric and material variations).For mode 1 and mode 2, the higher deflection region occurs on both sides of the rubbing surface with two nodal diameters. This is because the bottom sides are furthest away from the restraints. Both are having 900 repetitions of rotational over the rubbing surface at one axis of symmetry that is two nodal diameters of normal modes of vibration. A circumferential mode for reading 3 can bedescribed as a compression wave in the disc circumference similar to longitudinal mode of solid bar. At mode 3, the higher deflection is restrained at outer region of rubbing surfaces throughout the circular disc. Modes 4 and 5 having a rotating pattern of 450with two axis of symmetric on the rubbing surface, which are 3nodal diameter modes. Higher deflection is restraint at 3different locations over the surface area of rubbing surfaces.
Figure3. Stabilization diagram for brake disc
The characteristics of a system that describe its response to excitation as a purpose of frequency is the frequency response function. Frequency of response for every excitation is measured as shown in fig 3. The phase of response in general case will be dissimilar than that of the excitation. The phase deviation between the response and the excitation will vary with frequency. Fig. 4 shows the resonant frequency for rotor which is chosen based on phase separation at that frequency. The peaks of amplitude correspond to the natural frequency of every mode. In fact, they correspond to the natural frequencies of the principal modes of the rotor that were excited, or participated in vibration of the rotor due to impacts.
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Table6. Comparison of FEM and EMA Results for different elements
Component
Natural frequency (Hz)
Description
FEM
EMA
Brake Pad
3041.1
3263
Brake Calliper
4390.2
4161
745.7
698
Mode shape
Calliper Bracket (Carrier)
Table 6 illustrates the natural frequencies obtained for different parts of the brake assembly through FEA and EMA.It is also observed that the percentage deviation is within the acceptable range and good agreement withthe results of the natural frequency. The fig. 4, 5 and 6 shows the resonant frequency for pad, Brake calliper and carrier respectively.This frequency is selected based on phase separation at that frequency.An ideal resonance should have a phase shift of +180° to -180°. But phase shifts above 90° are generally accepted at resonant frequency.Fig.5 shows peak amplitude at 3263Hz which indicates the natural frequency of the pad for the given excitation.Similarly, fig.6 indicates the peak amplitude at 4161Hz and 698 Hz which shows the natural frequency of brake calliper and carrier respectively.
Figure 4: Resonant frequency for brake pad.
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
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Figure 5: Resonant frequency for brake calliper
Figure 6: Resonance frequency for Carrie
5.Conclusions This paper presents the modal analysis of realistic floating calliper disc brake components using finite element model and experimentation (excitation). Reasonably good agreement is achieved between predicted and experimental results in terms of dynamic characteristics of the developed model. The material properties of brake disc play an important role towards the vibration mode patterns. From the finite element analysis, the result shows that the ratio between Young’s modulus over density increases the natural frequencies of vibration for the disc with respect to the number of modes and disc stiffness.The simulation results showed that materials having lower value of the modulus of elasticity and higher value of density have lower values of natural frequencies of vibration.Vibration mode and frequency of a squealing disc brake’s rotor are influenced by natural frequencies and modes of stationary rotor. Thus, brake squeal occurs in the vicinity of natural frequencies of the disc.
References [1] [2] [3] [4] [5] [6] [7] [8]
Von Wagner U, HochlenertD, and Hagedorn P, “Minimal Models for Disc Brake Squeal”, Journal of Sound and Vibration,302,.(2007),pp 527-539 Akay A, Acoustics of friction, Journal of the Acoustic Society of America (2002); 111(4): pp 1525-1548. Abendroth H and B. Wernitz, 2000, The integrated test concept dyno-vehicle; performance and noise, SAE Technical paper 2000-012774 Nishiwaki M, Harada H, Okamura H, Ikeuchi T, “Study on disc brake squeal”. Technical Report 890864. SAE paper, (1989). Matsuzaki M, Izumihara T, “Brake noise caused by longitudinal vibration of disc rotor”. Technical Report 930804. SAE, (1993). Sheng Yan, Gong Jing and RongQiang “Modal Analysis of Active Framed Structure” Journal of low frequency noise , vibration and active control” vol 29 No 3,pp 197-206 G.M.L.Gladwell and D. Vijay, “Natural frequencies of free finite –length circular cylinder” Journal of Sound and Vibration, vol. 42, Issue 3, (1975), pp. 387-397 J.C. Bae and J.A. Wickert, “Vibration free vibration of coupled Disc hat structure” Journal of Sound and Vibration. Vol.235, Issue 1, 2000), pp117-132,
4994 [9] [10] [11] [12] [13] [14] [15] [16]
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994 Tuchinda N.P, Hoffmann and D.J. Ewins “Mode lock in characteristics and instability of the pin on disc system”, Proceedings of the International Modal Analysis Conference- IMAC XIX, Vol.1, pp 71-77, (2001) Ibrahim R. A. “Friction induced vibration chatter, squeal and chaos” part-II: dynamics and modeling, ASME Applied Mechanics Reviews, 47, (1994),pp, 227-259 Liles G.D. Analysis of disc brake squeals using finite element methods. Technical Report. 891150, SAE: (1989). Lee, Y.S., Brooks, P.C., Barton D.C. and Crolla , D.A, A study of Disc Brake Squeal propensity using a parametric finite element model, (1998). Abubakar AR and Ouyang H. Complex eigenvalue analysis and dynamic transient analysis in predicting disc brake squeal.Int. J. Vehicle Noise Vibration, 143-155, (2006) Mario T J,Samir N.Y and Roberto J, Analysis of brake squeal noise using finite element method-A parametric study, Applied Acoustics, 69, (2008),pp147-162 Nouby M, Mathivanan D, Srinivasan K, A combined approach of complex eigenvalue analysis and design of experiments to study disc brake squeal, International Journal Of Engineering Science and Technology,Vol. 1,No. 1, (2009),pp 254-271 Belhocineali, Nouby M. Gazaly, Effect of Young’s modulus on disc brake squeal using finite element analysis, IIAV,2016
ScienceDirect Materials Today: Proceedings 5 (2018) 4986–4994
www.materialstoday.com/proceedings
ICMPC 2017
Effect of Material Properties On Disc Brake Squeal And Performance Using FEM and EMA Approach. N.K.Kharatea, Dr.S.S.Chaudharib a b
NDMVPSKBTCOE,Dept.Of Mechanical Engg,Gangapur Road,Nashik (M.S),422003,India YCCOE,Dept.Of Mechanical Engg,Hingna road,wanadongari,Nagpur (M.S),441110,India
Abstract This paper is concerned with the investigation of disc brake squeal with different materials for disc brake components.The objective of the present research is developing FE model of every component of the disc brake system for understanding the influence of material properties on the disc brake squeal and validated with experimental modal analysis. The aim of the research is to predict the squeal at the former phase of invention using a more realistic model. The results of FEM and EMA indicated that different material properties of disc brake components play a sustainable role in generating the brake squeal.
© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of 7th International Conference of Materials Processing and Characterization. Keywords: Brake squeal, Modal analysis, Natural frequency, Mode shapes, Frequency response function
1.
Introduction:
Squeal that generated in the disc brake of the automobile has been considered as a one of the major problem in the automotive industry due to the persistent complaints that reduces customer satisfaction.Most of the scientist and engineers have agreed that squeal noise in the disk brake is initiated by the instability due to friction forces, contributing to self-excited vibrations 1. With the help of industrial source,.
* Corresponding author. Tel.: +91 9822767671; fax: +91- 253- 2317016. E-mail address:[email protected]
2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of 7th International Conference of Materials Processing and Characterization.
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
4987
Nomenclature FFT Fast Fourier transforms FRF Frequency response function FEM Finite element method EMA Experimental modal analysis Akay 2 reviewed that warranty costs due to noise, vibration and harshness (NVH) including disc brake squeal, in the North America were up to one billion dollars. Similarly, Abendroth and Wernitz 3 noted that many friction material suppliers have to spend up to 50 percent of their engineering budget on the NVH issues. Therefore, the elimination of brake squeal noise is very significant as the problem leads to increases warranty costs as well as discomfort towards the vehicle occupants and walkers. There have been many related studies carried out on the behaviour of the disc brake through modal analysis. Finite element method has been used by the researcher to several conclusions. The most usual technique applied is to compute M and K matricesin the equation of motion + + + = 0 to determine the natural frequencies and mode shape of the brake system components4-6.In recent years, the finite element (FE) has reached wide acceptance to assist brake vibration and noise problem. Although substantial research and efforts with different theories and method ologiessuch as modifications in structure, material, and dimensions have been formulated and carried out since 1930’s in order to predict and eliminate the brake squeal, it is still difficult to predict its occurrence because of its interdisciplinary nature. For example, In 1975, G.M.L. Gladwell and D. K. Vijay7, uses a finite element modelling technique to find out the natural frequencies of a hollow cylinder5.Bae and Wickert, concentrated on the top-hat structure type of disc brake8. Finite element model of the brake rotor disc was developed to study the influence of the top hat structure on the modalities of the brake rotor disc.The result proves how the natural frequency of the structure relates to disc thickness and hat structure. Further research by Tuchinda et al 9, considered the same top hat structure type disc brake for their finite element analysis and indicated that the frequency of squealing are influenced by natural frequencies and modes of stationary rotors.Ibrahim10, in his literature, reviewed many theorems and mechanism such as stick-slip, sprag- slip, negative friction velocity slop and mode coupling of structures with several conclusions. Theoretically, it shows that the mechanism such as stick-slip, sprag- slip, and negative friction velocity slop can cause chaosand instability of the system. One of the earliest researches of Liles11 developed a finite element model of each brake component using solid elements and validated their accuracy using an experimental modal analysis. He showed that squeal propensity increases at higher friction coefficients. Lee et al.12reported that reducing the back plate thickness increases the squeal propensity with uneven contact pressure distribution. Abu Bakar et.al13 further elaborates the squeal phenomenon by considering surface topographies of two new and unworn pairs of brake pads. Both pairs of pads are tested under certain braking pressure by inserting pressure indicating film in between to investigate wear progress. He suggests that FE model is more practical and reliable method for simulating wear progress. According to Mario Triches Junior et al.14, disc brake squeal occurs when the system undergoes large amplitude vibration. In 2009, Noubyet al.15, in their research considered the complex eigenvalue analysis along with the design of experiments to find out the optimal design of the brake system.They reported that by increasing the Young’s modulus of the back plate and modifying the shape of friction material by adding chamfer and slots, brake squeal propensity can be reduced to a great extent.Recently in 2016, Belhocineali, NoubyM.Gazaly16concentrated on effect of young’s modulus on the stability of the disc brake system and squeal generation.They commented that increasing young’s modulus of the rotor, friction material, anchor bracket and back plate reduces the number of unstable frequencies and provides the better squeal performance. Although successful case studies and research with certain success have been conducted in the last few years but no real reliable brake noise prevention tool truly exists yet.In fact, research done on a special case of brake or on a fussy type of vehicle is not assignable to other types of brakes or vehicle.
4988
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
2.Finite Element Method and Modeling A detailed three dimensional finite element model of a commercial ventilated disc brake system parts such as rotor, caliper, bracket and pad aremodeled considering the realistic dimensions for better correlation of the consequences with the experimental.Each component of the brake assembly is examined considering the free-free boundary conditions as it allows the structure to vibrate freely without interference of the other parts. It also facilitates better visualization of mode shapes associated with each natural frequency.For validation of FE model one must recognize the dynamic properties such as modulus of elasticity, density and Poisson’s ratio of the components. The dynamic properties of the structure are obtained by mode analysis or by its evaluation 4. The Block Lanczos method is applied to specify the frequencies with the help of FE software.Only linear behavior is viewed in a modal analysis while Non-linear properties are neglected. 2.1FE Modal Analysis of Brake Rotor: Modal analysis of brake rotor has been carried out for four different materials such as Gray C.I-1, Gray C.I2,carbonceramic and steel as it is one of the essential parts of the brake system which contributes more in the generation of noise. First ten modes are extracted for the rotor for predicting the natural frequencies. Solid 45-3D structural solid element is utilized for the three dimensional modelling of structure. The element is defined by eight nodes having three degrees of freedom at each node. Material properties of different rotor material are shown in table 1.Role of element shape and order of interpolation decides the element selection. Table1: Material properties of different rotor material Rotor Material
Density (kg/m3)
Young’s Modulus
Poisson’s ratio
Gray C.I-1
7200
66
0.28
Gray C.I-2
7100
125
0.28
Carbon Ceramic
2450
30
0.3
Steel
7840
210
0.3
2.2Modal analysis of pad, calliper and bracket: Finite element modal analysis is done on the various elements of the magnetic disk brake system such as brake pad, calliper and carrier. Material properties of different components of disc brake are shown in table 2.The same process is practiced for the analysis as that used for brake disc. Table 2: Material properties of disc brake components. Component Description Back Plate Friction material Brake Calliper Calliper Bracket
Young’s Modulus (Mpa) 220 ×103 03×103 110×103 130×103
Density (Kg/m3) 7800 2500 6100 7850
Poisson Ratio 0.3 0.3 0.3 0.3
3. Validation of FE model using experimental modal analysis (EMA) approach Each part of a disk brake assembly is tested through the EMA with free – free boundary conditions.The observational approach to investigate the way patterns and natural frequencies of the structure through impact hammer test consists of the following steps. • • • • • • •
Generation of model. Model test setting Divide the structure inadequate number of points with the appropriate special distribution. Excite the structure with impact hammer. Taking the measurements Analysis of measured output data. Establishment with the FEM data.
N.K.Kharate et al./ Materials Today: Proceedings 5 (2018) 4986–4994
4989
The test equipment used for the experimentation is the Fast Fourier Transform (FFT) with sixteen channels along with data acquisition system made of Scadas Front End.The structure was excited using impact hammer (Dytran Make 5800B3) at all predefined locations as indicated in fig.1 and the response was collected using tri-axial accelerometer(PCB T356A02 & 356B21) at an identified driving point transfer function (DPTF) location. The type of EMA is known as the Frequency Response Function (FRF) method which evaluates the input excitation and output response simultaneously.The essence of all frequency response functions (FRF’s) are resolved to extract natural frequencies and mode shapes. Fig.1 shows the experimental modal analysis set up for rotor.
Figure1. Accelerometer localization for rotor
The same methodology has been used for obtaining the natural frequency of brake pad, calliper and bracket. The sum FRF was collected and worked out to discover out the natural frequency of the elements. The instrumentation for experimental modal analysis is shown in fig.2 (a) and (b)
(a)
(b)
Figure2. EMA set up fora) Calliper Bracket b) Brake Pa
4. Results and discussion Natural frequencies obtained for different disc material using FEM for first ten modes are presented in the table 4.While table 3 shows the values of deformation i.e. displacement of disc at particular mode From table 6, it is observed that amongst the four materials the gray cast iron-1has acceptable lower natural frequency for first ten modes with the help of FEA. In fact, as per the definition of squeal range prescribed by the various researchers and
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experts found in the literature, GCI-1 does not much contribute to the generation of brake squeal. Finally, it is noted that gray cast iron-1 is considered as the best material composition for the disc rotor. It is also observed that the natural frequencies for the material carbon ceramic are less, but their shift at each modality is more as compared to rest of the materials as indicated in table 6.It is observed that for all types of materials, the oscillation (Vibrational) behaviour of the disc is same but with different values of natural frequencies and deformations. This is because of the two styles are differentiated by the fact that their in-plane displacements is different as shown in below Table 4. Table 3: Natural frequency for first ten modesofrotor. Gray Cast Iron 1
Gray Cast Iron 2
Carbon ceramic
Freq. (Hz)
Freq. (Hz)
Freq. (Hz)
Mode No.
Steel Freq. (Hz)
1
1093.9
1557.6
1264.3
1918.1
2
1098.1
1562.3
1269.2
1924.
3
1960.4
2930.6
2265.8
3630.
4
2239.4
3261.3
2588.3
4012.5
5
2239.6
3263.5
2588.5
4015.1
6
2331.9
3395.4
2695.2
4181.2
7
2365.4
3433.9
2733.8
4228.7
8
2475.6
3729.2
2861.2
4612.5
9
2478
3762.1
2864.
4653.4
10
2945
4649.3
3403.8
5742
Confirmation has also pulled in for the effects of natural frequencies of two different materials of the same model (Mode1) obtained in the FEA in terms of damping ratio coefficients which is the ratio of modulus of elasticity and compactness. For gray C.I 1modulus of elasticity (Ea) = 66Gpaand density (ρa) = 7200 Kg/m3.Similarly for, Gary C.I 2 modulus of elasticity (Eb) = 125Gpa and density (ρb) = 7100 Kg/m3.Thusthe ratio of natural frequencies and damping ratio coefficient of these two materials is equal to 0.7and are calculated by using the relation ⁄ and × × respectively.Likewise, for carbon ceramic and steel, natural frequency ratio and damping ratio coefficient is 0.67 for mode no 1.As the ratio between natural frequencies of two dissimilar types of materials are equal to the damping ratio coefficient, which is the ratio of modulus of elasticity and density, therefore it confirms the modes of frequencies obtained through Finite element modelling. Table 4: Minimum and Maximum Deformation of rotor for First 10 Modes in mm
Gray Cast Iron 1 Sr. No
Min.
Gray Cast Iron 2 Max.
Min.
Max.
Carbon ceramic Min.
Max.
Steel Min.
Max.
1
0.105
39.15
9.35
1230
5.73
2122.4
9.14
1171.9
2
0.036
39.13
11.09
1232
1.96
2121.3
10.93
1174.8
3
0.151
29.4
59.37
985.05
8.19
1593.8
55.86
936.17
4
0.044
44.26
3.42
1437
2.39
2399.6
3.17
1369.3
5
0.061
44.21
2.65
1417.7
3.32
2396.8
3.04
1351.4
6
1.736
31.34
58.56
1012.4
94.14
1699.3
56.88
962.04
7
1.745
32.19
52.23
1043.6
94.62
1745.1
49.62
991.3
8
0.134
36.64
31.15
1203.6
7.26
1986.6
32.65
1143.2
9
0.165
36.94
57.03
1230.1
8.95
2002.9
54.73
1168.7
10
0.189
99.27
1.50
3483.5
10.26
5381.6
1.44
3324.6
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Table 5.Natural frequencies for a Gray C. I- 2disc material
Mode
Natural Frequency
Deviatio
(Hz)
n
No
Mode Shapes
(%)
FEM
EMA
1
1557.6
1526
2
2
2930.6
3092 .7
3
3261.3
4
3263.5
Natural Mod
Frequency
Deviation
e No
(Hz)
( %)
FEM
EMA
5
3395. 4
3379
0
-5.24
6
3433. 9
3392. 8
1.21
3233 .2
0
7
3729. 2
3811. 6
-2.16
3266 .2
0
8
4649. 3
4659. 2
0
Mode shapes
As discussed earlier, a commercial disc was tested with the aid of experimental modal analysis. As a consequence, the natural frequencies and mode shapes obtained are really much nearer to the gray cast iron -2 materials. Therefore, it is reasoned that the rotor material examined in EMA is the gray cast iron-2.Table 5 shows the comparison of FEA and EMA results for a gray cast iron 2 material for the first eight modes. The FEM analysis deviation is considered acceptable as it fits within the scope.(Most of the deviation is zero) Small deviation is noted due to component production variability.(Geometric and material variations).For mode 1 and mode 2, the higher deflection region occurs on both sides of the rubbing surface with two nodal diameters. This is because the bottom sides are furthest away from the restraints. Both are having 900 repetitions of rotational over the rubbing surface at one axis of symmetry that is two nodal diameters of normal modes of vibration. A circumferential mode for reading 3 can bedescribed as a compression wave in the disc circumference similar to longitudinal mode of solid bar. At mode 3, the higher deflection is restrained at outer region of rubbing surfaces throughout the circular disc. Modes 4 and 5 having a rotating pattern of 450with two axis of symmetric on the rubbing surface, which are 3nodal diameter modes. Higher deflection is restraint at 3different locations over the surface area of rubbing surfaces.
Figure3. Stabilization diagram for brake disc
The characteristics of a system that describe its response to excitation as a purpose of frequency is the frequency response function. Frequency of response for every excitation is measured as shown in fig 3. The phase of response in general case will be dissimilar than that of the excitation. The phase deviation between the response and the excitation will vary with frequency. Fig. 4 shows the resonant frequency for rotor which is chosen based on phase separation at that frequency. The peaks of amplitude correspond to the natural frequency of every mode. In fact, they correspond to the natural frequencies of the principal modes of the rotor that were excited, or participated in vibration of the rotor due to impacts.
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Table6. Comparison of FEM and EMA Results for different elements
Component
Natural frequency (Hz)
Description
FEM
EMA
Brake Pad
3041.1
3263
Brake Calliper
4390.2
4161
745.7
698
Mode shape
Calliper Bracket (Carrier)
Table 6 illustrates the natural frequencies obtained for different parts of the brake assembly through FEA and EMA.It is also observed that the percentage deviation is within the acceptable range and good agreement withthe results of the natural frequency. The fig. 4, 5 and 6 shows the resonant frequency for pad, Brake calliper and carrier respectively.This frequency is selected based on phase separation at that frequency.An ideal resonance should have a phase shift of +180° to -180°. But phase shifts above 90° are generally accepted at resonant frequency.Fig.5 shows peak amplitude at 3263Hz which indicates the natural frequency of the pad for the given excitation.Similarly, fig.6 indicates the peak amplitude at 4161Hz and 698 Hz which shows the natural frequency of brake calliper and carrier respectively.
Figure 4: Resonant frequency for brake pad.
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Figure 5: Resonant frequency for brake calliper
Figure 6: Resonance frequency for Carrie
5.Conclusions This paper presents the modal analysis of realistic floating calliper disc brake components using finite element model and experimentation (excitation). Reasonably good agreement is achieved between predicted and experimental results in terms of dynamic characteristics of the developed model. The material properties of brake disc play an important role towards the vibration mode patterns. From the finite element analysis, the result shows that the ratio between Young’s modulus over density increases the natural frequencies of vibration for the disc with respect to the number of modes and disc stiffness.The simulation results showed that materials having lower value of the modulus of elasticity and higher value of density have lower values of natural frequencies of vibration.Vibration mode and frequency of a squealing disc brake’s rotor are influenced by natural frequencies and modes of stationary rotor. Thus, brake squeal occurs in the vicinity of natural frequencies of the disc.
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