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2、rom, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be revised, reaffirmed, stabilized, or cancelled. SAE invites your written comments and suggestions.Copyright 2012 SAE International All rights reserved. No part of this pub
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4、(outside USA) Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.orgSAE values your input. To provide feedback on this Technical Report, please visit http:/www.sae.org/technical/standards/J3013_201210SURFACEVEHICLERECOMMENDEDPRACTICEJ3013 OCT2012 Issued 2012-10Friction Ma
5、terial Elastic Constants Determination through FRF Measurements and OptimizationRATIONALEFriction material elastic constants are required inputs to brake NVH simulations, whether at component (e.g., pad assembly FRFs) or system levels (e.g., squeal simulations). Friction materials are anisotropic (a
6、pproximately transversely isotropic) and inhomogeneous (including elastic constants and densities).Measuring elastic constants locally has its own difficulties and limitations, when used for NVH simulations: There is no known measurement method that can measure a complete set of elastic constants of
7、 a single sample. The prevailing measurement method used in automotive brake industry is the ultrasonic method (SAE J2725), which requires measurements of TWO separate samples to calculate a set of elastic constants (while the elastic constants and densities of these two samples are generally differ
8、ent). There is no known measurement method, not just for a complete set of elastic constants but also densities, that is nondestructive. Measuring multiple samples from multiple pads then calculating their averages, while beneficial, does not ensure adequate correlation (pad assembly vibration simul
9、ation vs. measurement) see referenced publications. Besides, the averaged values are no longer “local” properties, anyway. The FRF (Frequency Response Function) measurement based method has been in use in practice for brake NVH simulations, either to provide elastic constants directly or to improve
10、averaged elastic constants calculated based on ultrasonic measurements (see referenced publications). Therefore, it seems both necessary and beneficial to document the procedures and standardize as much as possible. FOREWORDThe FRF measurement based procedure described in this standard is intended t
11、o provide a set of homogeneous (equivalent averaged values) and anisotropic (transversely isotropic) elastic constants for brake NVH simulations (not for quality control). The objective is to ensure pad assembly vibration correlation between simulation and measurement. It is an alternative to, and d
12、oes not require, ultrasonic measurement results. However, elastic constants from ultrasonic method, if available, can be used as initial inputs. It can also be used to improve calculated average elastic constants from ultrasonic methods. SAE J3013 Issued OCT2012 Page 2 of 13 1. SCOPE This SAE Standa
13、rd specifies necessary procedures and control parameters in estimating anisotropic elastic constants of friction material based on pad assembly FRF measurements and optimization. It is intended to provide a set of elastic constants as inputs to brake NVH simulation, with the objective of ensuring pa
14、d assembly vibration correlation between simulation and measurements. 2. REFERENCES 2.1 Applicable Documents The following publications form a part of this specification to the extent specified herein. Unless otherwise indicated, the latest issue of SAE publications shall apply. 2.1.1 SAE Publicatio
15、ns Available from SAE International, 400 Commonwealth Drive, Warrendale, PA 15096-0001, Tel: 877-606-7323 (inside USA and Canada) or 724-776-4970 (outside USA), www.sae.org.Lou, G, Lee, L, and Malott, B., “Introduction of Anisotropic Lining Elastic Constants Optimization (ALCO) Method for Friction M
16、aterials”, SAE Congress, Detroit, MI, 2007; SAE 2007-01-0591 Lee, L., Lou, G., and Malott, B., “Development and Applications of ALCO Method for Acquiring Elastic Constants of Friction Materials,“ SAE Technical Paper 2007-01-3958, 2007, doi:10.4271/2007-01-3958. Liu, W., “Improving Finite Element Mod
17、els of Brake Pads Through Material Optimization,“ SAE Technical Paper 2007-01-3946, 2007, doi:10.4271/2007-01-3946. SAE J2598 Automotive Disk Brake Pad Natural Frequency and Damping Test SAE J2725 Road Vehicles Friction Materials Elastic Properties Measurements 3. GENERAL DESCRIPTIONS 3.1 Main Steps
18、 and Flow There are 3 main steps: (1) Pad FRF measurements; (2) Optimization; (3) Verification (see Figure 1 below). SAE J3013 Issued OCT2012 Page 3 of 13 FIGURE 1 - FLOW DIAGRAM OF FRF MEASUREMENT BASED PROCEDURE FOR ELASTIC CONSTANTS Following sections describe these procedures and criteria more i
19、n detail. 4. PAD FRF MEASUREMENTS 4.1 Pad Assembly Full pad assemblies, without insulator, are used for FRF measurements. It is desirable to use the same pad assembly geometry as those intended for noise testing. If pads without slot and chamfer are readily available, they can be used, as slots and
20、chamfers may add additional part-to-part variations (the variations are small as found in practice. Therefore, it is not advised to make pads just for this purpose). Changes in chamfers and/or slots typically do not require reacquiring the elastic constants. However, if and when parts are available,
21、 confirmation of FRF correlation between measurements and simulation is always recommended, regardless of how the elastic constants are obtained (whether from FRF measurements or ultrasonic measurements) If parts for the intended program are not available yet, elastic constants obtained from a diffe
22、rent pressure plate and pad geometry can be used. Even though there are successful application cases (see referenced publications), the overall FRF correlation (of all modes) between measurement and simulation is no longer ensured. When parts become available, FRF correlation should be verified, and
23、 if necessary, elastic constants re-measured using the pads for the intended program. SAE J3013 Issued OCT2012 Page 4 of 13 4.2 FRF measurements Multiple pads (minimum 3) should be measured. Typical pad-to-pad frequency variations are expected 3%, otherwise further investigation is recommended (befo
24、re using this standard), for example, poor bonding between pressure plate and friction material / underlayer may cause larger frequency variations. Excitation: an impact hammer is typically used. Response: typically an accelerometer is used, though laser vibrometer can also be used. Full modal analy
25、sis is not required, as long as major modes of interest can be identified (bending, torsional and in-plane). Refer to SAE J2598 for more information on pad FRF measurements. Multiple measurement points (locations), in both out-of-plane and in-plane directions should be considered. The more modes cap
26、tured and main vibration identified correctly (bending, torsional, in-plane), the better. Frequency range ideally should go up to 16,000 Hz. If the quality (and modal information) of a particular mode (or modes) is in doubt, the mode (modes) can be excluded. The user needs to ensure, e.g., in the Ve
27、rification step (Section 6), that there is no mismatch of modes between measurement and simulation. 4.3 FRF Measurement Results Measured frequencies from these multiple pads are averaged. These frequencies are then divided into two sets (Optimization Set and Verification Set):4.3.1 Optimization Set
28、These modes are used in the Optimization Step (Section 5): Since there are 5 independent elastic constants, at least 6 modes (frequencies) are required. The more modes used (if available), the better. At least one in-plane mode should be included in the Optimization Set. The selected modes do not ne
29、ed to be consecutive (in frequencies). The remaining modes (not included in Optimization Set) are used in Verification Set. 4.3.2 Verification Set The remaining modes are used in the Verification Step (Section 6): All remaining modes (not included in Optimization Set) are included in Verification Se
30、t. At least one mode should be reserved for Verification Set. The more modes in the Verification Set, the higher confidence with the results from optimization process, especially when the elastic constants need to be used for other programs (different pressure plate and pad geometry). SAE J3013 Issu
31、ed OCT2012 Page 5 of 13 5. OPTIMIZATION 5.1 Finite Element Analysis (FEA) FEA model is required for both Optimization Step and Verification Step (Section 6). 5.1.1 Geometry Same geometry as FRF measured parts (Section 4) should be used, including chamfers and slots. 5.1.2 FEA Model Element Type The
32、commonly used element types in brake NVH are either 2ndorder (10-node) tetrahedral element or 1storder (8-node) brick element, both are acceptable. For similar modal analysis quality, 1storder brick element model would be much smaller in size, therefore requires much less solver time. The 2ndorder t
33、etrahedral element is, on the other hand, much easier to mesh (typically auto-meshing). Element and Model Size It is beneficial, though not required, to use the same FEA model as the intended brake NVH simulation model, if possible. When the intended NVH simulation model is not available (e.g., exte
34、rnal users), the element and model size should be similar as an actual brake NVH simulation would require. Pressure Plate material properties for pressure plate (Youngs Modulus, Poissons Ratio and Density) are required input, and should be the same as the material being used (e.g., steel), and docum
35、ented / reported (see Table 2). The user needs to ensure good agreement between CAD / FEA model and actual pressure plate, in dimensions (especially thickness) and material properties (e.g., Youngs Modulus). Friction Material Density Density (average / nominal) can be calculated, based on pad / pres
36、sure plate volumes (CAD model), total pad assembly mass (average of multiple pad assemblies), and pressure plate density. It should also be documented / reported (see Table 1). FEA Model Coordinate System the pad assembly FEA model can use any global coordinate orientations. However, the user must e
37、nsure that its friction material property orientations are defined consistently (using local coordinate system if necessary), as in Figure 2 and Equations (1): FIGURE 2 - PAD COORDINATE SYSTEM (ORIENTATIONS) y zxSAE J3013 Issued OCT2012 Page 6 of 13 5.2 Elastic Stress-strain relationship for transve
38、rsely isotropic materials can be described as Equations (1): ,000000000000665544332322131211=zxyzxyzyxzxyzxyzyxCClSymmetricaCCCCCCC(Eq. 1) where x, y, zand xy, yz, zxare normal and shear stresses; x, y, zand xy, yz, zx, are normal and shear strains, correspondingly. The C matrix is Elastic Coefficie
39、nt Matrix, where C11, C12, C13, C22, C23, C33C44, C55and C66are elastic constants.For transversely isotropic material, C11= C22, C13= C23, C55= C66. C12and C44satisfy Equation (2); therefore, either C44or C12can be calculated. ().21;2121144441112CCCorCCC = (Eq. 2) The C matrix in Equation (1) can be
40、 simplified as in Equation (3). The 6 elastic constants C11, C12, C13, C33, C44and C55are required inputs to NVH simulations. ,000000000000555544331311131211=CClSymmetricaCCCCCCCC (Eq. 3) In Equation (3), there are only 5 independent elastic constants, due to the constraint of Equation (2). 5.3 Init
41、ial/Starting Point The user needs to provide an initial set of elastic constants as a “starting point” for the optimization procedure: (C11, C12,C13, C33, C44and C55)0, with either C12or C44calculated by Equation (2). This can simply be a “guess”, and there is no rigid requirement. Even a “bad guess
42、” does not fundamentally prevent the optimization converge to the same “optimized” answer as a good “guess” (see SAE 2007-01-3958) While not required, prior knowledge of the friction material (hence its elastic constants) is beneficial, and should be used if available. Other knowledge, such as elast
43、ic constants of a similar material, or averaged values calculated from ultrasonic measurements (SAE J2725), can also be used.SAE J3013 Issued OCT2012 Page 7 of 13 5.4 Optimization This step runs FEA modal analysis iteratively to improve the elastic constants (from Starting Point), until converging,
44、i.e. the specified Objective achieved (optimized), and all constraints successfully met (without any violations), based on the provided FRF measurements (Optimization Set). 5.4.1 FEA Solver Any commercial FEA software (e.g., NASTRAN, ABAQUS, etc.), or internal programs (if already in use and verifie
45、d in brake NVH simulations) are all acceptable. 5.4.2 Optimization Algorithm Following algorithms have been tested with satisfactory performance (see referenced publications for details): 5.4.2.1 Optimization algorithms used by SAE 2007-01-0591 and SAE 2007-01-3958: Sequential Quadratic Programming
46、(SQP) default algorithm (recommended) Nonlinear Least Squares Curve-Fitting Multi-Objective Goal Attainment 5.4.2.2 Optimization algorithms in MSC/NASTRAN with satisfactory performance (SAE 2007-01-3946) Modified Method of Feasible Directions Sequential Quadratic Programming 5.4.3 Optimization Objec
47、tive While individual optimization algorithm can be different in its optimization objective(s), the overall objective is to minimizethe frequency differences between measured modes and FEA calculated ones. Equation (4) is a typical optimization objective by SQP method: ;min2, i iTestiTestiFEAfffDefa
48、ult tolerance value for optimization at 0.001 (Eq. 4) WhereiFEAf,andiTestf,are the corresponding mode (i) from FEA and measurement, respectively. SAE 2007-01-0591 and SAE 2007-01-3958 use all modes in the optimization set in Equation (4). SAE 2007-01-3946 shows that with only a few selected higher modes in Equation (4) can also lead to satisfactory optimization results. (The remaining modes are used in optimization constraints.) 5.4.3.1 Mode Matching Th
