1、_ SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising there
2、from, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions. Copyright 2011 SAE International All rights reserved. No part of this publication m
3、ay be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: +1 724-776-4970 (outside U
4、SA) Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.orgSAE values your input. To provide feedbackon this Technical Report, please visit http:/www.sae.org/technical/standards/J2933_201103SURFACEVEHICLERECOMMENDEDPRACTICEJ2933 MAR2011 Issued 2011-03 Verification of Brake
5、 Rotor Modal Frequencies RATIONALE Braking systems industry uses modal testing of brake rotors for design validation, production validation, and quality control purposes. Several vendors provide equipment to facilitate this measurement. Currently, there exists no standard procedure that brings unifo
6、rmity to these measurements. This procedure addresses this need by providing the guidelines necessary for making these measurements comparable. TABLE OF CONTENTS 1. SCOPE 31.1 Purpose . 32. REFERENCES 32.1 Related Publications . 33. DEFINITIONS . 34. PROCEDURE . 44.1 Preparation 44.1.1 Set Up: Free
7、Condition 44.1.2 Excitation Method 44.1.3 Response Sensor 44.1.4 Setup Documentation 44.2 Setup Configurations . 44.2.1 Impact and Microphone. 44.2.2 Impact and Accelerometer 54.2.3 Impact and Laser Vibrometer 54.2.4 Optional Set Up for Drums 64.3 Data Acquisition 64.3.1 Dynamic Analyzer . 64.3.2 Eq
8、uipment Input Amplifier . 64.3.3 Digitization . 64.3.4 Equipment Signal to Noise Ratio 64.3.5 Triggering 64.3.6 Windowing . 64.3.7 Differential Input 64.4 Signal Processing . 74.4.1 Averaging 74.4.2 Frequency Resolution . 74.4.3 Transfer Function 7SAE J2933 Issued MAR2011 Page 2 of 94.5 Reporting .
9、74.5.1 Modal Classification 74.5.2 Results Tabulation 84.6 Statistical Inferences . 84.6.1 Normality of Batch Measurements 84.6.2 Base Line Variability 84.6.3 Mean Shift of Lower Mode for Known Population . 84.6.4 Mean Shift of Lower Mode for Unknown Population . 84.6.5 Mean Shift of Higher Modal Fr
10、equencies (when only lower mode is measured) . 94.6.6 Mean Shift of Higher Modal Frequencies when Multiple Frequencies are Measured. . 95. NOTES 95.1 Marginal Indicia . 9FIGURE 1 IMPACT AND MICROPHONE SETUP . 4FIGURE 2 IMPACT AND ACCELEROMETER CONFIGURATION . 5FIGURE 3 IMPACT AND LASER VIBROMETER CO
11、NFIGURATION . 5FIGURE 4 SET UP FOR DRUMS 6FIGURE 5 ROTOR PLATE OUT OF PLANE MODES . 7FIGURE 6 ROTOR PLATE IN-PLANE RADIAL MODES . 7FIGURE 7 ROTOR PLATE IN-PLANE CIRCUMFERENTIAL MODES . 8TABLE 1 SAMPLE TABULATION OF RESULTS 8SAE J2933 Issued MAR2011 Page 3 of 91. SCOPE Provide description of standard
12、 test methods, analysis methods, and reporting methods for measuring the resonant modes of automotive disc brake rotors and drums for purpose of design and production verification of these components. 1.1 Purpose This procedure may be used for verification of production capability of a plant to prod
13、uce brake rotors that are consistent with Production Part Approval Process (PPAP). The procedure may be used to fingerprint parts used for design validation process. 2. REFERENCES 2.1 Related Publications The following publications are provided for information purposes only and are not a required pa
14、rt of this SAE Technical Report.Bosch Technical Report, Tim Kraus, Mohamed Khalid Abdelhamid, “Detection of IP and OP modes of vented rotors with fiber laser modal analysis“ Abdelhamid, M.K. and Denys, E., “Brake Rotor Modal Frequencies: Measurement and Control,“ SAE Technical Paper 2010-01-1688, 20
15、10, doi:10.4271/2010-01-1688. Hyeongill Lee, Rajendra Singh: ”Acoustic radiation from out-of-plane modes of an annular disk using thin and thick plate theories” Michael Yang, Abdul-Hafiz Afaneh and Peter Blaschke: “A study of disc brake high frequency squeals and disc in-plane/out-of-plane modes” 3.
16、 DEFINITIONS 3.1 FREQUENCY RESPONSE FUNCTION (FRF) FRF In simple terms describes the magnitude and phase of the test structure dynamic response as normalized by the exciting force. A FRF measurement consists of measuring the excitation force, using a force transducer, and the response, typically by
17、using a motion transducer (displacement, velocity, or acceleration). Other physical measurements such as sound pressure, air particle speed may also be used. 3.2 ACQUISITION TIME Total time required to collect a measurement. Denoted as T, acquisition time is equal to the block size (the number of sa
18、mples acquired), multiplied by t (the time between samples). 3.3 SPECTRAL LINES Spectral lines are the maximum number of spectral frequency lines. It is related to the number of time samples 3.4 BANDWIDTH The bandwidth is limited by the maximum frequency (Hz) measured. According to the Nyquist sampl
19、ing theorem, the maximum frequency is equal to 1/2 the sampling frequency. Most front-ends are equipped with their own anti-aliasing filter (typically 3 dB per octave) at 80% of the bandwidth. Above 80% of the bandwidth errors in amplitude and phase can be expected. Therefore data within the high ra
20、nge of the bandwidth should be used with caution. SAE J2933 Issued MAR2011 Page 4 of 93.5 FREQUENCY RESOLUTION The frequency resolution is the frequency difference (f), between spectral lines. f is equal to the bandwidth divided by spectral lines. When Fast Fourier Transform is used to calculate FRF
21、, f is also the inverse of Acquisition time. 4. PROCEDURE 4.1 Preparation 4.1.1 Set Up: Free Condition Free condition is the rotor support condition intended for this procedure. The actual support method used needs to simulate free conditions as closely as possible. Validation tests of the setup sha
22、ll be conducted to prove that free conditions are met. The reference free condition is a rotor hanging by a finger from the rotor hat as depicted in SAE paper 2010-01-1688. The support setup used must not induce a frequency shift of more than 1% from the reference free condition. Ambient temperature
23、 should be 20 C 1 C. 4.1.2 Excitation Method An impact device (instrumented or not) with a steel tipped end shall be used to impart a single pulse of short duration. The rotor should be impacted in one or more directions depending on the targeted modes. One of these directions should be normal to th
24、e brake plate. 4.1.3 Response Sensor Response sensor shall sense rotor plate motion or the sound radiated from this motion. 4.1.4 Setup Documentation Document the used rotor setup with a picture and a value for variation from the reference free condition. 4.2 Setup Configurations 4.2.1 Impact and Mi
25、crophone In this configuration, an impact device is used to excite rotor vibration and a microphone placed close to the brake plate is used to measure the sound radiated from rotor vibration. This is illustrated in Figure 1. The response captured by the microphone includes contributions from rotor i
26、n-plane and out-of-plane modes. In order to differentiate between modes, a separate finite element analysis or an experimental modal analysis is required to associate frequencies with specific mode shapes. FIGURE 1 - IMPACT AND MICROPHONE SETUP SAE J2933 Issued MAR2011 Page 5 of 94.2.2 Impact and Ac
27、celerometer In this configuration, an impact device is used to excite rotor vibration and one or more accelerometers are placed on the rotor brake plate to measure rotor vibration. Figure 2 illustrates use of tri-axial accelerometer to identify out of plane versus in plane vibration. This setup may
28、be sufficient to classify rotor modes, since motion in normal, radial, and tangential directions are observed. Impact position shall not coincide with a node of a mode that is under consideration. The mass of the attached accelerometer(s) shall be small enough so that they do not alter the frequency
29、 or modes of the rotor or drum. The attachment method used to secure the accelerometer to the surface should not interfere with the transmission of the compression or shear wave components into the accelerometer body. FIGURE 2 - IMPACT AND ACCELEROMETER CONFIGURATION 4.2.3 Impact and Laser Vibromete
30、r In this configuration, an impact device is used to excite rotor vibration and one or more laser beams are targeted onto the rotor brake plate to measure rotor vibration. Figure 3 illustrates use of two laser beams to identify out of plane versus in plane vibration. This setup can differentiate bet
31、ween in-plane and out-of-plane rotor modes. Impact position shall not coincide with a node of a mode that is under consideration. FIGURE 3 - IMPACT AND LASER VIBROMETER CONFIGURATION SAE J2933 Issued MAR2011 Page 6 of 94.2.4 Optional Set Up for Drums Drums are used in drum brakes similar to rotors i
32、n disk brakes. This test procedure may be used for drum brakes and the following setup illustrated in Figure 4 is an optional set up that may use microphone, accelerometer, or laser sensors. FIGURE 4 - SET UP FOR DRUMS 4.3 Data Acquisition 4.3.1 Dynamic Analyzer A dynamic analyzer is the preferred m
33、eans of collecting transfer functions for rotor modal frequencies. 4.3.2 Equipment Input Amplifier Dynamic range of the input channels is preferred to be with variable gain type. 4.3.3 Digitization If enough bit resolution is available, a fixed range input channel may be used. 4.3.4 Equipment Signal
34、 to Noise Ratio Signal to noise ratio of the vibration signal should be better than 72 dB. 4.3.5 Triggering A pre-trigger capability is preferred. 4.3.6 Windowing A rectangular window for impact input signal and exponential window for vibration signal is the preferred setting. 4.3.7 Differential Inp
35、ut Use test equipment that have signal differential input if voltage type sensors are used. SAE J2933 Issued MAR2011 Page 7 of 94.4 Signal Processing 4.4.1 Averaging Averaged transfer function is the preferred analysis process. 4.4.2 Frequency Resolution Frequency resolution should be better than 3
36、Hz. (This may be obtained by sampling at 12.8 kHz, collecting 6400 points for a duration of 0.5 s frame and carrying FFT analysis using the full 6400 points resulting a resolution of 2 Hz over 6400 Hz.) 4.4.3 Transfer Function Transfer function may be used in its accelerance (a/f), mobility (v/f), o
37、r compliance (x/f) forms. Sound pressure may be also used as output (Pa/N), but no differential is allowed in this case. 4.5 Reporting 4.5.1 Modal Classification It is recommended that rotor modes be classified before reporting. Classification shall be based on plate vibration shape as shown in Figu
38、res 5, 6, and 7. FIGURE 5 - ROTOR PLATE OUT OF PLANE MODES FIGURE 6 - ROTOR PLATE IN-PLANE RADIAL MODES SAE J2933 Issued MAR2011 Page 8 of 9FIGURE 7 - ROTOR PLATE IN-PLANE CIRCUMFERENTIAL MODES 4.5.2 Results Tabulation Table 1 provides a guideline for listing modal information. Use a unique number i
39、dentifying the rotor and document the test date. Mass is reported to a gram of resolution. Frequencies are reported to a 1 Hz, even though resolution of measurement may be larger (3 Hz). First 3 OPD modes, 3 IPR modes, and 1 IPC modes are reported for tests with no prior knowledge on tested data, or
40、 if verification requires these modes. For quality control of larger batches, mass and first mode may be sufficient TABLE 1 - SAMPLE TABULATION OF RESULTS Rotor ID General Identification Masskg OPD1(0,2)Freq Hz OPD2(0,3)Freq Hz OPD3(0,4) Freq Hz IPC1Freq Hz IPR1Freq Hz 4.6 Statistical Inferences 4.6
41、.1 Normality of Batch Measurements It is recommended that batch normality and variance of first mode and mass be checked for new batches. Only reasonably normally distributed batches shall be considered. 4.6.2 Base Line Variability For new products or undocumented production lines, rotors and drums
42、normal control limits shall be 3% of nominal modal frequencies. 4.6.3 Mean Shift of Lower Mode for Known Population Student t-test may be used for checking frequency shift of first mode if base line population is established. The population shall be estimated based large number of samples (over 300)
43、 collected at several intervals spread over a calendar year. 4.6.4 Mean Shift of Lower Mode for Unknown Population Use 3% of baseline mean frequency as your control limits in a capability check to establish mean shift. SAE J2933 Issued MAR2011 Page 9 of 94.6.5 Mean Shift of Higher Modal Frequencies
44、(when only lower mode is measured) A rotor that conforms to mean (or median) of the batch is to be chosen and comparison of its higher modes to baseline is used to measure frequency shift of higher modes. Same evaluation method in the last sections should be used. 4.6.6 Mean Shift of Higher Modal Fr
45、equencies when Multiple Frequencies are Measured. Same evaluation method used for lower mode in the last sections may be used for evaluating shift of higher modal frequencies. 5. NOTES 5.1 Marginal Indicia A change bar (l) located in the left margin is for the convenience of the user in locating are
46、as where technical revisions, not editorial changes, have been made to the previous issue of this document. An (R) symbol to the left of the document title indicates a complete revision of the document, including technical revisions. Change bars and (R) are not used in original publications, nor in documents that contain editorial changes only. PREPARED BY THE SAE NOISE, VIBRATION AND HARSHNESS STANDARDS COMMITTEE
