Reference numberISO 18431-4:2007(E)©ISO 2007INTERNATIONAL STANDARD ISO18431-4First edition2007-02-01Mechanical vibration and shock — Signal processing — Part 4: Shock-response spectrum analysis Vibrations et chocs mécaniques — Traitement du signal — Partie 4: Analyse du spectre de réponse aux chocs Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---ISO 18431-4:2007(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobe s licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobe s licensing policy. The ISO Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. © ISO 2007 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO s member body in the country of the requester. ISO copyright office Case postale 56 • CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail

[email protected] Web www.iso.org Published in Switzerland ii © ISO 2007 – All rights reservedCopyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---ISO 18431-4:2007(E) © ISO 2007 – All rights reserved iiiContents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references . 1 3 Terms and definitions. 1 4 Symbols and abbreviated terms . 2 5 Shock-response spectrum fundamentals 2 6 Shock-response spectrum calculation. 7 7 Sampling frequency considerations. 12 Bibliography . 16 Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---ISO 18431-4:2007(E) iv © ISO 2007 – All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 18431-4 was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and condition monitoring. ISO 18431 consists of the following parts, under the general title Mechanical vibration and shock — Signal processing: ⎯ Part 1: General introduction ⎯ Part 2: Time domain windows for Fourier Transform analysis ⎯ Part 4: Shock-response spectrum analysis The following parts are under preparation: ⎯ a part 3, dealing with bilinear methods for joint time-frequency analysis ⎯ a part 5, dealing with methods for time-scale analysis Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---ISO 18431-4:2007(E) © ISO 2007 – All rights reserved vIntroduction In the recent past, nearly all data analysis has been accomplished through mathematical operations on digitized data. This state of affairs has been accomplished through the widespread use of digital signal-acquisition systems and computerized data processing equipment. The analysis of data is, therefore, primarily a digital signal-processing task. The analysis of experimental vibration and shock data should be thought of as a part of the process of experimental mechanics that includes all steps from experimental design through data evaluation and understanding. ISO 18431 (all parts) assumes that the data have been sufficiently reduced so that the effects of instrument sensitivity have been included. The data covered in ISO 18431 (all parts) are considered to be a sequence of time samples of acceleration describing vibration or shock. Experimental methods for obtaining the data are outside the scope of ISO 18431 (all parts). This part of ISO 18431 is concerned with methods for the digital calculation of a shock-response spectrum. The analysis is by no means restricted to signals that can be characterized as shocks. On the contrary, it is, in a strict sense, meaningless to analyze a shock according to the definition in ISO 2041, where a shock is defined as a sudden event, taking place in a time that is short compared with the fundamental periods of concern. Such a shock has no frequency characteristics in the frequency range of concern. It is only characterized by its time integral, the impulse, corresponding to constant frequency content. The notation “shock-response spectrum” has been kept, however, although a better term would be maximum-response spectrum. Historically, the shock-response spectrum was initially used to describe transient phenomena, at the time called shocks. Response analysis in general is a method to characterize a vibration or shock when other frequency analysis methods are inadequate. This can be the case, for instance, when different kinds of vibration are compared. Spectrum analysis based on the Fourier Transform produces spectra that are incompatible when the signals analyzed are of different kinds, such as periodic, random or transient. The typical use of a shock-response spectrum is to characterize a dynamic mechanical environment. The vibration (or shock) characterized is recorded in digital form, commonly as acceleration. The data are analyzed into a shock-response spectrum. This spectrum can then be used to define a test for equipment that is required to endure the environment in question. There exist International Standards that describe how to design tests from given shock-response spectrum specifications, for example IEC 60068-2-81. (See the bibliography for additional information.) When measurements to characterize a vibration and/or shock environment are performed, it is necessary to take certain measures, for instance to ascertain a proper dynamic load in the measurement points. These measures are beyond the scope of this part of ISO 18431. There are many good handbooks and recommended practices that are helpful in this area[1],[2]. Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---INTERNATIONAL STANDARD ISO 18431-4:2007(E)© ISO 2007 – All rights reserved 1Mechanical vibration and shock — Signal processing — Part 4: Shock-response spectrum analysis 1 Scope This part of ISO 18431 specifies methods for the digital calculation of a shock-response spectrum (SRS) given an acceleration input, by means of digital filters. The filter coefficients for different types of shock-response spectra are given together with recommendations for adequate sampling frequency. NOTE The definition of a shock-response spectrum given in ISO 2041, implies that a shock-response spectrum can be defined in terms of an acceleration, velocity or displacement transfer function. This part of ISO 18431 deals only with acceleration input. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 2041, Vibration and shock — Vocabulary 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 2041 and the following apply. 3.1 maximax shock-response spectrum SRS where the maximum absolute value of the response is taken 3.2 negative shock-response spectrum SRS where the maximum value is taken in the negative direction of the response 3.3 positive shock-response spectrum SRS where the maximum value is taken in the positive direction of the response 3.4 primary shock-response spectrum SRS where the maximum value is taken during the duration of the input 3.5 residual shock-response spectrum SRS where the maximum value is taken after the duration of the input Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---ISO 18431-4:2007(E) 2 © ISO 2007 – All rights reserved4 Symbols and abbreviated terms a(s) Laplace transform of acceleration (m/s2)·s c damping constant in SDOF system N/(m/s) d(s) Laplace transform of displacement m·s fnnatural frequency for SDOF system Hz fssampling frequency, sampling rate Hz G(s) transfer function in s domain H(z) transfer function in z domain k spring constant in SDOF system N/m m mass in SDOF system kg, N/(m/s2) Q Q-value, resonance gain s Laplace variable, complex frequency rad/s SDOF single-degree-of-freedom system SRS shock-response spectrum T sampling time interval s v(s) Laplace transform of (vibration) velocity (m/s)·s z z-transform variable α digital filter denominator coefficient β digital filter numerator coefficient ωnangular natural frequency rad/s ζ damping ratio, fraction of critical damping 5 Shock-response spectrum fundamentals 5.1 Introduction In this part of ISO 18431, a shock-response spectrum is the response to a given acceleration of a set of single-degree-of-freedom, SDOF, mass-damper-spring oscillators. The given acceleration is applied to the base of all oscillators, and the maximum responses of each oscillator versus the natural frequency make up the spectrum; see Figure 1. Each single-degree-of-freedom system in Figure 1 has a unique set of defining parameters; mass, m, damping constant, c, and spring constant, k. The parameters of the system are the conventional ones, given in Clause 4. A given acceleration, a1, is applied to the base. If the response is measured as acceleration, a2, then the transfer function, G(s), for a SDOF system is given by Equation (1): 221()()()as cs kGsasms cs k+==++(1) Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---ISO 18431-4:2007(E) © ISO 2007 – All rights reserved 3where s is the Laplace variable (complex frequency) in radians per second. The single-degree-of-freedom system is normally characterized by its (undamped) natural frequency, fn, in hertz, as given in Equation (2), and the resonance gain, Q (Q-factor), as given in Equation (3): 12nkfm=π(2) kmQc= (3) ainput motion bresponse motion NOTE The responses of a set of single-degree-of-freedom (SDOF) mechanical systems define the shock-response spectrum. The combination of m, c and k differs among the systems. Figure 1 — Responses of a set of single-degree-of-freedom (SDOF) mechanical systems The transfer function may then be rewritten, as given in Equation (4): 22221()()()nnnnsas QGssassQωωωω+==++(4) with 2nnfω =π being the angular natural frequency in radians per second. The transfer function is given versus frequency in Figure 2, where the natural frequency is set to 1 Hz and Q = 10 as an example. Note the gain of Q at resonance. NOTE Equation (4) defines the transfer function used. The maximum is approximately Q and the maximum occurs approximately at fnHz. The larger the Q-value, the more accurate the approximation. Copyright International Organization for Standardization Provided by IHS under license with ISO Not for ResaleNo reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---ISO 18431-4:2007(E) 4 © ISO 2007 – All rights reservedKey X frequency, expressed in hertz Y transfer function Figure 2 — Transfer function of SDOF system as function