1、 g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58Part 4: Shock-response spectrum analysisICS 17.160Mechanical vibration and shock Signal processing
2、BRITISH STANDARDBS ISO 18431-4:2007BS ISO 18431-4:2007This British Standard was published under the authority of the Standards Policy and Strategy Committee on 29 June 2007 BSI 2007ISBN 978 0 580 52915 3Amendments issued since publicationAmd. No. Date Commentsrequest to its secretary.This publicatio
3、n does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application.Compliance with a British Standard cannot confer immunity from legal obligations.National forewordThis British Standard was published by BSI. It is the UK implementation of ISO
4、 18431-4:2007.The UK participation in its preparation was entrusted by Technical Committee GME/21, Mechanical vibration, shock and condition monitoring, to Subcommittee GME/21/2, Vibration and shock measuring instruments and testing equipment.A list of organizations represented on this committee can
5、 be obtained on Reference numberISO 18431-4:2007(E)INTERNATIONAL STANDARD ISO18431-4First edition2007-02-01Mechanical vibration and shock Signal processing Part 4: Shock-response spectrum analysis Vibrations et chocs mcaniques Traitement du signal Partie 4: Analyse du spectre de rponse aux chocs BS
6、ISO 18431-4:2007ii 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
7、. 16 BS ISO 18431-4:2007iv Foreword 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
8、 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 Comm
9、ission (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 technic
10、al 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 sha
11、ll 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 process
12、ing: 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 ana
13、lysis BS ISO 18431-4:2007vIntroduction 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 e
14、quipment. 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 underst
15、anding. 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 m
16、ethods 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
17、 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. I
18、t 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 t
19、ransient 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 Fourie
20、r 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
21、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
22、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 p
23、oints. 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 area1,2. BS ISO 18431-4:2007blank1Mechanical vibration and shock Signal processing Part 4: Shock-response spectrum analysis 1 Scope This part of ISO
24、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 def
25、inition 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
26、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
27、 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
28、.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
29、 the duration of the input BS ISO 18431-4:20072 4 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 ms fnnatural frequency for SDOF system Hz fssampling frequency, sampling rate Hz G(s) transf
30、er 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) La
31、place transform of (vibration) velocity (m/s)s z z-transform variable digital filter denominator coefficient digital filter numerator coefficient nangular natural frequency rad/s damping ratio, fraction of critical damping 5 Shock-response spectrum fundamentals 5.1 Introduction In this part of ISO 1
32、8431, 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
33、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
34、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) BS ISO 18431-4:20073where s is the Laplace variable (complex frequency) in radians per second. The single-degree-of-freedom system is normally cha
35、racterized 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=(2) kmQc= (3) ainput motion bresponse motion NOTE The responses of a set of single-degree-of-freedom (SDOF) mechanical systems define the sho
36、ck-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 QGssassQ+=+(4) with 2nnf = being the angular natu
37、ral 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
38、 occurs approximately at fnHz. The larger the Q-value, the more accurate the approximation. BS ISO 18431-4:20074 Key X frequency, expressed in hertz Y transfer function Figure 2 Transfer function of SDOF system as function of frequency Instead of the resonant gain, Q, the damping ratio, fraction of
39、critical damping, , may be used. is often expressed in “percent of critical damping,” as given in Equation (5): 122cQkm = (5) NOTE Critical damping, ccrit, is defined as crit2.ckm= To calculate the shock-response spectrum, the acceleration signal to be analyzed is applied to the base of a set of SDO
40、F systems characterized by their natural frequencies and Q-values. The responses are calculated; the maximum responses as a function of the natural frequencies compose the shock-response spectrum. In a basic version of the shock-response spectrum, the maximum taken is the maximax, which is the maxim
41、um of the absolute value of the response. In the calculation of a shock-response spectrum, the natural frequencies are selected in a logarithmic fashion. The same Q-value is used for all SDOF systems. The number of natural frequencies depends on the Q-value (or damping). For a common Q-value of 10,
42、corresponding to a damping ratio of 5 %, a minimum of six frequencies per octave, corresponding to 20 frequencies per decade, is recommended. A finer resolution can be warranted if a smaller value of damping is assumed. As an example, Figure 3 shows the (maximax) shock-response spectrum for a half-s
43、ine pulse with duration 11 ms and amplitude of 10 gn. BS ISO 18431-4:20075Key X frequency, expressed in hertz Y maximax acceleration SRS, expressed in g-values Figure 3 Shock-response spectrum for a half-sine pulse with amplitude 10 gn, duration 11 ms and Q = 10 5.2 Variations of the shock-response
44、spectrum 5.2.1 Introduction In the basic shock-response spectrum, the maximax value of the acceleration response of the SDOF system is calculated. Variations of the basic shock-response spectrum are created when other responses are considered, such as relative velocity or relative displacement. Apar
45、t from that, different maximum values may be considered, such as the maximum value (largest positive value) or the minimum value (largest negative value). If the maximum is taken in the positive direction, the spectrum is called a positive shock-response spectrum. If the maximum is taken in the nega
46、tive direction, the spectrum is called a negative shock-response spectrum. If the maximum absolute value is taken, the spectrum is called a maximax shock-response spectrum. In some cases, a distinction is made between the maximum value occurring during the duration of the input (especially if it has
47、 a pulse character) and the maximum value occurring after the pulse. The former is called primary shock-response spectrum while the latter is called residual shock-response spectrum. To avoid confusion, the type of spectrum calculated should be stated, for instance “relative-displacement maximax res
48、ponse spectrum.” BS ISO 18431-4:20076 5.2.2 Relative-velocity response spectrum When the response of the SDOF system is calculated as relative velocity between the SDOF system mass and the base, the transfer function becomes as given in Equation (6) or (7): 2121() ()()()vs vs msGsasms cs k =+(6) or
49、21221() ()()()nnvs vs sGssassQ =+(7) 5.2.3 Relative-displacement response spectrum When the response of the SDOF system is calculated as relative displacement between the SDOF system mass and the base, the transfer function becomes as given in Equation (8) or (9): 2121() ()()()ds ds mGsasms cs k =+ +(8) or 21221() () 1()()nnds dsGssassQ =+(9) 5.2.4 Pseudo-velocity response spectrum The relative-displacement response may be multiplied by the angular natural frequency, n
