A shock damage potential approach to shock testing D.H. Trepess Mechanical Subject Group, School of Engineering, Coventry University, Coventry CVl 5FB, UK A shock damage (excitation capacity) approach to shock testing has oeen undertaken. Shock tests usually specified are difficult if not impossible to implement and are generally not representative of shock environments. The experimental and theoretical work described here outlines how a transient waveform can be weighed so to poses similar damage potential properties as that possessed by another transient excitation. The benefits offered by this technique is to permit the application of the equivalence of a shock environment, where the specified shock environment is difficult to directly implement. 1 Introduction It is essential that electronic and mechanical equipment undergo shock tests to investigate their shock durability. Equipment may, during their lifetime experience shock motion. To avoid in service equipment failure pre-operation shock testing is necessary. Shock test specifications, testing methods and traditional shock test machines are presented and discussed in [1] and [2]. The main deficiencies of the tests are that actual defined transients are difficult to implement and they are unrepresentative of many shock environments or their environments damage capacity. Deficiencies of the shock test machine are their poor repeatability and controllability of a shock motion, and the machine is solely dedicated to the production of one type of shock excitation. Of course the main aim of the test specifications and the test machines is to impart into a structure a large amount of energy in a short time duration. This accounts for the problems outlined above. Shock testing would be more controllable and repeatable if the excitation energy was input to the test item over a longer duration. The resultant lower levels of excitation would be easier to implement and permits the employment of convention exciters, see [3]. Compensation for structural energy dissipation within a test item needs to be undertaken. This is necessary to maintain equal structural borne energy in the test item for transient excitations of differing durations. Care must be taken when increasing the excitation duration. If the duration of excitation is too long the input energy and the dissipation energy would balance and thus the excitation is steady state.
234 Structures Under Shock And Impact 1.1 Outline of work undertaken The paper describes how a rapid, linear frequency sweep [4] is employed to reproduce the damage capacity of a shock environment. A rapid frequency sweep is a transient waveform that sweeps between two defined frequency limits, the instantaneous frequency varying linearly with time. The benefits of the sweep are the spectral content of the excitation is readily controlled by way of the time domain and the waveform is easily realised on conventional electrodynamic exciters. Work described demonstrates how a shock environment was selected and measured. The necessary frequency sweep conditioning, to be representative of the environment is presented. The practical procedure needed to implement the test is detailed and the limitations of the technique are also described. To facilitate the comparison of the damage potential of the measured shock and its representative excitation an experiment was built. 2 Test rig A photograph of the test equipment is shown as figure 1. The test rig consisted of three types of responsive elements; Figure 1. Experimental test rig
Structures Under Shock And Impact 235 Relative displacement element: The mass spring arrangement is representative of a relative displacement component, for example equipment on shock mounts. The mass sliding up and down on the silvered steel shaft. The motion of the mass was measured by an accelerometer, see figure 1. Inertial loading element: The mass-shaft arrangement is representative of an inertially loaded component, for example equipment on rigid mounts. A strain gauge fixed onto the shaft between the base plate and the mass measured the loading in the shaft due to the inertial effects of the mass. Bending elements: Aluminium beams of various lengths (to have different natural frequencies) with all other properties (geometrical and material) being identical were employed. The utilisation of these beams achieved representation of bending elements, for example printed circuit boards. The bending stresses at the roots of the beams were measured by strain gauges, as indicated in the photograph figure 1. 3 Shock environment It was decided that the resultant test motion of a shock machine would be a good source of a shock environment. A shock test (half sine pulse) would be performed The resultant table motion and equipment response being recorded. A rapid frequency sweep would then be constructed to be endowed with the Fourier spectrum modulus of the table motion. The equivalent swept sine wave additionally weighted so to be endowed with the same damage potential as the measured shock environment would be employed to excite the pre-mentioned equipment. The consequential equipment responses being compared with the shock machine induced responses. The test rig was attached to the shock machine. An accelerometer was mounted on the test rig, figure 1. This was used to measure the shock machine acceleration motion. The shock machine was set-up to attempt to produce the defined acceleration pulse motion. The actual acceleration motion of the machine table and the response dynamics of the experimentalrigelements were recorded. The resultant time history of the table motion is shown in figure 2. Clearly the shock machine table acceleration motion is not described by a half sine pulse. The initial motion consists of a double triangular type pulse, peaking at 250 m/s* (25.5 g) and a duration of about 20 ms. Clearly beyond the initial pulse further table motion occurs. The nature of the motion is predominantly a heavily damped sine wave, with a frequency of about 25 Hz. The experimental test rig had been fixed centrally to the shock machine table plate. It is felt that the oscillator motion observed was a result of the plate with a central mass (test rig) vibrating. The actual transient motion delivered by the shock machine and how it compares with the intended motion is not of great importance within the context of these tests. What is important is that a record of the actual
236 Structures Under Shock And Impact acceleration motion and the rig element responses are made. The recorded signals allow a rapid frequency sweep to be constructed and the comparison of the rig responses due to this sweep and excitation by the shock machine. 300 200 100 o -too 200-300 0.05 O.I T1ME/S 0.15 0.2 Figure 2. Shock machine table acceleration time history 4 Construction of a rapid frequency sweep to posses equivalent damage potential as the measured shock environment A comprehensive description of the test implementation procedure is presented in reference 3. The following presents an outline of the experimental technique employed for the construction of a sweep representation of the shock machine motion. [I] The Fourier transform modulus of the shock environment (shock machine motion figure 2) of interest wasfirstobtained, see section 3.2. [II] A unit amplitude linear, rapid frequency sweep was weighted and scaled by the required spectrum modulus (as derived in [I]). It is essential the frequency sweep encompasses the dominant spectral content of the required waveform. A rapid frequency sweep offrequencyrange 0 Hz to 200 Hz was chosen. A 2 second sweep duration was decided upon. A sweep of longer duration (3 seconds upwards) would not be a transient excitation, that is steady state excitation for all or part of the duration of excitation. To achieve transient excitation the level of damping of the structural elements is important. As the sweep duration increases the excitation energy
Structures Under Shock And Impact 237 and the energy dissipated by the experimental rig elements tend to equilibrium thus steady state excitation. The upper limit of the time duration of the excitation was constrained by the unusually high damping of the test structure. The high damping was due to the nature of the rig, i.e. strain gauges glued to the roots of the beams and friction between the shaft and the sliding mass of the spring/mass. A simple impulse excitation test was performed on the substructures of the rig. Analyse of the decay rate of free vibration yielded an a viscous damping ratio for the rig. A shorter duration sweep would mean that less of the lower frequency excitation levels could be realised. For a shorter sweep the excitation level needs to be greater to attain the same spectral levels. The low frequencies (0 Hz to 20 Hz) acceleration excitation levels are dependant on the allowable stroke of the exciter, see part [IV]. [Ill] The sweep was then weighted, so contains the same damage potential as the shock environment. The weighting is introduced since the duration of the sweep was greater than for the measured shock. As the duration is longer additional energy needs to be supplied to the equipment so to compensate for energy dissipation. This will maintain the level of structural borne energy in the test rig. The energy dissipation compensation technique is described in [5]. [IV] The frequency response characteristics of the generating system, i.e. power amplifier, electro-dynamic exciter etc. must be compensated for. The compensation is achieved by using the technique outlined in reference [4]. The procedure is to weight the required exciter table motion by the inverse of the transfer function between the exciter table motion and the signal from the function generator. When this compensated signal, is used to drive the electrodynamic exciter via a power amplifier, the exciter table motion will be that shown in figure 3. 100-50 2 LU _J LU U -50-100 - 0.4 0.8 1.6 TIME/S Figure 3 Rapid frequency sweep representation of shock environment
238 Structures Under Shock And Impact It was necessary that the amplitude of the resultant sweep should be windowed for the first and final parts the sweep. The resultant effect is such to reduce the start-up spurious transient of the exciter and to obtain the neutral position of the exciter upon signal termination. An Additional reason for a start up window is to elimination from the driving signal the possibility of the exciter table displacement exceeding its limits. The exciter employed had a stroke peak to peak of 1 inch. The exciter being displacement limited up to about 22 Hz. With the 1 inch displacement limit the acceleration was limited up to about 22 Hz. [V] The instrumented shock test rig of figure 1 was then attached to the electro-dynamic exciter. Consequently the exciter table and the test rig experienced the acceleration motion derived above and described by figure 3. The dynamic responses of each element of the experimental test rig were recorded. 5 Comparison of dynamic responses of the test rig elements 5.1 Mass/Spring element Figures 4 and 5 present the motion of the mass of the mass/spring element for the base excitations. Figure 4 portrays the motion due to the shock machine excitation and figure 5 the resultant motion from the rapid frequency sweep. The time history figure 4 is a measure of the absolute motion of the mass, whereas the response shown in figure 5 is the relative motion between the mass and the rig base. ISO - 1 o I 100 - so - o - -so - -100 - Figure 4 Acceleration of the mass due to shock machine motion
Structures Under Shock And Impact 239 too - 50 o U -50-100 - 0.4 0.8 1.2 TIME / S 1.6 2.4 Figure 5 Acceleration of the mass due to frequency sweep The two time histories contain spikes (non linear motion), this was due to the mass impacting onto the fully closed spring. The time history of figure 4 (that associated with the shock machine excitation) exhibits an initial peak response of about 150 m/s. The movement of the mass was in the same direction as the motion of the initial pulse from the shock machine. The duration of the initial response pulse and the initial excitation pulse are very similar. The maximum relative acceleration of the mass can be deduced by simple visual comparison of the two time histories. The peak relative excitation is about 115 m/s occurring at about 0.08 s from the start of the shock excitation. The time history of figure 5 is relative mass motions. The base motion having been removed from the accelerometer recorded signal. The maximum accelerations exhibited by these traces are about 100 m/s. The comparison of the two peak responses is good. 5.2 Mass/shaft element The peak recorded longitudinal strains in the shaft, for each excitation are 133 HE for the shock machine and 128 ie for the representative shock. 5.3 Bending elements The dynamic bending strain responses at the roots of the longest cantilevered beam is presented in figures 6 and figure 7. Figure 6 is the strain time historv due to shock machine motion and figure 7 is the response due to
240 Structures Under Shock And Impact the sweep excitation. Observing figure 6 the peak strain in the beam is 830 ue. The peak strain recorded in figure 7 is 800 us. CO z te 0.03 0.06 0.09 TIME / S 0.12 0.15 0.18 Figure 6 Strain in beam 1 due to shock machine motion 900 600 OJ a. Z 300 0-300 -600-900 0.4 0.8 1.2 TIME / S 1.6 2.4 Figure 7 Strain in beam 1 due to frequency sweep
Structures Under Shock And Impact 241 For ease of referral each beam has been allocated a number, 1 to 4. The numbers in ascending order being allocated to the beams of increasing resonance frequency (decreasing length) that is 1 the longest and 4 the shortest. The comparison of the dynamic peak bending strains resulting from the two excitations is presented in table 1 below. Table 1. Peak bending strain of the beams due to the excitations Beam 1 2 3 4 PEAK BENDING STRAIN / is shock machine frequency sweep 830 800 550 400 260 200 240 120 6 Discussion of results The results obtained are on the whole good. There was approximately a 10 % difference in the peak acceleration of the mass, of the mass/spring arrangement, resulting from the two types of excitation. For the mass/shaft arrangement there was about a 4 % difference in the resultant peak strain induced by the two forms of excitation. The percentage difference between the responses of beams 1,2,3 and 4 for the shock machine excitation and the sweep with a similar modulus are 8 %, 27 %, 23 % and 50 % respectively. Further investigation of the representative rapid frequency sweep should improve the correlation of the resultant responses. The formation of a rapid frequency sweep to possess the same Fourier spectrum modulus as that of the shock motion means that the residual shock spectra of both the excitations are the same. For a system excited by a half sine pulse, the maximum response will occur during the pulse if the natural time of the system is less than the duration of the excitation pulse. The main initial excitation pulse duration is about 0.01 s. Therefore for any system with a natural frequency above 100 Hz the maximum response should occur during the pulse. It appears that the fundamental natural frequency of beam 1 was less than 100 Hz, for beam 2 is about 100 Hz and for beams 3 and 4 the fundamental naturalfrequencieswere greater than 100 Hz. The natural frequency values were deduced as follows; knowing the frequency range of the sweep to be 0 Hz to 200 Hz with duration of 2 s then at 1 s the sweep instantaneous frequency is 100 Hz (linear sweep). The resonance response of beam 1 due to the rapid frequency excitation occurred prior to the 1 s point of the sweep. Therefore the resonance frequency of beam 1 appears to be less than 100 Hz. For beam 2 the resonance response occurs just beyond the 1 s point. Therefore the resonance frequency of beam 2 is about 100 Hz.
242 Structures Under Shock And Impact Beams 3 and 4 were shorter in length than beam 2 other parameters being the same (physical and geometrical) then their resonance frequencies must have been greater than 100 Hz. To allow for peak response occurring during excitation it is necessary to consider the maximum shock spectrum of the excitation. A maximum shock spectrum approach would however produce and overtest. Thus a combination of the two spectra would prove beneficial. A maximum shock spectrum is the maximisation of the combination of the initial shock spectrum and residual shock spectrum. The initial shock spectrum is the maximum response of a set a single degree of freedom systems whilst the excitation shock pulse is still acting. The residual shock spectrum is the maximum response after the pulse has stopped acting. 7 Conclusion The excitation capacity (damage potential) of a shock environment has been reasonably reproduced on a conventional electro-dynamic exciter. A piece of equipment was subjected to the excitation of a shock environment and to a rapid frequency sweep, predicted to be comparable to the shock environment. The responses of the substructures of the equipment compared. The measured responses due of the excitations compared favourably. It is therefore now possible to design a transient waveform excitation which when used to support excite a structure induces equal damage potential within the structure. References 1. B.S. 2001. Methods for the environmental testing of electronic components 2. E.W. Clements, I. Vigness and J.R. Sullivan: "Shock Testing Machines", Shock and Vibration Handbook, Ed C.M. Harris, 3rd ed., ch. 26, McGraw-Hill. 3. Trepess, D.H. and White, R.G. "Practical Shock Testing Utilising Shock Response Emulation". 10th International Conference on Experimental Mechanics, Lisbon, Portugal, 1994. 4. White, R.G. and RJ. Pinnington 1982. Practical application of the rapid frequency sweep technique for structural frequency response measurement. Aeronautical Journal. 5. Trepess, D.H. and White, R.G. "Shock Testing using a Rapid Frequency Sweep". Proceedings of the AIAA 31st Structural Dynamics & Materials Conference, Long Beach, California, 1990. 6. Trepess, D.H. and White, R.G. "Shock testing with electrodynamic exciters using oscillatory transient excitation". Proceedings of the Third International Conference on Recent Advances in Structural Dynamics, Vol. II, University of Southampton, 1988.