JOURNAL OF GUIDANCE,CONTROL, AND DYNAMICS Vol. 21, No. 5, September–October 1998 New Tools for Structural Testing: Piezoelectric Impact Hammers and Acceleration Rate Sensors C. K. Lee, ¤ C. T. Lin, † C. C. Hsiao, † and W. C. Liaw † National Taiwan University, Taipei, Taiwan 10764, Republic of China Small-size ultra-high-precision mechanical systems demand special testing methodologies, such as a better high- frequency response, a precise impact position, an extremely high repeatability, etc. Utilizing the fact that signals obtained from piezoelectric sensing elements are strongly inuenced by the interfacing circuitry, piezoelectric sensors that can be used to measure acceleration rate were developed. Both analytical and experimental results indicate that acceleration rate sensors can detect the arrival of realistic shock earlier than conventional accelerome- ters can. An ultra-high-precision high-speed piezoelectric impact system with an on-line load cell was also modeled, designed, and built. The sensitivity of this on-line load cell was calibrated by using a standard quartz load cell. This innovative high-speed impact hammer system was found to have a timing accuracy in the range of microseconds and a positioning accuracy in the range of micrometers. Introduction A CCOMPANYING high-tech development comes the devel- opment of high-performance miniature mechanical systems. These types of devices demand testing methodologies of differ- ent merits, such as better high-frequencyresponses, faster reaction times, etc. Early detection of shock arrival, which typically creates a negativeeffect on high-performancemechanicalsystems, can sig- nicantly improve structural system performance. In other words, improving the shock arrival detection is the same as improving the high-frequency response of the sensing system. A simple way to improve high-frequencysensor response is to measure the rate of changeof the quantityof interest.More specically, an acceleration rate sensor will have a better high-frequencyresponse than that of accelerometers because differentiation in the time domain equals multiplying j ! and the frequency spectrum, where j D p ¡1 and ! is the angular frequency. However, differentiation in the time do- main amplies the noise, which in turn reduces the accuracy of the rate signal. A method of improving the sensor high-frequency re- sponse by measuring the rate of change without deteriorating the signal-to-noiseratio is thus desirable. On the other hand, modal testing that can reveal the dynamic behavior and execute system identication of today’s high-perfor- mance mechanical systems is becoming more difcult to perform as impact forces are getting more difcult to apply to testing struc- tures. An impact hammer system with a positioningaccuracy in the micrometer range and a timing accuracy in the microsecond range to permit us to perform precise modal or accurate impact testing on miniature mechanical systems is becoming ever more important. The newly developed sensing and impacting systems, which are the accelerationrate sensorand the high-speedimpact hammer sys- tem, will be discussed in detail herein. Acceleration Rate Sensors Combining linear piezoelectric theory and Hook’s law yields the governing equation for traditional accelerometers. 1¡6 That is, the charge signal q .t / generated from a piezoelectric sensing el- ement is linearly proportional to the acceleration experienced by a piezoelectric sensing element in traditional accelerometers. Be- cause piezoelectricsensing elements are of high-outputimpedance, Received Nov. 11, 1996; presented as Paper 97-0687 at the AIAA 35th Aerospace Sciences Meeting, Reno, NV, Jan. 6–9, 1997; revision received Feb. 25, 1998; accepted for publication March 1, 1998. Copyright c ° 1998 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. ¤ Professor, Institute of Applied Mechanics, No. 1, Sec. 4, Roosevelt Road. Senior Member AIAA. † Graduate Research Assistant, Institute of Applied Mechanics, No. 1, Sec. 4, Roosevelt Road. the externallyobtainedsignalsfrom a piezoelectricsensingelement are stronglyinuenced by the interfacingcircuitry used. It has been identied that changing the charge amplier typically used in tra- ditional piezoelectric accelerometers to a current amplier is the equivalent of time differentiation. 4;6 In other words, the rate signal can be obtained by measuring the current signal i .t / D dq .t /=dt without using a mathematical differentiation process. This is the basic concept of the interfacing circuit used for the piezoelectric acceleration rate sensor. 6 Considering a realistic impact force that can appear in high- performance structural systems, the impact force amplitude is ini- tially zero and increases rapidly with time. That is, f .t ! 0 C / D f .0 C / C P f .0 C /t C O .t 2 / (1) where f .0 C / typicallyequals zero for a realisticimpact force due to the shock arrival time constraintin a mechanicalsystem. Physically, any shock excitationsource has a nite rising time such as a sudden hertz impact. Consider the contribution of a realistic impact force on a simple mass-spring system m R x C k P x D f .t /, where m and k are the mass and stiffness of the mass-spring system, respectively, and under the initial conditions x .0 ¡ / and P x .0 ¡ / D 0. The response of this spring-mass system can be shown to be 6 x .t ! 0 C / D lim t ! 0 C P f .t / 6m t 3 C O.t 4 / (2) where O .¢/ denotes the big- O notation.DifferentiatingEq. (2) sev- eral times with respect to time yields the governing equations for acceleration R x .t ! 0 C / D lim t ! 0 C P f .t / m t C O .t 2 / (3) and the accelerationrate d R x dt .t ! 0 C / D lim t ! 0 C P f .t / m C O .t / (4) From the preceding equations, it is clear that the acceleration rate has a nite value at t ! 0, whereas the accelerometer output sig- nal equals zero as t ! 0. Thus, theoretically, the acceleration rate can be detected earlier than acceleration. From this viewpoint, the acceleration rate is a better sensing variable than acceleration itself for shock detection or even shock control. An impact testing experimentalsetup as shown in Fig. 1 was cre- ated to examine the performance of the acceleration rate sensor vs that of the accelerometer. The acceleration rate sensor was created by replacing the Endevco Model 22 accelerometer 7 charge ampli- er interfacing circuit with a Keithley 427 current amplier. 8 The 692