The motivation for this work is to mitigate shock levels on vehicle components, through testing new designs of equipment. The objective is to generate a time history to perform shock testing on military and commercial ground vehicle components. The time histories are used to drive hydraulic actuators coupled to a test specimen.

Figure 1. “Sawtooth” Classical Shock

The Military Standard 810g Method 516.7 (MIL-STD) prescribes actual event data as the first choice. However, that is usually not an option as most components haven’t been tested in actual shock events. Therefore, the second procedure called out in the MIL-STD is the best choice for the lab. That second procedure is Shock Response Spectrum (SRS) based testing, which was the focus of this research. The SRS was used to generate the time history.

Another procedure defined in the MIL-STD is called classical shock, which was the method used by the lab prior to this work. It defines pre-developed acceleration time histories for one to control the test to. An example of classical shock waveform is shown in Figure 1. As seen in the figure, the acceleration is all positive, therefore high velocities are reached when running these profiles.

In order to stop the actuator from over extending after the pulse is complete, a “post pulse” negative acceleration needs to be applied. These post pulses can be just as harsh, or worse, on the actuator and the test item. The step change in acceleration is also hard to control on hydraulic actuators.

The post pulses are one of the items desired to be eliminated by using the SRS as a testing base. The time history that’s synthesized can be tailored to have no residual velocity and still match the reference SRS. This will stop the displacement from continuing to increase after the pulse is played out.

Figure 2. SRS Synthesis

A shock response spectrum is a method for characterizing the shock properties of a transient time history. A SRS is similar to Power Spectral Density (PSD), in that they both involve the frequency domain, however the PSD can be transformed into, and back from, a waveform time history mathematically. While a SRS can be derived easily, there’s no well-defined unique inverse method for an SRS back into a time history. Figure 2 shows a graphical depiction of how the SRS is generated from a single input waveform.

Each mass damper system is representative of each frequency of interest, and the max amplitude of each mass damper’s response is a point on the SRS curve. However, through this process a lot of the information of the initial waveform is lost. Converting an SRS back into a waveform requires an iterative mathematical approach.

The method chosen for generating a time history from an SRS, is to compose a time history from a set of basis-functions parameterized by a set of variable amplitudes and delays. This time history acts as a starting point for iterations. A SRS is generated from the time history, and compared to the MIL-STD SRS, then the variables of the time history are changed to reduce the error between the optimized SRS, and the reference SRS. Through these iterations, an optimized time history results. This optimized time history has an SRS nearly identical to the MIL-STD SRS.

This work was done by Samuel Allen for the Army Combat Capabilities Development Command. ARL-0223

This Brief includes a Technical Support Package (TSP).
Waveform Synthesis for Shock Response Spectrum Replication, Applied to Ground Vehicle Component Testing

(reference ARL-0223) is currently available for download from the TSP library.

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