Random Vibration Test for Brake Shield and Fatigue life Estimation
Structures and mechanical components are frequently subjected to the oscillating loads which are random in nature. Random vibration theory has been introduced for more than three decades to deal with all kinds of random vibration behavior. Since fatigue is one of the primary causes of component failure, fatigue life prediction has become a most important issue in almost any random vibration problem. Traditionally fatigue damage is associated with time dependent loading, usually in the form of stress or strain. However, there are many design scenarios when the loading, or fatigue damage process, cannot easily be defined using time signals. In these cases the design engineer usually has to use a test based approach to evaluate the fatigue life of his component. Alternatively, a frequency based fatigue calculation can be utilized where the loading and response are categorized using Power Spectral Density (PSD) functions. This paper discuss one of such project in which brake shield is subjected to a dynamic load and the fatigue life of the component is predicted and correlated with physical testing. The finite element analysis and experimental techniques which are employed to study the Durability of the Brake shield which is subjected to random vibration loading conditions. In this case the loading is defined in terms of its magnitude at different frequencies in the form of a power spectral density (PSD) plot. A frequency domain fatigue calculation can be utilized where the random loading and response are categorized using power spectral density functions and the dynamic structure is modeled as a linear transfer function. During Product development stage the brake shield is tested based on the PSD loads given in Subsystem technical specification in the lab. The same math model was discretized as Finite Elements and simulated using Abaqus software. The simulation model is first fine tuned by correlating the natural frequencies, mode shapes and transmissibility functions with experimentally measured lab test results. The model is then used to simulate both sinusoidal and random vibration tests to obtain the stress and the response spectrum at critical and test measured locations respectively. FEA response is compared with the test response at measured locations and is able to correlate with the test failure locations. Since the failure is observed in the FEA as well in the rig test, Optimized design is proposed which meets the durability requirements. The proposed analysis technique is capable of determining premature products failure phenomena. Therefore, it can reduce cost, product development time; improve product durability and customer confidence. 1. TECHNICAL BACKGROUND Finite Element based tools for fatigue life prediction are now widely available. The basic aim of such tools is to enable fatigue life calculations to be done at the design stage of a development process. A very important part of these new FEA based tools is a vibration fatigue capability. It is necessary to clarify the term vibration fatigue as the estimation of fatigue life when the stress or strain histories obtained from the structure or component, are random in nature and therefore best specified using statistical information about the process. The same approach can also be described using the terms spectral fatigue analysis, or frequency based fatigue techniques. Nearly all structures or components have traditionally been designed using time based structural and fatigue analysis methods. However, by developing a frequency based fatigue analysis approach, the true composition of the random stress or strain responses can be retained within a much optimized fatigue design process. This can yield many advantages, the most important being, (i) an improved understanding of system behavior, (ii) the capability to fully include the true structural behavior rather than a potentially inadequate simplified version and (iii) a more computationally efficient fatigue analysis procedure. Most designers, if asked to specify a random loading input, or response output, for a structural system would specify the random time history shown in Figure 1. This process can be described as random and in the time domain. The process is described as random because, strictly SIMULIA India Regional Users Meeting ,11 Page 2 of 10 speaking, it can only be determined statistically. A second sample taken for the same process would obviously have different values to the first. Figure .1 Figure .2 There are several alternative ways of specifying the same random process. Fourier analysis allows any random loading history of finite length to be represented using a set of sine wave functions, each having a unique set of values for amplitude, frequency and phase. Such a representation is called deterministic (Figure 2) because the individual sine waves can be determined precisely at any given point in time. It is still time based and so is therefore specified in the time domain. As an extension of Fourier analysis, Fourier transforms allow any process to be represented using a spectral formulation such as a PSD function. Such a process is described as a function of frequency and is therefore said to be in the frequency domain (see Figure 1) It is still a random specification of the function. For the vast majority of engineering problems, if you have one form of the above three loading specifications you can quite easily get to one of the two alternative specifications. These transformations rely on the assumption that the process is stationary, random and Gaussian. Fortunately, most engineering processes conform reasonably well to these assumptions. 2. LOADING INFORMATION The usual way to describe the severity of damage for random vibration is in terms of its power spectral density (PSD) a measure of a vibration signal"s power intensity in the frequency domain. Looking at the time history plot in Figure 1, it is not obvious how to evaluate the constantly changing acceleration amplitude. The way to evaluate is to determine the average value of all the amplitudes within a given frequency range. Although acceleration amplitude at a given frequency constantly changes, its average value tends to remain relatively constant. This powerful characteristic of the random process provides a tool to easily reproduce random signals using a vibration test system. Random vibration analysis is usually performed over a large range of frequencies from 20 to 2,000 Hz, for example. Such a study does not look at a specific frequency or amplitude at a specific moment in time but rather statistically looks at a structure"s response to a given random vibration environment. Certainly, we want to know if there are any frequencies that cause a large random response at any natural frequencies, but mostly we want to know the overall response of the structure. The square root of the area under the PSD curve in Figure 3 gives the root mean square (RMS) value of the acceleration, or Grms, which is a qualitative measure of intensity of vibration.