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A previous SAE paper (2018-01-1396), (see ref 5) introduced the concept of using the frequency domain for exhaust system analysis under road excitation as a fast and efficient approach. During the intervening period further benchmarks have confirmed the validity of the approach for several exhaust systems comparing the results of simulations performed in the time domain and frequency domain for different applications. This paper will present that data and also introduce a new technique which has been developed to create, from the originating road load data (RLD), the cutting plane loads at any desired section of the exhaust system. Those loads can be used directly to determine safety factors against load capacities based, for example, on part SN curves from current or former hardware testing or even derived from statistics.

Multi-axial loaded parts like lower control arms are routinely tested in the laboratory for durability verification. But the full anticipated complex road load data is not normally applied because it would be too expensive and complex to test all parts this way. Instead, a simplified loading condition is used. Ideally, this will be as simple as a single sine wave loading applied to one loading point and in one direction. The specification of which hard point to use, which loading direction, and which frequency and load magnitude, requires very good engineering judgement and a high degree of experience. Even then, it is unlikely that the optimum solution will be obtained and the risk of creating a non-representative test is high. Recently, a new FEA technique has been developed which simultaneously derives both an optimum loading profile (surrogate load) and loading direction (vector direction) from full Proving Ground [PG] real loading conditions.

Most automotive companies validate their vehicle designs by running vehicle on the durability proving grounds. Part fractures and collisions between two components are common failures observed during proven ground testing. Laboratory testing and FEA simulation are used to validate designs in the concept stage as it consumes less time and cost as compared to proven ground testing. The lab testing and simulation process both have their own limitations. It is difficult to incorporate effect of multi-direction input loading (x, y, z) with single direction loading in laboratory testing due to restrictions with electrodynamic shaker testing. However, in simulation, multi direction input can be easily incorporated but often actual vehicle measured test track data is not available in the early design stage. In the present work, Modern methodologies have been employed [ref 1, 2] in frequency domain to validate design in FEA simulation.

The time domain is currently the most widely chosen option in fatigue testing to fully represent random events occurring in multiple simultaneous input channels. In vehicles for example, time domain tests can represent the same conditions of the road, by applying the same loads at the hard points of the vehicle along a time history. The main drawback of this methodology is the extensive testing duration and hardware cost. Time domain based fatigue tests are composed of a complex hardware, which requires servo motors to work, in order to induce the specific amount of load at a specific time window. These tests are time consuming, since they require the same length duration of the event they are reproducing, times the required repetitions. The frequency domain method for fatigue testing, on the other hand, requires simpler hardware, since there are no need for servomotors and the test length is reduced, since there is no need to run the full event times the required repetitions.

Frequency domain methods of analysis are now being used for the evaluation of fatigue for large vehicle systems and these methods offer advantages over equivalent time domain approaches in a number of ways, including analysis efficiency and the usefulness of derived results. One big potential advantage is to be able to do localized sub-component analysis using “cascaded” loads. Such sub-components can be analysed with refined parameters such as more sophisticated damping or a different frequency range. Local parts can also be re-analysed at a different phase in the design program. This paper will demonstrate the approach and show examples of the method.

Conventional approaches for the fatigue life evaluation of automotive parts like headlamps involves the evaluation of random stress conditions in either the time or frequency domain. If one is working in the frequency domain the fatigue life can be evaluated using one of the available methods like the Rayleigh (Narrow Band) approach or the more recent Dirlik method. Historically, the random stresses needed as input to these methods have been evaluated by the FEA solver (eg Abaqus, or Nastran) and these “in built” stress evaluations have limitations which relate to the fact that the stress conditions are complex and so the common “equivalents” for stress like von-Mises or Principal have not been available. There have also been limitations in the location and method of averaging for such stresses. In addition, the fatigue calculation approach for doing the evaluation has been constrained to the linear stress based (S-N) method.