Prosig Signal Processing Blog

By James Wren, Application Engineer, Prosig

The following application note describes the test and measurement process for the fatigue testing and development cycle of a component. Strain gauges were used to monitor the strain levels in a particular suspension component. The component had been known to fail at various intervals. A predicted life for the component was required to analyse the feasibility of the its continued use or to see if a design change was required. The component under test (Figure 1) was an automotive suspension component, specifically a tie rod. The testing was carried out by a major automotive manufacturer.

Figure 1: Vehicle suspension under test	Figure 2: Strain gauge mounted on component under test

First, the vehicle was instrumented and data acquired whilst the vehicle was on a test track. The vehicle under test was then mounted on a four-post shaker rig that simulates actual road conditions. Particular sections of the actual test run from the test track could be replicated for much longer periods than otherwise would be possible, additionally this could all be done in the controlled conditions of the test laboratory.

This article will focus on the capture of the strain type data and the processing of this resultant data to use ‘Stress Life’ and ‘Fatigue Life Prediction’ methods to predict the potential life of the component.

Initially the vehicle was instrumented with strain gauges, using a Prosig P8000 portable data acquisition system. The vehicle was driven around a test track and data from the strain gauges acquired with the P8000 data acquisition unit. The data capture and signal processing procedure can be seen and followed from start to finish.

Figure 2 shows an example of a strain gauge attached to the component under test by adhesive. In this case the gauge is a two wire device.

Upon launching the Prosig Data Acquisition software several fields must be filled in. In this case only one strain gauge is to be used to assist in clarity for this application note. The signal names and types are entered, for this example a single strain gauge in a quarter bridge completion configuration is used. It is a 120 Ohm gauge and an excitation of 10VDC has been selected to be applied as shown in Figure 3.

Figure 3: Acquisition setup screen	Figure 4: Real time display of data

Next the Prosig P8000 and acquisition software is used to capture the strain data from the vehicle as it traverses the test track. The real time display, Figure 4, shows the micro strain and in this case the reciprocal nature of the data as it is being captured.

Figure 5: Strain v time	Figure 6: Peak and trough data

Once this data capture was completed it was possible to return to the testing laboratory and use the vehicle shaker test rig. It was then possible to use the DATS signal processing software to select particular frequencies and amplitudes of strain data that the vehicle had been subject to on the test track and use the P8000 to ‘replay’ the signals into the shaker to ‘mimic’ particular parts of the test track using the analogue output feature of the P8000. This allows test engineers to control the amount of time the component under test will be subjected to particular frequencies or amplitudes. On the test track, in any one hour period the component will only be subject to some particular characteristics for several seconds. But by capturing this data and using the shaker rig it is possible to subject the component to an accelerated saturation of particular frequencies and amplitude characteristics.

For this application note the suspension component was subject to 180 seconds of excitation. This was captured with the P8000 and opened in the DATS signal processing software (Figure 5).
At this stage the strain data is with respect to time, the amount of micro strain that the component was subject to can be seen over time.

In order to begin with the fatigue life prediction it is necessary to analyse the peak and trough content of the captured data. This is easily achieved using the DATS Fatigue Life Analysis software tool kit.

The peak and trough data was then produced as shown in Figure 6.

Figure 7: Peak & Trough analysis section	Figure 8: S-N curve analysis selection	Figure 9: S-N curve generation parameters

Next, it was required to generate an S-N curve for the component. It is important to note that this is not an S-N curve for the material used in fabricating the component, but the S-N curve for the component itself.

At this stage data is available for failure rates but this information is rough and sporadic. This, however, will not be used to produce the S-N curve at this point. The failure data will be used later to refine the S-N curve.

Using the DATS Fatigue Life Analysis module for S-N curve generation (Figures 9 & 10) it is possible to produce an S-N curve.

S-N curves are by their nature very simple, they can usually be approximated by two intersecting straight lines on a graph of log stress verses log cycles. In this case three points are used to create the curve.

Figure 10: S-N curve values	Figure 11: Generated S-N curve

A set number of cycles to failure and stress levels are required. As mentioned the S-N curve will be refined later. At this stage, the values for the ‘Weld Classification’ are used. These are arbitrarily chosen as it is a known curve that closely follows that of the material under test.
The generated S-N curve is then created as shown in Figure 11.

With the peak trough data and S-N curve it is possible to complete a fatigue life prediction, using the ‘Stress Life Fatigue Prediction’ analysis module (Figure 12). To complete this analysis both the S-N curve and the initial peak and trough data are required.

Figure 12: Stress Life Prediction analysis selection	Figure 13: Stress Life Prediction parameters

When the analysis module begins it prompts the user for certain values (Figure 13).

The fatigue life prediction analysis module requires a young’s modulus for the material, in this case 2.07×10⁴ MPa and a rain flow algorithm must be selected, in this case the ASTM1094. (American Society for Testing and Materials, Revision 1985).

The conversion from Micro Strain to Stress uses the following formula, the micro strain values, µe, are translated into stress, S, by solving

Where
E is Young’s Modulus
K’ is Strain Hardening Coefficient
n’ is Strain Hardening Exponent
If K’ or n’ or both are zero then the module uses
S = eE

This analysis takes two input datasets, the peak and trough count and the S-N curve. The resultant ‘Stress Life Fatigue Prediction’ damage curve is shown in Figure 14, with a fatigue life prediction of 5.36×10²³ seconds.

The results of the Fatigue Life prediction also show more detailed results as Named Elements, these are shown highlighted in blue in Figure 15. These include Damage, Duration of original time sample, Number of cycles and so on.

Figure 14: Stress Life Prediction data	Figure 15: Stress Life Prediction data (Named Elements)

To summarise thus far, it has been possible to complete a fatigue life prediction from a sample of strains over a specific time period.

This has given a predicted life of 5.36×10²³ seconds.

As discussed earlier the S-N curve was not refined and was almost arbitrary in its construction. This could potentially lead to errors. Therefore at this stage the S-N curve must be refined to allow the recalculation of the results and thus remove any potential errors.

The component in question has been reported to fail in the field after various time periods, hence the reason for the trial. Although the stress and strain levels are not known for these failures the time to failure is important. Because it is possible to apply the expected strain level for general use to the component for the known period of time, it is, therefore, possible to extrapolate the stress levels. Note, the stress levels and cycles to failure are not known for these situations. Only the time to failure is known.

The component has also been tested to failure, with failures occurring at the following intervals. As these failures were under controlled test environments they can be considered more accurate than that discussed previously. These have time to failures of,

Time to failure 6.48×10⁵ seconds with a stress of 0.003010 MPa

Time to failure 6.75×10⁷ seconds with a stress of 0.000165 MPa

The following have known time to failure, but with unknown strain levels. For these cases the known failure stress levels can be used, in this case 0.000165 MPa is chosen.

1.52×10⁷ seconds

7.78×10⁷ seconds

2.64×10⁶ seconds

The cycles of the vehicle suspension component, importantly not the material cycles were at 2Hz. However, the material cycles were, from the peak and trough calculations in the captured data 3253 in a 180 second snap shot.

Therefore, it is possible to calculate the number of material cycles for the known failure times. It is then possible to accurately adjust our initial S-N curve.

It is also possible to calculate cycles to failure for the situations where the known failure times do not have strain information. This can be done because it is possible, from experimental testing, to deduce what the expected or average use and therefore strains will be.

It is now possible to refine the original S-N curve (Figure 16) with the 5 pairs of values calculated,

0.003010 MPa and 11710800 cycles to failure
0.000165 MPa and 1219875000 cycles to failure
0.000165 MPa and 274697777 cycles to failure
0.000165 MPa and 1406018888 cycles to failure
0.000165 MPa and 47710666 cycles to failure

Therefore it is possible to extrapolate what the S-N curve could have been.

And thus re-process the results using the automatic reprocessing features of DATS as shown in Figure 16.

Figure 16: Recalculated S-N curve	Figure 17: Recalculated life prediction

The result of the re-processed fatigue life prediction is 21.3×10⁶ seconds.

The conclusion is that after approximately 246 days of use at the expected level of 10 hours use per day, this component could be expected to fail. Clearly this is a fragile component that is likely to fail in an unacceptably low amount of time for an automotive manufacturer and a technical design change and further testing are required.

It is clear to see that the more testing to failure that is carried out the more accurate the final life prediction will be.

[This article has been reduced in complexity compared to the original tests and uses deliberately modified initial strain values]