The following application note shows the steps taken to perform a structural analysis using a hammer impact test on an automotive exhaust pipe structure with the aim of improving the structural damping properties of the exhaust pipe mount. This application note is a follow up to a previous article – “Preventing Component Failure In The Fast Lane”.
A recent signal processing application note described how the Prosig sponsored Dalmeny Racing Formula Ford Team, whilst contesting the UK Formula Ford 1600cc championship, suffered several minor structural failures on a particular part of an exhaust pipe mount. Prosig dispatched a team of engineers and after a brief survey of the damage the Prosig engineers made an outline assessment “Our initial thoughts are that the exhaust itself might be resonating at particular engine speeds, thus causing some shear forces in the mount, which could then in turn cause stresses in the material leading to cracking and eventually failure.”
In order to prove this hypothesis a series of simple experiments were carried out. The testing produced a set of frequency response functions that were applied to an operating deflecton model. The animated model displayed the motion at each of the measurement positions over a range of frequencies. In effect, the team were able to visualize the exhaust pipe vibration and analyze exactly the type of motions that were occurring at different frequencies and thus were able to deduce which engine speeds were contributing the most to the problem.
With the use of Prosig equipment and expertise, a modified mount, which included a damping element was developed that greatly reduced the likelihood of further component failure.
The structural testing and development was successfully completed, but the racing team had no time to complete extensive retests until the off-season. During the off-season the aerodynamic rules governing the formula were changed and the entire exhaust structure had to be completely redesigned and modified.
The team retained the developed damping mount and used it with the redesigned exhaust structure. In general vehicle testing it did not fail and was assumed to be acceptable. However, the team’s engineers, in the following off-season thought it worthwhile to retest the new structure in order to see how the design changes had been affected by the performance of the damping mount. It was, after all, in effect a completely new exhaust structure; the previous damping mount could potentially have been doing as much harm as good.
A failure in the previous type of mount had not occurred during the use of the new exhaust structure. But with the benefit of hindsight and the painful experience of component failures in the past the team felt a complete retest was wise before there was any chance of new failure.
The method for testing required a “before and after“ approach. In order to evaluate the effectiveness of the exhaust mount damper, it was necessary to obtain the responses of the structure with and without the damping. This would show if the damper was providing the correct amount of damping at the correct frequencies, and would confirm, or otherwise, if the new structure was properly supported and damped by the new mount.
A similar test was carried out: once with the damping material removed and again with the damping material fitted, so that comparisons could be drawn with respect to this new exhaust structure.
So, again the Prosig engineers set off for the Dalmeny Racing headquarters armed with the P8012 data acquisition hardware and the DATS signal processing and analysis software.
Having carried out a hammer impact test in the past on the previous design of the exhaust structure, the Prosig team already had experience of testing such structures. In the previous testing a single axis accelerometer was used for measuring motion along the axis thought to contribute most to the problem.
The axis thought to be contributing the largest magnitude and causing the greatest stress was the Y axis. This was because of the way the structure was supported and the nature of the previous failures. These had occurred in the same place and in a position that made it clear the structure was moving in the Y axis. The orientation of the Y axis is shown on the original structure in figure 1.
In the latest test the Prosig engineers used a tri-axial accelerometer, mounted on the exhaust structure perpendicular to the direction of force in the mount as this was thought to be, and was subsequently proved to be, the plane most excited as in the previous test. The accelerometer is shown in blue in figure 2.
However, since the team were using a tri-axial accelerometer for this test the orientation of the transducer was not as critically important as it was in the original test. This is because in this test all three axes of acceleration are captured not just one.
The next step required the excitation of the exhaust pipe in order that the acceleration response could be measured and recorded. For clear repeatability and accuracy, each excitation had to be carried out three times at each point and then the average of the three readings used. All of the measurement, averaging and analysis is carried out by the DATS Hammer Impact Test Software. This greatly reduces the time required for the testing. A typical screenshot of the DATS Hammer software is shown in Figure 3.
The hammer used for excitation, as shown in figure 4, is a rubber-based hammer with a force transducer built inside the head. The force transducer is quite simply a form of piezo electric crystal. When this crystal is put under compression a small voltage is generated. This voltage is captured by the P8012 data acquisition system and converted into a value equal to the force applied by the hammer.
The team marked the structure using masking tape; the tape had previously been labelled with positions indicating the locations for the input excitation. It was arbitrarily chosen to have 8 points on the mount and 21 on the exhaust structure in order to give a reasonable spatial resolution for representing the structure. This is shown in figure 5.
The hammer was used at each input point to excite the structure. As a tri-axial accelerometer was being used it was possible to get all three transfer functions per response position. A transfer function is basically a mathematical representation of a relationship between an input and an output. The input is the force that the hammer puts into the system and the output is the acceleration measured by the accelerometer. A transfer function normally has one input and one output, so for each measurement position the calculation is carried out 3 times, once for each axis.
In its basic form the transfer function H(s) is the relationship between the input signal or excitation x(t) and the output signal or response y(t).
X(f) is the frequency spectrum of x(t)
Y(f) is the frequency spectrum of y(t)
The fact that all three axes can be captured and calculated enhances the visualization animation as all three axes can be animated at the same time. This allows for a more detailed analysis of the complete structure and how it is deflecting.
The first test was with no damping material present and the second was with the originally developed damping material present.
There are two sets of 87 responses from this test capture, these are used as the inputs for the operational deflection animation comparison. However, simply comparing some of these response functions provides some interesting initial results.
Using the response functions the Prosig team constructed a model using the DATS Structural Animation Editor. This enabled them to construct a 3D model of the new structural layout of the exhaust. This process is briefly shown in figures 6 and 7.
In order to analyze the structure, it is important to understand the structure, the point of failure was known from previous experience. This is shown in figure 8 and figure 9. The point of failure is the point of highest stress, hence the failure. But it is not the point of the largest deflection. It was known from previous experience the location of the initial crack that caused the failures. From this it was obvious in which axis the force and therefore stress was being exerted.
Although much time had been spent taking data from the whole structure the most important component was the mount itself not the exhaust. The dynamics of the exhaust were important to understand what was exciting the mount.
The point of highest deflection shows the most obvious differences when comparing the responses with and without damping. However it is not the most important position. The most important position is where the largest stress concentration occurs. The position with the largest stress concentration is the failure point or in this case the 29th point of excitation during the testing. This is shown in figure 8 and figure 9.
From the rotational speeds of the components in the automotive engine when it is running, it is possible to deduce the frequencies that the exhaust structure responds to when the vehicle is in use. For this particular race car the frequencies of interest are from 15Hz to 250Hz. This is because the fundamental speeds of the engine are from 1000 RPM to 7500 RPM. This gives a basic frequency spread of 15Hz to 125Hz. However the 2nd order components of the engine, like the cam shaft run at twice those frequencies, namely 30Hz to 250Hz. For completeness the frequency range of interest in the structure is analyzed from 0Hz to 500Hz.
|Figure 10: Entire frequency range||Figure 11: Frequency range of interest (dB scale)|
|Figure 12: Frequency range of interest (linear scale)|
Figure 10 shows the complete frequency range of interest on a logarithmic scale. The blue line is the response of the structure at the highest stress point with the damper fitted, the green line is the same point without the damper fitted. It can be seen that the key effects of the damper being fitted are the distinct reductions of two large excitations at around 100Hz and 475 Hz.
The comparison in figure 11, plotted on a logarithmic scale in dB’s, shows the largest variation between the damped and the undamped structures over a reduced frequency range. This frequency range was chosen because it contained the largest excitation in the undamped mount. This is shown in figure 11 where linear values illustrate the difference more clearly. The blue line can hardly be seen.
Although a tri-axial accelerometer was used, the Y-axis was clearly the axis with the most harmful excitation, resulting in cracks being caused in that plane.
The results of the testing and analysis show the damper is effective in reducing the deflections and therefore stress forces exerted on the exhaust mount. These results were deduced by the analysis of the operational deflection structural animations and the individual analysis of the response functions. Although the final results were gleaned from the raw analysis and comparison of two transfer functions the structural animation directed the engineers in the correct direction. It was possible to see from the animations which location was the most excited and which location therefore would have the largest forces imposed upon it.
In the previous article, “Preventing Component Failure In The Fast Lane”, the structure of the exhaust was fundamentally different. The frequencies and magnitudes of excitation were different. A relatively small redesign had changed the fundamentals of the structure making it in effect a completely new structure.
The mount that was developed from the previous test results proved acceptable for the new exhaust structure. Although different fundamental frequencies were at work the basic fact that the exhaust mount had gone from having no damping to having some damping was a great improvement. Coupled to this, the original testing and retesting to find the best damping material meant that the new structure was being well supported and damped by the previously untested antivibration mount. In this case no further development or testing was necessary. As can be seen from figure 10 the largest magnitudes of deflection are being reduced by large factors in the damped mount.
The reason for the fundamental frequency with the largest excitation being much lower than in the original article was because the exhaust structure was less rigid and therefore excited the mount at lower frequencies.
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