LAB LESSONS LEARNED—PART 3: TIRE MODAL IMPACT TESTING AND FORCED-RESPONSE ANALYSIS

Projects are carried out each spring by groups of students enrolled in a class called ME597A ‘‘Practical Experiences in Vibration’’ at Purdue University in the School of Mechanical Engineering. As the final installment of a three-part series, the student team’s project studied the differences in tire response due to excitations across the tread width using modal impact testing and transmissibility analysis.

This course and others like it at institutions across the country recognize that experimental vibrations and acoustics are best learned if students are required to work in groups to conceptualize, design, conduct, and analyze their own experiments. Multiple offerings of this course at Purdue University have demonstrated that1 students retain more knowledge of measurement systems, signal processing, frequency response estimation, modal analysis, and other topics in experimental dynamics if they experience the frustrations and revelations of testing firsthand. Students sometimes find testing tedious; however, they always come away from the course with a solid understanding of the basics in structural dynamic testing: What is modal impact testing? How can it be used to obtain information about the free vibration response of a structure? What signal processing issues can cause problems in the analysis of data?

In this experimental vibrations course, the instructor serves primarily as a ‘‘measurement coach’’ by providing students with quick tutorials and suggestions at various points throughout the semester. By working together, students usually troubleshoot and solve their own measurement challenges. In fact, different groups often consult for one another during the semester, leading to a highly collaborative learning environment.

In addition to benefiting students, this type of experiential and cooperative learning approach also benefits industry. In fact, the course at Purdue University is sponsored by notable industry partners (including Arvin Meritor, General Motors, Lord Corporation, The Modal Shop, PCB Piezotronics, among others) who have provided test structures, measurement instrumentation, and expertise in kind. Surveys of these sponsors from both industry and federal laboratories with an interest in structural dynamics2 indicate that by allowing students to conceptualize and design their own experiments, open-ended lab experiences provide students with the trainingnecessary to hit the ground running when they enter the workplace. For example, students are exposed to the latest sensing, data acquisition, and data analysis (software) technologies during the semester-long course at Purdue University. VXI Technologies 1432 data acquisition systems with multireference impact testing and X-Modal interfaces, which were created by the University of Cincinnati Structural Dynamics Research Laboratory, are used by every student in the course. This exposure to multichannel dynamic measurement systems helps demystify experimental techniques so the student can quickly learn whichever system they are expected to use in industry. Surveys and hiring histories associated with programs, where hands-on, open-ended labs are offered, demonstrate that employers are more likely to hire undergraduate and graduate students who have participated in such programs.

TIRE RESPONSE TO TREAD EXCITATIONS

Steel-belted radial tires are complicated structures that pose numerous structural dynamic testing challenges. In fact, a search in the engineering literature database Compendex with the keywords ‘‘tire’’ and ‘‘testing’’ results in over 3000 hits. The tire industry is also extremely competitive; therefore, when solutions to testing challenges are found, they are sometimes not shared with the testing community due to concerns about intellectual property rights. There are over 1800 patents listed on the US Patent and Trade Office listing dealing with tire vibrations.

The students who carried out this project chose to study the following issues taken from a long list of potential challenges to investigate in tire dynamic testing:

• One challenging aspect to address in tire testing is that each point on the tire responds in multiple directions when the rolling tread is excited by the road surface. For example, modal impacts made normal to the direction of the tread in the radial direction cause the tire tread to vibrate primarily in the radial direction and the sidewall to vibrate in the lateral direction. In addition, excitations from the road occur both in the radial direction and in the slip and lateral directions. Therefore, the students used a triaxial accelerometer in order to adequately measure the multiple response degrees of freedom at a given point on the tire.
   
• Another challenge that was particularly interesting to the students is that rubber is a compliant material, making it difficult to excite tires in the higher frequency range with modal impact testing. Impacts made to the tire usually result in long contact times between the hammer tip and the tire as shown in Fig. 1a. These long contact times produce low-frequency bandwidth excitations as shown in Fig. 1b. An improved impacting method that produces shorter impacts would aid in exciting a greater number of natural frequencies and mode shapes.

Fig. 1: (a) Impact time history when striking rubber tread on tire and (b) impact frequency spectrum magnitude showing inverse relationship between contact time and frequency bandwidth.

Fig. 2: (a) Transmission of force acting on tire patch to force acting on spindle and (b) transmission of motion of tire patch to corresponding motion at spindle

Lesson Learned #1

This inverse relationship between time domain and frequency domain signals is always clearer to students after they have conducted a few modal impacts and then examined the load cell data from the hammer tip. Impacts that are long in the time domain, that is, long T, are short in the frequency domain, that is, small F, where T is the length of the impact time history and F is the length of the main lobe in the impact frequency spectrum. By changing hammer tips or by striking the tire on the rim and then the tread, this inverse relationship between the time and the frequency domain representations of the impact force can be observed.

• Because the frequency bandwidth of the modal impact force for a compliant structure like a tire is usually limited as shown in Fig. 1b, experimental results for the natural frequencies and mode shapes of the tire will be limited as well. In contrast, there is usually no limit to the number of natural frequencies and mode shapes that can be computed analytically. An additional limitation in experimentally obtained tire modal parameters is that it is difficult to exert modal impacts on the tire in directions other than the radial direction normal to the tire patch. When comparing experimental and analytical modal parameters, it is important to keep these experimental limitations in mind.

Lesson Learned #2

It is always a challenge in structural dynamic testing to apply an excitation force that is ‘‘persistent.’’ The word persistent implies that an experimentally applied force adequately excites a structural system so that its response can be fully characterized. For example, a persistent input force in the case of a tire should excite the tire with a nearly constant amplitude over the entire frequency range of interest; otherwise, the modal properties at certain frequencies (higher) may be characterized less accurately than the modal properties at other frequencies (lower). A persistent input force for the tire should also excite the tire in all directions of interest; otherwise, the modal properties in those response directions (e.g., tangential to the tire) cannot be characterized. In analytical work, the theoretical excitation force can always be modeled perfectly by analysts. In experimental work involving modal impact testing, the excitation force is always different from what the experimentalist would like.

• An additional challenge that the students addressed in this project is that frequency response function (FRF)measurements between input forces on the tire tread and output response accelerations on the tire or rim did not really provide the forced-response information of primary interest to examine in ride and handling performance of tires. For example, it would be more desirable to make measurements that relate the force that acts on the tire patch to the force that transmits through the spindle. This measurement would correspond to the transmissibility function for the tire as shown in Fig. 2a. In some cases, it would be of more interest to know how small motions of the tire patch as it rolls over an obstacle transmit into corresponding motions of the spindle (Fig. 2b). Students discovered that they could manipulate FRF measurements in order to obtain the desired transmissibility measurements for forced-response analysis as explained below.

Fig. 3: (a) Tire experimental setup and (b) measurement degrees of freedom

Fig. 4: Tangential response measurement (in volts) for longer and shorter time windows showing oscillations, with clipping at 5 volts followed by exponential decay

Other challenges in tire testing that were observed by students but not addressed in their project included issues related to the tire rim, which is a boundary condition that possesses inertia and is somewhat compliant. The student objectives of the project were: first, to identify the transverse, radial, and tangential mode shapes and natural frequencies of the tire and, second, to determine if the forced response changes appreciably when the tread is excited by the road on the inner, center, or outer tread segments. The students referred to papers by Guan et al.,3 Yam et al.,4 and others to complete the project.

Fig. 5: (a) Roll-off of modal impact autopower and (b) steel patch and coin used to overcome challenges with impact testing

Fig. 6: (a) Modal impact radial FRF magnitudes and (b) ordinary coherence functions with (red) and without (blue) steel patch for impact at location 3 showing improvement in coherence beyond 500 Hz and below 100 Hz

Figure 3a shows the experimental setup used for modal impact testing of the tire. This setup was designed to simulate a free–free boundary condition. The free–free boundary condition produced a 10-Hz resonance compared to the first resonance at 100 Hz exhibited by the tire.

Lesson Learned #3

The effect of the free–free boundary condition was minimized by reducing the frequency at which the test structure inertia resonated along with the bungee cords. The students were initially surprised when they saw the 10- Hz mode in the measured frequency response data. It is issues like this that must be considered when comparing experimental and theoretical vibration results; a free– free boundary condition is perfect in analytical models, but that is not the case in experimental fixtures. The students chose to mount the tire in this direction because none of the radial modes were affected by the bungee cords using this configuration.

A single impact location was used for the Modally Tuned ICP impact hammer (PCB Piezotronics model 086C03, Depew, NY, 10 mV/lb) along with one tri-axial ICP accelerometer(PCB Piezotronics model T356B08, 100 mV/g) that was roved to 16 response locations along the circumference of the tire as shown in Fig. 3b. Initially, a higher sensitivity tri-axial ICP accelerometer (PCB Piezotronics model T356B18, 1 V/g) was used; however, it was overloading causing the ‘‘ski slope’’ phenomenon shown below in Fig. 4. This phenomenon was caused by an overload to the analog to digital converter that saturates and then discharges in a similar manner to an RC low-pass filter.

Lesson Learned #4

After acquiring an initial dataset with the high-sensitivity accelerometer, the students noticed some unusual characteristics in their response data. They later discovered that the accelerometer was clipping at 5V, producing discontinuities in their data. The students were surprised that the tire responded so strongly to such small modal impacts. As they continued their project, they discovered that tires have low damping that led to the high response amplitudes observed in these impact response measurements using the higher sensitivity accelerometers.

Data were acquired with a 1-s time window and 800-Hz low-pass filter given that the desired frequency range was anticipated to be 200 Hz or less based on evidence in the literature.3 As explained above, the students were required to overcome the severe roll-off of the radial impact excitations to the tire along the tread. Their concern was that if the input power spectrum rolled off at 200 Hz, it would not be possible to identify higher frequency modes of vibration.

Figure 5a (dashed line) shows the impact force autopower spectrum when the tire was struck directly with the modal impact hammer. The low-frequency roll-off due to the compliance of the tire is clearly seen in this input spectrum. To extend the modal impact spectrum out to higher frequencies, the students attached a small steel rectangular patch with superglue to the tread. Figure 5b shows the tire tread instrumented with this patch. It is seen in Fig. 5a (solid line) that this patch extended the frequency range of the hammer strike out to 800 Hz by locally stiffening the impact site.

Lesson Learned #5

The students discovered that they could modify the properties of the modal impact (excitation) without affecting the properties of the test structure (tire) using this steel patch. This modification gave them a four times improvement in the excitation bandwidth over what seemed to be possible in the modal testing literature on tires. Once again, the students were able to observe that proper experiment design and performance is the key to obtaining useful data.

In addition to improving the excitation autopower spectrum as shown in Fig. 5a, the steel patch also improved the coherence associated with these FRF measurements. Figure 6 shows the improvement obtained in one of the FRFs (a) and the coherence function (b) when the patch was used. After obtaining these FRFs, the tire modal frequencies and mode shapes were identified.

The radial modes of vibration were identified using FRF data for impacts on the center tread and response measurements along the center tread. Students felt that this combination of impact and response locations would be less influenced by the sidewall stiffness of the tire. The modal frequencies were extracted using the eigensystem realization algorithm.

Fig. 7: Modal deflection shapes using response measurements along the center tread and excitation along the center tread

Fig. 8: Modal deflection shapes using response measurements along the center, inner, and outer treads

Fig. 9: Transmissibility function magnitudes along center tread

Lesson Learned #6

As with all modal parameter algorithms, the results obtained using Eigensystem Realization Algorithm (ERA) were sensitive to the segments of time data used to extract the modal parameters. Students observed that as the model orderwas changed in the algorithm, the stability of the resultant modal parameters changed. They concluded that it was best to select time data over relatively short-time segments where the response amplitudes were smaller to avoid subtle nonlinear bias in the estimated parameters.

Figure 7 shows the radial deflection shapes using modal impacts and responses along the center of the tread for the tire up to 250 Hz. Students noted that as the number of nodal lines increased, the quality of the estimated mode shape decreased due to spatial aliasing. To determine the effect of exciting the outer or inner treads (rather than the center one), the modal properties were also extracted for impacts on these treads accordingly. Figure 8 shows that these results are very similar to those for the center tread, suggesting that the tire is very uniform in the lateral direction and that the effects of the sidewall are small in this frequency range.

Lesson Learned #7

The limitations associated with measurement degrees of freedom in experimental modal testing were vividly observed by students in the mode shapes shown in these figures. As the natural frequency increased, the mode shape became less clear due to the lack of response degrees of freedom along the tire circumference.

In order to study the tire forced response due to excitations at different parts of the tread on the tire patch, FRFs were collected on the tire using the input at the steel patch and response measurements along the tread lines at different radial positions. Then, these FRFs were used to compute tread force and motion transmissibility functions that directly indicate how the tire will transmit force/motion from the excited tread location to any point of interest on the tire or rim. For example, it might be of interest to understand how an impact on one tread by a perturbation in the road affects the response of another tread that follows in the path of the first tread in the rolling tire footprint. FRFs were simply divided in order to determine these transmissibility functions.

Figure 9 shows the transmissibility to the center tread at locations 1–5 along the circumference when the tire is impacted at the center tread at point 1. Interestingly, this figure shows that the second point, which is closest to the input location, will have much higher response for frequencies around 20 Hz. At 20 Hz, all the points on the center tread show more displacement (or force) than the input point. This frequency corresponds to the antiresonance at low frequency in the FRF of the radial response at the first location. In contrast, the second point will not move much relative to the input point when the frequency is close to 50 Hz.

The students also wanted to investigate the differences in transmissibility to different tread lines on the tire. The transmissibility from the center tread to the inner and outer treads at locations 1–5 for impacts on the center tread at location 1 are shown in Fig. 10 for the center (blue), inner (red), and outer (green) treads. It is evident that the three treads patterns produce similar transmissibilities for these center impacts once again suggesting that the tire behaves similarly along these three tread lines.

Lesson Learned #8

The students discovered that by simply taking the ratio of measured FRFs, it was possible to calculate transmissibilities that help assess the forced response of tires in various excitation scenarios. Students also learned that the peaks of transmissibility functions depend on the location of the excitation. However, the peaks in FRFs, which are the natural frequencies of the structure (tire), are global properties of the structure and do not depend on the impact location.

CONCLUSION

It was concluded that a steel patch installed on the tire tread could be used to increase the frequency bandwidth of the modal impact excitation by a factor of nearly four. The patch also significantly improved the coherence of the FRF measurements. It was also determined that the forced-response characteristics of the center, inner, and outer tread lines were very similar for the tire tested.

Students learned lessons about many aspects of modal impact testing. They first observed the inverse relationship between modal impact time and frequency domain data. Then, they experienced the limitations of experimental model testing relating to the lack of a persistent excitation as a function of frequency and direction. When designing their experimental setup, students also faced issues related to the free–free boundary condition, clipping of the response data, and tuning of the excitation bandwidth by modifying the stiffness of the tire locally where the impact was applied. The sensitivity of modal parameter estimation algorithms to the time/frequency data used by the algorithm was also demonstrated. Spatial aliasing due to the lack of response data along the circumference of the tire also reminded students about the experimental limitations of modal impact testing. Last, student realized that by forming the ratios of FRF data, it was possible to compute transmissibility functions that were helpful in understanding the forced response of the tire.

Fig. 10: Transmissibility across the tire at locations (a) 1, (b) 2, (c) 3, (d) 4, and (e) 5 with respect to impact on center tread at location 1