Structural Surface Intensity as a Diagnostic Indicator of Machinery Failure

Jeffrey C. BanksGraduate Program in Acoustics

Stephen HambricApplied Research Laboratory

The Pennsylvania State UniversityState College, PA 16801

Abstract:

Many time and frequency based analysis techniques are available to predict mechanical faults. The primary function of these techniques is to evaluate wear that affects machinery reliability and to predict subsequent failure. The focus of this research is to develop a metric that is more responsive to the mechanical condition of a structure than existing vibration analysis methods. Structural surface intensity is a quantity that indicates vibrational energy flow through a structure. Evaluating the energy level and its direction could possibly lead to a sensitive and effective indicator of mechanical condition. Since this technique has had limited use as an applied method of fault analysis, structural intensity measurements have been made on a gearbox casing in the ARL Penn State Machinery Diagnostic Test Bed (MDTB) as the gear set is run to failure. The changes in energy flow are analyzed and characterized to provide preliminary criteria for fault detection. Preliminary results indicate that significant changes in structural surface intensity occur as geartooth faults develop.

Keywords: Diagnostic metric; gear failure; intensity; and predictive maintenance.

Introduction:

This research is being conducted to develop a diagnostic indicator that is more sensitive to mechanical system conditions then other techniques. Many time and frequency based diagnostic techniques use a single parameter, such as vibration, to evaluate the condition of the system. Traditional fault analysis methods for rotating and reciprocating elements are based on evaluating discrete fault frequencies and levels, which are directly affected by speed and load. The difficulty with this type of analysis is that the fault frequency that is being scrutinized may not appear or change until a fault has occurred. A more sensitive metric is needed to assess the condition of a mechanical element or system. There has been extensive experimental research conducted using intensity to measure energy flow through a structure. The experimental work conducted previously concerned itself with developing intensity measurement methods and analyzing energy flow through simple structures like beams and plates. Because intensity is a vector that provides magnitude and direction of the energy through the structure, it may prove to be a very insightful diagnostic metric.

Testing is conducted on the ARL Penn State Mechanical Diagnostic Test Bed (MDTB) [1], which is specifically designed as a gearbox wear platform to experimentally simulate the accelerated fault evolution in mechanical gearbox power transmission components.

Figure 1: Mechanical Diagnostics Test Bed facility located at the Pennsylvania State University Applied Research Lab

The test bed, shown in Figure 1, consists of two AC electric motors for driving and loading the single reduction gearbox. The test gearbox is instrumented with input and output torque cells, accelerometers, thermocouples, acoustic emission, and oil debris sensors to log measurement data for post-test processing. During break-in and testing of the gearbox, it is run at a standard design speed of 1750 RPM and variable load profiles from 0 to 5 times the rated torque of the test gearbox. The MDTB can create duty cycle profiles for any speed and load desired for testing. Some of the previous work conducted on the MDTB by the ARL Penn State Conditioned Based Maintenance group include interstitial processing to analyze transitional failure data [2], method development to fuse vibration and oil analysis data to provide better estimation of failure mode identification [3], and wavelet analysis of vibration spectra to forecast geartooth failure [4].

Structural Surface Intensity:

The intensity measurement approach used in this research was developed by G. Pavic [5]. This method is based on the fact that sensor access is limited to the surface of the structure, hence the term structural surface intensity (SSI). Most intensity techniques are developed specifically for beam and plate-like structures and are not applicable to complicated geometries like gearbox housings. The strength of the SSI technique is that it is insensitive to the geometry of the structure. Although SSI does not indicate the total power level within a structure, it still provides insight into the energy flowing through its surface. The SSI method requires the use of an array of transducers, including two accelerometers in the X and Y planes (planar to the surface) and three strain gauges in a rosette pattern of 0-45-90 degrees to the Y-axis (which is inline with the drive axis.) Three groups of sensors attached to the gearbox housing in the MDTB are shown in Figure 2.

Figure 2: Three sensor arrays attached to test gearbox housing.

Pavic developed equivalent structural surface intensity algorithms that can be implemented in the time and the frequency domains.

The time domain based intensity equations are:

where:

G is the shear modulus is the intensity in direction i, is the particle velocity in direction i, is the shear strain,

is the normal strain in direction x is Poisson’s ratio.

The frequency domain based intensity equations are:

where:

is the cross spectral density between strain in direction i and velocity in direction j.

Since the two methods should yield equivalent results, they can be applied using the same data to confirm that the algorithms are implemented correctly. Once the methods were validated, the frequency domain method was used for analysis, since it will allow for easier facilitation of variable bandwidth analysis in the future. This involves analyzing the frequency bandwidth that is most affected by the condition of the system to gain optimum sensitivity.

Pavic measured structural surface intensity on a motor and gearbox system at two different running conditions. The different conditions involved running the motor with and without the gearbox attached and data was taken on the motor/gearbox support structure using a transducer array configuration similar to that shown in Figure 2. The intensity changed significantly between the two states. This simple application test shows the potential of applying the method as a diagnostic technique. It is hoped that developing failures, such as gear tooth breakage, will cause substantial changes in structural intensities well before failure.

Test Structure:

To maximize the effectiveness of the SSI diagnosis approach, the behavior of the MDTB gearbox was analyzed. A modal analysis of the single reduction (3.3:1) gearbox housing was performed to determine its natural frequencies and mode shapes. Since the gearbox is a relatively complex structure, the modal analysis gives insight into which frequency range has the highest modal density relative to good coherence levels. The analysis also helps determine which modes are most responsive, and helps differentiate between local and global modes. This analysis shows that a rectangular shaped portion of the housing connected to the output shaft bearing support provides an adequate test area with good modal response of six frequencies for a bandwidth of 0 – 3200 Hz. The resonant frequencies of this portion of the housing are grouped within 1500 – 3200 Hz as shown in the sample FRF in Figure 3.

Figure 3: Sample Frequency Response Function of test area using impact hammer and accelerometer.

The natural frequencies for the test section of the gearbox were measured using an impact hammer and accelerometer and are shown in Table 1.

Table 1: Gearbox housing resonance frequencies.

Frequencies: 1800 Hz 2090 Hz 2310 Hz 2790 Hz 2950 Hz 3070 Hz

The standard test speed of the gearbox is 1750 RPM, which based on the number of gearteeth, generates a gearmesh frequency of 613 Hz. There are resonance frequencies at 1800 Hz and 3070 Hz, which are close to 3 times and 5 times the gearmesh frequency respectively. These modes may be excited by energy emanating from a degradation of geartooth condition. The frequency domain SSI method (Eqs.3 & 4) encompasses a selected frequency range of interest, which may bracket selected modes to optimize the sensitivity of SSI to changes in excitation due to developing faults. In this study, however, the entire frequency range is included, in the analysis.

To optimize the sensor placement, an intensity analysis with a single known drive was conducted on the test section of the gearbox. An electro-dynamic shaker excited the gearbox housing at a constant frequency of 613 Hz, while the X and Y plane response of the test area at 49 discrete points (7 by 7 grid) was measured with an accelerometer. The acceleration data was converted to velocity and differentiated over space to approximate strain in order to estimate the intensity vector for each point within the test area using Eqs.1-4. The analysis reveals high intensity levels at several locations within the test area, which provides a basis for positioning the sensor arrays. Due to the size of each sensor and to the limited amount of test surface area it was decided to use three array positions at locations shown to have high intensity levels. As mentioned previously, the sensor array consists of a triaxial accelerometer and a rosette configuration of three strain gages. Special consideration was given to the strain gauge selection since preliminary testing revealed that the sensitivity of the conventional foil strain gauges was not high enough for this application. It was found that PCB dynamic strain sensors (model # 740B02) have the sensitivity and the bandwidth to function properly for this application.

Experiment:

The experimental test runs began with a four hour prebreak-in run at 1750 RPM and 416 in-lbs. (0.75 times maximum rated load) to comply with manufacturer specification criteria. Following the prebreak-in and an oil change, the break-in run consisted of running the gearbox at 1750 RPM and 555 in-lbs. (1 times maximum rated load) for 20 hours to establish a standard wear pattern on the gearset. The test run involved running the gearbox at 1750 RPM with a load of 1665 in-lbs. (3 times maximum rated load) in order to accelerate the wear life of the gearset. The test run lasted for 11 hours concluding with a tooth failure on the output gear. Previous gearbox tests have lasted anywhere from 2 to 180 hours based on the gearsets and bearing tolerances and how well the gearbox was aligned to the test apparatus. Test data was taken in one to two hour increments throughout the entire test cycle until the gearbox failed.

Preliminary Analysis:

The 3 times maximum rated load test data was post-processed to compute intensity vectors using Eqs.3 & 4 at the three test areas and these values were evaluated with the accelerometer and strain gauge data at their respective locations over time. The primary goal is to look for significant and correlated changes in the processed data. A preliminary look at the SSI data shows a significant change in the intensity data before a change is seen in either the accelerometer or strain gauge data. The seven X and Y plane intensity, accelerometer and strain data sets shown in Tables 2 - 4 are given in voltage and are presently uncalibrated, but the calibration factors will not change the overall trends shown in the Tables.

Table 2: Sensor Array No. 1

Hours Int x Int y Accel x Accel y Strain x Strain 45 Strain y4 -0.89 0.45 1.64 2.54 0.284 0.256 0.2326 -0.85 0.60 1.61 2.42 0.284 0.261 0.2397 -0.35 0.87 1.46 2.44 0.277 0.258 0.2278 -1.01 2.26 1.60 2.59 0.280 0.254 0.2209 -0.61 2.12 1.61 2.62 0.266 0.247 0.22010 -0.28 2.12 2.10 3.47 0.460 0.423 0.38010.5 -0.25 2.15 2.10 3.40 0.470 0.422 0.374Note: Accel x denotes mean accelerometer voltage in the X-plane.

The acceleration and strain gauge data shows a significant change in level for all three sensor positions starting at hour 10. The data set at hour 10.5 was taken shortly before the MDTB test rig was shut down for inspection. A boroscope examination of the gearset revealed that a tooth from the output gear was missing. Sensor array number 1 shows a significant change in the Y-plane intensity level approximately 2 hours before the accelerometer or strain gauge position number 1 data is affected.

Table 3: Sensor Array No. 2

Hours Int x Int y Accel x Accel y Strain x Strain 45 Strain y4 1.53 -1.87 8.39 10.72 0.199 0.330 0.2166 1.58 -1.84 8.15 10.29 0.203 0.339 0.2217 -0.94 -5.00 7.69 9.83 0.188 0.332 0.2128 -3.66 -4.05 8.56 10.97 0.194 0.318 0.2089 -4.15 -4.92 8.38 10.79 0.193 0.330 0.21110 -3.60 -6.96 11.61 15.20 0.293 0.513 0.34111 -3.74 -7.71 11.50 15.00 0.288 0.508 0.331

The second sensor array reveals a significant change in the X and Y plane intensity levels approximately 3 hours before the accelerometer or strain gauge position number 2 data.

Table 4: Sensor Array No. 3

Hours Int x Int y Accel x Accel y Strain x Strain 45 Strain y4 -0.038 -0.034 0.083 0.087 0.229 0.187 0.1276 -0.042 -0.039 0.081 0.084 0.236 0.193 0.1277 -0.060 -0.049 0.079 0.083 0.219 0.183 0.1318 -0.050 -0.072 0.084 0.090 0.227 0.186 0.1279 -0.054 -0.068 0.084 0.090 0.225 0.183 0.12510 -0.054 -0.075 0.113 0.129 0.299 0.276 0.19911 -0.067 -0.078 0.112 0.127 0.301 0.273 0.199

The third sensor array shows a less significant change in the Y-plane level approximately 2 hours before the accelerometer number 3 data.

Conclusions:

Based on the preliminary results presented here, SSI shows great promise as a metric for diagnosing impending machinery failures. SSI appears to be more sensitive to developing geartooth faults than acceleration or strain gauge levels alone. Further analysis will be conducted to determine why the intensity in the Y direction appears to be more sensitive to geartooth condition than the intensity in the X direction and to evaluate the significance of changes of intensity level compared to intensity direction. Additional analysis will focus on qualifying the optimum bandwidth for measuring intensity and to determine which modes contribute most to the intensity level during normal and damaged operation. Future work should focus on using SSI for prognosis as well as diagnosis.

Acknowledgement:

This research was supported by the Multidisciplinary University Research Initiative for Integrated Predictive Diagnostics (Grant Number N00014-95-1-0461) sponsored by the Office of Naval Research. A special thanks to PCB Piezotronics for donating the Dynamic ICP Strain Sensors and signal condition electronics used in this research.

References:

1. Kozlowski, J.D., and Byington, C.S., “Mechanical Diagnostics Test Bed for Condition Based Maintenance”, ASNE Intelligent Ships Symposium II, November 25-26, 1996.

2. Maynard, K.P., “Interstitial Processing: The Application of Noise Processing to Gear Fault Detection”, International Conference on Condition Monitoring, April 12-15, 1999.

3. Byington, C.S., Merdes, T.A., and Kozlowski, J.D., “Vibration and Oil Debris Feature Fusion in Gearbox Failures”, 53rd Meeting of the Society for Machinery Failure prevention Technology (MFPT), April 1999.

4. Miller, A.J., and Reichard, K.M., “A New Wavelet Basis for Automated Fault Diagnostics of Gear Teeth,” Proceedings of Internoise 99, pp.1597-1602, 1999.

5. G.Pavic, “Structural Surface Intensity: An Alternate Approach in Vibration Analysis and Diagnosis”, Journal of Sound and Vibration, 1987, Vol.115, pp.405-422.