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Gear cracks are typically difficult to diagnose with sufficient warning time. Significant damage must he present before algorithms detect the damage. A new feature extraction and two new detection techniques are proposed. The time synchronous averaging concept was extended from revolution-based to tooth engagement-based. The detection techniques are based on statistical comparisons among the averages for the individual teeth. These techniques were applied to a series of three seeded fault crack propagation tests. These tests were conducted on aerospace quality spur gears in a test rig. The tests were conducted at speeds ranging from 2500 to 7500 revolutions per minute and torque from 184 to 228 percent of design load. The inability to detect these cracks with high confidence may be caused by the high loading required to initiate the cracks. The results indicate that these techniques do not currently produce an indication of damage that significantly exceeds experimental scatter.
Health and Usage Monitoring System research and development involves analysis of the vibration signals produced by a gearbox throughout its life. There are two major advantages of knowing the actual lifetime of a gearbox component: safety and cost. In this report, a technique is proposed to help extract the critical data and present it in a manner that can be easy to understand. The key feature of the technique is to make it independent of speed, torque and prior history for localized, single tooth damage such as gear cracks. This extraction technique is demonstrated on two sets of digitized vibration data from cracked spur gears. Standard vibration diagnostic parameters are calculated and presented for comparison. Several new detection algorithms are also presented. The results of this study indicate that crack detection methods examined are not robust or repeatable. The proposed techniques provide a limited improvement to existing diagnostic parameters. Current techniques show that the cracks progressed at a much faster rate than anticipated which reduced available time for detection.
Robust gear designs consider not only crack initiation, but crack propagation trajectories for a fail-safe design. In actual gear operation, the magnitude as well as the position of the force changes as the gear rotates through the mesh. A study to determine the effect of moving gear tooth load on crack propagation predictions was performed. Two dimensional analysis of an involuted spur gear and three-dimensional analysis of a spiral-bevel pinion gear using the finite element method and boundary element method were studied and compared to experiments. A modified theory for predicting gear crack propagation paths based on the criteria of Erdogan and Sih was investigated. Crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction techniques using a simple static analysis in which the tooth load was located at the highest point of single tooth contact was validated. For three-dimensional analysis, however, the analysis was valid only as long as the crack did not approach the contact region on the tooth.
Design guidelines have been established to prevent catastrophic rim fracture failure modes when considering gear tooth bending fatigue. Analysis was performed using the finite element method with principles of linear elastic fracture mechanics. Crack propagation paths were predicted for a variety of gear tooth and rim configurations. The effects of rim and web thicknesses, initial crack locations, and gear tooth geometry factors such as diametral pitch, number of teeth, pitch radius, and tooth pressure angle were considered. Design maps of tooth/rim fracture modes including effects of gear geometry, applied load, crack size, and material properties were developed. The occurrence of rim fractures significantly increased as the backup ratio (rim thickness divided by tooth height) decreased. The occurrence of rim fractures also increased as the initial crack location was moved down the root of the tooth. Increased rim and web compliance increased the occurrence of rim fractures. For gears with constant pitch radii, coarser-pitch teeth increased the occurrence of tooth fractures over rim fractures. Also, 250 pressure angle teeth had an increased occurrence of tooth fractures over rim fractures when compared to 200 pressure angle teeth. For gears with constant number of teeth or gears with constant diametral pitch, varying size had little or no effect on crack propagation paths.
The fatigue life of a gear tooth can be thought of as the sum of the number of cycles required to initiate a crack, N(sub i), plus the number of cycles required to propagate the crack to such a length that fracture occurs, N(sub p). The factors that govern crack initiation are thought to be related to localized stress or strain at a point, while propagation of a fatigue crack is a function of the crack tip parameters such as crack shape, stress state, and stress intensity factor. During a test there is no clear transition between initiation and propagation. The mechanisms of initiation and propagation are quite different and modeling them separately produces a higher degree of accuracy, but then the question that continually arises is 'what is a crack?' The total life prediction in a fracture mechanics model presently hinges on the assumption of an initial crack length, and this length can significantly affect the total life prediction. The size of the initial crack is generally taken to be in the range of 0.01 in. to 0.2 in. Several researchers have used various techniques to determine the beginning of the crack propagation stage. Barhorst showed the relationship between dynamic stiffness changes and crack propagation. Acoustic emissions, which are stress waves produced by the sudden movement of stressed materials, have also been successfully used to monitor the growth of cracks in tensile and fatigue specimens. The purpose of this research is to determine whether acoustic emissions can be used to define the beginning of crack propagation in a gear using a single-tooth bending fatigue test. Wheitner, Jeffrey A. and Houser, Donald R. Unspecified Center ACOUSTIC EMISSION; ACOUSTIC MEASUREMENT; BENDING FATIGUE; CRACK PROPAGATION; FATIGUE LIFE; FATIGUE TESTING MACHINES; FRACTURE MECHANICS; GEAR TEETH; NONDESTRUCTIVE TESTS; BEND TESTS; CRACKS; DETECTION; FATIGUE TESTS; STIFFNESS; STRESS WAVES...
This book gathers contributions presented at the 9th Workshop on Cyclostationary Systems and Their Applications, held in Gródek nad Dunajcem, Poland in February 2016. It includes both theory-oriented and practice-oriented chapters. The former focus on heavy-tailed time series and processes, PAR models, rational spectra for PARMA processes, covariance invariant analysis, change point problems, and subsampling for time series, as well as the fraction-of-time approach, GARMA models and weak dependence. In turn, the latter report on case studies of various mechanical systems, and on stochastic and statistical methods, especially in the context of damage detection. The book provides students, researchers and professionals with a timely guide to cyclostationary systems, nonstationary processes and relevant engineering applications.
Health and Usage Monitoring System research and development involves analysis of the vibration signals produced by a gearbox throughout its life. There are two major advantages of knowing the actual lifetime of a gearbox component: safety and cost. In this report, a technique is proposed to help extract the critical data and present it in a manner that can be easy to understand. The key feature of the technique is to make it independent of speed, torque and prior history for localized, single tooth damage such as gear cracks. This extraction technique is demonstrated on two sets of digitized vibration data from cracked spur gears. Standard vibration diagnostic parameters are calculated and presented for comparison. Several new detection algorithms are also presented. The results of this study indicate that crack detection methods examined are not robust or repeatable. The proposed techniques provide a limited improvement to existing diagnostic parameters. Current techniques show that the cracks progressed at a much faster rate than anticipated which reduced available time for detection. Decker, Harry J. Glenn Research Center NASA/TM-2002-211492, NAS 1.15:211492, E-13260, ARL-TR-2682
Explores the detailed steps necessary to determine the causes of failure. First, the physical characteristics of a gear are studied: where the stress points are, from what directions the forces are applied, where the movement of material progresses, and where strain patterns exist. Second, all external conditions and forces are considered. With this background information, a systematic examination is described from beginning to end, the end being a conclusion about the mode and cause of failure.