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This paper complements recent investigations [Handschuh et al. (2014), Talbot et al. (2016)] of the influences of tooth indexing errors on dynamic factors of spur gears by presenting data on changes to the dynamic transmission error. An experimental study is performed using an accelerometer-based dynamic transmission error measurement system incorporated into a high-speed gear tester to establish baseline dynamic behavior of gears having negligible indexing errors, and to characterize changes to this baseline due to application of tightly-controlled intentional indexing errors. Spur gears having different forms of indexing errors are paired with a gear having negligible indexing error. Dynamic transmission error of gear pairs under these error conditions is measured and examined in both time and frequency domains to quantify the transient effects induced by these indexing errors. These measurements are then compared against the baseline, no error condition, as a means to quantify the dynamic vibratory behavior induced due to the tooth indexing errors. These comparisons between measurements indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks and mesh harmonics, are complemented by non-mesh orders of transmission error due the transient behavior induced by indexing errors. In addition, the tooth (or teeth) having indexing error imparts transient effects which dominate the vibratory response of the system for significantly more mesh cycles than the teeth having errors are in contact. For this reason, along with the results presented in Talbot et al. (2016), it was concluded that spur gears containing indexing errors exhibit significant deviations from nominal behavior, at both a system and time-domain level.
Noise and vibration performance of a gear system is critical in any industry. Vibrations caused by the excitations at the gear meshes propagate to the transmission housing to cause noise, while also increasing gear tooth stresses to degrade durability. As such, gear engineers must seek gear designs that are nominally quiet with low vibration amplitudes. tudes. They must also ensure that this nominal performance is robust in the presence of various manufacturing errors. This thesis research aims at an experimental investigation of the influence of one type of manufacturing error, namely random tooth spacing errors, on the vibratory responses of spur and helical gear pairs. For this purpose, families of spur and helical gear test specimens having intentionally induced, tightly controlled random spacing error sequences are fabricated. These specimens are paired and assembled in various ways to achieve different sequences of composite spacing errors. Static and dynamic motion transmission error measurements from these tests are compared to the baseline case of “no error” gear to quantify the impact of random spacing errors on the dynamic response. These comparisons show that there is a significant, quantifiable impact of random spacing errors on both spur and helical gear dynamics. In general, vibration amplitudes of gear pairs having random spacing errors are higher than those of the corresponding no-error gear pairs. In the frequency domain, gears having random spacing errors exhibit broad-band spectra with significant non-mesh harmonics, pointing to potential noise quality issues.
Abstract: In this study, theoretical and experimental investigations of the effect of tooth spacing errors on the motion transmission error and root stresses of spur gear pairs are performed. A test setup with dedicated instrumentation for the measurement of the static transmission error and root stresses is devised. A number of experiments are performed with gears having deterministic spacing errors (at one or two teeth only) and random spacing errors (all teeth having a random distribution of errors as in a typical production gear). A test matrix defined by a range of torque at a very low speed is executed with each error configuration to experimentally quantify the influence of spacing errors on the static transmission error and the gear tooth root stresses. The results of these experiments form an extensive database on the impact of spacing errors on the static transmission error (a typical noise metric) and the root stresses (a durability metric). These experiments are simulated by using two existing gear contact models to demonstrate their accuracy and describe the empirical trends physically. A methodology is proposed at the end to relate increases in root stresses to the spacing error magnitudes directly. Closed-form expressions resulting from this methodology allow determination of the stress amplification factors due to a certain range of spacing error tolerances as well as quantifying how much spacing error can be tolerated within a user defined stress limit.
This book presents papers from the International Gear Conference 2014, held in Lyon, 26th-28th August 2014. Mechanical transmission components such as gears, rolling element bearings, CVTs, belts and chains are present in every industrial sector and over recent years, increasing competitive pressure and environmental concerns have provided an impetus for cleaner, more efficient and quieter units. Moreover, the emergence of relatively new applications such as wind turbines, hybrid transmissions and jet engines has led to even more severe constraints. The main objective of this conference is to provide a forum for the most recent advances, addressing the challenges in modern mechanical transmissions. The conference proceedings address all aspects of gear and power transmission technology and range of applications (aerospace, automotive, wind turbine, and others) including topical issues such as power losses and efficiency, gear vibrations and noise, lubrication, contact failures, tribo-dynamics and nano transmissions. - A truly international contribution with more than 120 papers from all over the world - A judicious balance between fundamental research and industrial concerns - Participation of the most respected international experts in the field of gearing - A wide range of applications in terms of size, power, speed, and industrial sector
Experimental Techniques, Rotating Machinery & Acoustics, Volume 8: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015, the eighth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Experimental Techniques Processing Modal Data Rotating Machinery Acoustics Adaptive Structures Biodynamics Damping
Abstract: In this study, an experimental investigation is performed to investigate the impact of various gear errors on transmission error and root fillet stresses. A test set-up is devised to operate a pair of spur gears under loaded, low-speed conditions. Two measurement systems; one an optical encoder-based transmission error measurement system and the other a multi-channel strain measurement system, are developed and implemented with the test set-up. A set of test gears having various types and tightly-controlled magnitudes of manufacturing errors are designed and procured. These errors include indexing errors of different tooth sequences, pitch line run-out errors and lead wobble errors. An extensive test matrix is executed to quantify the impact of these errors on the loaded static transmission error and the root stresses of the spur gears. At the end, the same test conditions are simulated by using a recent feature of gear analysis model (LDP) to assess the accuracy of its predictions.
The dynamic load of gears with regular type of spacing error such as full-sine and half-sine type has been analyzed in several previous research works. In this study, the irregular type of tooth spacing error is incorporated with the regular type ones to determine their effect on gear dynamic response. Linear and Parabolic tooth profile modification are applied to evaluate their influence on the dynamic loads of gear systems with regular or irregular tooth spacing errors. All dynamic analyses are conducted using the NASA gear dynamics code, DANST program.The objective of this study is to examine the relationship between gear dynamic load, type and extent of tooth spacing error, and profile modifications. Results obtained from this study can provide proper tooth profile design to minimize the dynamic response of the spur gear systems for a better transmission design.
Abstract: Power Transmission systems are widely used in automotive and aerospace industries. These systems are often operated under relatively high rotational speeds and hence their dynamic behavior, especially its impact on the gears, becomes a relevant issue. Dynamic behavior of gear systems is important for two main reasons: durability and noise. In this study, two different dynamic models, a finite elements-based deformable-body model and a simplified discrete model, are developed to predict dynamic behavior of spur gear pairs. The deformable-body model will have the ability to predict both DTE and DF based on mesh and tooth forces as well as dynamic gear tooth bending stresses. The discrete model will rely on the deformable-body model for computation of gear mesh parameters under quasi-static conditions and will predict both DTE and DF based on mesh and tooth forces. Dynamic transmission error (DTE) and dynamic factors (DF) defined based on the gear mesh loads, tooth loads and bending stresses are computed for a number of unmodified and modified spur gears within a wide range of rotational speed for different involute contact ratios and torques. Both models are validated by comparing their DTE predictions with experimental data obtained from a set of tests using spur gear having unmodified and modified tooth profiles. The predicted Dc DF and DTE values are related to each other through simplified formulas. Impact of nonlinear behavior such as tooth separations and jump discontinuities on DF is also quantified.