Download or read book Development of a Digital Data Acquisition and Analysis System for the Measurement of Dynamic Transmission Error of Spur and Helical Gear Pairs written by Michael Heskamp and published by . This book was released on 2007 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In this thesis, digital data acquisition software is developed and implemented with an accelerometer-based instrumentation for the measurement of motion transmission errors of parallel-axis gear pairs operating under dynamic conditions. This system digitizes the acceleration signals from diametrically opposed tangential transducers mounted on each gear wheel to determine angular accelerations of both the mating gears. These signals are combined and integrated twice to obtain the dynamic transmission error (DTE) along the line of action. The measured DTE is processed under constant speed or sweep-up and sweep-down conditions to determine the harmonic content of the steady-state vibration response as well as transient response in the form of waterfall plots. The DTE values obtained by using the digital method are compared to those obtained from an analog system to show a good correlation. The digital data acquisition and analysis system is then used to measure the DTE of a number of example spur and helical gears having different modifications and contact ratios. At the end, capabilities and limitations of this approach for measuring DTE are discussed.
Download or read book A Dynamic Load Distribution Model for Helical Gear Pairs Having Various Manufacturing Errors written by Michael Alan Benatar and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation research focuses on developing and experimentally validating a three-dimensional load distribution model for helical gear pairs that is suitable for both quasi-static and dynamic conditions. As one phase of this research, the modeling work is carried out in two main steps. The first step focuses on quasi-static conditions by (i) developing a generalized procedure to define instantaneous contact lines along the gear mesh interface, (ii) formulating the flexibility introduced by the support structures such as bearings and shafts in a systematic way, and (iii) including gear blank related manufacturing errors such as eccentricity and wobble. The contact problem under these conditions, governed by compatibility and equilibrium equations, are solved by using an iterative elastic contact algorithm. In the second step, dynamic effects are included in the model of the first step to develop a dynamic load distribution model of a helical gear pair having the same novel features of the quasi-static model. For this, the compatibility equations of the quasi-static model are coupled to the equations of motion in the state-space representation and solved by using a backward Euler method. The other phase of this research is focused on validation of the quasi-static and dynamic load distribution models. As very little experimental helical gear data is available in the literature, an experimental study is conducted to generate an extensive database for validation of the models of this study as well as for guiding future helical gear modeling efforts. The experimental study considers a family of unity-ratio helical gear pairs having varying amounts of micro-geometry modifications as well as several spur gears having certain manufacturing errors. An encoder-based measurement system is devised to quantify the static transmission error at various transmitted torque levels to form Harris charts and define the design load values. An accelerometer-based measurement system is also incorporated with the same setup to evaluate the dynamic transmission error of the same test articles within wide speed ranges of operation. The predictions of the proposed models are compared to the experimental measurements to demonstrate that the models are accurate under both quasi-static and dynamic conditions, with or without gear blank related manufacturing errors. Given their computational efficiency, the proposed models with their novel capabilities are suitable for design optimizations studies.
Download or read book An Experimental Investigation of the Effect of Spacing Errors on the Loaded Transmission Error of Spur Gear Pairs written by Brian Anichowski (Jr.) and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analysis of the Influence of Errors and Stiffness on Dynamic Loads Developed in Spur and Helical Gears written by Donald Russell Houser and published by . This book was released on 1969 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Study on the Relationship Between the Dynamic Factor and the Dynamic Transmission Error of Spur Gear Pairs written by Venkata Krishna Tamminana and published by . This book was released on 2005 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A New Measuring System for Investigating Gear Transmission Error written by Jian Xu Wang and published by . This book was released on 1987 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Performance Based Gear Metrology written by William D. Mark and published by John Wiley & Sons. This book was released on 2012-11-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous explanation of how manufacturing deviations and damage on the working surfaces of gear teeth cause transmission-error contributions to vibration excitations Some gear-tooth working-surface manufacturing deviations of significant amplitude cause negligible vibration excitation and noise, yet others of minuscule amplitude are a source of significant vibration excitation and noise. Presently available computer-numerically-controlled dedicated gear metrology equipment can measure such error patterns on a gear in a few hours in sufficient detail to enable accurate computation and diagnosis of the resultant transmission-error vibration excitation. How to efficiently measure such working-surface deviations, compute from these measurements the resultant transmission-error vibration excitation, and diagnose the manufacturing source of the deviations, is the subject of this book. Use of the technology in this book will allow quality spot checks to be made on gears being manufactured in a production run, to avoid undesirable vibration or noise excitation by the manufactured gears. Furthermore, those working in academia and industry needing a full mathematical understanding of the relationships between tooth working-surface deviations and the vibration excitations caused by these deviations will find the book indispensable for applications pertaining to both gear-quality and gear-health monitoring. Key features: Provides a very efficient method for measuring parallel-axis helical or spur gears in sufficient detail to enable accurate computation of transmission-error contributions from working-surface deviations, and algorithms required to carry out these computations, including examples Provides algorithms for computing the working-surface deviations causing any user-identified tone, such as ‘ghost tones,’ or ‘sidebands’ of the tooth-meshing harmonics, enabling diagnosis of their manufacturing causes, including examples Provides explanations of all harmonics observed in gear-caused vibration and noise spectra. Enables generation of three-dimensional displays and detailed numerical descriptions of all measured and computed working-surface deviations, including examples
Download or read book An Experimental Investigation of the Impact of Random Spacing Errors on the Transmission Error of Spur and Helical Gear Pairs written by Muhammad Nevin Anandika and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book NASA SP written by and published by . This book was released on 1993 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Loaded Transmission Error Measurement System for Spur and Helical Gears written by Zachary Harrison Wright and published by . This book was released on 2008 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The majority of loaded static transmission error test stands developed in the past had little success generating accurate results versus analytical predictions for parallel-axis gearing. Design flaws historically caused issues with speed and torque control, ultimately, leading to erroneous results. Fortunately, some of these issues were corrected through the years, most recently by Schmitkons [1], for loaded transmission error testing of bevel gears sets. The original goal of this thesis was to translate those successes into a test rig for parallel-axis gearing that can measure static transmission error and shaft deflections to take a look at transmission error, shuttling and friction force excitations. However, due to difficulties in achieving a good comparison between experimental results and analytical predictions, the goal was shifted towards simply assessing the performance of the new test stand. By using virtually the same control setup and measurement setup as the loaded bevel gear static transmission error test stand, the new test stand generated static transmission error results for both spur and helical gears at various torque levels. Those results were compared to analytical prediction software codes (WindowsLDP, RomaxDesigner and Helical3D), using optimal and measured micro-geometry topographies. The static transmission error results compared well at low torque values, but deviated from the predicted trends at higher torque values. Ultimately, lessons learned from this test setup will be reflected in future experimental work in order to better assess the accuracy of prediction tools.
Download or read book Effect of Sliding Friction on Spur and Helical Gear Dynamics and Vibro acoustics written by Song He and published by . This book was released on 2008 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This study examines the salient effects of sliding friction on spur and helical gear dynamics and associated vibro-acoustic sources. First, new dynamic formulations are developed for spur and helical gear pairs based on a periodic description of the contact point and realistic mesh stiffness. Difficulty encountered in existing discontinuous models is overcome by characterizing a smoother transition during the contact. Frictional forces and moments now appear as either excitations or periodically-varying parameters, since the frictional force changes direction at the pitch point/line. These result in a class of periodic ordinary differential equations with multiple and interacting coefficients. Predictions match well with a benchmark finite element/contact mechanics code and/or experiments. Second, new analytical solutions are constructed which provide an efficient evaluation of the frictional effect and a more plausible explanation of dynamic interactions in multiple directions. Both single- and multi-term harmonic balance methods are utilized to predict dynamic mesh loads, friction forces and pinion/gear displacements. Such semi-analytical solutions explain the presence of higher harmonics in gear noise and vibration due to exponential modulations of periodic parameters. This knowledge also analytically reveals the effect of the tooth profile modification in spur gears under the influence of sliding friction. Further, the Floquet theory is applied to obtain closed-form solutions of the dynamic response for a helical gear pair, where the frictional effect is quantified by an effective piecewise stiffness function. Analytical predictions are validated using numerical simulations. Third, an improved source-path-receiver vibro-acoustic model is developed to quantify the effect of sliding friction on structure-borne noise. Interfacial bearing forces are predicted for the spur gear source sub-system given two whine excitations (static transmission error and sliding friction). A computational model of the gearbox, with embedded bearing stiffness matrices, is developed to characterize the motilities of structural paths. Radiated sound pressure is then estimated by using the Rayleigh integral method and a substitute source technique. Predicted pressures match well with measured noise data over a range of operating torques. In particular, the proposed vibro-acoustic model quantifies the contribution of sliding friction, which could be significant when the transmission error is minimized through tooth modifications.
Download or read book A Transmission error based Gear Dynamic Model written by Nina Sainte-Marie and published by . This book was released on 2019 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noise measurements have shown that helicopters main gearboxes highly contribute to the overall cabin noise. Gear mesh vibrations propagate through the shafts to the rolling element bearings and the casing which becomes a source of radiated noise. The latter is characterized by high-amplitude tones emerging from broadband noise whose frequencies lie in the range of maximum human ear sensitivity. In the context of continuous improvement in the acoustic comfort of helicopter passengers, it is therefore necessary to analyse and optimize gearbox vibrations in order to reduce casing noise radiations. The research work presented in this memoir is focused on the development of a numerical model dedicated to the prediction of gear system dynamic behaviour, comprising several gear stages and different types of gears. This model relies on classic beam and lumped parameter elements along with specific two-node gear elements for both cylindrical (spur, helical) and spiral-bevel gears. The equations of motion are developed based on time-varying functions representative of mesh excitations which comprise: (a) mesh stiffness functions, (b) quasi-static transmission error under load, and (c) kinematic (or no-load) transmission error. A number of comparisons with benchmark numerical and experimental results from the literature are presented which demonstrate that the proposed approach is sound as far as single-stage systems with spur, helical or spiral-bevel gears are considered. Validations are then extended to double-stage gears and, here again, it is confirmed that the proposed transmission error based formulation is accurate and can account for tooth shape modifications. In the second part of the memoir, several examples of application are presented and commented upon. First, the combined influence of tooth pitch errors and load on the dynamic behaviour of gear transmissions is tackled. An extended three-dimensional model and a reduced torsional version are then confronted in order to investigate the dependency between dynamic transmission errors and mesh force / root stress dynamic factors. Further investigations on bearing dynamic response in two-stage spur gear systems are conducted and the particular contributions of profile modifications are analysed. Finally, a system combining a cylindrical gear and a spiral-bevel gear is considered and particular attention is paid to the dynamic couplings between the various meshes and their influence on bearing dynamic responses.
Download or read book Measurement of Vibrations of Gears Supported by Compliant Shafts written by Ma Ru Kang and published by . This book was released on 2009 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In this study, an accelerometer-based measurement method is proposed for measurement of motions of parallel-axis gears in torsional, translational and rotational directions. This method uses a family of tri-axial accelerometers that are mounted on a shaft flange at a given radius. Acceleration signals from the accelerometers are processed based on a novel formulation to quantify the motions of a gear in the torsional, rotational (rocking), transverse (line-of-action and off-line-of-action) and axial directions. With the similar instrumentation implemented on the mating gear, the dynamic transmission error of the gear pair is also measured. This measurement system is applied for example to spur and helical gear pairs held by different shafts representative of different support compliances. The transverse motions of the spur pinion in the line-of-action direction, as well as line-of-action, rocking and axial motions of helical gears are shown to be significant when they are supported compliantly. At the end, the same experiments are simulated by using a previously developed gear-shaft-bearing dynamics model to identify the shapes of the modes excited and to show the agreement between the predicted and measured forced responses.
Download or read book Mobility Analysis of a Spur Gear Pair and the Examination of Sliding Friction written by Allison Holub and published by . This book was released on 2005 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Linear vibro-acoustic models of a geared system are developed to comparatively examine the effect of the static transmission error and sliding friction excitations. Mobility synthesis is applied to a spur gear pair system with six degrees-of-freedom, describing only the line-of-action dynamics. The frequency responses are validated using direct inversion for assumed transmission error excitation. Simplified analytical expressions for natural frequencies and dynamic bearing forces are derived using the mobility model and compared to the work presented by Steyer (1987). The transmission error and sliding friction sources are compared in terms of the gear mesh harmonic amplitudes predicted by a computer program called Load Distribution Program. To simplify the friction excitation, an empirical equation describing a variable coefficient of friction, as a function of roll angle, is employed and then a mean value of the coefficient is obtained for various operating conditions. An eight degree-of-freedom model incorporating the off-line-of-action direction is also developed for the spur gear pair, in which the friction force excitation is assumed to act externally with a given amplitude for all frequencies. Using this model, the dynamic bearing forces are evaluated in both the line-of-action and off-line-of-action directions. A simple noise prediction model for the gearbox based on experimentally measured structural-acoustic transfer functions is presented. The sound pressure levels are predicted at the gear mesh harmonics to examine the role of the static transmission error and sliding friction excitations. The predictions are qualitatively compared to measurements performed at NASA Glenn Research Center as well.
Download or read book Computerized Generation and Simulation of Meshing of Modified Spur and Helical Gears Manufactured by Shaving written by and published by . This book was released on 2001 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modification of geometry of spur and helical gears with parallel axes and helical gears with crossed axes is proposed. The finishing process of gear generation is shaving. The purposes of modification of the gear geometry are to localize and stabilize the bearing contact, and to reduce noise and vibration. The goals mentioned above are achieved by using profile crowning and plunging the shaver by a prescribed motion during pinion generation. The pinion becomes double crowned. The gear member is generated as a conventional involute gear. A tooth contact analysis (TCA) program for simulation of meshing and contact was developed and the analysis is illustrated with TCA results for spur and helical gears.
Download or read book Aeronautical Engineering written by and published by . This book was released on 1993 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: A selection of annotated references to unclassified reports and journal articles that were introduced into the NASA scientific and technical information system and announced in Scientific and technical aerospace reports (STAR) and International aerospace abstracts (IAA).
Download or read book A Theoretical and Experimental Study of Static and Dynamic Transmission Error for Spur and Helical Gears with Various Modifications and Contact Ratios written by James M. Graber and published by . This book was released on 1994 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
