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Gearbox NoiseCorrelation with Transmiion Error and Influence of Bearing Preload
ABSTRACT The five appended papers all deal with gearbox noise and vibration.The first paper presents a review of previously published literature on gearbox noise and vibration.The second paper describes a test rig that was specially designed and built for noise testing of gears.Finite element analysis was used to predict the dynamic properties of the test rig, and experimental modal analysis of the gearbox housing was used to verify the theoretical predictions of natural frequencies.In the third paper, the influence of gear finishing method and gear deviations on gearbox noise is investigated in what is primarily an experimental study.Eleven test gear pairs were manufactured using three different finishing methods.Transmiion error, which is considered to be an important excitation mechanism for gear noise, was measured as well as predicted.The test rig was used to measure gearbox noise and vibration for the different test gear pairs.The measured noise and vibration levels were compared with the predicted and measured transmiion error.Most of the experimental results can be interpreted in terms of measured and predicted transmiion error.However, it does not seem poible to identify one single parameter,such as measured peak-to-peak transmiion error, that can be directly related to measured noise and vibration.The measurements also show that disaembly and reaembly of the gearbox with the same gear pair can change the levels of measured noise and vibration considerably.This finding indicates that other factors besides the gears affect gear noise.In the fourth paper, the influence of bearing endplay or preload on gearbox noise and vibration is investigated.Vibration measurements were carried out at torque levels of 140 Nm and 400Nm, with 0.15 mm and 0 mm bearing endplay, and with 0.15 mm bearing preload.The results show that the bearing endplay and preload
influence the gearbox vibrations.With preloaded bearings, the vibrations increase at speeds over 2000 rpm and decrease at speeds below 2000 rpm, compared with bearings with endplay.Finite element simulations show the same tendencies as the measurements.The fifth paper describes how gearbox noise is reduced by optimizing the gear geometry for decreased transmiion error.Robustne with respect to gear deviations and varying torque is considered in order to find a gear geometry giving low noise in an appropriate torque range despite deviations from the nominal geometry due to manufacturing tolerances.Static and dynamic transmiion error, noise, and housing vibrations were measured.The correlation between dynamic transmiion error, housing vibrations and noise was investigated in speed sweeps from 500 to 2500 rpm at constant torque.No correlation was found between dynamic transmiion error and noise.Static loaded transmiion error seems to be correlated with the ability of the gear pair to excite vibration in the gearbox dynamic system.Keywords: gear, gearbox, noise, vibration, transmiion error, bearing preload.ACKNOWLEDGEMENTS This work was carried out at Volvo Construction Equipment in Eskilstuna and at the Department of Machine Design at the Royal Institute of Technology(KTH)in Stockholm.The work was initiated by Profeor Jack Samuelon(Volvo and KTH), Profeor Sören Anderon(KTH), and Dr.Lars Bråthe(Volvo).The financial support of the Swedish Foundation for Strategic Research and the Swedish Agency for Innovation Systems – VINNOVA – is gratefully acknowledged.Volvo Construction Equipment is acknowledged for giving me the opportunity to devote time to this work.Profeor Sören Anderon is gratefully acknowledged for excellent guidance and encouragement.I also wish to expre my appreciation to my colleagues at the Department of Machine Design, and especially to Dr.Ulf Sellgren for performing simulations and contributing to the writing of Paper D, and Dr.Stefan Björklund for performing surface finish measurements.The contributions to Paper C by Dr.Mikael
Pärinen are highly appreciated.All contributionsto this work by colleagues at Volvo are gratefully appreciated.1 INTRODUCTION 1.1 Background Noise is increasingly considered an environmental iue.This belief is reflected in demands for lower noise levels in many areas of society, including the working environment.Employees spend a lot of time in this environment and noise can lead not only to hearing impairment but also to decreased ability to concentrate, resulting in decreased productivity and an increased risk of accidents.Quality, too, has become increasingly important.The quality of a product can be defined as its ability to fulfill customers’ demands.These demands often change over time, and the best competitors in the market will set the standard.Noise concerns are also expreed in relation to construction machinery such as wheel loaders and articulated haulers.The gearbox is sometimes the dominant source of noise in these machines.Even if the gear noise is not the loudest source, its pure high frequency tone is easily distinguished from other noise sources and is often perceived as unpleasant.The noise creates an impreion of poor quality.In order not to be heard, gear noise must be at least 15 dB lower than other noise sources, such as engine noise.1.2 Gear noise This diertation deals with the kind of gearbox noise that is generated by gears under load.This noise is often referred to as “gear whine” and consists mainly of pure tones at high frequencies corresponding to the gear mesh frequency and multiples thereof, which are known as harmonics.A tone with the same frequency as the gear mesh frequency is designated the gear mesh harmonic, a tone with a frequency twice the gear mesh frequency is designated the second harmonic, and so on.The term “gear mesh harmonics” refers to all multiples of the gear mesh frequency.Transmiion error(TE)is considered an important excitation mechanism for gear whine.Welbourn [1] defines transmiion error as “the difference between
the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate.” Transmiion error may be expreed as angular displacement or as linear displacement at the pitch point.Transmiion error is caused by deflections, geometric errors, and geometric modifications.In addition to gear whine, other poible noise-generating mechanisms in gearboxes include gear rattle from gears running against each other without load, and noise generated by bearings.In the case of automatic gearboxes, noise can also be generated by internal oil pumps and by clutches.None of these mechanisms are dealt with in this work, and from now on “gear noise” or “gearbox noise” refers to “gear whine”.MackAldener [2] describes the noise generation proce from a gearbox as consisting of three parts: excitation, transmiion, and radiation.The origin of the noise is the gear mesh, in which vibrations are created(excitation), mainly due to transmiion error.The vibrations are transmitted via the gears, shafts, and bearings to the housing(transmiion).The housing vibrates, creating preure variations in the surrounding air that are perceived as noise(radiation).Gear noise can be affected by changing any one of these three mechanisms.This diertation deals mainly with excitation, but transmiion is also discued in the section of the literature survey concerning dynamic models, and in the modal analysis of the test gearbox in Paper B.Transmiion of vibrations is also investigated in Paper D, which deals with the influence of bearing endplay or preload on gearbox noise.Differences in bearing preload influence a bearing’s dynamic properties like stiffne and damping.These properties also affect the vibration of the gearbox housing.1.3 Objective The objective of this diertation is to contribute to knowledge about gearbox noise.The following specific areas will be the focus of this study: 1.The influence of gear finishing method and gear modifications and errors on noise and vibration from a gearbox.2.The correlation between gear deviations, predicted transmiion error, measured transmiion error, and gearbox noise.3.The influence of bearing preload on gearbox noise.4.Optimization of gear geometry for low transmiion error, taking into consideration robustne with respect to torque and manufacturing tolerances.2 AN INDUSTRIAL APPLICATION − TRANSMISSION NOISE REDUCTION 2.1 Introduction This section briefly describes the activities involved in reducing gear noise from a wheel loader transmiion.The aim is to show how the optimization of the gear geometry described in Paper E is used in an industrial application.The author was project manager for the “noise work team” and performed the gear optimization.One of the requirements when developing a new automatic power transmiion for a wheel loader was improving the transmiion gear noise.The existing power transmiion was known to be noisy.When driving at high speed in fourth gear, a high frequency gear-whine could be heard.Thus there were now demands for improved sound quality.The transmiion is a typical wheel loader power transmiion, consisting of a torque converter, a gearbox with four forward speeds and four reverse speeds, and a dropbox partly integrated with the gearbox.The dropbox is a chain of four gears transferring the powerto the output shaft.The gears are engaged by wet multi-disc clutches actuated by the transmiion hydraulic and control system.2.2 Gear noise target for the new transmiion Experience has shown that the high frequency gear noise should be at least 15 dB below other noise sources such as the engine in order not to be perceived as disturbing or unpleasant.Measurements showed that if the gear noise could be decreased by 10 dB, this criterion should be satisfied with some margin.Frequency analysis of the noise measured in the driver's cab showed that the dominant noise from the transmiion originated from the dropbox gears.The goal for transmiion noise was thus formulated as follows: “The gear noise(sound preure level)from the dropbox
gears in the transmiion should be decreased by 10 dB compared to the existing transmiion in order not to be perceived as unpleasant.It was aumed that it would be neceary to make changes to both the gears and the transmiion housing in order to decrease the gear noise sound preure level by 10 dB.2.3 Noise and vibration measurements In order to establish a reference for the new transmiion, noise and vibration were measured for the existing transmiion.The transmiion is driven by the same type of diesel engine used in a wheel loader.The engine and transmiion are attached to the stand using the same rubber mounts that are used in a wheel loader in order to make the installation as similar as poible to the installation in a wheel loader.The output shaft is braked using an electrical brake.2.4 Optimization of gears Noise-optimized dropbox gears were designed by choosing macro-and microgeometries giving lower transmiion error than the original(reference)gears.The gear geometry was chosen to yield a low transmiion error for the relevant torque range, while also taking into consideration variations in the microgeometry due to manufacturing tolerances.The optimization of one gear pair is described in more detail in Paper E.Transmiion error is considered an important excitation mechanism for gear whine.Welbourn [1] defines it as “the difference between the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate.” In this project the aim was to reduce the maximum predicted transmiion error amplitude at gear mesh frequency(first harmonic of gear mesh frequency)to le than 50% of the value for the reference gear pair.The first harmonic of transmiion error is the amplitude of the part of the total transmiion error that varies with a frequency equal to the gear mesh frequency.A torque range of 100 to 500 Nm was chosen because this is the torque interval in which the gear pair generates noise in its design application.According to Welbourn [1], a 50% reduction in transmiion error can be expected to reduce gearbox noise by 6 dB
(sound preure level, SPL).Transmiion error was calculated using the LDP software(Load Distribution Program)developed at the Gear Laboratory at Ohio State University [3].The “optimization” was not strictly mathematical.The design was optimized by calculating the transmiion error for different geometries, and then choosing a geometry that seemed to be a good compromise, considering not only the transmiion error, but also factors such atrength, loes, weight, cost, axial forces on bearings, and manufacturing.When choosing microgeometric modifications and tolerances, it is important to take manufacturing options and cost into consideration.The goal was to use the same finishing method for the optimized gears as for the reference gears, namely grinding using a KAPP VAS 531 and CBN-coated grinding wheels.For a specific torque and gear macrogeometry, it is poible to define a gear microgeometry that minimizes transmiion error.For example, at no load, if there are no pitch errors and no other geometrical deviations, the shape of the gear teeth should be true involute, without modifications like tip relief or involute crowning.For a specific torque, the geometry of the gear should be designed in such a way that it compensates for the differences in deflection related to stiffne variations in the gear mesh.However, even if it is poible to define the optimal gear microgeometry, it may not be poible to manufacture it, given the limitations of gear machining.Consideration must also be given to how to specify the gear geometry in drawings and how to measure the gear in an inspection machine.In many applications there is also a torque range over which the transmiion error should be minimized.Given that manufacturing tolerances are inevitable, and that a demand for smaller tolerances leads to higher manufacturing costs, it is important that gears be robust.In other words, the important characteristics, in this case transmiion error, must not vary much when the torque is varied or when the microgeometry of the gear teeth varies due to manufacturing tolerances.LDP [3] was used to calculate the transmiion error for the reference and optimized gear pair at different torque levels.The robustne function in LDP was used to analyze the sensitivity to deviations due to manufacturing tolerances.The “min, max, level” method involves aigning three levels to each parameter.2.5 Optimization of transmiion housing Finite element analysis was used to optimize the transmiion housing.The optimization was not performed in a strictly mathematical way, but was done by calculating the vibration of the housing for different geometries and then choosing a geometry that seemed to be a good compromise.Vibration was not the sole consideration, also weight, cost, available space, and casting were considered.A simplified shell element model was used for the optimization to decrease computational time.This model was checked against a more detailed solid element model of the housing to ensure that the simplification had not changed the dynamic properties too much.Experimental modal analysis was also used to find the natural frequencies of the real transmiion housing and to ensure that the model did not deviate too much from the real housing.Gears shafts and bearings were modeled as point maes and beams.The model was excited at the bearing positions by applying forces in the frequency range from 1000 to 3000 Hz.The force amplitude was chosen as 10% of the static load from the gears.This choice could be justified because only relative differences are of interest, not absolute values.The finite element analysis was performed by Torbjörn Johansen at Volvo Technology.The author’s contribution was the evaluation of the results of different housing geometries.A number of measuring points were chosen in areas with high vibration velocities.At each measuring point the vibration response due to the excitation was evaluated as a power spectral density(PSD)graph.The goal of the housing redesign was to decrease the vibrations at all measuring points in the frequency range 1000 to 3000 Hz.2.6 Results of the noise measurements The noise and vibration measurements described in section 2.3 were performed after optimizing the gears and transmiion housing.The total sound power level decreased by 4 dB.2.7 Discuion and conclusions It seems to be poible to decrease the gear noise from a transmiion by
decreasing the static loaded transmiion error and/or optimizing the housing.In the present study, it is impoible to say how much of the decrease is due to the gear optimization and how much to the housing optimization.Answering this question would have required at least one more noise measurement, but time and cost iues precluded this.It would also have been interesting to perform the noise measurements on a number of transmiions, both before and after optimizing the gears and housing, in order to determine the scatter of the noise of the transmiions.Even though the goal of decreasing the gear noise by 10 dB was not reached, the goal of reducing the gear noise in the wheel loader cab to 15 dB below the overall noise was achieved.Thus the noise optimization was succeful.3 SUMMARY OF APPENDED PAPERS 3.1 Paper A: Gear Noise and Vibration – A Literature Survey This paper presents an overview of the literature on gear noise and vibration.It is divided into three sections dealing with transmiion error, dynamic models, and noise and vibration measurement.Transmiion error is an important excitation mechanism for gear noise and vibration.It is defined as “the difference between the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate” [1].The literature survey revealed that while most authors agree that transmiion error is an important excitation mechanism for gear noise and vibration, it is not the only one.Other poible time-varying noise excitation mechanisms include friction and bending moment.Noise produced by these mechanisms may be of the same order of magnitude as that produced by transmiion error, at least in the case of gears with low transmiion error [4].The second section of the paper deals with dynamic modeling of gearboxes.Dynamic models are often used to predict gear-induced vibrations and investigate the effect of changes to the gears, shafts, bearings, and housing.The literature survey revealed that dynamic models of a system consisting of gears, shafts, bearings, and gearbox casing can be useful in understanding and predicting the dynamic behavior of a gearbox.For
relatively simple gear systems, lumped parameter dynamic models with springs, maes, and viscous damping can be used.For more complex models that include such elements as the gearbox housing, finite element modeling is often used.The third section of the paper deals with noise and vibration measurement and signal analysis, which are used when experimentally investigating gear noise.The survey shows that these are useful tools in experimental investigation of gear noise because gears create noise at specific frequencies related to the number of teeth and the rotational speed of the gear.3.2 Paper B: Gear Test Rig for Noise and Vibration Testing of Cylindrical Gears Paper B describes a test rig for noise testing of gears.The rig is of the recirculating power type and consists of two identical gearboxes, connected to each other with two universal joint shafts.Torque is applied by tilting one of the gearboxes around one of its axles.This tilting is made poible by bearings between the gearbox and the supporting brackets.A hydraulic cylinder creates the tilting force.Finite element analysis was used to predict the natural frequencies and mode shapes for individual components and for the complete gearbox.Experimental modal analysis was carried out on the gearbox housing, and the results showed that the FE predictions agree with the measured frequencies(error le than 10%).The FE model of the complete gearbox was also used in a harmonic response analysis.A sinusoidal force was applied in the gear mesh and the corresponding vibration amplitude at a point on the gearbox housing was predicted.3.3 Paper C: A Study of Gear Noise and Vibration Paper C reports on an experimental investigation of the influence of gear finishing methods and gear deviations on gearbox noise and vibration.Test gears were manufactured using three different finishing methods and with different gear tooth modifications and deviations.Table3.3.1 gives an overview of the test gear pairs.The surface finishes and geometries of the gear tooth flanks were measured.Transmiion error was measured using a single flank gear tester.LDP software from Ohio State University was used for transmiion error computations.The test rig described in Paper B was used to measure gearbox noise and vibration for the different test gear pairs.The measurements showed that disaembly and reaembly of the gearbox with the same gear pair might change the levels of measured noise and vibration.The rebuild variation was sometimes of the same order of magnitude as the differences between different tested gear pairs, indicating that other factors besides the gears affect gear noise.In a study of the influence of gear design on noise, Oswald et al.[5] reported rebuild variations of the same order of magnitude.Different gear finishing methods produce different surface finishes and structures, as well as different geometries and deviations of the gear tooth flanks, all of which influence the transmiion error and thus the noise level from a gearbox.Most of the experimental results can be explained in terms of measured and computed transmiion error.The relationship between predicted peak-to-peak transmiion error and measured noise at a torque level of 500 Nm is shown in Figure 3.3.1.There appears to be a strong correlation between computed transmiion error and noise for all cases except gear pair K.However, this correlation breaks down in Figure 3.3.2, which shows the relationship between predicted peak to peak transmiion error and measured noise at a torque level of 140 Nm.The final conclusion is that it may not be poible to identify a single parameter, such as peak-to-peak transmiion error, that can be directly related to measured noise and vibration.3.4 Paper D: Gearbox Noise and Vibration −Influence of Bearing Preload The influence of bearing endplay or preload on gearbox noise and vibrations is investigated in Paper D.Measurements were carried out on a test gearbox consisting of a helical gear pair, shafts, tapered roller bearings, and a housing.Vibration measurements were carried out at torque levels of 140 Nm and 400 Nm with 0.15 mm and 0 mm bearing endplay and with 0.15 mm bearing preload.The results shows that the bearing endplay or preload influence gearbox vibrations.Compared with bearings
with endplay, preloaded bearings show an increase in vibrations at speeds over 2000 rpm and a decrease at speeds below 2000 rpm.Figure 3.4.1 is a typical result showing the influence of bearing preload on gearbox housing vibration.After the first measurement, the gearbox was not disaembled or removed from the test rig.Only the bearing preload/endplay was changed from 0 mm endplay/preload to 0.15 mm preload.Therefore the differences between the two measurements are solely due to different bearing preload.FE simulations performed by Sellgren and Åkerblom [6] show the same trend as the measurements here.For the test gearbox, it seems that bearing preload, compared with endplay, decreased the vibrations at speeds below 2000 rpm and increased vibrations at speeds over 2000 rpm, at least at a torque level of 140 Nm.3.5 Paper E: Gear Geometry for Reduced and Robust Transmiion Error and Gearbox Noise In Paper E, gearbox noise is reduced by optimization of gear geometry for decreased transmiion error.The optimization was not performed strictly mathematically.It was done by calculating the transmiion error for different geometries and then choosing a geometry that seemed to be a good compromise considering not only the transmiion error, but also other important characteristics.Robustne with respect to gear deviations and varying torque was considered in order to find gear geometry with low transmiion error in the appropriate torque range despite deviations from the nominal geometry due to manufacturing tolerances.Static and dynamic transmiion error as well as noise and housing vibrations were measured.The correlation between dynamic transmiion error, housing vibrations, and noise was investigated in a speed sweep from 500 to 2500 rpm at constant torque.No correlation was found between dynamic transmiion error and noise.4 DISCUSSION AND CONCLUSIONS Static loaded transmiion error seems to be strongly correlated to gearbox noise.Dynamic transmiion error does not seem to be correlated to gearbox noise in speed
sweeps in these investigations.Henrikon [7] found a correlation between dynamic transmiion error and gearbox noise when testing a truck gearbox at constant speed and different torque levels.The different test conditions, speed sweep versus constant speed, and the different complexity(a simple test gearbox versus a complete truck gearbox)may explain the different results regarding correlation between dynamic transmiion error and gearbox noise.Bearing preload influences gearbox noise, but it is not poible to make any general statement as to whether preload is better than endplay.The answer depends on the frequency and other components in the complex dynamic system of gears, shafts, bearings, and housing.To minimize noise, the gearbox housing should be as rigid as poible.This was proposed by Rook [8], and his views are supported by the results relating to the optimization of a transmiion housing described in section 2.5.Finite element analysis is a useful tool for optimizing gearbox housings.5 FUTURE RESEARCH It would be interesting to investigate the correlation between dynamic transmiion error and gearbox noise for a complete wheel loader transmiion.One challenge would be to measure transmiion error as close as poible to the gears and to avoid resonances in the connection between gear and encoder.The dropbox gears in a typical wheel loader transmiion are probably the gears that are most easily acceible for measurement using optical encoders.See Figure 5.1.1 for poible encoder positions.Modeling the transmiion in more detail could be another challenge for future work.One approach could be to use a model of gears, shafts, and bearings using the transmiion error as the excitation.This could be a finite element model or a multibody system model.The output from this model would be the forces at the bearing positions.The forces could be used to excite a finite element model of the housing.The housing model could be used to predict noise radiation, and/or vibration at the attachment points for the gearbox.This approach would give absolute values, not just relative levels.REFERENCES [1] Welbourn D.B., “Fundamental Knowledge of Gear Noise −A Survey”, Proc.Noise & Vib.of Eng.and Trans., I Mech E., Cranfield, UK, July 1979, pp 9–14.[2] MackAldener M., “Tooth Interior Fatigue Fracture & Robustne of Gears”, Royal Institute of Technology, Doctoral Thesis, ISSN 1400-1179, Stockholm, 2001.[3] Ohio State University, LDP Load Distribution Program, Version 2.2.0, http://www.daodoc.com/ , 2007.[4] Borner J., and Houser D.R., “Friction and Bending Moments as Gear Noise Excitations”,SAE Technical Paper 961816.[5] Oswald F.B.et al., “Influence of Gear Design on Gearbox Radiated Noise”, Gear Technology, pp 10–15, 1998.[6] Sellgren U., and Åkerblom M., “A Model-Based Design Study of Gearbox Induced Noise”, International Design Conference – Design 2004, May 18-21, Dubrovnik, 2004.[7] Henrikon M., “Analysis of Dynamic Transmiion Error and Noise from a Two-stage Gearbox”, Licentiate Thesis, TRITA-AVE-2005:34 / ISSN-1651-7660, Stockholm, 2005.[8] Rook T., “Vibratory Power Flow Through Joints and Bearings with Application to Structural Elements and Gearboxes”, Doctoral Thesis, Ohio State University, 1995.
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