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Gearbox NoiseCorrelation with Transmission Error and Influence of Bearing PreloadDoctoral Thesis in Machine DesignTRITA-MMK 2008:19ISSN 1400-1179ISRN/KTH/MMK/R-08/19-SEDepartment of Machine DesignRoyal institute of TechnologySE100 44 Stockholm, Sweeden© Mats Åkerblom 2008ABSTRACTThe 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. Transmission 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 transmission error. Most of the experimental results can be interpreted in terms of measured and predicted transmission error. However, it does not seem possible to identify one single parameter,such as measured peak-to-peak transmission error, that can be directly related to measured noise and vibration. The measurements also show that disassembly and reassembly 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 transmission error. Robustness 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 transmission error, noise, and housing vibrations were measured. The correlation between dynamic transmission error, housing vibrations and noise was investigated in speed sweeps from 500 to 2500 rpm at constant torque. No correlation was found between dynamic transmission error and noise. Static loaded transmission 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, transmission error, bearing preload.ACKNOWLEDGEMENTSThis 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 Professor Jack Samuelsson (Volvo and KTH), Professor Sören Andersson (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.Professor Sören Andersson is gratefully acknowledged for excellent guidance and encouragement.I also wish to express 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 Pärssinen are highly appreciated. All contributionsto this work by colleagues at Volvo are gratefully appreciated.1 INTRODUCTION1.1 BackgroundNoise is increasingly considered an environmental issue. 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 expressed 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 impression 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 noiseThis dissertation 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.Transmission error (TE) is considered an important excitation mechanism for gear whine. Welbourn 1 defines transmission 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.” Transmission error may be expressed as angular displacement or as linear displacement at the pitch point. Transmission error is caused by deflections, geometric errors, and geometric modifications.In addition to gear whine, other possible 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 process from a gearbox as consisting of three parts: excitation, transmission, and radiation. The origin of the noise is the gear mesh, in which vibrations are created (excitation), mainly due to transmission error. The vibrations are transmitted via the gears, shafts, and bearings to the housing (transmission). The housing vibrates, creating pressure 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 dissertation deals mainly with excitation, but transmission is also discussed in the section of the literature survey concerning dynamic models, and in the modal analysis of the test gearbox in Paper B. Transmission 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 bearings dynamic properties like stiffness and damping. These properties also affect the vibration of the gearbox housing.1.3 ObjectiveThe objective of this dissertation 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 transmission error, measured transmission error, and gearbox noise.3. The influence of bearing preload on gearbox noise.4. Optimization of gear geometry for low transmission error, taking into consideration robustness with respect to torque and manufacturing tolerances.2 AN INDUSTRIAL APPLICATION TRANSMISSION NOISE REDUCTION2.1 IntroductionThis section briefly describes the activities involved in reducing gear noise from a wheel loader transmission. 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 transmission for a wheel loader was improving the transmission gear noise. The existing power transmission 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 transmission is a typical wheel loader power transmission, 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 transmission hydraulic and control system. 2.2 Gear noise target for the new transmissionExperience 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 transmission originated from the dropbox gears. The goal for transmission noise was thus formulated as follows: “The gear noise (sound pressure level) from the dropbox gears in the transmission should be decreased by 10 dB compared to the existing transmission in order not to be perceived as unpleasant. It was assumed that it would be necessary to make changes to both the gears and the transmission housing in order to decrease the gear noise sound pressure level by 10 dB.2.3 Noise and vibration measurementsIn order to establish a reference for the new transmission, noise and vibration were measured for the existing transmission. The transmission is driven by the same type of diesel engine used in a wheel loader. The engine and transmission 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 possible to the installation in a wheel loader. The output shaft is braked using an electrical brake.2.4 Optimization of gearsNoise-optimized dropbox gears were designed by choosing macro- and microgeometries giving lower transmission error than the original (reference) gears. The gear geometry was chosen to yield a low transmission 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.Transmission 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 transmission error amplitude at gear mesh frequency (first harmonic of gear mesh frequency) to less than 50% of the value for the reference gear pair. The first harmonic of transmission error is the amplitude of the part of the total transmission error that varies with a frequency equal to the gear mesh frequency. A torque range of100 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 transmission error can be expected to reduce gearbox noise by 6 dB (sound pressure level, SPL). Transmission 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 transmission error for different geometries, and then choosing a geometry that seemed to be a good compromise, considering not only the transmission error, but also factors such asstrength, losses, 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 possible to define a gear microgeometry that minimizes transmission 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 stiffness variations in the gear mesh. However, even if it is possible to define the optimal gear microgeometry, it may not be possible 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 transmission 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 transmission 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 transmission error for the reference and optimized gear pair at different torque levels. The robustness function in LDP was used to analyze the sensitivity