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Gear Noise and Vibration – a Literature Survey

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Gear Noise and Vibration – a Literature Survey GEAR NOISE AND VIBRATION – A LITERATURE SURVEY Mats Åkerblom [email protected] Volvo Construction Equipment Components AB SE–631 85 Eskilstuna, Sweden Abstract This paper is a survey of the literature on gear noise and vibration. It is divided into three parts, “Transmission error”, “Dynamic models” and “Noise and vibration measurement”. Transmission error (TE) is considered to be an important excitation mechanism for gear noise and vibration. The definition of transmission error is “The difference between the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate”. Dynamic models of the system consisting of gears, shafts, bearings and gearbox casing are useful in order to understand and predict the dynamical be- haviour of a gearbox. Noise and vibration measurement and signal analysis are important tools when experimentally investigating gear noise because gears create noise at specific frequencies, related to number of teeth and the rotational speed of the gear. Keywords: gear, noise, vibration, transmission error, dynamic models. CONTENTS 1 TRANSMISSION ERROR.................................................................................................2 1.1 Introduction to transmission error....................................................................................2 1.2 Transmission error theory................................................................................................2 1.3 Transmission error measurement.....................................................................................5 1.4 Gear inspection using transmission error measurement ..................................................7 1.5 Transmission error calculation.........................................................................................8 1.6 Correlation between calculated TE, measured TE and measured noise and vibrations 10 1.7 Other noise and vibration measurements.......................................................................14 1.8 Friction and bending moments as gear noise excitations...............................................15 2 DYNAMIC MODELS.......................................................................................................15 2.1 Introduction to dynamic models ....................................................................................15 2.2 Lumped parameter dynamic models..............................................................................15 2.3 Dynamic models of complete gearboxes .......................................................................17 2.4 Experimental investigations...........................................................................................18 2.5 Noise prediction models (equations) .............................................................................19 3 NOISE AND VIBRATION MEASUREMENT..............................................................20 3.1 Introduction to noise and vibration measurement..........................................................20 3.2 Gear noise measurement................................................................................................20 3.3 Gear fault detection........................................................................................................21 4 CONCLUSIONS................................................................................................................21 REFERENCES.....................................................................................................................22 1 1 TRANSMISSION ERROR 1.1 Introduction to transmission error The most frequently used type of gear profile is the involute. It is used for cylindrical spur and helical gears as well as for conical gears like beveloid, hypoid and spiral bevel gears. Some characteristics of involute (cylindrical) gears that have made them so common are: • Uniform transmission of rotational motion, independent of small error in centre distance. • The sum of the contact forces is constant and the direction of the total contact force al- ways acts in the same direction. • An involute gear can work together with mating gears with different number of teeth. • Manufacturing is relatively easy and the same tools can be used to machine gears with different numbers of teeth. (Applies to hobs, shaper cutters, grinding worms, shaving cut- ters but not to profile tools like milling cutters and profile grinding wheels). If the gears were perfectly rigid and no geometrical errors or modifications were present, the gears would transmit the rotational motion perfectly, which means that a constant speed at the input shaft would result in a constant speed at the output shaft. The assumption of no friction leads to that the gears would transmit the torque perfectly, which means that a constant torque at the input shaft would result in a constant torque at the output shaft. No force variations would exist and hence no vibrations and no sound (noise) could be created. Of course, in real- ity, there are geometrical errors, deflections and friction present, and accordingly, gears some- times create noise to such an extent that it becomes a problem. 1.2 Transmission error theory Transmission error (TE) is considered to be an important excitation mechanism for gear noise and vibration. The definition of transmission error made by Welbourn [20] is “The difference between the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate”. This may be expressed as angular displacement or as linear displacement at the pitch point. An example of a typical transmission error signal is shown in figure 1.1. 2 50 Pinon run out Twice per tooth-pass error Once per tooth-pass error 0 Gear run out -50 -100 Total TE -150 Tooth to tooth TE -200 Figure 1.1 Example of typical transmission error signal and its component’s. The causes of transmission error are deflections, geometrical errors and geometrical modifica- tions. Examples of deflections: • Contact deformations (hertzian) in the gear mesh • Gear teeth bending deflections • Gear blank deflections • Shaft deflections • Bearing and gearbox casing flexibility Examples of geometrical errors: • Involute alignment deviations • Involute form deviations • Lead deviations • Lead form deviations • Gear tooth bias • Pitch errors • Run-out • Error in bearing position in the casing 3 Examples of some common geometrical modifications: • Lead crowning • Helix angle modification • Profile crowning • Tip relief and root relief Transmission error can be measured statically or dynamically (low or high speed), unloaded or loaded (light or heavy load) see table 1.1. Static unloaded transmission error is the most commonly used for gear quality inspection purposes because it gives information about the gears manufacturing errors. Static loaded measurement also includes the deflections. The most relevant transmission error measurements for noise and vibration predictions are proba- bly the dynamic (loaded or unloaded). When measuring dynamic transmission error, the gears should be in the gearbox, because the dynamical properties of the system consisting of gears, shafts, bearings and casing are important. In production gearboxes it is often difficult to measure transmission error, due to the inaccessibility of free shafts [12]. Load (torque) Low High Static Static Low Unloaded Loaded Speed Dynamic Dynamic High Unloaded Loaded Table 1.1 Static/dynamic, loaded/unloaded transmission error. The frequency content of the transmission error signal is often acquired by frequency analysis using FFT (Fast Fourier Transform) [1] [6] [25]. Usually it is the tooth mesh frequency and its harmonics that causes gear noise. The once per revolution transmission error is seldom a problem itself because the frequency is relatively low, but the once per revolution transmission error, due to for example run-out, causes side- bands to the gear mesh frequency, with the frequency of tooth mesh frequency +/- the shaft rotational frequency [1]. In addition to the tooth contact frequency, there are sometimes “ghost” or “phantom” fre- quencies, as a result of cyclic errors in the master worm wheel drive in the grinding machine used to finish cut the gears. These errors are imprinted onto the gear teeth as a helix undula- tion on each tooth and they are sometimes an important source of transmission error [5]. “Phantom” frequencies may also originate from the dressing wheel, used for dressing the grinding wheel, when grinding gears [4]. The diamond grains on the dressing wheel causes undulations on the grinding wheel surface and when grinding the gear, also the gear flank surface will have undulations (waviness). These undulations typically have wavelengths of about 0.5 mm and amplitudes of approximately 4μm. 4 Kohler and Regan [7] investigated the effect of pitch errors on transmission error of a gear pair. They stated that other researchers were wrong when they assumed that if pitch errors alone are present, the frequency spectrum of the corresponding transmission error will have no component’s either at the tooth mesh frequency or any of its harmonics. It was showed (theoretically) that, in general, tooth contact harmonics of significant amplitudes will exist, except for unity contact ratio gears (εα=1). The results of Kohler and Regan [7] were ques- tioned by Welbourn [8]. The need for experimental evidence of theoretical results was em- phasised. In Welbourn’s earlier analyses of how pitch
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