Tooth Mesh Frequency Research Articles

Experimental assessment of the effective working area of a robot of a parallel structure with stepped motors

Negative effects arising from the operation of parallel structure mechanisms near special positions of the first kind are considered, as well as an approach that makes it possible to build effective working zones for such mechanisms in terms of speed, which is experimentally tested on a model of a five-link robot. Keywords: parallel structure mechanism, working area, vibrations, stepper motor, tooth mesh frequency, five-link mechanism.

Development and validation of a dynamic model for a two-stage speed-reducer

This paper presents the development and validation of a six degree of freedom (DOF) dynamic model of a two-stage parallel shaft gearbox, without flaws, which is able to determine the reaction of gearbox components to varying torque inputs and loads. The model utilises flexible shafts and gears rather than using a rigid assumption, to further understand the effect of varying mesh stiffness. The paper replicates the results presented by Diehl and Tang, and improves the number of frequencies that can be analysed. The gear meshing frequencies were expected to dominate the result, however due to the use of a sinusoidal approximation of the varying tooth mesh frequency, the presented model shows the additional gear generated frequencies are present and analysable in the data.

Precise modeling of complex tooth surface microtopography and multi-degree-of-freedom nonlinear friction dynamics for high-performance face gear.

Face gear transmission is a kind of space-meshing mechanism that is mainly used in the field of aviation. Compared with traditional transmission, it has the advantages of stability, reliability, low noise, and strong carrying capacity. However, owing to its complex tooth surface, there are no means to accurately model the face gear. Likewise, research based on the geometry is difficult. Therefore, the tooth surface equation of the face gear is derived in this article based on the meshing theory. Based on the equations, the point cloud of the face gear tooth surface is calculated, the complex tooth surface is generated, and the face gear is accurately modeled. Moreover, taking tooth surface friction excitation into consideration, a multi-degree-of-freedom nonlinear dynamic model of face gear transmission system is established, using the adaptive variable step length Runge-Kutta method. As shown in the results, the bifurcation diagram, phase diagram, time history diagram, and Poincaré section diagram are combined to analyze the influence of tooth surface friction and meshing frequency on the dynamic characteristics of the system.

Residual signal feature extraction for gearbox planetary stage fault detection

AbstractFaults in planetary gears and related bearings, e.g. planet bearings and planet carrier bearings, pose inherent difficulties on their accurate and consistent detection associated mainly to the low energy in slow rotating stages and the operating complexity of planetary gearboxes. In this work, statistical features measuring the signal energy and Gaussianity are calculated from the residual signals between each pair from the first to the fifth tooth mesh frequency of the meshing process in a multi‐stage wind turbine gearbox. The suggested algorithm includes resampling from time to angular domain, identification of the expected spectral signature for proper residual signal calculation and filtering of any frequency component not related to the planetary stage. Two field cases of planet carrier bearing defect and planet wheel spalling are presented and discussed, showing the efficiency of the followed approach and the possibility of characterizing a fault as localized or distributed. Copyright © 2017 John Wiley & Sons, Ltd.

Investigation on Modulation Sidebands in a K-H-V Planetary Gear with Double-Enveloping Cycloid Drive Vibration

In this paper, modulation sidebands about the tooth meshing frequency in a two stages planetary gear reducer vibration are investigated. The two stages gear reducer is developed using double-enveloping cycloid drive with a K-H-V planetary gear. Firstly, the double-enveloping cycloid drive and the meshing characteristics are introduced. Secondly, the meshing frequencies and the sidebands of this prototype gear reducer are calculated based on a model, which explains the modulation in terms of the motion of the planets relative to the location of the transducer. Thirdly, the experiment vibration spectrums are compared with the calculated results. And the comparisons between the simulation and calculation results show good agreement.

Torsional Vibration of Machines with Gear Errors

Vibration and noise induced by errors and faults in gear meshes are key concerns for the performance of many rotating machines and the prediction of developing faults. Of particular concern are displacement errors in the gear mesh and for rigid gears these may be modelled to give a linear set of differential equations with forced excitation. Other faults, such as backlash or friction, may also arise and give non-linear models with rich dynamics. This paper considers the particular case of gear errors modelled as a Fourier series based on the tooth meshing frequency, leading immediately to non-linear equations of motion, even without the presence of other non-linear phenomena. By considering the perturbed response this system may be modelled as a parametrically excited system. This paper motivates the analysis, derives the equations of motion for the case of a single gear mesh, and provides example response simulations of a boiler feed pump including phase portraits and power spectra.

1217 振動法と油中摩耗粉検知による歯車故障診断(OS1-5 振動(3))

To prevent the machine plant from breaking down, there are many methods such as acoustic emission, vibration, noise, ultrasound, temperature, and so on. In this study, both vibration method and detection of iron powder in the oil using magnet were applied to detect the failure of steel gear sets. The wavelet Transform (WT) is a method for the time-frequency analysis. A failed tooth could be found out by the change of WT intensity of the vibration acceleration, giving attention to the frequency band near the tooth meshing frequency. When the plural teeth were failed by pitting, the output of the iron powder sensor using magnet was changed. However, the increase in the iron power did not detected at the initial fatigue stage.

Application of the wavelet transform to health monitoring and evaluation of dynamic characteristics in gear sets

This paper deals with health monitoring and evaluation of dynamic characteristics in gear sets. The wavelet transform (WT) is the method used for the time-frequency analysis. The dynamic characteristics of both steel and sintered gears were measured using a power circulating gear testing machine and were analysed in the time-frequency domain using continuous and discrete WTs. Furthermore, health monitoring of gear sets was carried out and tooth surface failure by pitting was diagnosed using WTs. The vibration acceleration characteristics of the gearbox could be divided into two different behaviours above and below the tooth mesh frequency. A failed tooth could be found by a change in WT intensity of the vibration acceleration, taking the tooth meshing into consideration. Since the discrete WT is able to provide the signal with the component of tooth mesh frequency, it was found to be superior to the continuous WT. In the case of failure at the dedendum surface of a driven gear, the amplitude of the vibration acceleration with the component of tooth mesh frequency became larger as after meshing of the failed tooth. Therefore, not only the vibration of the gear sets but also the condition of tooth meshing would have to be taken into consideration to diagnose failed teeth.

Evaluation Method of Gear Dynamic Performance Using Information in Time-Frequency Domain.

The wavelet transform (WT) is a method for the time-frequency analysis of signals. It is possible to detect the change in each frequency through a sampling period by the WT. In this study, in order to discuss an evaluation method for the gear dynamic performance using the time-frequency analysis, the dynamic performance of both sintered and steel gears were measured using a power circulating gear testing machine in the range of the rotational speeds of 1600 to 10000 rpm. The measured signals of dynamic performance, which are tooth root strain, vibration and sound of gear box, were analyzed in the time-frequency domain by the continuous WT based on the Gabor function, and the signals of the dynamic performance were decomposed and reconstructed by the discrete WT based on the cardinal B-spline function. The validity on the new evaluation method using both continuous and discrete WTs was discussed. The dynamic performance can be divided between two frequency regions over and under the tooth mesh frequency fz. Consequently, it was clarified that the dynamic performance over the fz indicated the condition of the torsional vibration of gear system, and the dynamic performance under fz depended on the rotational speed of gear.

Behavior of Aerodynamic Sound of Spur Gears : Determination of Similarity Law and Source Locations

Tooth mesh frequency sound generated aerodynamically in the region of meshing was investigated to determine the general characteristics of the sound emission as well as its detailed source locations. Sound pressure response measurement for various facewidths revealed that emission is expressed in terms of a similarity law as a function of a parameter b/λ, the ratio of facewidth to wavelength of the sound. The effect of dimensions such as the module and number of teeth were derived by means of a dimensional analysis with respect to pumping action of the cavity between driving and driven gears. Throughout several kinds of experiments, one source was located at the middle of the meshing exit, which becomes prominent as the axial air flow reaches a certain speed. Another source is estimated to spread over both faceends, of which the radiation characteristics are closely related to the distribution and the solid boundary of the gear pair.

Reduction of Partial-Load Rattling Noise of an Oil-Injected Screw Compressor.

This paper describes a study of partial-load rattling noise of an oil-injected air screw compressor and its reduction method. Rotational vibrations of the male and female rotors were measured to detect the noise source. Relative rotational angle between the rotors greatly oscilated in a sharp sawtooth wave form of tooth-meshing frequency, corresponding to the rattling noise emission. The observations indicate that the rattling noise comes from the tooth separating vibration of the rotors due to decrease in the transmission torque. A rotor profile was so selected that the transmission torque never became negative even at a no-load operation, and this profile was applied to the compressor. As the result, neither rattling noise nor abnormal rotational vibrations were generated at partial load, as well as at full load.

Behavior of Aerodynamic Sound of Spur Gears. Determination of Similarity law and Source Locations.

Tooth mesh frequency sound generated aerodynamically at the region of meshing was investigated to find out a genaral characteristis of the sound emissioin as well as its detailed source locations. Sound pressure response measurement for various facewidth revealed that emission is expressed in terms of a similarity law as a function of a parameter b/λ, the ratio of facewidth to the wavelength of the sound. The effect of dimensions such as module, number of teeth were derived by means of a dimensional analysis with respect to a pumping action of the cavity between driving and driven gears. Throughout several kinds of experiments, one source is located at the middle of the exit of meshing, which becomes prominent ad the axial air fiow reaches to a certain speed. Another source is estimated to spread over both face ends, whose radiation characteristics are closely related to the distribution and the solid boundary of the gear pair.

Representative form accuracy of gear tooth flanks on the prediction of vibration and noise of power transmissions.

In order to develop a better method of predicting gear noise of automotive power transmission as a function of gear accuracy, the correlation between the amplitude of the tooth mesh frequency component of measured noise and that of the simulated single flank rolling test of gears using the measured form accuracy of the tooth flank was investigated. Experimental and simulated results show, when the worst composite error surface of meshing tooth flanks is chosen as representative among many different composite error surfaces for possible combinations of meshing tooth pairs and the simulation is worked out under the hypotheses, that this worst composite error surface exists at every meshing of teeth, a very good correlation between simulated results of the single flank rolling test of the pair of gears and measured noise level of power transmission can be obtained. This result indicates that the development of the gear production method to minimize the scattering of deviation of tooth flank accuracy at each tooth of a gear is more effective in producing noiseless power transmission than in improving the average quality of tooth flank accuracy of gears.

Examination of a technique for the early detection of failure in gears by signal processing of the time domain average of the meshing vibration

An existing technique for the signal processing of the time domain average of the tooth meshing vibration of gears is examined with application to the early detection of failure. It is shown that the “regular” signal extracted from the time domain average of the gear vibration by the elimination of all except the fundamental and harmonics of the tooth meshing frequency forms the time domain average of the vibration of a single tooth. The “residual” signal which is obtained by subtracting the regular signal from the original time domain average gives the departures of the vibration from the average. Numerical and practical examples are given.

The sound radiated from gears. On the existence of aerodynamic sound.

The behaviour of tooth mesh frequency sound radiated from a tooth mesh point of a spur gear pair was investigated to see how it is generated. after examining the effect of bottom clearance, torque and material (steel or nylon) upon the radiation, the sound proved to be an aerodynamic sound; i.e., the sound is born from the pumping action of the clearance between meshing teeth, under high speed conditions. Especially towards the exit side of meshing, the radiation is prominent, with a level trough feature, which occurs due to the existence of two sorts of sounds having a phase difference of 180° near the meshing point. It has also become clear that this aerodynamic sound can not necessarily be reduced by increasing the clearance, after a consideration based on an analogy to the fluctuation of the flow rate of a gear pump.

The sound radiated from gears. 2nd, report On the existence of aerodynamic sound.

The behaviour of tooth mesh frequency sound radiated from a tooth mesh point of a spur gear pair was investigated to see how it is generated. After examining the effect of bottom clearance, torque and material (steel or nylon) upon the radiation, the sound proved to be an aerodynamic sound ; i.e., the sound is born from the pumping action of the clearance between meshing teeth, under high speed conditions. Especially in the direction of the exit side of meshing, the radiation is prominent, with a feature of level trough, which occurs due to the existence of two sorts of sounds having the phase difference of 180° nearby the meshing point. It has become also clear that the aerodynamic sound can not necessary be reduced by increasing clearance, after an analogical consideration on the fluctuation of the flow rate of a gear pump.

An Explanation for the Asymmetry of the Modulation Sidebands about the Tooth Meshing Frequency in Epicyclic Gear Vibration

The vibration spectra of epicyclic gears commonly exhibit considerable asymmetry of the modulation sidebands and even complete suppression of the component at the tooth meshing frequency. A model is proposed which explains these observations in terms of the relationship between the vibrations generated by each of the planet gears as they move relative to the transducer location. Comparisons of the predictions of the model with measured vibration spectra for several epicyclic gearboxes show good agreement.

歯車の偏心誤差と騒音スペクトル(第2報)

In gears with eccentric errors, the tooth-meshing frequency is subjected to both amplitude modulation and frequency modulation at the same time. Consequently, the noise spectrums consist of a large number of sidebands. The general equation about sideband levels is derived in the case the modulation signals include the high order harmonics of the angular frequency of the eccentric gear. The value of the parameter in the general equation is estimated from the change of the amplitude of the tooth-meshing noise and the fluctuation of the angular velocity of the input and the output shaft. The appropriateness of the general equation is shown by comparing the spectrum of the actual tooth-meshing noise with the calculated one by the general equation.

On the Running Noise of Toothed Belt Drive : 1st Report, Mechanism of Noise Generation

As the first step to find the noise reduction methods for toothed belt drive, the authors investigated the characteristics of the noise and its generating mechanism experimentally. The results obtained are as follows: (1) In general running condition the impact sound which is generated periodically with tooth meshing frequency is the most powerful component in the noise. And it was ascertained that the impact sound is caused by the collision of tooth tips of the driving wheel against bottom lands of the toothed belt. (2) When the belt tension is large enough the transverse vibration (string vibration) of belt resonates badly with the meshing frequency and this resonant sound sway the noise level. (3) In a case where both impact and resonant sound are not predominant, the toothed belt drive runs silent enough.