Shigeki Matsumura

Utilization of synchronous averaging for inspection of tooth surface undulations on gears (localization of nonmesh harmonic components to individual gear)

Cyclic undulation of the gear tooth surface is one of the important sources of gear noise and vibration. It has been known that vibration caused by this source can appear at the nonmesh harmonic frequency components (ghost components). As there are no relationships between the frequency of this vibration and any gear specifications, the gear noise source is hard to detect. This paper proposes the utilization of the synchronous averaging technique for diagnosis of the source of nonmesh harmonic vibration components on a gear pair, and shows the possibility of using this technique for inspection of tooth surface undulation. The method for practically applying this technique is discussed in detail. Results demonstrated in the form of spectrum showed good agreement with the undulation assessed from precise tooth surface measurement over the whole surface of every tooth. The effect of the direction of the arrangement of cyclic undulation on tooth surface and gear vibration is also discussed in this paper. Finally the limitation to the synchronous averaging technique was discussed with respect to gear ratio.

Estimating Gear Tooth Surface Geometry by Means of the Vibration Measurement: Distinction of the Vibration Characteristics of Gears With Tooth Surface Form Error

Tooth surface measurement is an important way to verify the quality of produced gears. To reduce inspection time and cost, only a few tooth profiles and traces on some teeth are inspected. Measured data are not likely representatives of all gear teeth because errors may occur in assembly procedure and affect tooth contact condition. Frequently, tooth surface measuring data cannot show contact condition and used to predict gear vibration accurately. Field inspection method whose measured results relate directly to the messing condition is required. This paper derives the relationship between meshing vibration components and the common gear tooth surface geometries of helical gears. The tooth surface geometries considered here are lead crowning, profile convex, pressure angle error, and bias-in modification. The polar plot representation, which plots meshing components in a complex plane, is proposed here to distinguish vibration characteristics of gears with various tooth surface forms. It is found that the vector of the second order of meshing component is valuable for classifying the type of tooth surface geometry.

Estimation Method of Mesh Excitation Waveform of a Gear System (Hybrid Estimation With Vibration Measurement and Simulation)

We propose estimation method of frequency response function and mesh excitation waveform combining vibration measurement and simulation. It can be used to estimate tooth surface contacting condition on running gear unit. It may become possible to verify gear vibration simulation. For the verification of proposed method, vibration measurements are done both on the driven gear and on the gearbox simultaneously. Though frequency response functions are different between these two measurement results, estimated excitation wave form become almost the same as expected.Copyright

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.

An Alternative Method for Evaluating Gear Tooth Surface Geometry Based on Synchronous Average of Vibration of a Gear Pair

Low noise and vibration in the gearing operation is always required. Inspection by measuring gear tooth surface is a common way to investigate the source of noise and vibration. However many problems probably occur during assembling procedure, or are attributed to the bearing condition of the tooth pairs that certainly cannot be detected when inspecting each gear separately. In this paper, the newly developed method to evaluate gear tooth surface geometry based on vibration measurement is proposed. This method can be done in field. Moreover measured vibration also relates directly with the tooth bearing condition. In this method, vibration of the gear pair is measured and processed by the synchronous averaging technique to extract only the signal of interest. Then the system transfer function obtained experimentally is applied to the averaged-meshing vibration to estimate vibration excitation. Consequently tooth surface geometry directly relating with the vibration excitation can be inversely evaluated. The effectiveness of this method was verified by many experiments done by measuring the vibration of helical gears with various kinds of tooth surface forms at various operating conditions. The evaluated vibration excitations were plotted in the polar coordinate. The changes of amplitude and phase angle of the second order components were found to be suitable and could be used as an indicator to evaluate gear tooth surface form.Copyright

Pressure Measurement of Ambient Air in the Root Space of Helical Gears for the Purpose of Understanding Fluid Flow to Improve Lubrication Efficiency

Lubricant supply in gearing gives excess power loss due to churning as well as lubrication system. Since the behavior of lubricant at the mesh region is still unclear, much greater amount of oil than required is used for cooling because most part is thrown away by centrifugal force. For lower loss due to lubrication, it is necessary to discover the location of supplying nozzle. Authors have measured the pressure variation during the mesh process, which will give us an idea how we can deliver the lubricant properly with minimal but efficient cooling. Pressure measurement was done for several pairs of helical gears, that had a pressure gage installed at the bottom of root space. A sucking action is found to distribute along the tooth width especially at the recess side of meshing. Although there is global axial flow due to helix angle, which is directed from the leading side towards the trailing side, there is the opposite flow at a part at the trailing side.Copyright

Utilization of Synchronous Averaging of Vibration for Diagnosis of Gear System to Estimate Tooth Error

Generally, gear vibration behavior has base frequencies equal to meshing frequency and its harmonics. But it has become known that slight undulation even on ground gear surface sometimes generate peculiar vibration behavior that is non-integer order of meshing frequency, and it is called ‘ghost noise’. In the normal cases, the gear pair that is the source of vibration can be located by considering mesh frequencies of each gear pair and their harmonics. But if ghost noise components exist, it becomes difficult to detect which gear pair is the source. Therefore diagnosis method to detect ghost noise source with measuring vibration is required. In this study, we proposed the utilization of synchronous averaging to distinguish the source of ghost noise components. With this method, we could separate the effect of driving and driven gear from each other. The estimation results with synchronous averaging were verified with precise tooth surface measurements.Copyright

Experimental Investigation of the Possibility of a Self-Vacuuming Gearbox for Reducing Windage Loss

Reducing windage loss can be achieved by vacuuming the gear box. This study examines the possibility of implementing a gear pump characteristic with a working helical gear pair inside the gear box itself. An air-tight gear box is constructed and its vacuuming ability, windage loss, and temperature rise in speed range up to 60 m/s are investigated. The vacuuming ability is satisfactory, as it can reduce the pressure to less than 0.02 MPa (absolute), but large heat is generated by adiabatic compression associated with the temperature elevation of about 200°C. This presents excess loss and is due to the pressure difference before and after mesh engagement. Since this loss is proportional to the speed, further higher-speed condition will make total loss smaller than the expected windage loss which is proportional to the third power of the speed. In addition, this self-vacuuming ability can be improved with the assistance of a small vacuum pump to maintain the interior pressure at the beginning of engagement as small as possible. Finally, the feasibility of lubricant feeding is also examined.Copyright

A discussion on feeding cooler lubricant to the mesh exit region of a helical gear pair based on flow visualization experiments

Efficient lubrication for cooling of tooth surfaces immediately after meshing, when a rather wide helical gears runs fast, is discussed. Focusing mesh recess region the transparent helical gear pair was examined in water to realize slower dynamic motion of medium. Flow visualization results are introduced with using dispersed/injected particles and summarized. After clarifying the suction movement at mesh ending region, optimal way to feed lubricant to the tooth surfaces is discussed. Especially, the smaller the drop size of oil, the greater the effect of fluid motion due to suction on the oil delivery.

Dynamic Behavior of Helical Gears with Effects of Shaft and Bearing Flexibilities

This study presents a numerical model of helical gears to consider the effects of shaft and bearing flexibility. A primary feature of this study is that the time-varying mesh stiffness is not just determined by the geometry of gear pair but also updated for each iteration according to the change of center distance. The effects of shaft and bearing flexibilities are discussed by comparing the dynamic response of gear pairs supported with a rigid and a flexible bearing-shaft system. The results show that the pressure angle and contact ratio are significantly changed due to the center-distance variation of gears and the gear pair with a flexible bearing-shaft system has much larger vibration. Finally, experimental tests are conducted to validate the proposed model. The predicted results show good agreement with the experimental data.