A Coupling Dynamics Analysis Method for Two-Stage Spur Gear under Multisource Time-Varying Excitation

A new modeling method is proposed to simulate the dynamic response of a two-stage gear transmission system using the finite element method (FEM). The continuous system is divided into four modules: shaft-shaft element, shaft-gear element, shaft-bearing element, and gear-gear element. According to the FEM, the model is built with each element assembled. Meanwhile, the model considers the time-varying mesh stiffness (TVMS), bearing time-varying stiffness (BTVS), and the shaft flexibility. The Newmark integration method (NIM) is used to obtain the dynamic response of the spur gear system. Results show that vibration amplitude and the number of frequency components decrease after considering shaft flexibility through comparing the gear dynamic response under the condition of flexible shaft and rigid shaft. When the effect of bearing stiffness is considered, there will be a bearing passing frequency component in the frequency spectrum. In addition, the result shows that the simulation and experimental test of the frequency component are basically consistent. Furthermore, the theoretical model is validated against an experimental platform of the two-stage gear transmission system and the dynamic responses are compared under the condition of increasing speed. Additionally, the increase of shaft stiffness not only changes some of the dominant mode shapes (torsional mode shapes) but also makes the number of primary resonance speeds added. The method can be used to guide the design of gear systems.

THE SELECTION OF PRELOAD IN ANGULAR CONTACT BALL BEARINGS ACCORDING TO THE DURABILITY CRITERION

The regulation of the preload of angular contact ball bearings is mentioned in specialist literature, but only as a practical activity carried out based on experience, still without selection methodology. At present, there exists no widely accessible method of this load selection. Neither the literature on the subject nor catalogues of bearings producers give recommendations for the selection of this parameter, which is most often perceived intuitively. Still, it is known that its wrong selection can have a catastrophic influence on the durability of bearings. In consequence, there exists a problem of the accurate choice of preload (i.e. of such a preload that the durability of bearings will not be significantly decreased). The aim of the study is to determine the maximum preload in angular contact ball bearings by the criterion of durability, taking into account shaft flexibility and the flexibility of bearings. In order to determine a general influence of preload on fatigue life of bearings, numerous calculations were made for different locations of the plane of load.

The Influence of the Pinion-Shaft Deflection on the Dynamic Characteristics of Helical Gear Pairs

This study presents a dynamic model of helical gears for analyzing the effect of pinion-shaft flexibility on the dynamic behavior of helical gears. In the analysis, the time-varying mesh stiffness is determined in relation with the geometry of the gear pair and incorporates the deflection of the pinion–shaft. A comparison analysis is presented for the dynamic transmission error response of gear pairs supported with a rigid and a flexible shaft system. The results show that the pinion-shaft deflection must be included in the dynamic analysis since they can strongly affect the dynamic characteristics of helical gear pairs.

On the mechanics of the golf swing

A perspective of the golf swing is defined, and current knowledge of swing mechanics is reviewed. The implications of previous research are collected. A conventional arm–club simulation model is set up and used to show that an apparently important result from the literature is incorrect. The swing model is fitted, through a parametric optimization process, to data relating to expert golfers. The kinematic deficiencies of the arm–club model are pointed out and a shoulder–arm–club simulation model with shaft flexibility is developed. Parameters of the shoulder–arm–club model for best matching the expert-golfer data are found by optimization. The torques generated by the golfers are deduced. The shoulder–arm–club model is then applied for finding whether or not improvements to the observed torque histories are possible, with a positive result. A pattern for the optimal use of available driving torques is established. Scaling of the problem to help the understanding of the relationship between large and small players is studied through dimensional analysis. Several contributory conclusions are drawn.

Additional Investigations Into the Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System

Traditional rotor dynamics analysis programs make the assumption that disk components are rigid and can be treated as lumped masses. Several researchers have studied this assumption with specific analytical treatments designed to simulate disk flexibility. The general conclusions reached by these studies indicated disk flexibility has little effect on critical speeds but significantly influences natural frequencies. This apparent contradiction has been reexamined by using axisymmetric harmonic finite elements to directly represent both disk and shaft flexibility along with gyroscopic effects. Results from this improved analysis show that depending on the thickness-to-diameter (slenderness) ratio of the disk and the axial position of the disk on the shaft, there are significant differences in all natural frequencies, for both forward and backward modes, including synchronous crossings at critical speeds.