Dynamic Behavior of Gear Systems and Variation of Coefficient of Friction and Efficiency During the Engagement Cycle

In this work, the instantaneous and average efficiency and coefficient of friction of gear drives operating at low, medium, and moderately high speeds were experimentally and analytically investigated. First, using the gear testing machine specially designed for this type of investigation, the frictional losses in gearing during the engagement period were obtained experimentally. Based upon the obtained data, the values of efficiency and coefficient of friction were evaluated. A mathematical model simulating the gear testing machine was then developed and employed for the analysis of the dynamic behavior of the gear train system and analytical evaluation of gear system efficiency. The results obtained from this model were compared to those obtained directly from experiments, and a close correlation was achieved. The influence of such factors as diametral pitch, contact ratio, magnitude of transmitted load, and speed upon the efficiency of gear drives and the coefficient of friction in gearing was investigated. This investigation showed that the suggested method may be used to predict the dynamic behavior and efficiency of gear systems if a coefficient of friction is known or assumed. This investigation also gives some promise for power gear transmission design with improved capacity when scoring is the limiting criterion for capacity.</jats:p

A Multi-Purpose Planetary Gear Testing Machine for Studies of Gear Drive Dynamics, Efficiency, and Lubrication

Feasibility of a multi-purpose testing machine for research studies in gearing has been demonstrated with construction of a unique gear testing machine with a differential planetary gear drive. This machine was used in such interdependent studies as determination of instantaneous gear tooth engagement loads, minimum film thicknesses, and gear efficiencies. With minimal structural and mechanical modifications, this gear research machine can be used for studies of surface durability, thermal distribution in gear meshing zones, and effects of variable torques and torsional oscillations on performance of gearing. Most of these studies could be conducted simultaneously. Upon selection of appropriate gear ratios, this machine was operated either with one or two stationary gears. Presence of stationary gears simplified greatly the measurement techniques and increased the reliability of tests. This machine can accommodate spur, helical or any special type of gearing. Design and operational characteristics of this machine, as well as a short summary of research projects performed on this machine, are presented in this paper.</jats:p

The Synthesis of Tooth Profile Shapes and Spur Gears of High Load Capacity

In this work a method is presented for the synthesis of high capacity noninvolute spur gears and tooth profiles. Two gear capacity criteria are used in the synthesis: (1) the capacity based on maximum allowable Hertz stress and (2) the capacity based on the bending strength of the tooth. These capacity criteria are related to a generalized noninvolute gear geometry which includes the factors number of teeth and contact ratio. It was found that there are certain optimal relationships which exist among the noninvolute parameters which lead to a solution, for a maximum capacity noninvolute gear pair. For a speed ratio of one to five it was found that a significant capacity advantage exists for the synthesized noninvolute gear pair (compared to a 20-deg involute spur gear pair) for moderate as well as high hardness values. For a speed ratio of one to one a capacity advantage was found for moderate hardness but the advantage decreased significantly for high hardness.</jats:p

Efficiency of Gear Transmissions With Flexibly Connected Gears Subjected to Axial Vibrations

The axial vibrational motion of one of the engaged gears increases the mechanical efficiency of a gear system by reducing the frictional resistance in the plane of gear rotation. The purpose of this investigation was to determine the effect of axial vibrations on the frictional losses in gear systems which are operated under the conditions of boundary lubrication. Two basic cases were investigated: the case when all four gears were rigidly connected to the shaft, and the case in which two of the four gears in the drive were mounted to the shaft in such a manner that they had a certain degree of freedom in the axial direction. In the second case, the relative axial displacement between the engaged gears may be smaller than the amplitude of the shaft vibrations, and the effect of the axial vibrations on the frictional losses in a gear system may be reduced. The influence of the following factors upon the efficiency of the gear train were investigated: the magnitude of the force transmitted by the train, the weight of the flexibly connected gears with the masses attached to them, the frequency of the axial vibration of the shaft, and the amplitude of this vibration.</jats:p

A Method of Controlling the Shaft Misalignment in a Gear Testing Machine by “Prestressed” Externally Pressurized Journal Bearings

“Prestressed” externally pressurized journal bearings employing capillary restrictors as compensating elements are installed on a four-square gear testing machine for the purpose of investigating the frictional phenomena in gearing. The bearings are designed so that the position of the shafts can be aligned with the geometric axes of the bearings by operating the bearing system at zero, positive, or negative eccentricities. These operating conditions are made possible by employing capillary restrictors whose conductance is larger on the loaded side of the bearings than on the unloaded side. Analytical data are presented which give the load capacity, lubricant flow rate requirements, and stiffness of the bearing for given geometry of the bearing and capillary restrictors and for a given eccentricity ratio. In addition, analytical and experimental data are presented from which, for a given load, the required supply pressure can be selected so that the bearing system, on the gear testing machine, operates at zero eccentricity.</jats:p