Design of the conjugated straight-line internal gear pairs for fluid power gear machines

Abstract

The conjugated straight-line internal gear pair, including a pinion with straight-line profile and an internal gear with profile conjugated to the pinion profile, is the key components to the conjugated straight-line internal gear pumps. Truninger [ Truninger gear pump. Patent 3491698, USA, 1970] pointed that this kind of gear pairs leads to a very small trapped volume, which is 10 times smaller than that of the conventional involute internal gear pumps. Therefore, it can yield significant reduction in noise levels of the pumps. However, to the authors’ knowledge, there is no research on the design of these gear pairs until now. First, our study describes the straight-line profile of the pinion mathematically with definitions of some geometric parameters. Second, according to the theory of gearing, the mathematical models of the rack-cutter and the conjugated internal gear are derived. Then, the condition to avoid overcutting is obtained for the generation of the pinion by a rack-cutter. Finally, the condition to avoid interference in the internal gear pair is derived as a non-linear equation system and an algorithm is developed to find a numerical solution. Two examples are presented to demonstrate how to determine tooth numbers of the internal gears for avoiding interference. It is hoped that the study in this article should be helpful to the designers of the conjugated straight-line internal gear pairs. Moreover, it could provide a prepared knowledge for the researchers to investigate the performances of the fluid power gear machines, pumps, and motors, with the conjugated straight-line internal gear pumps.

Lumped Parameters Model of a Crescent Pump

“…With reference to the Figure 3 and according to the Equation (6) the square of the vector ray belonging to the driving gear relative to the contact point P 1 is: (13) while for the driven gear the vector ray is:…”

“…The same authors [12] optimized the floating plate for the axial clearance compensation of a water hydraulic internal gear pump by means of a finite element analysis. Moreover, in [13] the authors studied the conjugated straight-line profiles for internal gear pumps, with a specific focus on the non-interference condition.…”

Investigation of fluid delivery and trapped volume performances of Truninger gear pump by a discretization approach

“…Before the derivation of the line of action, the mathematical models of the conjugated straight-line internal gear pair obtained in the Song and Zhou 31 are listed in the following…”

“…Although the Truninger gear pumps have such extraordinary performances in the fluid noise and service life, few literatures have been found for the systematical investigation on the flowrate characteristics of Truninger gear pumps. In the previous article, 31 the authors derived the mathematical models of the conjugated straight-line internal gear pairs and also carried out overcutting and interference analysis based on the gearing theory. 32 With those mathematical models, this article presents a discretization approach to obtain the fluid delivery and trapped volume performances of Truninger gear pumps.…”

Generation and Meshing Analysis of a New Type of Double Helical Gear Transmission

“…The analytical model was proposed to capture the excitation from tooth profile modifications at the sunplanet and ring-planet meshes. Song et al [9] designed the conjugated straight-line internal gear pairs for fluid power gear machines. The conjugated straight-line internal gear pair includes a pinion with straight-line profile and an internal gear with profile conjugated to the pinion profile.…”