Geometric Design Using Hypotrochoid and Nonundercutting Conditions for an Internal Cycloidal Gear

Abstract

This paper uses the theory of gearing to derive the mathematical model of an internal cycloidal gear with tooth difference. Whereas the outer rotor profile is based on a curve equidistant to a hypotrochoidal (or extended hypocycloid) curve, the inner rotor design generally depends upon type of use—e.g., when used as a speed reducer, it is a pin wheel. Therefore, this analysis proposes designs for both a gerotor and a speed reducer. Specifically, for an inner rotor used as a gerotor pump, it outlines a mathematical model to improve pump efficiency and derives a dimensionless equation of nonundercutting. For the speed reducer, it develops and demonstrates with numerical examples, a feasible design region without undercutting on the tooth profile or interference between the adjacent pins.

Geometry generation principle and meshing properties of a new gear drive

“…As shown in Fig.4, the coordinate systems are established according to the right-hand rule (Hwang, 2007), (Li, 2014), S f1 (O f1 -x f1 , y f1 , z f1 ) and S f2 (O f2 -x f2 , y f2 , z f2 ) are the fixed coordinate systems. Respectively, conjugate curves Γ 1 and Γ 2 are defined by using the two movable coordinate systems S 1 (O 1 -x 1 , y 1 , z 1 ) and S 2 (O 2 -x 2 , y 2 , z 2 ) which are connected to the pinion 1 and wheel 2.…”

“…Cycloid drive, which has big transmission ratio, compact size and large load capacity including high bending and contact strength, has been the popular gear reducers of small teeth difference planetary applied in precision transmission such as robot and aerospace areas (Li, 2014). A lot of researches about cycloid drives, including conjugate theory (Chang, 2003), meshing characteristics (Hwang, 2007) and mechanical properties (Biernacki, 2015), have been reported. It should be a valuable research topic that a new type of cycloid profile which have these disadvantages in the external drive can be developed.…”

Experimental vibration test of the cycloidal gearbox with different working conditions

“…The empirical equation relating to machining tolerance with backlash and effective torque ripple was presented in [4] and a mathematical model that includes kinematics parameters and machining step to output moment calculations compared with experimental data was studied in [5]. Propositions of a cycloid generation with the elimination of lobes undercutting was proposed at [6][7][8][9][10][11]. There is also some work dedicated to the power loss and efficiency calculation [12][13][14].…”

The selection of optimal parameters of gerotor pump by application of factorial experimental design

“…They have proposed a mathematical model applied to simulate the gerotor pump and cycloidal speed reducer [7][8][9]. Tong and others are the first to design non circular internal gerotor gear and develop the complete theory, as well as, the algorithm for designing non circular internal gerotor [10].…”