Modeling of the Meshing of Trochoidal Profiles With Clearances
01 Apr 2012-Journal of Mechanical Design (American Society of Mechanical Engineers)-Vol. 134, Iss: 4, pp 041003
TL;DR: In this article, the authors developed a general mathematical model of trochoidal gearing that can be applied for Gerotor pumps and cyclo reducers, where the inner gear profile is described by peritrochoid equidistance and the outer gear profile by circular arc.
Abstract: This paper explains development of the general mathematical model of trochoidal gearing that can be applied for gerotor pumps and cyclo reducers. The model analyzes geometry and physics of the gearing pair in trochoidal pump where the outer gear has one tooth more than the inner gear. The inner gear profile is described by peritrochoid equidistance and the outer gear profile by circular arc. Mathematical model of gearing with clearances is based on the principle of an ideal profile development. Minimum clearance height between teeth profiles in relation to instantaneous gear ratio is determined. The influence of gear profile geometrical parameters on gearing process, clearance height change, and pulsation of drive moment is analyzed and presented in numerical examples. Obtained results can be used for the design of the trochoidal gearing where accurate and silent operation is required. [DOI: 10.1115/1.4005621]
Citations
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TL;DR: In this article, a review of the different methodologies used in the last years for the simulation of the flow rates generated by Gerotor, external gear and crescent pumps is presented.
Abstract: Gear pumps represent the majority of the fixed displacement machines used for flow generation in fluid power systems. In this context, the paper presents a review of the different methodologies used in the last years for the simulation of the flow rates generated by gerotor, external gear and crescent pumps. As far as the lumped parameter models are concerned, different ways of selecting the control volumes into which the pump is split are analyzed and the main governing equations are presented. The principles and the applications of distributed models from 1D to 3D are reported. A specific section is dedicated to the methods for the evaluation of the necessary geometric quantities: analytic, numerical and Computer-Aided Design (CAD)-based. The more recent studies taking into account the influence on leakages of the interactions between the fluid and the mechanical parts are explained. Finally the models for the simulation of the fluid aeration are described. The review brings to evidence the increasing effort for improving the simulation models used for the design and the optimization of the gear machines.
76 citations
TL;DR: In this article, a method for analyzing the contact dynamics of the multi-tooth meshing in a cycloidal-pin gear transmission was proposed considering the influences of the turning-arm cylindrical roller bearing.
65 citations
TL;DR: In this article, a system dynamics analysis model of a cycloidal speed reducer is constructed, together with dynamics analysis models for two design types: a traditional pinwheel design and a nonpinwheel design (i.e., a design in which a cycloid internal gear replaces the pinwheel).
Abstract: Cycloidal speed reducers are composed primarily of an eccentric shaft, output parts, and a set comprising a cycloidal gear and pinwheel with pins or a cycloidal gear and cycloid internal gear. This paper investigates the contact and collision conditions of these components, as well as their stress variations during the transmission process. To do so, a system dynamics analysis model of a cycloidal speed reducer is constructed, together with dynamics analysis models for two design types: A traditional pinwheel design and a nonpinwheel design (i.e., a design in which a cycloid internal gear replaces the pinwheel). Based on the theory of gearing, a mathematical model of the pinwheel with pins, cycloidal gear, and cycloid internal gear is then built from which the component geometry can be derived. These dynamics analysis models, constructed concurrently, are used to investigate the components' movements and stress variations, and determine the differences between the transmission mechanisms. The results indicate that the nonpinwheel design effectively reduces vibration, stress value, and stress fluctuation, thereby enhancing performance. An additional torsion test further suggests that the nonpinwheel design's output rate is superior to that of the traditional pinwheel design.
61 citations
TL;DR: A computer-aided procedure using the Monte Carlo method is established to analyze the distribution of kinematic error and tolerance design of cycloidal gear reducers and the tolerances of the parameters are optimized with the objective of minimizing the manufacturing cost.
61 citations
TL;DR: In this paper, a generalised dynamic model is proposed for bearing-cycloid-pinwheel transmission mechanisms (BCPTMs) that are used in robot joint rotate vector (RV) reducers, which can be used to investigate the effect of changing the geometrical design parameters of the cycloidal gear and turn-arm bearings on the dynamic contact response and internal load transmission characteristics.
57 citations
References
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TL;DR: In this article, the generation and design of cycloidal gearings that have found application in Wankel engine, Root's blowers and pumps are considered, and computer programs in support to proposed analytical solutions have been developed.
126 citations
"Modeling of the Meshing of Trochoid..." refers methods in this paper
...They derived parametric equations of cycloid and equidistance in addition to equations for curvature radius and stationary points of cycloid [15]....
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TL;DR: In this article, the effect of machining tolerances on backlash and torque ripple on cycloidal speed reducer was investigated and it was found that both the backlash and the torque ripple are inherent periodic functions of the input crank angle.
Abstract: The cycloidal speed reducer, or cycloid drive, is an epicyclic gear train in which the profile of the planet gear is an epitrochoid and the annular sun gear has rollers as its teeth. The cycloid drive has very high efficiency and small size, in comparison with a conventional gear mechanism, making it an attractive candidate for limited space applications. In this paper an analytical model is developed which models the cycloid drive with machining tolerances. Consequently, the effect of machining tolerances on backlash and torque ripple are investigated. It is found that both the backlash and the torque ripple are inherent periodic functions of the input crank angle
96 citations
"Modeling of the Meshing of Trochoid..." refers background in this paper
...The angle between theoretical and real position of the inner gear is called the lag angle [9], and it is marked as Dhi on the Fig....
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...[9–11], authors present different approaches to cycloid reducers design and provide the complex analysis of their profiles, effects of tolerances to clearances and consequent torque pulsations, as well as stress analysis, all aimed at their optimization....
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TL;DR: In this article, a new geometry of the rotor profiles of a cycloidal pump is proposed to provide that only one pair of teeth is in mesh at every instant, and to avoid tooth interference and rapid wearing that occur in the case of a conventional pump whereas all the rotor teeth are in mesh.
94 citations
"Modeling of the Meshing of Trochoid..." refers background in this paper
...[20]...
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...They also identified analytical conditions for appearance of singularity points at theoretical cycloidal profiles and conjugated envelope and developed software for analysis of contact conditions of gearing pairs [20]....
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TL;DR: In this paper, a unified set of equations is presented to optimize cycloid drive design, including profile reduction, backlash and torque ripple, and maximum gear-ratio, and stress, efficiency, and moment of inertia.
Abstract: Cycloid drives are compact, efficient speed reducers. In this paper, a unified set of equations is presented to optimize their design. The conceptual framework and profile design are described. Sources and effects of tolerance are then introduced, including profile reduction, backlash and torque ripple, and maximum gear-ratio. Equations for stress, efficiency, and moment of inertia are provided.
92 citations
"Modeling of the Meshing of Trochoid..." refers background in this paper
...[9–11], authors present different approaches to cycloid reducers design and provide the complex analysis of their profiles, effects of tolerances to clearances and consequent torque pulsations, as well as stress analysis, all aimed at their optimization....
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TL;DR: In this paper, a two-stage cycloidal speed reducer with a simple combination of singlestage cycloid speed reducers is presented, which is characterized by good load distribution and dynamic balance.
Abstract: A new design of a two-stage cycloidal speed reducer is presented in this paper. A traditional two-stage cycloidal speed reducer is obtained by the simple combination of singlestage cycloidal speed reducers. A single-stage reducer engages two identical cycloid discs in order to balance dynamical loads and to obtain uniform load distribution. Consequently, the traditional two-stage reducer has four cycloid discs, in total. The newly designed two-stage cycloidal speed reducer, presented in this paper, has one cycloid disc for each stage, that is, two cycloid discs in total, which means that it is rather compact. Due to its specific concept, this reducer is characterized by good load distribution and dynamic balance, and this is described in the paper. Stress state analysis of cycloidal speed reducer elements was also realized, using the finite elements method (FEM), for the most critical cases of conjugate gear action (one, two, or three pairs of teeth in contact). The results showed that cycloid discs are rather uniformly loaded, justifying the design solution presented here. Experimental analysis of the stress state for cycloid discs was realized, using the strain gauges method. It is easy to conclude, based on the obtained results, that even for the most critical case (one pair of teeth in contact) stresses on cycloid discs are in the allowed limits, thus providing normal functioning of the reducer for its anticipated lifetime. [DOI: 10.1115/1.4004540]
85 citations
"Modeling of the Meshing of Trochoid..." refers background in this paper
...[9–11], authors present different approaches to cycloid reducers design and provide the complex analysis of their profiles, effects of tolerances to clearances and consequent torque pulsations, as well as stress analysis, all aimed at their optimization....
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