Design of a two-stage cycloidal gear reducer with tooth modifications

Dynamic modeling and contact analysis of a cycloid-pin gear mechanism with a turning arm cylindrical roller bearing

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.

Dynamics Analysis of Cycloidal Speed Reducers With Pinwheel and Nonpinwheel Designs

Kinematic error analysis and tolerance allocation of cycloidal gear reducers

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]

Modeling of the Meshing of Trochoidal Profiles With Clearances

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]

A New Design of a Two-Stage Cycloidal Speed Reducer

Numericka i eksperimentalna analiza stanja naprezanja ciklozupcanika Izvorni znanstveni clanak U ovom radu izvrsena je analiza stanja naprezanja ciklozupcanika numerickim i eksperimentalnim metodama za najkriticniji slucaj sprezanja - slucaj jednostrukog zahvata. Ciklozupcanik predstavlja vitalni element cikloreduktora - mehanickog prijenosnika snage i gibanja novije generacije sa sve vecom primjenom u industrijskoj praksi. Izrađen je 3D kompjuterski model jednog konkretnog jednostupanjskog cikloreduktora. Zatim je definiran citav niz razlicitih numerickih modela ciklozupcanika u programskim paketima FEMAP i NASTRAN radi određivanja sto realnijeg stanja naprezanja uporabom metode konacnih elemenata (MKE). U cilju verifikacije dobivenih rezultata numerickim putem, izvrsena je eksperimentalna analiza koristenjem metode mjernih traka. Napravljen je fizicki model ciklozupcanika kao i ostalih elemenata cikloreduktora koji su s njim u direktnom kontaktu kako bi se dobili sto realniji uvjeti u postupku eksperimentalne analize. Dobiveni eksperimentalni rezultati pokazuju dobru sukladnost s numerickim rezultatima. Cak i za najnepovoljniji teorijski slucaj sprezanja (jednostruki zahvat), koji se kod cikloreduktora u praksi gotovo i ne javlja, vrijednosti naprezanja su u dopustenim granicama i osiguravaju pouzdan rad prijenosnika tijekom predviđenog radnog vijeka. Kljucne rijeci: cikloreduktor, ciklozupcanik, eksperimentalna analiza, numericka analiza

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Numerical and experimental analysis of the cycloid disc stress state

Experimental determination of fatigue properties and fatigue life of S355J2+N steel grade

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Experimental and numerical strength analysis of wagon for transporting bulk material

The problem of internal forces that occur on the cycloid disc during the cycloid speed reducer operation so far has not been considered in a way that reflects its actual workloads and stresses in the cycloid disc itself. This paper presents a dynamic analysis of the stress-strain state of a cycloid disc by using experimental and numerical methods. The following cases of meshing are presented in the paper: a single-tooth, double-tooth, and triple-tooth meshing of the cycloid disc and the ring gear. The cycloid disc was chosen for this study because it is one of the main elements and the most critical element of the cycloid speed reducer. An experimental physical model of the cycloid disc and the meshing elements of the cycloid speed reducer was made based on a previously performed 3D CAD model. The numerical analysis of the stress-strain state of the cycloid disc was performed with the identically defined external load using the transient stress method. The paper presents a comparative analysis of the experimental and numerical results, which gives a solid insight into what is happening in the cycloid disc during the cycloid speed reducer operation. The experimental and simulation results both give the results with a deviation between 3% and 15%. After the detailed analyses, it is shown that the most critical element of cycloid speed reducer are output rollers, which need further study.

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Aleksandar Disic

Papers

A New Design of a Two-Stage Cycloidal Speed Reducer

Numerical and experimental analysis of the cycloid disc stress state

Experimental determination of fatigue properties and fatigue life of S355J2+N steel grade

Experimental and numerical strength analysis of wagon for transporting bulk material

A Dynamic Analysis of the Cycloid Disc Stress-Strain State