Basic Theoretical Research Of The Curve-surface Meshing Planetary Gear Drive With Small Tooth Number Difference

Gear is extremely an important key element in manufacturing equipment andnational defense industry, and is also considered to be an industrial symbol. With thedevelopment of science and technology, more attentions are paid to gear transmissionperformance such as load capacity, efficiency, reliability, accuracy, etc.. So it is ofgreatly significant to develop the study on principle of gearing and it provides thetheoretical basic and technical support for improving the gear performance.A new meshing theory namely that curve-surface meshing is proposed based on theprinciple of gearing. The general principle can be described that the smooth curveselected on one of the mated tooth surfaces with given motion law is considered as theridge line and thereby a new meshing tubular tooth surface which is establishedaccording to the enveloping method can engage with another. The curve-surfacemeshing has the characteristic of point contact and the motion process characterized byengagement with approximate pure rolling, the smaller sliding ratio, the highertransmission efficiency, etc.. can be realized through constructing the suitablecurve-surface gear pair. It has important theoretical significance and practical value tosystematically carry out the study on curve-surface meshing theory, the general designmethod, manufacturing key technology and experiment, then lays the basic of itsengineering applications.The main content of this paper is as follows:(1) The concept of curve-surface meshing is presented and its forming method isalso proposed. The geometric theory is established based on the theoretical derivation.The new generation method of tooth surface is developed in terms of the envelopingtheory that a sphere with approximate radius moves along the given equidistant one ofcontact curve. The equations of tubular tooth surfaces and contact curves are derived,and the selected conditions are also demonstrated simultaneously.(2) The definition of cycloid planetary drive with curve-surface meshing is providedand the generation method of engagement pair is also developed. The geometric theoryabout this gearing is discussed subsequently. Moreover, the general equations ofengagement pair such as tooth profile of original surface, the meshing equation, toothprofile of new generated surface, and the actual meshing curve are developed. A designexample of cycloid planetary drive with curve-surface meshing is presented and the selected conditions of parameters and its meshing characteristics are analyzed.(3) The definition and generation method of curve-surface meshing involuteplanetary transmission with small tooth difference are proposed and the geometrictheory about this gearing is also discussed. The general equations of engagement pairsuch as tooth profile of original surface, the meshing equation, tooth profile of newgenerated surface, and the actual meshing curve are developed. A design example of ispresented. Similarly, the selected conditions of parameters and the meshingcharacteristics of this gear drive are analyzed.(4) The general formula of calculation of sliding ratio between the gear pair isderived based on the equations of conjugate contact curves, and it can be applied toarbitrary engagement pair of gear drive. The sliding ratio of conventional cycloidplanetary drive and involute planetary transmission with small tooth difference arederived by means of equations of tooth profile, respectively. Then, the schematic curveof sliding ratio is got in terms of the Mathematica software. Meanwhile, the sliding ratioof curve-surface meshing cycloid planetary drive and curve-surface meshing involuteplanetary transmission with small tooth difference are also derived. The sliding ratio ofcurve-surface meshing pair is greatly reduced compared with that of conventional gearpair. It shows that the motion with approximate pure rolling can be realized between thiscurve-surface meshing pair and the transmission efficiency is also improved.(5) The models of finite element analysis aimed to curve-surface meshing cycloidplanetary drive and curve-surface meshing involute planetary transmission with smalltooth difference are built, respectively. The results are solved in terms of ANSYS solverand the characteristic of point contact is revealed according to the analysis solution.(6) The forming envelop CNC grinding method which is utilized to manufacture thetubular tooth profile of curve-surface meshing cycloid planetary drive is developed. Thereducer prototype of this gearing is researched and the structures of laboratory bench arecompleted. The confirmatory test study is also carried out and the results indicate thatthe curve-surface meshing pair can significantly improve the transmission efficiency.