Study On Meshing Characteristics Of The Double-enveloping Planetary Gear Drive With Small Tooth Number Difference And Analysis Of Its Dynamic Behavior

Planetary gear drive with small tooth number difference has been used widely inmany industrial areas for power transmission, such as metallurgical machinery, hoistingand conveying machinery, construction machinery, chemical machinery and textilemachinery, etc., due to its superior characteristics: large transmission ratio, compactstructure, small size, light weight, high transmission efficiency and high load capacity,etc.. In recent years, it has been also used more and more widely in precisiontransmission because of its outstanding averaging effect of errors which can lead to highprecision caused by the multi-tooth meshing. In order to meet the requirement of thehigh precision and the low vibration for the gear transmission because of thedevelopment of the industrial areas, the researchers home and abroad have paid moreand more attention to the dynamic analysis of the gear transmission. Thedouble-enveloping cycloid drive with small tooth number difference is a new type ofplanetary gear drvie which is generated by the double-enveloping method based on thesecondary action phenomenon. The main characteristics of the double-envelopingconjugated tooth pair are the double contact lines simultaneously in a certain meshingarea and the good meshing characteristics. The deep and systematical research on themeshing characteristics and the dynamic behavior of the double-enveloping planetarygear drive with small tooth number difference has the theoretical significance andengineering practice value for the development and the design of the new type of hightransmission performance planetary gear drive with high effiency, high precision andlow vibration, etc..In this paper, the research is mainly on the conjugated surfaces, the meshingcharacteristics, the theoretical dynamic analysis and the experimental research about thedouble-enveloping planetary gear drive with small tooth number difference. The maincontents are as the following:(1) Based on the differential geometry and gear geometry theory, the meshcharacteristics of the double-enveloping cycloid drive are studied; the incompletedouble-enveloping cycloid drive is proposed according to the superior characteristics ofthe second contact line and the sensitivity to the errors of the double contact lines, theequations of the meshing and the tooth profiles for the incomplete cycloid drive arederived, the meshing characteristics are calculated; the characteristics of the tooth profiles, the contact lines and the induced normal curvature among the incompletedouble-enveloping cycloid drive, the double-enveloping ccycloid drive and theconventional cycloid drive are compared with each other, the results show that thedouble-enveloping conjugated tooth pair has superior characteristics than theconventional conjugated tooth pair, and the meshing characteristics of the incompletedouble-enveloping cycloid drive is a little better than that of the double-envelopingcycloid drive; the parabolic type double-enveloping conjugated tooth pair is proposedand the equations of its meshing and tooth profiles are presented.(2) The structure of the double-enveloping planetary gear drive with small toothnumber difference is creatively designed,4physical prototypes are designed andmanufactured; a physical prototype with two stages of which the second stage is thedouble-enveloping cycloid drive, is selected as the research object, the characteristics ofits structure, conjugated surfaces and the relationship among the components areanalyzed, based on the model of the sideband frequency calculation the meshingfrequencies for the two stages and the sideband frequencies are calculated.(3) The dynamic behavior of the double-enveloping planetary gear drive with smalltooth number difference is theoretically analyzed: based on the Hertz theory, the meshstiffness calculation model of the double-enveloping cycloid conjugated tooth pair isestablished, the calculation formulas of the normal stiffness, the arm length and thetorsional stiffness are derived; the meshing stiffness of the double-envelopingconjugated tooth pair for the prototype is calculated compared with that of theconventional cycloid drive, and the comparison results show that the meshing stiffnessof the double-enveloping cycloid tooth pair has both larger average value and largerfluctuation value than that of the conventional cycloid drive; based on the lumpedparameter method, the rotation vibration model with five freedoms for the physicalprototype is established and the motion equations are derived, the natural frequenciesand the modes of the free vibration are calculated, the motion equations are solved usingRunge-Kuta method under that he variation mesh stiffness is considered as the internalexcitation, the rotation vibrations of the different parts of the physical prototype areanalyzed, the natural frequencies and the vibrations are compared with that of theconventional cycloid drive, the comparision results show that the natural frequecnciesand the vibrations of the two types of cycloid drive are almost the same, and the rotationvibration of the double-enveloping cycloid drive are smaller than that of theconventional cycloid drive. (4) The experiment test rig is put up for the dynamic analysis of thedouble-enveloping planetary gear drive: firstly, based on the test principle, the generalscheme is designed; secondly, the types and the detail parameters of the motor, loaddevice and the test instrument are determined; then the equipments for the test aredesigned, such as cradle and the connection couplings; finally, the experiment test rig isinstalled and adjusted.(5) The experiment test rig is put up for the dynamic experimental research on thedouble-enveloping planetary gear drive with small tooth number difference, and thedynamic tests on the prototype are carried out including modal test, translationalvibration test and rotation vibration test of the output plate; the phenomenon of themodulation sidebands is analyzed and compared with the theoretical calculation results,the comparision results show that the experimental results and the theoretical resultshave good agreement；the experiment data of the output plate rotation vibration isanalyzed and the results show that the gear mesh vibration of the first stage of theprototype is the main source of the whole gear reducer vibration.