Meshing Theory Investigations On Composite Cycloid Gear Transmission

The earliest applied cycloid profile curve has been used widely in many industrial machinery,such as roots pumps,helical-lobe compressor,horologe,instruments,cycloid-pin reducer,cycloid pump.However,due to lower carrying capacity and contact ratio,external cycloid gear drive is not suitable for power transmission.Gear transmission performances are determined largely by conjugate profile curves.Therefore,in order to improve the insufficient and transmission performance of tradition drive type,investigations on the geometric design and meshing theory of new profile curve are the key to solve these problems.In this paper,the composite cycloid,that has a relatively strong controllability in geometry,is put forward by explaining cycloid principle with trajectory curve of equivalent link mechanism.With the composite cycloid application on geometrical element,the profile curve is constructed.After that the high performance gear drive types are proposed,including composite cycloid external gear and small tooth difference planetary drive.Then,the research is mainly focused on the conjugated mesh theories,meshing properties,mechanical loading properties and planetary gear design study.The researching contents construct an important part and a key element of innovation and development for gear basic research,and these contents also have great theoretical significance and engineering practice.In this thesis,the prime contents are as follows.?1?The geometric theory of composite cycloid that can be applied on tooth profile of gear transmission are studied.The cycloid principle is deduced.Geometrical mechanism of cycloid evolution is revealed.And an equivalent link mechanism is developed to describe the geometric principle of cycloid by introducing the motion transforming method.The new cycloid type is defined by introduced the concept of order.Then the path curve of n-order cycloid motion is raised using n+1 link generalized mechanism.Geometrical conditions that new cycloid can be applied as profile in both external meshing drive of parallel axis and internal tooth with small tooth difference planetary drive.Theoretical expansion accordingly,motion laws of n-order epicycloid,n-order hypocycloid and n-order composite cycloid are came up with n+1link in expansibility.The mathematic relation model between equation variables and profile design parameters of composite cycloid.Using both qualitative analysis of equation variables and quantitative analysis of profile case,geometric characteristic of composite cycloid profile are studied.The research results shows that forth order composite cycloid has a relatively strong controllability in geometry and utilization potentiality of transmission gear profile.?2?Meshing theory investigations on composite cycloid cylindrical gears for external driving are carried out.Its conjugate meshing theory is established by deduced meshing equation,conjugate profile equation and meshing line equation.The meshing properties,such as pressure angle,contact ratio,curvature,undercut and sliding ratio of the composite cycloid gear driving are conducted.The composite cycloid gears are modeled,and the strength characteristic of this drive is evaluated by FEM method simultaneously.In research results,the relationship between the pressure angle of reference circle and regulation coefficient f₁ of tooth profile is obtained.Meanwhile,meshing properties and mechanics properties,including concave-convex tooth surface meshing in line contact,greater contact ratio,smaller sliding ratio and relatively higher both bending stress and contact stress of the new gear,are represented.?3?Experimental investigations on transmission efficiency of composite cycloid gear with external meshing are completed.In order to test transmission efficiency accurately,and in view of the low test precision of load torque and only double rotational speed control of standard FZG gear test bed.Based on this FZG test bed,the new gear test bed which has the function of double torque sensors and variable speed is proposed.The torque sensor is added at the pinion of test gearbox to test transmission efficiency accurately,the bigger power and high speed servo motor is employed to realize more working condition speeds.Then the new gear test bed is set up,gear samples are machined,and transmission efficiencies under different operating conditions are measured in the test rig.The results indicate that the higher transmission efficiency show a remarkable engineering application value.The basic conditions that this new gear can be served on power transmission are verified,and the basic experimental datas on this new gear are acquired?4?Meshing theory investigations on small tooth difference planetary drive with composite cycloid internal tooth profile are performed.The meshing equation of conjugate gear drive,the conjugate profile equation with small tooth difference and action line equation are deduced to establish its basic meshing principle.Based on it,the solving method on the meshing boundary point and the actual meshing profile of composite cycloid internal profile is presented.And the analysis of meshing boundary properties based on parameter transformation is conducted.The undercutting judgement equation for determining that singularity appeared on conjugate profile is derived.It also provides an effective theoretical method for the optimize design of internal tooth dedendum and the non-undercutting design of conjugate profile.Meshing properties including action line,contact ratio,pressure angle,induced normal curvature and sliding ratio of this new gear drive are investigated.Sensitivity analysis methods on induced normal curvature and sliding ratio in certain meshing range are put forward.The changing law of meshing properties with respect to control-parameter of profile c₂ is reveal.And the multi-tooth meshing,force transmitting,lubrication,capacity and anti-wear of gear drive are evaluated.In the results,better meshing performances are indicated.The accurate model of composite cycloid planetary gear is established.And mechanical contact capacity,which is analyzed with FEA method,shows relatively low contact stress.Based on the variable profile curvature and meshing theory of composite cycloid.Extendedly,a novel planetary drive with small tooth difference,which using variable curvature ellipse as internal tooth profile,is presented.Numerical examples are provided for the illustration and validation of new gear meshing theory.?5?The research on the innovative design on transmission structure of composite cycloid with small tooth number difference is carried out.Based on better meshing characteristics of the composite cycloid planetary gear drive with small tooth difference,and considering the gear ratio range,transmission efficiency,lightweight design,geometric design space,and load performance.The gear pair is applied as the core transmission parts to construct the planetary transmission structure and design the transmission mechanism.And N-type,NN-type and RV-type planetary gear transmission design with small tooth difference of composite cycloid gear are accomplished.Moreover,on the basis of this,the four innovative designs of the transmission structure are carried out.A new steel ball ring groove N-type double planetary gear transmission is proposed;Expansively,based on the transmission medium properties of the steel ball as the rolling element,the cylindrical and conical ring groove N-type double planetary gear transmission scheme is proposed.Based on the view of NN multistage planetary transmission,a pin NN-type transmission is proposed.Considering the power split,multisource power input,reduction of the crankshaft partial load and improvement of the input torque stability with small tooth difference,a two stage split type RV transmission is proposed.Corresponding design examples have been completed for different structure.And on this basis,the structure design method on both the experimental prototype and the engineering application of novel composite cycloid gear are provided.