Research On Tooth Surface Design Method Of Spur Face-Gear Pairs And Load-Sharing Characteristics Of Dual Branch Transmission Systems With Spur Face-Gear Pairs

The face-gear drive has been successfully applied to the helicopter branch transmission system in foreign countries,which has significantly improved the characteristics of the helicopter branch transmission system.This technology is of great significance for the development of helicopter power transmission technology in China.But at present,there is still a long way to go for the actual application of distance face-gear drive in the aviation field,especially in the design and processing of the high-performance face-gear pair and the load-sharing design of the face-gear branch transmission,there is still a certain gap compared with foreign countries.The outstanding advantages of the spur face-gear pair are that the cylindrical pinion has free axial position,no axial force,no anti-dislocation design,and can be installed radially floating,so the spur face-gear pair has the most advantageous in the helicopter branch transmission system.Based on this background,this dissertation has carried out systematically the research on tooth surface design method of spur face-gear pairs and load-sharing characteristics of the dual branch transmission system with spur face-gear pairs according to the space gear-meshing theory,the technology of Tooth Contact Analysis(TCA)and Loaded Tooth Contact Analysis(LTCA).The main research contents and achievements are as follows:(1)The unified tooth surface model of non-orthogonal,offset and profile-shifted(NOP)spur face-gear drive is established,and the limiting tooth width of general NOP spur face-gear is derived.The TCA model,LTCA model and the analysis model of the full tooth surface flash temperature of general NOP spur face-gear are established.The results show that the small shaft angle and positive profile-shifted coefficient are beneficial to increase the tooth width of face gears;the tolerance of the shaft angle error is the worst in the three types of installation errors,so the shaft angle error should be strictly controlled;the positive profile-shifted coefficient is beneficial to reduce the contact stress and bending stress of the pinion,and the larger offset can reduce the contact stress and bending stress of the gear and pinion;the profile-shifted coefficient and offset have great influences on the maximum tooth surface flash temperature,so it is necessary to design them reasonably.(2)A novel design and optimization method for tooth modifications on pinions for spur face-gear drives is proposed.The design method not only includes three modification types of profile,axial and topology modification,but also can directly and accurately controls the modification amount,modification lengths and deviation surface.A tooth profile and axial modification curve on a spur pinion are designed as a three-segment combined curves and the topologically modified tooth surface of the pinion can be expressed as a superposition of the theoretical tooth surface and the deviation surface.From two aspects of vibration reduction and noise reduction,improvement of anti-scuffing ability,the optimization models of tooth modifications under different load conditions are established by combining genetic algorithm.The results show that in the optimization models of different objectives,through the optimization of the parameters of the modification curves on the spur pinion,the modified tooth surface of the pinion that satisfies each optimization objective can be obtained,thereby improving the meshing performance.(3)The forces of general NOP spur face-gear pair and the layouts of dual branch transmission and the meshing phase differences of the system are analyzed.The deformation coordination conditions of the system are derived.Simultaneously combining deformation coordination conditions,torque balance conditions and elastic support conditions,the static torque distribution model of the dual branch transmission system with general NOP spur face-gears is established.The factors such as meshing phase differences,time-varying comprehensive meshing stiffness,installation errors and elastic deformations are considered in the model.The results show that the static uneven loading of the system without errors is mainly caused by the meshing phase differences in the system;the greater the installation errors,the greater static load-sharing coefficient of the system;when there is installation error,the static load-sharing coefficient decreases with the increase of the input load;the smaller the support stiffness of the input pinion,the torsional stiffness of the elastic shaft and the meshing stiffness wave amplitude,the more conducive to the uniform loading of the system.(4)Taking into account such factors as meshing phase differences,time-varying comprehensive meshing stiffness,installation errors,damping and elastic deformations,a bending-axial-torsional coupled dynamic model of the dual branch transmission systems with general NOP spur face-gear pairs is established based on the lumped mass method.The Runge-Kutta numerical integration method is used to solve the dynamic differential equations and the dynamic load-sharing coefficient of the system is obtained.By analyzing the influences of the parameters on the dynamic load-sharing characteristics of the system,it is found that the dynamic uneven loading of the system is caused by the gear vibration besides the meshing phase differences;the dynamic load-sharing coefficient of the system is extremely sensitive to the input speed.In order to reduce the dynamic load-sharing coefficient of the system,it can be achieved by optimizing the natural frequencies of the system through the structural design to avoid the resonance region;in addition to the input speed,the influences of other parameters on the dynamic load-sharing characteristics of the system are basically consistent with that of the static load-sharing characteristics.(5)Considering four aspects of meshing phase differences,installation errors,input pinion based on spline clearance floating and tooth surface modifications,the realization methods of even loading for dual branch transmission system are analyzed.For example,if the meshing phase differences of both split-torque stage and combine-torque stage are designed to be π,and the number of teeth of both input pinion and output gear should be designed to be an odd at high input speed;by actively designing installation errors of the gears in the system,a part of the uneven load-sharing caused by the installation errors can be offset each other;the input pinion can be designed as a floating structure,which is installed on the input shaft through a spline connection,and the torque is transmitted by the spline;the tooth surface modifications on the gear pairs of both split-torque stage and combine-torque stage are performed to reduce the wave amplitude of the time-varying comprehensive meshing stiffness.(6)A test-bed is built to test the load-sharing performance of the dual branch transmission system with the orthogonal spur face-gear pairs,and the torque distributions of the dual branch transmission system under different installation errors,input loads and input pinion support stiffness are tested.By comparing and analyzing the experimental results and theoretical calculation results,the correctness of the method described in this dissertation is preliminarily verified.