Research On Geometry Design Methodology And Mesh Characteristic Analysis Of Hypoid Gear In Low Crossed Shaft Angle Configuration

The gear transmission with non-parallel axis has gradually become a hot-spot in gear transmission area.The low shaft angle transmission has the irreplaceable advantages and extensive application which can be found in the fields of high-speed ship power transmission,four-wheel drive vehicle power split transmission,aero-engine accessory transmission,helicopter middle reduction.Compared with beveloid gear,hypoid gear has more compact structure,larger bearing capacity,wider application range of intersecting angle and preset meshing characteristics in low shaft angle configuration,which has better comprehensive mesh behavior and application prospect.However,due to the extreme value of shaft angle and offset,the relationship between tooth profile evolution and meshing theory are complicated and unclear.There is no machining reference which can be found for hypoid gears with long pitch cone distance,and the traditional design method based on right-angle condition is not applicable,which seriously limits application.This thesis focused on the technical difficulties which involving meshing theory,the tooth surface generating method and tooth contact analysis to research the pitch cone design,machine-tool calculation and mesh behavior under low shaft angle configuration.The mesh model of hypoid gear with low shaft angle configuration considering pitch cone design has been established,the relationship between gear evaluation and mesh theory has been researched.The calculated model considering machine-tool setting calculation has been established,the methodology of machine-tool calculation based on enhancement of local synthesis method has been proposed to find the target of pinion surface in low shaft angle configuration.The influences of different geometry parameters and assembly parameters on mesh behavior have been investigated.The software based on the whole design and calculation process for low shaft angle configuration has been developed by application of C#.The efficient system of hypoid gear in low shaft angle configuration involving geometry design,machine-tool calculation,gear flank optimization and experiment has been proposed.The research results have a significant enhancement for geometry design,machine-tool setting calculation and gear surface optimization of hypoid gear in low shaft angle configuration,those results also provide the reference to technical staff in industry of gear manufacturing.The main results are shown as follow(1)The mathematical model of mating hyperboloid surface with instantaneous axis under extremely working condition have been proposed.The influence of different intersected angle between hyperboloid surface and instantaneous axis on the position of tangent point has been investigated.The main three geometry law and relationship between limited curvature of gear flank and limited pressure angle has been established.The iterated process of hypoid gear in low shaft angle condition which considering spiral angle of wheel and auxiliary angle of pinion as iterated values has been established,here,the final judgement is offset and limited curvature.The standard tooth taper has been proposed to solve the limitation issue of long pitch cone distance hypoid gear.The calculated method of gear blank parameters has been derived.(2)Based on the machining process of hypoid gear and spiral bevel gear,the generating methodology and movement rules of traditional machine tool and five-axis CNC machine has been researched.The related position of cutter is applied to simulate the generating process of gear flank.The mathematical model of face-milled hypoid gear based on those two types of machine tools have been established.Based on the enhancement of local synthesis method,the mesh behavior control approach with can be used in low shaft angle condition have been proposed.This method can find the unique solution of machine-tool settings of pinion which can mate the target wheel and achieve the preset mesh characteristics.(3)An accurate meshing model of gear pair has been established,and a tooth contact analysis method based on Sheveleva discrete theory has been proposed to improve the efficiency and convergence of tooth surface meshing analysis.The mean contact position on the tooth surface is evenly distributed around the preset conjugated point,the contact mark position center is consistent with the preset conjugate point position,the contact ellipse length is consistent with the given value,the peak-to-peak value of transmission error presents a parabolic shape.(4)A synthetic optimization method of tooth surface has been proposed to avoid undercutting,opposite hand,top-land pointing and unsoomthness root part.The theoretical contact model of hypoid gear transmission with low crossed shaft angle considering different basic geometric parameters has been established to reveal the influence law of different basic geometric parameters on the geometric morphology of tooth surface at extreme condition.The technical route and closed diagram for calculating the boundary of basic parameters of hypoid gear with low crossed shaft angle has been proposed.The selected range system of basic geometric parameters of hypoid gear with low crossed shaft angle considering safety factor has been constructed.(5)Combining the finite element analysis and tooth contact analysis,the effect of different misalignments on mesh characteristics of hypoid gear has been investigated for the low crossed shaft angle configuration.It is the first time to put forward a method to compensate the installation errors by considering the axial displacement of large and small wheels.The methodology is verified by tooth contact analysis and loaded tooth contact analysis.The conclusion is that the axial position errors of large and small wheels can be compensated mutually,and the offset and shaft angle errors can be compensated by the position errors of pinion and wheel.(6)A demonstration platform of low crossed shaft angle has been built,a machining method of long pitch spiral bevel gear based on multi-axis CNC technology has been proposed.The corresponding relationship of machining parameters between traditional mechanical machine tool and CNC machine tool has been revealed.The relationship between machining parameters of long pitch spiral bevel gear and machine stroke has been studied.The hypoid gear with low crossed shaft angle has been generated.