Research On Generating Methods Of Tangent-Contact Oriented Twin-Curves And Its Relative Motion

Twin-curve with tangent-contact is widely exist in mechanical field,such as in the transmission of eccentric gear,internal gear pump and co-rotating extruder and the following grinding of non-circle profile and crankshaft pin.Movement and power transmission can be realized and the non-circle profile can be generated in the process of relative motion of twincurve with tangent-contact.Oriented from the tangent-contact relationship,the model of parametric eccentric gear transmission,equivalent instantaneous tangent-contact,parallelogram mechanism used in co-rotating profiles,operator of normal vector and four-bar mechanism used in crankshaft following grinding etc.were established.Based on the above model,the issue of accurate non-uniform motion of eccentric gear transmission,tooth profile overlap interference in linear internal gear pump,generation of smooth co-rotating profile,tool path generation of noncircle using two-axis and crankshaft pin using three-axis in following grinding were researched.Main results of research are as follow.(1)Parametric model of eccentric gear transmission was established directly using the tangent-contact relationship.Numerical simulation indicated the asymmetric characteristics in eccentric gear transmission.The asymmetric and non-uniform characteristics are enhanced with the increase of eccentricity.In the factor which influenced the feature of non-uniform transmission,eccentricity is biggest,pressure angle and working pressure angle is less,tooth number has almost no effect.(2)The equivalent model of instantaneous tangent-contact and the approximation method using straight line and involute curve based on instantaneous tangent-contact were proposed,.The parametric conjugated tooth profile model was established based on linear approximation method and the critical of tooth profile overlap interference was proposed.The internal gear pump with linear and circular arc tooth profile was obtained.The eccentric gear transmission model using equivalent involute curves was established,which provides a new approach for calculation and analysis of eccentric gear transmission.(3)The kinematic model of co-rotating tooth profile was established.The characteristic of co-rotating profile was indicated that the normal line is always parallel to the center line.The generation method of co-rotating profiles was established.The result indicated that the profiles of ellipse and its conjugated co-rotating profiles are not the same.A method of generating the same co-rotating profile with smooth arc conjugated profile was established,which using parametric parallelogram model.The family of co-rotating profile was induced and the theoretical foundation of co-rotating profiles generation was provided.(4)The offset operator was established based on tangent-contacted which can be used to generating the tool path of non-circle following grinding with two-axis.The principle error of CNC instruction execution was revealed via the CNC instruction execute analyses,and the error control method was given.The method of the influence of grinding precision caused by matching constant error was analyzed.The normal angle operator was proposed,and the improved spline method using normal angle operator is established which solved the problem of precision calculation of normal angle of discrete curve and improving the precision of tool path using in the following grinding.The tool path generating methods was verified by the two-axis following grinding experiment.(5)Model of crankshaft pin following grinding using parameterized four-bar mechanism was proposed.The instantaneous tangent-contact relationship was naturally ensured by parameters constraint.The generation of three-axis tool path of following grinding was converted to the crank angle mating its corresponding special connecting rod curve.The corresponding optimization kinematics index is proposed.Character and the best parameter range of in-line slider crank model,parallelogram model and reverse parallelogram mechanism model were analyzed.Finally,the error sensitivity analysis model about motion error was established.The results indicate that the three motion errors satisfy the principle of linear superposition using numerical simulation.That is the base of the additional y-axis can be used as error compensation.Experiment result shows that the models and method is correct.