| With the transformation and upgrading of equipment manufacturing industry,the performance of gear transmission system,which is widely used in equipment manufacturing industry,has been put forward higher requirements.Accurate calculation of various characteristics of gear pairs is the basis for the design and manufacture of high-performance gear transmission system.Affected by the process of gear design,processing and assembly,the gear pair will inevitably have misalignment errors after installation,and cannot be eliminated.Therefore,the error characteristics become the inherent attributes of gear pairs,and accurate calculation and evaluation of the performance of gear pairs with error characteristics is a difficult point in gear calculation theory.Different from the existing finite element model or the international and national standard coefficient method based on ideal model,a new spatial analytical calculation theory and method of gear pairs with multi-degree-of-freedom error characteristics are proposed in the paper,as well as the meshing and mechanical characteristics.Specifically,as follows:Firstly,a mathematical model of spatial meshing of gear pairs with multi-degree-of-freedom error characteristics is established.Based on the theory of gear processing and coordinate transformation,the parametric equation of curved surface profile in meshing coordinate system is defined,and a new slice model of gear pair is established based on the geometric projection principle,taking the installation position of gear as the reference ideal position.The model consists of several groups of sliced gear meshing pairs,each of which consists of a standard large gear slice and a non-standard pinion slice.In addition,a method for calculating the initial meshing angle with error characteristics is proposed for the new model.Secondly,the analytical method of time-varying meshing stiffness of gear pairs with multi-degree-of-freedom error characteristics is studied.According to the meshing mathematical model of gear pair with error characteristics,the profile shape and equation of gear and pinion slices in their respective local coordinate systems are obtained.Based on the energy method,the formulas for calculating the stiffness of each component of the slices are derived,and the corresponding solving methods are put forward through mechanical theory and geometric deformation compatibility equation.Finally,the meshing stiffness of gears under different error conditions is calculated and compared with the results of the finite element model verified by physical experiments,which verifies the correctness of the new analytical calculation model.Then,a new analytical model is proposed for calculating contact stress of modified gears.Based on the meshing mathematical model of gear pair with error characteristics,the precise profile equation of modified gear is derived.Combining with contact mechanics theory,the geometric deformation compatibility equation of gear pair during meshing is established,and the calculation formula of contact stress on the tooth surface of modified gear is deduced.The contact stresses of gear teeth under the conditions of no modification,different loads,different modification ranges and different modification exponents are calculated respectively.The results are compared with those of the finite element model under the same conditions,and the correctness of the new analytical model is verified.In addition,on the basis of meshing mathematical model and meshing stiffness calculation model of gear pairs with error characteristics,a new analytical calculation model of tooth contact stress with multi-degree-of-freedom error characteristics is established,and the correctness of the new analytical model is verified by comparing with the corresponding finite element model.Besides,with the meshing mathematical model of gear pairs with multi-degree-of-freedom error characteristics,a new analytical model for calculating the maximum stress of the root and the crucial section locations in ideal state with high accuracy and rapidity is established.The root stresses and crucial section locations under different teeth number,modulus,pressure angle,and tooth height modification coefficient and edge radius of cutter are calculated.Compared with those of ISO 6336-3,AGMA 2101-D04 and finite element model published by American Gear Manufacturing Association,the new analytical model has higher accuracy.On this basis,combined with the analytical calculation model of meshing stiffness and contact stress of gear pairs with multi-degree-of-freedom error characteristics,an analytical calculation method for calculating the root stress and crucial section location of gear teeth under multi-degree-of-freedom error conditions is proposed,and the root stress and crucial section locations of gear teeth under different error conditions are studied and analyzed.Similarly,the new analytical calculation model is validated by the finite element model.Lastly,based on the analytical meshing mathematical model,meshing stiffness and contact stress calculation model of gear pairs with multi-degree-of-freedom error characteristics,a method for calculating transmission error of gear pairs under multi-degree-of-freedom conditions is proposed,and transmission errors under different error types and parameters are calculated.The correctness of the new analytical calculation model is verified by comparing the results of the corresponding finite element model. |
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