Research On 3D Deviations Characterization & Atlas Of Gears

Gear errors has a direct impact on its service life and performance.With the continuous improvement of gear processing accuracy,measurement accuracy and measurement efficiency,gear information obtained through measurement is becoming more and more comprehensive and complete.Because traditional gear errors characterization only uses the partial information of the gear,its limitations and deficiencies are gradually being highlighted.There is an urgent need to propose a new gear errors characterization method.This method can use a lot of useful information in the measurement,and can intuitively clarify the relationship between gear errors,gear errors and gear pair errors.This thesis takes gear errors as the research object.The actual gear 3D point cloud data obtained by modern measurement methods calculates the flank normal deviations.and converted to the meshing surface coordinate system.Orthogonal polynomials are used to characterize the normal deviation,and then the gear characteristic lines that can reflect the performance of the gear is expressed by a unified model,which realizes the characterization and decomposition of the 3D deviations of the gear,and provides theoretical support for obtaining new indicators of the flank quality evaluation.On this basis,the relationship between the typical 3D deviations of the gear and the individual deviations of the gear,the individual deviations of the gear and the comprehensive errors,and the relationship between the individual deviations of the gear and the integrated errors are further analyzed.The discovery of the correlation law between errors,clarified the quantitative relationship between the 3D deviations of various forms of gears,and represented the complex relationship between the deviations in the form of graphics.Graphical and serialized "gear single topological deviation atlas" and "gear comprehensive error atlas" have been formed.The main research contents of this paper are as follows:(1)Propose the method of obtaining the normal deviation of flank and the unified model of gear characteristic error.This paper first calculates the normal deviation of the flank according to the actual data of the flank,and uses the relationship between the gear coordinate system and the meshing surface coordinate system during the gear meshing process to convert the 3D gear deviations to 2D,and establish it in the meshing surface coordinate system.The unified characterization model of each characteristic line proposes a method of extracting characteristic lines on the flank under 3D measurement.This model realizes the rapid extraction of various characteristic lines at any position on the 3D flank,simplifies the evaluation of the 3D deviations of the flank,and is of great significance to the gear error theory,and provides a theoretical basis for the rapid evaluation of the gear under the 3D measurement.(2)Propose a method to characterize the 3D deviations of gears.In this paper,through theoretical and method innovations,a full-information 3D deviations representation model of gears is established.The flank deviation is directly evaluated in the normal direction reflecting the transmission quality.After the flank normal deviations is converted to the meshing surface coordinate system,in order to realize the process parameter adjustment and process error traceability,a kind of gear based on Legendre orthogonal polynomial is proposed.The surface error decoupling method establishes the relationship between the coefficients of the orthogonal polynomial and the various characteristic errors on the gear flank,and realizes the separation of the various errors on the flank.The characterization and decomposition method in this paper is compatible with the traditional "dot-line feature" characterization of gears,and has the function of evaluating the entire flank profile.After experimental verification,this method realizes the characterization and decomposition of the 3D deviations of the flank.(3)A "Gear Topological Deviations Atlas" is proposed to analyze the coupling relationship between various types of gear errors.On the basis of the 3D characterization and unified model of gears,common gear errors are summarized as representative characteristic errors,the coupling relationship between various gear errors is analyzed,and the tooth profile deviation,helix deviation,and pitch deviation are systematically studied.The relationship between the deviation of the normal meshing tooth profile and the deviation of the contact line,and the map of the single topological deviations of the gear is proposed.(4)The relationship between the shape of the gear deviation atlases and the polynomial expansion coefficient is studied.When the size of the characteristic deviations and the pose of the characteristic deviations change,the expansion coefficient of the polynomial will change.It is found that when the nature of the deviations does not change,such as the degree of the first-order slope or the second-order middle crowing remains unchanged,the expansion coefficient representing the size of the characteristic deviations remains unchanged;when the deviations only changes in pose,other related expansion coefficients are caused,the law of change is given.Some explorations were made on the problem of process errors traceability in CNC gear hobbing.Taking typical CNC gear hobbing as an example,the relationship model between gear deviations atlas and hobbing deviations in gear hobbing and the position and attitude deviations of hobbing was established,to obtain the corresponding inverse adjustment parameters of gear hobbing,which provides a new idea for the analysis of the process deviations of CNC gear hobbing.(5)The 3D gear transmission errors model based on orthogonal polynomials is studied.This model is the mathematical foundation of the theory of gear synthetic deviations atlas.Establish a method to calculate the transmission errors of a single gear based on the topological deviations of the tooth flank.Through the analysis of the single deviation atlases of the gear,the abstract gear errors and the coupling relationship between the deviations are expressed in the form of atlas,and various comprehensive deviations atlas under the characteristic deviations on gear are given.(6)The measurement test of the gear 3D deviations characterization and evaluation software and the characteristic gear has been completed.On the basis of the aforementioned research content,an application software including the 3D deviations characterization and decomposition of gears,and the extraction and evaluation of gear characteristic deviations under a unified model has been developed.The software provides a general method for characterizing and evaluating 3D gear errors.The above theoretical research provides visual verification results;completed the individual deviations measurement test and transmission errors measurement test of the characteristic gear with specific deviations,and verified the 3D deviations characterization and decomposition of the gear,the unified model of the gear characteristic deviations,and the single topological deviations of the gear,the comprehensive deviations atlas of the gear.