| Gears are the key basic components for motion and power transmission,and the gear machining accuracy directly decides the service performance of the gear.The higher the machining accuracy of the tooth surface,the more accurate the motion and power transmission,and the better the load capacity and fatigue life of the gear.Therefore,the manufacturing level of gears also determines the service performance and core competitiveness of high-end equipment including automobiles,aircraft carriers,helicopters,wind power,heavy-load engineering machinery,etc.,and represents the overall level of the national industry and national defense equipment.With the increase in gear machining requirements and the reduction in the cost of the gear grinding process,the hobbing-grinding process has gradually replaced the traditional hobbing-shaving process to be the main machining method for high-precision gears.Gear grinding is a finishing process after rough hobbing,can correct hobbing errors and heat treatment distortion errors,and determines the final accuracy level of the gear.The CNC gear profile grinding machine(GPGM),as key equipment for fine grinding of the tooth surface after hobbing,has significant advantages including high grinding efficiency,easy tooth profile modification,no undercutting,simplicity of operation,etc.At present,the mapping law and quantitative influence of the numerous error elements of the CNC GPGM on the tooth surface grinding errors are not clear.There is also a lack of effective traceability means for sensitive errors that have a significant influence on grinding accuracy.The accuracy design and quality control of grinding machines rely heavily on the empirical method or the safety factor method,leading to the lack of reliable theoretical basis and model support for the guarantee and improvement of gear grinding accuracy.Therefore,for the CNC GPGM,investigating the quantitative mapping law between the multi-source errors represented by geometric errors and the tooth surface grinding errors,establishing a coupling mapping model from the geometric errors to the tool posture errors and then to the tooth surface errors,and proposing new methods for error measurement and identification,sensitive error traceability analysis,and sensitive error high-efficiency compensation will be of great importance to improve the machining accuracy of the GPGM.In this paper,the researches on the geometric error coupling modeling and sensitive error traceability compensation for the CNC GPGM are conducted and the main contents are as follows.(1)Coupling mapping modeling of the geometric error-tooth surface error of the CNC GPGM.Based on the definition and positional relation of the geometric errors of the motion axis of a CNC machine tool,a geometric error modular modeling method for the motion axis based on the homogeneous transformation matrix is first proposed.Then,according to the actual kinematic chain considering the geometric errors of the CNC GPGM,the actual forward kinematics model of the machine tool is rapidly established by reconstructing the geometric error modules of the motion axes.It reveals the actual posture transformation relationships between the grinding wheel and the gear coordinate systems under the influence of geometric errors.After that,the forward and inverse numerical calculation methods between the helical tooth surface of the gear and the axial profile of the grinding wheel in the gear profile grinding process are studied,and the machining characteristics such as spiral grinding and conjugate contact are then considered to sequentially establish the geometric error-tool posture error model and the geometric error-tooth surface error model.They reveal the coupling mapping law from the geometric errors to the tool posture errors and then to the gear grinding errors and lay a theoretical foundation for the follow-up research on the sensitive error traceability and compensation of gear grinding.(2)Geometric error measurement and identification method for the CNC machine tools and the sensitive error traceability method of the tooth surface.To avoid the error interference of the non-identified axes and simplify the identification model,an identification method of the geometric errors of a rotary axis based on the single-axis motion measurement is proposed.The single-axis motion measurement mode of the double ball bar following the measured rotation axis is used to replace the traditional linkage measurement mode with multiple linear axes following the measured rotary axis.Based on the homogeneous transformation matrix,the mathematical model for the bar length change under the influence of the geometric errors of the worktable is first constructed,and the new identification scheme is designed according to the parameter analysis of the double ball bar and the column full-rank requirement of the identification matrix,thus establishing the error identification model of the rotary axis.Besides,due to the randomness and the mutual coupling characteristics of geometric errors,a sensitive error traceability method based on the improved Sobol method is proposed.The improved Sobol method replaces the pseudo Monte-Carlo sequence in the traditional Sobol method with the quasi Monte-Carlo sequence and further modifies it according to the actual distribution of geometric errors.It can calculate the sensitivity indices of each error element and obtain the sensitive errors and parts for each tooth surface error component.Finally,by comparing the sensitive error traceability results with that of the modified Morris method and conducting the sensitive error correction simulation experiment,the effectiveness of the traceability method is proved.(3)Sensitive error compensation method towards gear grinding accuracy enhancement.Firstly,the traditional actual inverse kinematics compensation model towards tool posture errors is established.It first decouples and separates the actual motion instructions of the A and C rotary axes after error compensation according to the mapping equation between the tool axis vector data in the workpiece and tool coordinate systems,and then according to the mapping equation of the tool position data,the actual motion instructions of the X,Y,and Z linear axes after error compensation can be decoupled and separated.Then,the topological tooth surface errors are calculated by the surface interpolation and the topology meshing method based on the geometric error-tooth surface error model.The necessary inspection indicators of gear accuracy such as tooth profile accuracy and tooth helix accuracy are calculated according to the international standard ISO 1328-1:2013.The improved Sobol method is used to trace the corresponding sensitive errors.Finally,by substituting the sensitive errors into the actual inverse kinematics compensation model towards tool posture errors,the analytical expressions of the actual motion instructions of the motion axes towards the compensation of specific accuracy indicators such as the tooth profile deviation and the tooth helix deviation can be directly derived out for realizing the sensitive error compensation towards gear grinding accuracy enhancement.(4)Sensitive error traceability and compensation tests for the CNC GPGM.Based on the proposed measurement and identification method for geometric errors and the sensitivity error traceability method of the tooth surface,the geometric error measurement and identification experiments on the CNC GPGM are carried out using a laser interferometer and a double ball bar.The sensitive error elements regarding the tooth profile and helix accuracy are traced,and their quantitative influences on the left and right tooth surface topological errors,the tooth profile deviations,and the tooth helix deviations are analyzed.Besides,the sensitive error compensation models towards the tooth profile deviation and the tooth helix deviation are established,and the improved effects of the tooth profile accuracy and the tooth helix accuracy before and after the sensitive error compensation are simulated and analyzed.Finally,the grinding tests for sensitive error compensation towards tooth helix accuracy enhancement are carried out.The left and right total tooth helix deviations of the ground tooth grooves before and after compensation are greatly reduced,from 18.6 μm and 28.2 μm to 5.5 μm and 7.7 μm,respectively.The helix accuracy increases by 2 levels on average and thus verifying the effectiveness of the compensation method. |
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