大型数控滚齿机加工误差及补偿研究
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摘要
大型数控滚齿机主要应用于航空、船舶、风力发电、重载车辆及工程机械等领域齿轮加工，这些行业所需齿轮结构尺寸大、精度要求高，但加工成本高风险大，故对滚齿机的安全性能与加工质量要求较高，特别对加工精度指标要求很高。
由于大型数控滚齿机结构尺寸比较大，部件种类与数量多，机床外支架伸出较长，滚刀与工件主轴结构尺寸长，机床各种系统配置多，以及机床滚削结构系统与受力情况均较复杂，故影响齿轮加工精度的因素多而复杂。因此，展开大型数控滚齿机加工误差与性能研究，对提高与改善机床加工精度，减小齿轮加工误差具有十分重要意义。
为了全面实现大型数控滚齿机高速、高效及高精度的大齿轮加工，本学位论文主要从以下五个方面对滚齿机加工误差的产生机理及补偿技术进行深入研究与探讨工作：
①研究大型数控滚齿机滚削力对主轴变形的影响，是减小或控制大型齿轮加工误差的方向之一。本文根据滚齿工艺参数、坐标变换方法及弯曲变形理论推导了滚刀、工件主轴变形及中心距X方向变化量计算公式。针对某具体型号大型数控滚齿机，由实际结构与滚削参数计算出滚削力、主轴变形及中心距变化量数据，获得了滚削力与主轴转速、进刀深度及主轴变形关系曲线，揭示了滚削变形规律。表明该研究可为滚齿机的结构优化、滚齿工艺参数选择、加工误差预测及补偿提供理论依据。
②为了掌握滚齿机由滚削动态特性引起主轴及主轴中心距X方向变形量对齿轮加工精度的影响状况。本文从滚齿机结构、滚齿工艺参数、动态特性、动力学原理及Euler-BernouHi梁振动理论出发，建立起滚齿机主要部件及主轴系统的模态、谐响应及振动特性理论相关数学模型。根据理论模型、滚齿工艺参数及振动测试数据，研究与分析了滚刀与工件主轴振动位移响应参数跟滚削工艺参数间的相互关系，揭示了滚齿机由振动引起的滚刀与工件主轴中心距X方向变化规律以及该变形量对齿轮加工精度的影响程度。
③系统地对大型数控滚齿机，由热变形引起滚刀与工件主轴中心距X方向位置偏差变化情况进行了研究。针对大型滚齿机结构特点，在金属材料热膨胀原理、构件轴线可伸长理论及温度分布不均匀梁的Euler-Bernoulli和Kirchhoff平截面假定理论基础上，提出一种滚齿机的热变形计算新模型，并提出基于变形微元与隔离体法的滚齿机立柱轴向变形与弯曲变形耦合理论。基于理论研究提出一套滚齿机的热变形与温度测试系统，建立了实验平台，测试与分析滚齿机的热变形位移与温度实验数据，揭示出滚齿机的热变形理论与实际规律，得出滚刀与工件主轴中心距位移偏差与齿轮齿向偏差轨迹曲线。
④在大型数控滚齿机振动模态、谐响应及滚削动态特性理论研究基础上，以某具体型号大型滚齿机为对象，建立起滚齿机约束模态及谐响应的动力学有限元仿真模型，提出了滚齿机动力学仿真的边界约束条件。结合滚齿工艺参数与材料特性参数进行了仿真计算。根据振动响应仿真云图与数据曲线，对滚刀与工件主轴中心距变化量及齿轮加工误差的影响进行了分析。仿真研究结果为滚齿机结构优化与装配位置调整提供了理论依据。
⑤在大型数控滚齿机热变形理论与实验研究基础上，采用模糊聚类法对滚齿机测试温度变量进行了筛选，利用多元回归法-最小二乘法，建立起滚齿机滚刀与工件主轴中心距热误差-温度的补偿模型。在数控自动编程系统中，对某具体型号的大型数控滚齿机进行了热误差补偿实验。研究结果表明，滚齿机主轴中心距热变形量得到大幅度降低，齿轮各项指标与精度显著提高。所建立的热误差补偿模型精度高，能有效预测和控制滚齿机的热变形及齿轮加工误差，可提高滚齿机加工精度与效率，表明该补偿系统与实验具有较强的实用价值。
本论文采用理论、实验及有限元研究方法，建立了大型滚齿机滚削变形、动力学振动位移及热变形的理论计算新模型。将齿轮加工工艺与实验测试、数控加工与计算机软件技术相结合，建立了滚齿机主轴中心距变化量的热误差补偿模型，成功地进行了热误差补偿试验研究。结果显示，滚齿机与齿轮加工精度得到极大地提高，表明这些研究为提升大型数控滚齿机高速、高效的加工能力，和全面实现滚齿机高精度的大型齿轮加工技术，奠定了理论基础和提供关键技术支持。
The large-scale numerical control （NC） gear hobbing machine is mainly used insome extremely important fields such as aviation industry, ship industry, wind powergeneration, heavy-duty vehicles and engineering machinery industry, in which thedemanded gears should be of large size with a low risk and cost and high precision.Accordingly, a large-scale NC gear hobbing machines will be needed high safetyperformance and processing quality, especially the machining precision.
Additionally, some factors such as its large structural size, varieties, largedimension between hob and workpiece spindle of gear hobbing machine, thecomplicated system configuration, also the complicated hobbing system and cuttingforce, have the significant influence upon gear of machining precision. Furthermore, theresearch of machining error and capability on the large-scale NC gear hobbing machinehas become increasingly significant to improve machining precision and decreasemachining error of gear.
In order to realize the large-scale gears of machining accurately and efficiently, thisthesis has finished some research on the machining error mechanism and correspondingcompensation technique of large-scale gear hobbing machine from the followingaspects:
①Research on the effect of spindle deformation which is caused by hobbing forceis an important way to diminish or control the machining tolerance of the large-scalegear. Based on the hobbing gear features, process parameters, the methods of changingcoordinate and theory of beam deflection, several formulae of hobbing and spindledeformation and centre distance variation are established through theoretical analysis.For certain typical gear hobbing machine with particular structure and machiningparameter, its hobbing force and spindle deformation and centre distance variationunder practical hobbing parameter are calculated by adopting the mentioned formulae.Further, the relationship curve of cutting force, spindle rotational speed, hobbing depthand deformation of spindle were obtained, and revealed the law of hobbing and cuttingdeformation. This research provides important basis for optimization design of machinetool structure, processing parameter and machining error prediction and compensationfor gear hobbing machine.
②To master the influence of spindle and spindle the centre distance radial deformation caused by dynamical properties of hobbing gear on machining precision forgear hobbing machines. Based on machine tool structure, processing parameter,dynamical properties of the machining gear, dynamical principle and Euler-BernouHibeam vibration theory, the related dynamical mathematical models were established inthis paper. According to the theoretical model, processs parameters and vibrationexperimental datum, this paper focused on the research and analysis of mutual relationbetween the response parameters of vibration displacement and hobbing processparameters for hob and workpiece spindle. By all the above analysis and research, thispaper reveal the radial deformation change law of the centre distance between hob andworkpiece spindle caused by the vibration of hobbing gear, and the influence on whichthe vibration displacement deformation exerts gears’ machining precision.
③Research on the deviation of the centre distance between hob and workpiecespindle and this deviation is caused by thermal deformation. Based on the structuralfeatures of large-scale NC gear hobbing machine, the theory of thermal expansiondeformation of metallic materials, the extensional beam theory, non-uniformtemperature distribution of the Euler-Bernoulli beam and Kirchhoff theory ofplane-section assumption, a novel model was proposed in this paper to calculate thebending thermal deformation of lathe bed and upright column of gear hobbing machinetheoretically, then, the research on the axial deformation and bending deformation of theupright column were also carried out by utilizing the deformation theory of thedeformation element and equilibrium element method. According to the theoreticalresearch, the testing system of temperature and thermal deformation for gear hobbingmachines were proposed, further, a experiment platform was established to test andanalyze the temperature and corresponding thermal deformation displacement data,eventually to reveal the theory and practical rule of thermal deformation, and to plot thedeviation curves of the centre distance between hob and workpiece spindle and geartooth trace deviation.
④Based on the theoretical research of the vibration mode, harmonic response andhobbing dynamical properties, the finite element of entity simulation model wereestablished about the restriction mode and harmonic response for gear hobbing machine,and proposed the restriction boundary conditions for dynamical simulation. The finitemodel was simulated by adopting the processing and material parameter. According tothe simulation cloud chart and data, the gear machining error and the variation of thecentre distance between hob and workpiece spindle were analyzed. These results of the simulation research provide theoretical basis for the structural optimization design andassembly position adjustment for gear hobbing machine.
⑤Based on the research of the thermal deformation theory and experiment, thetesting temperature variables were selected by using the method of fuzzy clustering, thethermal error compensation model of the center distance between hob and workpiecespindle of the Large-scale NC gear hobbing machine was set up by adapting themethods of multi-regressions and the least square regression. Meanwhile, theexperiment of the thermal error compensation for the certain typical Large-scale NCgear hobbing machine was carried out in the numerical control automatic programmingsystem. The result shows that the thermal deformation value of the centre distance ofhob and workpiece spindle reduces substantially and various indexes and precise ofmachining gear improve remarkably. The thermal error compensation model is higherprecision, the method not only upgraded the gear machining accuracy and the efficiencybut also effectively control and forecast the thermal deformation of the large-scale NCgear hobbing machine. Therefore, this compensation system and experiment have greatpractical value.
These novel calculation models were established about the hobbing deformation,dynamical vibration displacement and thermal deformation of large-scale NC gearhobbing machine abased on the analysis and research of theory, experiment and finiteelement method in this paper. Meanwhile, the thermal error compensation model of thecentre distance between hob and workpiece spindle of gear hobbing machine was set upby combining processing parameters and experimental datum, numerical machining andcomputer software’s technology, which successfully carried out the experiment ofthermal error compensation. the result show that the machining precision of gears aregreatly improved, Above all these researches lay the theoretical basis and provide keytechnological support for promoting the high speed and efficiency of machiningcapability, and for overall realizing the large-scale gear of high precision of machiningtechnology of large-scale NC gear hobbing machine.
由于大型数控滚齿机结构尺寸比较大，部件种类与数量多，机床外支架伸出较长，滚刀与工件主轴结构尺寸长，机床各种系统配置多，以及机床滚削结构系统与受力情况均较复杂，故影响齿轮加工精度的因素多而复杂。因此，展开大型数控滚齿机加工误差与性能研究，对提高与改善机床加工精度，减小齿轮加工误差具有十分重要意义。
为了全面实现大型数控滚齿机高速、高效及高精度的大齿轮加工，本学位论文主要从以下五个方面对滚齿机加工误差的产生机理及补偿技术进行深入研究与探讨工作：
①研究大型数控滚齿机滚削力对主轴变形的影响，是减小或控制大型齿轮加工误差的方向之一。本文根据滚齿工艺参数、坐标变换方法及弯曲变形理论推导了滚刀、工件主轴变形及中心距X方向变化量计算公式。针对某具体型号大型数控滚齿机，由实际结构与滚削参数计算出滚削力、主轴变形及中心距变化量数据，获得了滚削力与主轴转速、进刀深度及主轴变形关系曲线，揭示了滚削变形规律。表明该研究可为滚齿机的结构优化、滚齿工艺参数选择、加工误差预测及补偿提供理论依据。
②为了掌握滚齿机由滚削动态特性引起主轴及主轴中心距X方向变形量对齿轮加工精度的影响状况。本文从滚齿机结构、滚齿工艺参数、动态特性、动力学原理及Euler-BernouHi梁振动理论出发，建立起滚齿机主要部件及主轴系统的模态、谐响应及振动特性理论相关数学模型。根据理论模型、滚齿工艺参数及振动测试数据，研究与分析了滚刀与工件主轴振动位移响应参数跟滚削工艺参数间的相互关系，揭示了滚齿机由振动引起的滚刀与工件主轴中心距X方向变化规律以及该变形量对齿轮加工精度的影响程度。
③系统地对大型数控滚齿机，由热变形引起滚刀与工件主轴中心距X方向位置偏差变化情况进行了研究。针对大型滚齿机结构特点，在金属材料热膨胀原理、构件轴线可伸长理论及温度分布不均匀梁的Euler-Bernoulli和Kirchhoff平截面假定理论基础上，提出一种滚齿机的热变形计算新模型，并提出基于变形微元与隔离体法的滚齿机立柱轴向变形与弯曲变形耦合理论。基于理论研究提出一套滚齿机的热变形与温度测试系统，建立了实验平台，测试与分析滚齿机的热变形位移与温度实验数据，揭示出滚齿机的热变形理论与实际规律，得出滚刀与工件主轴中心距位移偏差与齿轮齿向偏差轨迹曲线。
④在大型数控滚齿机振动模态、谐响应及滚削动态特性理论研究基础上，以某具体型号大型滚齿机为对象，建立起滚齿机约束模态及谐响应的动力学有限元仿真模型，提出了滚齿机动力学仿真的边界约束条件。结合滚齿工艺参数与材料特性参数进行了仿真计算。根据振动响应仿真云图与数据曲线，对滚刀与工件主轴中心距变化量及齿轮加工误差的影响进行了分析。仿真研究结果为滚齿机结构优化与装配位置调整提供了理论依据。
⑤在大型数控滚齿机热变形理论与实验研究基础上，采用模糊聚类法对滚齿机测试温度变量进行了筛选，利用多元回归法-最小二乘法，建立起滚齿机滚刀与工件主轴中心距热误差-温度的补偿模型。在数控自动编程系统中，对某具体型号的大型数控滚齿机进行了热误差补偿实验。研究结果表明，滚齿机主轴中心距热变形量得到大幅度降低，齿轮各项指标与精度显著提高。所建立的热误差补偿模型精度高，能有效预测和控制滚齿机的热变形及齿轮加工误差，可提高滚齿机加工精度与效率，表明该补偿系统与实验具有较强的实用价值。
本论文采用理论、实验及有限元研究方法，建立了大型滚齿机滚削变形、动力学振动位移及热变形的理论计算新模型。将齿轮加工工艺与实验测试、数控加工与计算机软件技术相结合，建立了滚齿机主轴中心距变化量的热误差补偿模型，成功地进行了热误差补偿试验研究。结果显示，滚齿机与齿轮加工精度得到极大地提高，表明这些研究为提升大型数控滚齿机高速、高效的加工能力，和全面实现滚齿机高精度的大型齿轮加工技术，奠定了理论基础和提供关键技术支持。
The large-scale numerical control （NC） gear hobbing machine is mainly used insome extremely important fields such as aviation industry, ship industry, wind powergeneration, heavy-duty vehicles and engineering machinery industry, in which thedemanded gears should be of large size with a low risk and cost and high precision.Accordingly, a large-scale NC gear hobbing machines will be needed high safetyperformance and processing quality, especially the machining precision.
Additionally, some factors such as its large structural size, varieties, largedimension between hob and workpiece spindle of gear hobbing machine, thecomplicated system configuration, also the complicated hobbing system and cuttingforce, have the significant influence upon gear of machining precision. Furthermore, theresearch of machining error and capability on the large-scale NC gear hobbing machinehas become increasingly significant to improve machining precision and decreasemachining error of gear.
In order to realize the large-scale gears of machining accurately and efficiently, thisthesis has finished some research on the machining error mechanism and correspondingcompensation technique of large-scale gear hobbing machine from the followingaspects:
①Research on the effect of spindle deformation which is caused by hobbing forceis an important way to diminish or control the machining tolerance of the large-scalegear. Based on the hobbing gear features, process parameters, the methods of changingcoordinate and theory of beam deflection, several formulae of hobbing and spindledeformation and centre distance variation are established through theoretical analysis.For certain typical gear hobbing machine with particular structure and machiningparameter, its hobbing force and spindle deformation and centre distance variationunder practical hobbing parameter are calculated by adopting the mentioned formulae.Further, the relationship curve of cutting force, spindle rotational speed, hobbing depthand deformation of spindle were obtained, and revealed the law of hobbing and cuttingdeformation. This research provides important basis for optimization design of machinetool structure, processing parameter and machining error prediction and compensationfor gear hobbing machine.
②To master the influence of spindle and spindle the centre distance radial deformation caused by dynamical properties of hobbing gear on machining precision forgear hobbing machines. Based on machine tool structure, processing parameter,dynamical properties of the machining gear, dynamical principle and Euler-BernouHibeam vibration theory, the related dynamical mathematical models were established inthis paper. According to the theoretical model, processs parameters and vibrationexperimental datum, this paper focused on the research and analysis of mutual relationbetween the response parameters of vibration displacement and hobbing processparameters for hob and workpiece spindle. By all the above analysis and research, thispaper reveal the radial deformation change law of the centre distance between hob andworkpiece spindle caused by the vibration of hobbing gear, and the influence on whichthe vibration displacement deformation exerts gears’ machining precision.
③Research on the deviation of the centre distance between hob and workpiecespindle and this deviation is caused by thermal deformation. Based on the structuralfeatures of large-scale NC gear hobbing machine, the theory of thermal expansiondeformation of metallic materials, the extensional beam theory, non-uniformtemperature distribution of the Euler-Bernoulli beam and Kirchhoff theory ofplane-section assumption, a novel model was proposed in this paper to calculate thebending thermal deformation of lathe bed and upright column of gear hobbing machinetheoretically, then, the research on the axial deformation and bending deformation of theupright column were also carried out by utilizing the deformation theory of thedeformation element and equilibrium element method. According to the theoreticalresearch, the testing system of temperature and thermal deformation for gear hobbingmachines were proposed, further, a experiment platform was established to test andanalyze the temperature and corresponding thermal deformation displacement data,eventually to reveal the theory and practical rule of thermal deformation, and to plot thedeviation curves of the centre distance between hob and workpiece spindle and geartooth trace deviation.
④Based on the theoretical research of the vibration mode, harmonic response andhobbing dynamical properties, the finite element of entity simulation model wereestablished about the restriction mode and harmonic response for gear hobbing machine,and proposed the restriction boundary conditions for dynamical simulation. The finitemodel was simulated by adopting the processing and material parameter. According tothe simulation cloud chart and data, the gear machining error and the variation of thecentre distance between hob and workpiece spindle were analyzed. These results of the simulation research provide theoretical basis for the structural optimization design andassembly position adjustment for gear hobbing machine.
⑤Based on the research of the thermal deformation theory and experiment, thetesting temperature variables were selected by using the method of fuzzy clustering, thethermal error compensation model of the center distance between hob and workpiecespindle of the Large-scale NC gear hobbing machine was set up by adapting themethods of multi-regressions and the least square regression. Meanwhile, theexperiment of the thermal error compensation for the certain typical Large-scale NCgear hobbing machine was carried out in the numerical control automatic programmingsystem. The result shows that the thermal deformation value of the centre distance ofhob and workpiece spindle reduces substantially and various indexes and precise ofmachining gear improve remarkably. The thermal error compensation model is higherprecision, the method not only upgraded the gear machining accuracy and the efficiencybut also effectively control and forecast the thermal deformation of the large-scale NCgear hobbing machine. Therefore, this compensation system and experiment have greatpractical value.
These novel calculation models were established about the hobbing deformation,dynamical vibration displacement and thermal deformation of large-scale NC gearhobbing machine abased on the analysis and research of theory, experiment and finiteelement method in this paper. Meanwhile, the thermal error compensation model of thecentre distance between hob and workpiece spindle of gear hobbing machine was set upby combining processing parameters and experimental datum, numerical machining andcomputer software’s technology, which successfully carried out the experiment ofthermal error compensation. the result show that the machining precision of gears aregreatly improved, Above all these researches lay the theoretical basis and provide keytechnological support for promoting the high speed and efficiency of machiningcapability, and for overall realizing the large-scale gear of high precision of machiningtechnology of large-scale NC gear hobbing machine.
引文
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