螺旋锥齿轮磨削误差产生机制及修正技术研究
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摘要
螺旋锥齿轮是机械传动的基础元件,其空间形状和加工过程相当复杂。数控技术的发展,为螺旋锥齿轮简化调整和进一步提高加工质量提供了方便。而螺旋锥齿轮加工质量的控制一直是其加工中的一个关键问题。目前国外螺旋锥齿轮数控加工质量控制技术仅为少数公司所拥有,国内尚处于起步阶段。为此,本文根据螺旋锥齿轮数控加工的特点,以提高其加工精度为目的,展开螺旋锥齿轮磨削误差机理及补偿技术的研究,具体内容如下所述。
螺旋锥齿轮加工方法及数控加工模型的研究。由于螺旋锥齿轮磨削加工与铣齿加工原理一致,本文根据其铣齿加工特点,结合相对微分和局部共轭法,分析了螺旋锥齿轮大轮展成法、成形法,小轮刀倾法、变性法的加工算法。另外根据摇台式机床加工的特点,分别建立了大轮展成法、成形法,小轮刀倾法、变性法的六轴五联动数控加工模型,为后述螺旋锥齿轮磨削误差及齿面误差修正的研究提供了理论基础。
六轴五联动螺旋锥齿轮数控磨床综合误差模型的研究。运用多体系统理论,研究了螺旋锥齿轮CNC磨床低序体阵列拓扑结构,进而采用齐次坐标矩阵变换方法,建立了CNC螺旋锥齿轮磨床综合空间误差的数学模型,获得了六个自由度方向的误差表达式。在此基础上,分析了六轴五联动螺旋锥齿轮磨床砂轮磨削点的误差变化规律以及与齿轮齿距、螺旋角、周节、齿形等形位误差生成的关系,提出了获得螺旋锥齿轮精确形位参量所需的机床关键误差控制条件。
螺旋锥齿轮磨齿加工齿面误差的影响研究。结合得到的误差综合模型,运用螺旋锥齿轮加工原理、齿轮啮合理论,进一步建立了含磨床各运动副误差的螺旋锥齿轮的齿面方程,对含磨床砂轮主轴运动副误差的齿面进行仿真并得到差曲面,进而分析了磨床砂轮主轴各运动副误差对螺旋锥齿轮齿面的影响。其次根据成形法加工螺旋锥齿轮的原理,运用空间坐标变换原理,建立了成形法加工时螺旋锥齿轮的齿面方程,研究了各个机床调整参数扰动时的差曲面,分析了机床调整误差对齿面误差的影响规律。上述研究查明了磨床误差及加工调整参数误差对螺旋锥齿轮齿面误差的影响机制。
基于截断奇异值分解法的齿面误差修正技术的研究。结合机床调整参数、齿轮啮合原理,建立了螺旋锥齿轮齿面误差修正模型。提出采用TSVD(截断奇异值分解)正则化方法与L曲线相结合求解此线性超越方程组,从而达到对齿面误差修正,其求解精度比采用的最小二乘法求解更高,误差修正更好,为高精度的齿面误差修正提供了有效方法。
螺旋锥齿轮误差修正试验研究。实验验证了本文齿面误差修正模型及提出的TSVD法求解的正确性,提高螺旋锥齿轮齿面加工质量。此外还进一步分析了修正前后五个联动轴的表达式系数的变化趋势以及对齿面误差的影响规律。
Spiral bevel gear is the mechanical transmission fundamental element.Its space shape and the machining process are very complicated.The developments of numerical control technology provide convenience for simplification adjustment and improvement processing quality of spiral bevel gear.But the quality control of spiral bevel gear processing has been the key problem in the processing.At present,the quality control technologies of spiral bevel gear NC processing are grasped only the minority companies in overseas and are still at the starting stage in domestic. Therefore,according to the numerical control processing characteristic of spiral bevel gear,taking increase processing accuracy as the goal,the paper carries out research in mechanism and compensation technology of spiral bevel gear grinding error.The concrete contents are as follows.
Study on the numerical control processing model and machining method of spiral bevel gear.Combined with relative derivation and the partial conjugate law, both the generated method and formatted method of gear were analyzed,both the tilted method and modified roll method of pinion were also analyzed.According to machining characteristic of a cradle-type universal machine,the six axis five linkage numerical control machining model of generated method,formatted method,tilted method and modified roll method were established.The above research provides theoretical basis for analysis of spiral bevel gear grinding error and correction tooth surface error.
Study on the synthesis error model of spiral bevel gear numerical control grinder with six axes five linkages.Based on the multi-body system theory and homogeneous coordinate matrix transformation method,the low foreword body array topology structure of spiral bevel gear CNC grinder was studied.The mathematical model of synthesis space error of spiral bevel gear CNC grinder was established,and the erroneous expressions of six degrees of freedom direction were obtained.Based on such expressions,the tool point erroneous change laws of spiral bevel gear machine with six axes five linkages were analyzed,and the influence of the grinding spot errors on the teeth pitch,helix angle,pitch,teeth profile and others was discussed.The control conditions of machine's key error were proposed to obtain the precise form and position parameter of spiral bevel gear.
Study on the effect of machining errors of spiral bevel gear-tooth surface.Based on the model of error synthesis,the tooth surface equation of spiral bevel gear including the error motion for machine tools was further proposed by the manufacture principle and meshing principle of spiral bevel gear.The simulation of tooth surface with or without error motion of the spindle was carried out and the difference surface was also obtained,then the effect of error motion of the spindle for tooth surface was analyzed.Based on the forming processing principle of spiral bevel gear and space coordinates transformation,the tooth surface equation using forming processing was build.The difference surfaces with the disturbances of each machine tool adjustment parameter were studied,and the influence law of machine tool adjustment errors on tooth surface errors was analyzed.The above research finds out the influence of grinder error and machining setting parameter error on tooth surface error of spiral bevel gear.
Study on the error correction technique of tooth surface using truncated singular value decomposition(TSVD).The error correction model of tooth surface was established by machine tool adjustment parameters and meshing principle.The solution to these linear transcendental equations based on regularization method of truncated singular value decomposition and L-curve method was proposed,while the tooth surface errors were corrected and the solving precision is higher than that using the least square method.The above research provides effective method for high precision correction of tooth surface error.
Experimental study on the error correction of spiral bevel gear.The error correction model of tooth surface and solving method using TSVD were verified experimentally,and the tooth surface machining quality of spiral bevel gear was improved.In addition,the change tendency of the pre and post correction of five axes linkage expression coefficients was analyzed,and the influence of change tendency on tooth surface geometrical error was also discussed.
螺旋锥齿轮加工方法及数控加工模型的研究。由于螺旋锥齿轮磨削加工与铣齿加工原理一致,本文根据其铣齿加工特点,结合相对微分和局部共轭法,分析了螺旋锥齿轮大轮展成法、成形法,小轮刀倾法、变性法的加工算法。另外根据摇台式机床加工的特点,分别建立了大轮展成法、成形法,小轮刀倾法、变性法的六轴五联动数控加工模型,为后述螺旋锥齿轮磨削误差及齿面误差修正的研究提供了理论基础。
六轴五联动螺旋锥齿轮数控磨床综合误差模型的研究。运用多体系统理论,研究了螺旋锥齿轮CNC磨床低序体阵列拓扑结构,进而采用齐次坐标矩阵变换方法,建立了CNC螺旋锥齿轮磨床综合空间误差的数学模型,获得了六个自由度方向的误差表达式。在此基础上,分析了六轴五联动螺旋锥齿轮磨床砂轮磨削点的误差变化规律以及与齿轮齿距、螺旋角、周节、齿形等形位误差生成的关系,提出了获得螺旋锥齿轮精确形位参量所需的机床关键误差控制条件。
螺旋锥齿轮磨齿加工齿面误差的影响研究。结合得到的误差综合模型,运用螺旋锥齿轮加工原理、齿轮啮合理论,进一步建立了含磨床各运动副误差的螺旋锥齿轮的齿面方程,对含磨床砂轮主轴运动副误差的齿面进行仿真并得到差曲面,进而分析了磨床砂轮主轴各运动副误差对螺旋锥齿轮齿面的影响。其次根据成形法加工螺旋锥齿轮的原理,运用空间坐标变换原理,建立了成形法加工时螺旋锥齿轮的齿面方程,研究了各个机床调整参数扰动时的差曲面,分析了机床调整误差对齿面误差的影响规律。上述研究查明了磨床误差及加工调整参数误差对螺旋锥齿轮齿面误差的影响机制。
基于截断奇异值分解法的齿面误差修正技术的研究。结合机床调整参数、齿轮啮合原理,建立了螺旋锥齿轮齿面误差修正模型。提出采用TSVD(截断奇异值分解)正则化方法与L曲线相结合求解此线性超越方程组,从而达到对齿面误差修正,其求解精度比采用的最小二乘法求解更高,误差修正更好,为高精度的齿面误差修正提供了有效方法。
螺旋锥齿轮误差修正试验研究。实验验证了本文齿面误差修正模型及提出的TSVD法求解的正确性,提高螺旋锥齿轮齿面加工质量。此外还进一步分析了修正前后五个联动轴的表达式系数的变化趋势以及对齿面误差的影响规律。
Spiral bevel gear is the mechanical transmission fundamental element.Its space shape and the machining process are very complicated.The developments of numerical control technology provide convenience for simplification adjustment and improvement processing quality of spiral bevel gear.But the quality control of spiral bevel gear processing has been the key problem in the processing.At present,the quality control technologies of spiral bevel gear NC processing are grasped only the minority companies in overseas and are still at the starting stage in domestic. Therefore,according to the numerical control processing characteristic of spiral bevel gear,taking increase processing accuracy as the goal,the paper carries out research in mechanism and compensation technology of spiral bevel gear grinding error.The concrete contents are as follows.
Study on the numerical control processing model and machining method of spiral bevel gear.Combined with relative derivation and the partial conjugate law, both the generated method and formatted method of gear were analyzed,both the tilted method and modified roll method of pinion were also analyzed.According to machining characteristic of a cradle-type universal machine,the six axis five linkage numerical control machining model of generated method,formatted method,tilted method and modified roll method were established.The above research provides theoretical basis for analysis of spiral bevel gear grinding error and correction tooth surface error.
Study on the synthesis error model of spiral bevel gear numerical control grinder with six axes five linkages.Based on the multi-body system theory and homogeneous coordinate matrix transformation method,the low foreword body array topology structure of spiral bevel gear CNC grinder was studied.The mathematical model of synthesis space error of spiral bevel gear CNC grinder was established,and the erroneous expressions of six degrees of freedom direction were obtained.Based on such expressions,the tool point erroneous change laws of spiral bevel gear machine with six axes five linkages were analyzed,and the influence of the grinding spot errors on the teeth pitch,helix angle,pitch,teeth profile and others was discussed.The control conditions of machine's key error were proposed to obtain the precise form and position parameter of spiral bevel gear.
Study on the effect of machining errors of spiral bevel gear-tooth surface.Based on the model of error synthesis,the tooth surface equation of spiral bevel gear including the error motion for machine tools was further proposed by the manufacture principle and meshing principle of spiral bevel gear.The simulation of tooth surface with or without error motion of the spindle was carried out and the difference surface was also obtained,then the effect of error motion of the spindle for tooth surface was analyzed.Based on the forming processing principle of spiral bevel gear and space coordinates transformation,the tooth surface equation using forming processing was build.The difference surfaces with the disturbances of each machine tool adjustment parameter were studied,and the influence law of machine tool adjustment errors on tooth surface errors was analyzed.The above research finds out the influence of grinder error and machining setting parameter error on tooth surface error of spiral bevel gear.
Study on the error correction technique of tooth surface using truncated singular value decomposition(TSVD).The error correction model of tooth surface was established by machine tool adjustment parameters and meshing principle.The solution to these linear transcendental equations based on regularization method of truncated singular value decomposition and L-curve method was proposed,while the tooth surface errors were corrected and the solving precision is higher than that using the least square method.The above research provides effective method for high precision correction of tooth surface error.
Experimental study on the error correction of spiral bevel gear.The error correction model of tooth surface and solving method using TSVD were verified experimentally,and the tooth surface machining quality of spiral bevel gear was improved.In addition,the change tendency of the pre and post correction of five axes linkage expression coefficients was analyzed,and the influence of change tendency on tooth surface geometrical error was also discussed.
引文
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