低刚度摆线轮缘高速铣削变形与铣削力建模方法
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摘要
为了解决高速铣削过程中薄壁结构件加工质量控制难的问题,针对低刚度摆线轮轮廓高精度的加工要求,建立了低刚度轮缘的铣削变形预测模型以及弹性铣削力模型。其中,低刚度摆线轮缘的铣削变形预测模型是控制摆线轮加工质量的关键理论,也是弹性铣削力建模的重要理论依据。该研究成果可为高精度薄壁机构件的加工质量控制提供重要的理论基础,对提升我国制造业整体水平,满足国家重点发展行业的需求具有重要意义。
建立了低刚度轮缘在静态铣削过程中弯扭剪耦合的铣削变形模型。该模型中针对低刚度摆线轮轮缘的多种耦合铣削变形,建立了切削啮合区的基本微分方程;推导了低刚度轮缘的弯曲、扭转耦合变形,以及横向力引起的剪切变形;结合低刚度轮缘超静定的结构特点,根据卡氏定理推导出支座反力及其所引起的变形。
建立了细长径铣刀的铣削变形方程。该模型中将刀具等效为Timoshenko梁结构,结合刀刃的惯性矩计算关系式,建立了铣刀的铣削变形方程;基于刀具的偏心角和偏心半径,给出刀具偏离理论中心的坐标关系式。
基于低刚度轮缘的铣削变形模型和细长径铣刀的铣削变形模型,建立了变曲率弹性铣削力模型。该模型中结合周铣自由轮廓时曲率沿路径连续变化的特点,建立了变曲率弹性工艺几何模型;基于低刚度工件的铣削变形和细长径铣刀的弹性铣削变形以及偏心跳动对瞬时铣削厚度和瞬时切削啮合角的影响,建立了低刚度工艺系统的铣削力模型;采用Newton-Raphson迭代算法,仿真出铣削摆线轮整个轮廓时的铣削力、铣削变形以及刀具的铣削变形,并结合铣削试验,验证了铣削变形模型和铣削变形测试结果,以及变曲率弹性铣削力与铣削力测试结果比较一致。
根据仿真和试验结果可知,低刚度工艺系统中工件的弹性铣削变形和工艺几何模型对瞬时切削啮合角、瞬时铣削厚度的影响较大,因此,对弹性铣削力的影响较大;铣削变形与轮盘的刚度、轮缘张角、轮廓的结构形式以及轮缘厚度密切相关,且轮盘厚度和轮缘厚度均具有均载作用,其中,轮盘厚度相对轮缘厚度的均载作用较大;另外,低刚度工件的铣削变形和细长径铣刀的弹性变形在高精度的铣削过程中对工件轮廓加工精度的影响较明显,铣削变形和铣削力之间关系复杂且密切相关,并进一步影响低刚度零件的加工精度。另外,铣削力与加工参数密切相关。
To resolve the problem of high accuracy profile for thin-wall component with complex profile during high speed milling process,a model for predicting tooth profile deflection and the flexible milling force model for low-rigidity component with cycloid gear profile is presented to solve the problem of controlling the machined quality in high speed milling. In this model, the key to controlling the machined quality lies in predicting tooth profile deflection for low-rigidity cycloid gear tooth rim. And it provides a theory basis for flexible cutting forces. The achievements of research provide significant in theory for the controlling the machined quality in high speed milling thin-wall component. And the modeling method and the conclusions have important significance in increasing the whole level of Manufacture and meeting the China key business.
A milling deflection model for predicting the bending-torsional coupled deflection based on low-rigidity cycloid tooth profile, to determine the relationship between deflection and milling force is approached. In the model a differential equation that describes the coupled deflection of the cutting immersed area on the low-rigidity cycloid tooth profile is provided. And a method is provided to identify the key processing characteristics of the coupled deflection which involves the bending deflection, torsional deflection and shearing deflection. According to the construction of the statically indeterminate low-rigidity tooth rim fixed two ends the supporting forces and deflections under the action of applied forces on the end are derived on Casfigliano’s Second Theorem.
Assuming the slender cutter as a Timoshenko beam consisting of the shank and the flute the cutter bending deflection is derived. In the bending deflection model, take into account the effects on the inertia of the cutter edges. In this paper, tool runout is presented. The method can be used to express the centre coordinates of tool due to the cutter runout.
A flexible force model suitable for cycloid gear profile is proposed based on the milling deflection in the workpiece-tool process. Taking into account the deflections of workpiece and cutter the expressions are derived for process geometries parameters in peripheral milling where curvature varies continuously along the tool path. Then modified cutting tooth immersion angle and undeformed chip thickness have been introduced due to the deflections and process geometries. In machining workpiece geometries, the milling force distribution, deflections of the gear rim and tool for are solved interatively by the modified Newton-Raphson method. According to the measured forces and deflections the results have shown good convergence between predicted and measured values.
From the present study it has shown that the cutting tooth immersion angle and undeformed chip thickness subject to the deflectons and process geometries parameters. These will influence the flexible force model. The study has shown that any of the values of the gear stiffness, disk dimension, angle responding to the thin-wall rim, tooth construction and rim dimension has a strongly effect on the milling deflection. It can be shown that the disk width of rim is shared with the cutting force much more than the rim width. When high speed mills the precision cycloid gear profile the deflections of the low-rigidity workpiece and slender tool bring about a great effect on the dimension stability of the finished parts. This is attributed to the complex relation between the milling force and the milling deflection, which will influence the precision of the part.
建立了低刚度轮缘在静态铣削过程中弯扭剪耦合的铣削变形模型。该模型中针对低刚度摆线轮轮缘的多种耦合铣削变形,建立了切削啮合区的基本微分方程;推导了低刚度轮缘的弯曲、扭转耦合变形,以及横向力引起的剪切变形;结合低刚度轮缘超静定的结构特点,根据卡氏定理推导出支座反力及其所引起的变形。
建立了细长径铣刀的铣削变形方程。该模型中将刀具等效为Timoshenko梁结构,结合刀刃的惯性矩计算关系式,建立了铣刀的铣削变形方程;基于刀具的偏心角和偏心半径,给出刀具偏离理论中心的坐标关系式。
基于低刚度轮缘的铣削变形模型和细长径铣刀的铣削变形模型,建立了变曲率弹性铣削力模型。该模型中结合周铣自由轮廓时曲率沿路径连续变化的特点,建立了变曲率弹性工艺几何模型;基于低刚度工件的铣削变形和细长径铣刀的弹性铣削变形以及偏心跳动对瞬时铣削厚度和瞬时切削啮合角的影响,建立了低刚度工艺系统的铣削力模型;采用Newton-Raphson迭代算法,仿真出铣削摆线轮整个轮廓时的铣削力、铣削变形以及刀具的铣削变形,并结合铣削试验,验证了铣削变形模型和铣削变形测试结果,以及变曲率弹性铣削力与铣削力测试结果比较一致。
根据仿真和试验结果可知,低刚度工艺系统中工件的弹性铣削变形和工艺几何模型对瞬时切削啮合角、瞬时铣削厚度的影响较大,因此,对弹性铣削力的影响较大;铣削变形与轮盘的刚度、轮缘张角、轮廓的结构形式以及轮缘厚度密切相关,且轮盘厚度和轮缘厚度均具有均载作用,其中,轮盘厚度相对轮缘厚度的均载作用较大;另外,低刚度工件的铣削变形和细长径铣刀的弹性变形在高精度的铣削过程中对工件轮廓加工精度的影响较明显,铣削变形和铣削力之间关系复杂且密切相关,并进一步影响低刚度零件的加工精度。另外,铣削力与加工参数密切相关。
To resolve the problem of high accuracy profile for thin-wall component with complex profile during high speed milling process,a model for predicting tooth profile deflection and the flexible milling force model for low-rigidity component with cycloid gear profile is presented to solve the problem of controlling the machined quality in high speed milling. In this model, the key to controlling the machined quality lies in predicting tooth profile deflection for low-rigidity cycloid gear tooth rim. And it provides a theory basis for flexible cutting forces. The achievements of research provide significant in theory for the controlling the machined quality in high speed milling thin-wall component. And the modeling method and the conclusions have important significance in increasing the whole level of Manufacture and meeting the China key business.
A milling deflection model for predicting the bending-torsional coupled deflection based on low-rigidity cycloid tooth profile, to determine the relationship between deflection and milling force is approached. In the model a differential equation that describes the coupled deflection of the cutting immersed area on the low-rigidity cycloid tooth profile is provided. And a method is provided to identify the key processing characteristics of the coupled deflection which involves the bending deflection, torsional deflection and shearing deflection. According to the construction of the statically indeterminate low-rigidity tooth rim fixed two ends the supporting forces and deflections under the action of applied forces on the end are derived on Casfigliano’s Second Theorem.
Assuming the slender cutter as a Timoshenko beam consisting of the shank and the flute the cutter bending deflection is derived. In the bending deflection model, take into account the effects on the inertia of the cutter edges. In this paper, tool runout is presented. The method can be used to express the centre coordinates of tool due to the cutter runout.
A flexible force model suitable for cycloid gear profile is proposed based on the milling deflection in the workpiece-tool process. Taking into account the deflections of workpiece and cutter the expressions are derived for process geometries parameters in peripheral milling where curvature varies continuously along the tool path. Then modified cutting tooth immersion angle and undeformed chip thickness have been introduced due to the deflections and process geometries. In machining workpiece geometries, the milling force distribution, deflections of the gear rim and tool for are solved interatively by the modified Newton-Raphson method. According to the measured forces and deflections the results have shown good convergence between predicted and measured values.
From the present study it has shown that the cutting tooth immersion angle and undeformed chip thickness subject to the deflectons and process geometries parameters. These will influence the flexible force model. The study has shown that any of the values of the gear stiffness, disk dimension, angle responding to the thin-wall rim, tooth construction and rim dimension has a strongly effect on the milling deflection. It can be shown that the disk width of rim is shared with the cutting force much more than the rim width. When high speed mills the precision cycloid gear profile the deflections of the low-rigidity workpiece and slender tool bring about a great effect on the dimension stability of the finished parts. This is attributed to the complex relation between the milling force and the milling deflection, which will influence the precision of the part.
引文
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