高速面铣刀模态参数及其对切削性能影响研究
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摘要
高速面铣刀主要应用于铸铁、铝合金等材料的平面粗、精加工,可满足汽车、航空航天、模具等工业高效加工的需要。随着高速加工中心等高性能机床的不断升级,对高速面铣刀的动态性能提出了更高技术要求。
高速面铣刀的结构具有直径大、齿数多的特点,其切削过程是断续的,在刀齿周期性切入、切出工件过程中,存在振动和冲击现象；每个刀齿的切屑层厚度随着面铣刀的旋转角度发生变化,产生的铣削力具有周期性、时变性的特点。面铣削过程中的离心力和动态铣削力等载荷激发面铣刀的受迫振动和自激振动,影响高速面铣刀的铣削稳定性和工件表面质量。
对高速面铣刀进行模态分析获取面铣刀的模态参数,研究模态参数对面铣刀铣削稳定性和工件表面粗糙度的影响规律,建立高速面铣刀的动态特性与其切削性能之间的联系,是改善面铣刀铣削稳定性和提高工件表面质量的主要研究内容。
对面铣刀振动系统性质及其阻尼特性进行分析,建立面铣刀的多自由度结构比例阻尼振动系统微分方程。通过对其特征值求解,得到面铣刀频响函数的解析表达式,为面铣刀有限元模态分析和实验模态分析提供理论基础。
由于可转位面铣刀具有装配结构的特点,选用具备接触建模功能的ABAQUS有限元分析软件,建立面铣刀有限元模型,提高模态分析结果的精确程度。
刀体是面铣刀尺寸和质量最大的零件,对刀体材料和刀齿密度对模态参数的影响进行重点研究,分析五种刀体材料及三种刀齿密度面铣刀的前六阶固有频率和振型,发现五种刀体材料面铣刀的一阶固有频率从高到低为碳素纤维增强塑料、40CrMo、45#钢、铝合金AlCuMg2和钛合金Ti6A14V。刀齿密度是影响刀体结构的重要因素,在推荐的刀齿数范围内,刀齿密度越小,固有频率越高,面铣刀安全稳定切削的转速范围越大。
根据高速面铣刀的结构特点,确定面铣刀模态实验分析的原理和方法。模态实验采用频域辨识法中的单输入单输出方式；激振器采用自制电子冲击力锤,使产生的冲击力具有可重复性和可调节性；支承方式采用自由模态法和工作模态法两种方式；对所获得的频率响应函数的实频图和虚频图,运用分量分析法进行参数辨识。通过实验模态分析法获得面铣刀模态参数之后,和有限元模态分析结果进行比较,验证面铣刀有限元模型的有效性。
根据组合结构系统设计法,运用二分量响应耦合子结构分析法(RCSA),在有限元模态分析和实验模态分析的基础上,求解获得“主轴-刀柄”和面铣刀的结合面参数(线性刚度Kx和线性阻尼Gx、旋转刚度Kθ和旋转阻尼Gθ),并对结合面参数进行实验验证。面铣刀采用工作模态法测试刀尖频响函数时,利用结合面参数可以消除机床的影响,间接获得面铣刀的模态参数；利用结合面参数和面铣刀有限元等效模型,可以分析在该机床上使用的高速面铣刀的动态性能。
面铣削稳定性是评价高速面铣刀切削性能的重要方面。分析了面铣刀切削角度对铣削过程的影响,根据再生颤振机理建立刀片径向瞬时切屑厚度模型和动态面铣削力模型,动态铣削力系数矩阵反映了面铣削力断续性、时变性和周期性变化的特点。根据面铣削系统频响函数的负实部,计算临界轴向切削深度,并绘制轴向切削深度和主轴转速之间的关系图,即面铣削稳定性极限图,实现对颤振现象的预报和控制。
设计面铣削实验系统和实验参数,通过三维面铣削力测试结果,以及测量、计算已加工工件表面硬化程度,并利用二维和三维工件表面形貌验证面铣削稳定性极限图预报的有效性和可靠性。对比不同面铣刀的稳定性极限图发现：在推荐的刀齿数范围内,随着一阶固有频率的降低和模态阻尼的减小,稳定切削域减小；随着刀齿密度的增加,面铣刀的铣削稳定性降低。
工件表面质量反映了高速面铣刀切削性能的优劣。工件表面质量一般由表面粗糙度值来评定。通过研究面铣削过程中对工件表面粗糙度的主要影响因素,考虑平面刃口型式刀片的径向和轴向跳动误差、每齿进给量、切削刃长度、刀尖圆弧半径、刀片主偏角、轴向切削深度、受迫振动引起的刀齿与工件间的轴向相对位移等动静态因素的影响,沿工件表面粗糙度值最大的方向建立了铣削工件表面粗糙度模型。根据所测得的刀齿径向和轴向跳动误差,依据静态表面粗糙度模型模拟计算出刀齿轨迹；结合模态实验和铣削实验的结果,求解面铣削振动微分方程,得到面铣刀刀齿和工件的轴向动态相对位移；将静态模型和动态模型分别预测的结果进行综合,预测出铣削工件表面轮廓,实现对面铣刀铣削工件表面质量的预估和评价。验证了工件表面粗糙度模型,同时发现在相同切削参数下,在推荐的刀齿数范围内,随着刀齿密度的增加,表面粗糙度值增加,表面质量恶化。
High-speed face-milling cutter is mainly used for machining flat surface, and widely used for rough and finish machining of cast iron, aluminum. For its high cutting speed, face-milling cutting process has been widely used in automotive, aerospace, mold and other manufacturing fields. With high speed CNC machining centers and other high-performance machine tools upgraded, more and more technical requirements has been purposed for improve the dynamic performance of face-milling cutter.
High speed face-milling cutter has the features of large diameter, more teeth, and its cutting process is intermittent. When cutting teeth periodically cut in and off of the workpiece, there exits phenomenon of the vibration and impact. The chip thickness of each cutting teeth changes with rotation angle, hence cutting force is cyclical and time varying. The forced and self-vibration generated by centrifugal force and dynamic cutting force during cutting process, has significant effect on milling stability and workpiece surface quality.
By applying modal analysis on face-milling cutter, the modal parameters are extracted in this paper. By analyzing the effect of modal parameters on milling stability and workpiece surface roughness, the relationship between the dynamic characteristic and cutting performance are established, which is the main research content of improve cutting stability and workpiece surface quality.
By analyzing the nature of face-milling vibration system and damping characteristic, the multi-freedom structural proportion damping vibration system differential equation is built. By solving of eigenvalue, the analytical expression of FRF is got, which can supply theory basis for FEM modal analysis and experimental modal analysis for face-milling cutter.
Owing to the assembly of structural features of indexable face-milling cutter, ABAQUS software is selected in this paper for its contact modeling function to improve the accuracy of the modal analysis results.
Because cutting tool body is the largest part of the face-milling cutter, in this paper, the effects on modal parameters by the materials'properties and the density of cutting teeth are investigated. There are five different cutting tool body materials and three different densities of cutting teeth for different face-milling cutters. The first six natural frequencies and modal of these face-milling cutters are analyzed in this paper. Results show that, for the five different materials, the natural frequencies from high to low are: carbon fiber reinforced plastics,40CrMo,45#steel, AlCuMg2and Ti6A14V.Density of cutting teeth are important factors of cutter structure, the lower of the density of the teeth, the higher of the natural frequency and the larger spindle speed range for safe and stable cutting within the recommended teeth range.
According to structural characteristics of the face-milling cutter, the principle and method of experimental modal analysis are determined. Modal experiments adopt single input and output method of frequency domain identification. Exciter adopts electronic impact hammer to induce repeatability and adjustability impact force. Supporting methods adopt two ways including free modal and work modal. For the FRF of the tool tip, component analysis is adopted to identify the parameters. The modal parameters get from experimental modal analysis are compared with FEM analysis results to validation the FEM model.
According to composite structure system design method and two-component response coupling substructure analysis, based on the FEM modal analysis and experimental modal analysis, the joint surface parameters between spindle/shank and face milling cutter are get (linear stiffness Kx, linear damping Gx, rotation stiffness Kg and rotation damping Ge). The contact surface parameters are then valid by experiments. When using work modal to get the FRF of tool tip, by using the contact surface parameters, the modal parameters of face-milling cutter can be get indirectly. The joint surface parameters and the equivalent FEM model can be used to analyze the dynamic characteristic of the face milling cutter fixed on the specific machine tools.
The stability of the face-milling process is important to estimate and evaluate the cutting performance of the face-milling cutter. By analyzing the effect of face-milling cutting angle on milling process, based on mechanism of renewable flutter, the model of radial instantaneous chip thickness and dynamic face-milling cutting force are established. The matrix of dynamic milling force coefficient reflects the features of milling force:intermittent, time-varying and periodicity.
According to the FRF negative real part of face-milling system, the critical axial depth-of-cut is calculated. The diagrams which reflect the relationship between axial depth-of-cut and spindle speed have also been drawn in this paper. The stability limit lobes of face-milling process can forecast and control the phenomenon of chatter.
In order to verify the validity and reliability of the stability limit lobes, face-milling experimental system and parameters are designed. Cutting force in three directions are tested, work hardening capacity are also measured and calculated, the two and three dimensional picture reflecting workpiece surface integrity are get. By comparing different stability limit lobes, it is found that with the decrease of natural frequency and modal damping, the stable cutting region decreases; with the increase of density of cutter teeth, the stability of the face-milling process decreases within the recommended teeth range.
The workpiece surface quality can reflect the cutting performance of face-milling cutter and be evaluated by the the surface roughness of workpiece. By studying the influencing factors'effect on surface roughness during face-milling process, including radial and axial runout of the teeth in the form of flat blade, feed per tooth, cutting edge length, nose radius, cutting lead angle, axial depth-of-cut, axial displacement between cutting tooth and workpiece caused by forced vibration, the surface roughness prediction models are established in the direction of the maximum value of surface roughness.
According to the measured radial and axial runout of the teeth in the form of flat blade, the trajectory of cutting teeth is calculated based on the static surface roughness model. By combining experimental and modal analysis results, the vibration differential equations are solved and the axial relative displacement between cutting teeth and workpiece are get. By integrating the prediction results of static and dynamic models, the surface roughness and contours are predicted. The predicted results can be used for estimation and evaluation of surface quality. The prediction surface roughness model is verified by experiments. At the same time, it is found that the surface roughness increases and the workpiece surface quality deteriorates with the increase of density of cutter teeth under the same cutting conditions within the recommended teeth range.
The project is supported by Major Science and Technology Program of High-end CNC Machine Tools and Basic Manufacturing Equipment (2011ZX04016-031).
高速面铣刀的结构具有直径大、齿数多的特点,其切削过程是断续的,在刀齿周期性切入、切出工件过程中,存在振动和冲击现象；每个刀齿的切屑层厚度随着面铣刀的旋转角度发生变化,产生的铣削力具有周期性、时变性的特点。面铣削过程中的离心力和动态铣削力等载荷激发面铣刀的受迫振动和自激振动,影响高速面铣刀的铣削稳定性和工件表面质量。
对高速面铣刀进行模态分析获取面铣刀的模态参数,研究模态参数对面铣刀铣削稳定性和工件表面粗糙度的影响规律,建立高速面铣刀的动态特性与其切削性能之间的联系,是改善面铣刀铣削稳定性和提高工件表面质量的主要研究内容。
对面铣刀振动系统性质及其阻尼特性进行分析,建立面铣刀的多自由度结构比例阻尼振动系统微分方程。通过对其特征值求解,得到面铣刀频响函数的解析表达式,为面铣刀有限元模态分析和实验模态分析提供理论基础。
由于可转位面铣刀具有装配结构的特点,选用具备接触建模功能的ABAQUS有限元分析软件,建立面铣刀有限元模型,提高模态分析结果的精确程度。
刀体是面铣刀尺寸和质量最大的零件,对刀体材料和刀齿密度对模态参数的影响进行重点研究,分析五种刀体材料及三种刀齿密度面铣刀的前六阶固有频率和振型,发现五种刀体材料面铣刀的一阶固有频率从高到低为碳素纤维增强塑料、40CrMo、45#钢、铝合金AlCuMg2和钛合金Ti6A14V。刀齿密度是影响刀体结构的重要因素,在推荐的刀齿数范围内,刀齿密度越小,固有频率越高,面铣刀安全稳定切削的转速范围越大。
根据高速面铣刀的结构特点,确定面铣刀模态实验分析的原理和方法。模态实验采用频域辨识法中的单输入单输出方式；激振器采用自制电子冲击力锤,使产生的冲击力具有可重复性和可调节性；支承方式采用自由模态法和工作模态法两种方式；对所获得的频率响应函数的实频图和虚频图,运用分量分析法进行参数辨识。通过实验模态分析法获得面铣刀模态参数之后,和有限元模态分析结果进行比较,验证面铣刀有限元模型的有效性。
根据组合结构系统设计法,运用二分量响应耦合子结构分析法(RCSA),在有限元模态分析和实验模态分析的基础上,求解获得“主轴-刀柄”和面铣刀的结合面参数(线性刚度Kx和线性阻尼Gx、旋转刚度Kθ和旋转阻尼Gθ),并对结合面参数进行实验验证。面铣刀采用工作模态法测试刀尖频响函数时,利用结合面参数可以消除机床的影响,间接获得面铣刀的模态参数；利用结合面参数和面铣刀有限元等效模型,可以分析在该机床上使用的高速面铣刀的动态性能。
面铣削稳定性是评价高速面铣刀切削性能的重要方面。分析了面铣刀切削角度对铣削过程的影响,根据再生颤振机理建立刀片径向瞬时切屑厚度模型和动态面铣削力模型,动态铣削力系数矩阵反映了面铣削力断续性、时变性和周期性变化的特点。根据面铣削系统频响函数的负实部,计算临界轴向切削深度,并绘制轴向切削深度和主轴转速之间的关系图,即面铣削稳定性极限图,实现对颤振现象的预报和控制。
设计面铣削实验系统和实验参数,通过三维面铣削力测试结果,以及测量、计算已加工工件表面硬化程度,并利用二维和三维工件表面形貌验证面铣削稳定性极限图预报的有效性和可靠性。对比不同面铣刀的稳定性极限图发现：在推荐的刀齿数范围内,随着一阶固有频率的降低和模态阻尼的减小,稳定切削域减小；随着刀齿密度的增加,面铣刀的铣削稳定性降低。
工件表面质量反映了高速面铣刀切削性能的优劣。工件表面质量一般由表面粗糙度值来评定。通过研究面铣削过程中对工件表面粗糙度的主要影响因素,考虑平面刃口型式刀片的径向和轴向跳动误差、每齿进给量、切削刃长度、刀尖圆弧半径、刀片主偏角、轴向切削深度、受迫振动引起的刀齿与工件间的轴向相对位移等动静态因素的影响,沿工件表面粗糙度值最大的方向建立了铣削工件表面粗糙度模型。根据所测得的刀齿径向和轴向跳动误差,依据静态表面粗糙度模型模拟计算出刀齿轨迹；结合模态实验和铣削实验的结果,求解面铣削振动微分方程,得到面铣刀刀齿和工件的轴向动态相对位移；将静态模型和动态模型分别预测的结果进行综合,预测出铣削工件表面轮廓,实现对面铣刀铣削工件表面质量的预估和评价。验证了工件表面粗糙度模型,同时发现在相同切削参数下,在推荐的刀齿数范围内,随着刀齿密度的增加,表面粗糙度值增加,表面质量恶化。
High-speed face-milling cutter is mainly used for machining flat surface, and widely used for rough and finish machining of cast iron, aluminum. For its high cutting speed, face-milling cutting process has been widely used in automotive, aerospace, mold and other manufacturing fields. With high speed CNC machining centers and other high-performance machine tools upgraded, more and more technical requirements has been purposed for improve the dynamic performance of face-milling cutter.
High speed face-milling cutter has the features of large diameter, more teeth, and its cutting process is intermittent. When cutting teeth periodically cut in and off of the workpiece, there exits phenomenon of the vibration and impact. The chip thickness of each cutting teeth changes with rotation angle, hence cutting force is cyclical and time varying. The forced and self-vibration generated by centrifugal force and dynamic cutting force during cutting process, has significant effect on milling stability and workpiece surface quality.
By applying modal analysis on face-milling cutter, the modal parameters are extracted in this paper. By analyzing the effect of modal parameters on milling stability and workpiece surface roughness, the relationship between the dynamic characteristic and cutting performance are established, which is the main research content of improve cutting stability and workpiece surface quality.
By analyzing the nature of face-milling vibration system and damping characteristic, the multi-freedom structural proportion damping vibration system differential equation is built. By solving of eigenvalue, the analytical expression of FRF is got, which can supply theory basis for FEM modal analysis and experimental modal analysis for face-milling cutter.
Owing to the assembly of structural features of indexable face-milling cutter, ABAQUS software is selected in this paper for its contact modeling function to improve the accuracy of the modal analysis results.
Because cutting tool body is the largest part of the face-milling cutter, in this paper, the effects on modal parameters by the materials'properties and the density of cutting teeth are investigated. There are five different cutting tool body materials and three different densities of cutting teeth for different face-milling cutters. The first six natural frequencies and modal of these face-milling cutters are analyzed in this paper. Results show that, for the five different materials, the natural frequencies from high to low are: carbon fiber reinforced plastics,40CrMo,45#steel, AlCuMg2and Ti6A14V.Density of cutting teeth are important factors of cutter structure, the lower of the density of the teeth, the higher of the natural frequency and the larger spindle speed range for safe and stable cutting within the recommended teeth range.
According to structural characteristics of the face-milling cutter, the principle and method of experimental modal analysis are determined. Modal experiments adopt single input and output method of frequency domain identification. Exciter adopts electronic impact hammer to induce repeatability and adjustability impact force. Supporting methods adopt two ways including free modal and work modal. For the FRF of the tool tip, component analysis is adopted to identify the parameters. The modal parameters get from experimental modal analysis are compared with FEM analysis results to validation the FEM model.
According to composite structure system design method and two-component response coupling substructure analysis, based on the FEM modal analysis and experimental modal analysis, the joint surface parameters between spindle/shank and face milling cutter are get (linear stiffness Kx, linear damping Gx, rotation stiffness Kg and rotation damping Ge). The contact surface parameters are then valid by experiments. When using work modal to get the FRF of tool tip, by using the contact surface parameters, the modal parameters of face-milling cutter can be get indirectly. The joint surface parameters and the equivalent FEM model can be used to analyze the dynamic characteristic of the face milling cutter fixed on the specific machine tools.
The stability of the face-milling process is important to estimate and evaluate the cutting performance of the face-milling cutter. By analyzing the effect of face-milling cutting angle on milling process, based on mechanism of renewable flutter, the model of radial instantaneous chip thickness and dynamic face-milling cutting force are established. The matrix of dynamic milling force coefficient reflects the features of milling force:intermittent, time-varying and periodicity.
According to the FRF negative real part of face-milling system, the critical axial depth-of-cut is calculated. The diagrams which reflect the relationship between axial depth-of-cut and spindle speed have also been drawn in this paper. The stability limit lobes of face-milling process can forecast and control the phenomenon of chatter.
In order to verify the validity and reliability of the stability limit lobes, face-milling experimental system and parameters are designed. Cutting force in three directions are tested, work hardening capacity are also measured and calculated, the two and three dimensional picture reflecting workpiece surface integrity are get. By comparing different stability limit lobes, it is found that with the decrease of natural frequency and modal damping, the stable cutting region decreases; with the increase of density of cutter teeth, the stability of the face-milling process decreases within the recommended teeth range.
The workpiece surface quality can reflect the cutting performance of face-milling cutter and be evaluated by the the surface roughness of workpiece. By studying the influencing factors'effect on surface roughness during face-milling process, including radial and axial runout of the teeth in the form of flat blade, feed per tooth, cutting edge length, nose radius, cutting lead angle, axial depth-of-cut, axial displacement between cutting tooth and workpiece caused by forced vibration, the surface roughness prediction models are established in the direction of the maximum value of surface roughness.
According to the measured radial and axial runout of the teeth in the form of flat blade, the trajectory of cutting teeth is calculated based on the static surface roughness model. By combining experimental and modal analysis results, the vibration differential equations are solved and the axial relative displacement between cutting teeth and workpiece are get. By integrating the prediction results of static and dynamic models, the surface roughness and contours are predicted. The predicted results can be used for estimation and evaluation of surface quality. The prediction surface roughness model is verified by experiments. At the same time, it is found that the surface roughness increases and the workpiece surface quality deteriorates with the increase of density of cutter teeth under the same cutting conditions within the recommended teeth range.
The project is supported by Major Science and Technology Program of High-end CNC Machine Tools and Basic Manufacturing Equipment (2011ZX04016-031).
引文
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