高速铣削稳定性及加工精度研究
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摘要
高速铣削加工技术是先进制造技术中最重要的基础技术之一,已成为21世纪先进制造技术的重要组成部分,被广泛应用于航空航天、汽车、模具、能源、轨道交通等众多领域。高速铣削实现高速、高效和高精度加工的关键限制因素之一,是铣削过程中的振动。本文以航空铝合金7050-T7451为研究对象,围绕高速立铣刀铣削过程中存在的多种振动形式,借助理论分析和试验研究等手段,以提高切削效率、保障加工精度为主要研究目标,对高速铣削过程中振动的产生机理、影响因素以及与加工精度的关系进行系统、深入地研究。
考虑每齿进给量、主轴-刀柄-刀具偏心、再生效应、刀具-工件静态变形和后刀面与已加工表面间的“耕犁力”或“刃口力”等因素的影响,建立整体硬质合金立铣刀高速铣削系统四自由度(4-DOF)动力学模型;将螺旋齿立铣刀的切削过程分为三部分,研究螺旋角对刀具-工件动态切削区的影响,并从动力学角度解释,当轴向切削深度等于齿距时,螺旋齿铣刀系统稳定性极限中不出现倍周期分叉的原因;利用有限元法,建立薄壁件铣削系统的时变参数周期延迟微分方程;考虑进给量和刀具振动对延迟时间的共同影响,建立2-DOF状态再生延迟动力学模型,根据Frechet微分理论,对该模型进行周期状态延迟微分方程的线性化研究。
通过变每齿进给量试验,针对航空铝合金7050-T7451,获得切削力模型中的切削力系数,同时运用试验模态分析方法,获得七种整体超细晶粒硬质合金立铣刀系统的模态参数;并探讨铣削过程中存在的振动频率及分叉形式;研究切削参数对系统稳定性的影响规律,建立铣削系统的三维稳定性极限曲面;探讨1-DOF、2-DOF和4-DOF铣削系统稳定性极限之间的关系;另外,在精确估计变速铣削系统延迟时间的基础上,从变速的影响机理出发,研究转速的调制幅度和调制频率对系统稳定性极限的影响规律,建立变速铣削系统的三维稳定性极限曲面,并对调制幅度和调制频率进行优化选择。
研究刀具主要结构参数对铣削系统稳定性的影响规律,建立考虑刀具悬伸长度的三维稳定性极限曲面;探讨不等齿距铣刀系统的稳定性问题,并研究此种铣刀对铣削颤振的抑制作用机理;建立薄壁件铣削系统的三维稳定性极限曲面,探讨薄壁件铣削稳定性极限与刀具加工位置的关系;另外,提出并建立基于铣削均匀性和稳定性结合的高速立铣刀结构参数设计理论。
根据共振区理论和前后连续两刀齿切削过程的相位差的三种临界状态,给出六种主轴转速,并将高速铣削稳定区划分为四部分;依据Floquet理论的单值矩阵的特征乘子与单位圆的关系,推导高速铣削系统的稳定性判据,给出高速铣削系统稳定性极限图的绘制方法;利用共振区与稳定区在稳定性极限图中的位置关系,提出一种适合试验现场的简单、快速获得系统稳定性较好的极限值的方法;以最大稳定性的材料切除率为优化目标,以加工过程稳定且非共振为约束条件,以系统的结构参数和切削参数为优化变量,提出一种同时考虑自激振动和强迫振动的动态优化方法,此优化方法适合粗加工或半精加工等对加工精度要求不太高的高效加工过程;基于平均切削力理论模型,提出一种获得最优径向切削深度的研究方法;利用最优控制理论,建立一种新的稳定区一最优稳定区,将传统稳定区进行细分;结合最优径向切削深度理论和最优稳定区理论,提出一种获得最优切削参数的研究方法,所获得的最优切削参数适合精密加工、超精密加工等加工精度要求较高、加工过程要求稳定且抗外界干扰能力较强的加工过程。
在切削稳定区内,从系统响应的角度,研究动态表面位置误差的产生机理;运用谐平衡法,计算获得强迫振动在工件已加工表面产生的动态表面位置误差,并研究各种系统参数(主轴转速、径向切削深度、刀具齿数、刀具螺旋角和刀具悬伸长度等)对动态表面位置误差的影响规律;另外,通过铣削试验,对比研究稳定非共振切削、稳定且共振切削和不稳定切削三种工况对薄壁件铣削加工前后和时效前后的变形量的影响规律;最后,研究振动对航空整体框类零件加工变形的影响规律,并探讨不等齿距铣刀对航空整体结构件加工变形的改善作用。
本课题得到国家自然科学基金重点项目“大型航空整体结构件加工变形机理及精度保障技术(50435020)”的支持。
High-speed milling (HSM), which is one of the advanced manufacturing technologies, has been become the important part of modern manufacture technology in 21 century and used in many different fields, e.g. aeronautics and astronautics, automobile, die and mould, energy, and rail transit. While the material removal rate (MRR), reflecting the machining efficiency, is often limited by the occurrence of an instability phenomenon called chatter in HSM processes. In order to increase the chatter-free MRR and surface accuracy, the numerical analysis and experimental researches are carried out through underlying and systematacial investigation of the occurring sources of the different types of vibrations, influencing factors, and machining accuracy in HSM processes.
An integrated four degree-of-freedom (DOF) dynamic model for HSM processes with solid carbide endmill is developed, including feed per tooth, tool eccentricity, regenerative effect, static deflection of tool-workpiece, and plouging effect. Dividing the cutting process into three cutting processes, the influence of the helix angle on dynamic cutting zone is considered. Unstable flip islands arise in the stability lobe diagram due to the helical flutes of the tool. The analysis of the directional cutting force factor gives a clear explanation for the existence of the unstable islands. The periodic delay differential equation with variable parameters for thin-walled workpiece milling process is proposed. Considering the feed motion and tool vibration, a 2-DOF dynamic model of regenerative chatter with state dependent time delay is developed in HSM processes. Based on the Frechet derivative theory, the linearization of periodic state-dependent delay different equation is investigated. For a system with practical milling paramters, it is shown that the incorporation of the state-dependent delay into the model does not essentially affect the linear stability properties of the system.
Cutting force coefficients and tool or workpiece modal parameters are found by using experiments with variable feed rates and experimental modal analysis (EMA), respectively. The vibration frequencies and bifurcations during milling processes are described. The influences of cutting parameters on stability limits are investigated in detail. The three dimensional stability limit map for different spindle speeds, different axial depths of cut, and different radial depths of cut are obtained. Two types of instability are predicted corresponding to quasiperiodic (Hopf) and periodic (flip) chatter. The stability lobes of 1 -DOF, 2-DOF, and 4-DOF milling processes are shown. It is shown that the stability behaviour depends strongly on the flexibility of system. In this dissertation, a better delay approximation has been used in the modeling of variable spindle speed (VSS) milling processes, and the benefits of VSS milling operations are discussed by comparing the stability charts of VSS milling operations with those obtained for constant spindle speed milling operations. The three dimensional stability limit map for different frequencies and amplitudes of the cosine speed variation at the speed 12000rpm is shown. From the graph, it is possible to select variable parameters that are adequate for the cutting conditions required.
The influences of different tool structural parametes on stability limits are investigated respectively. The tool frequency response function (FRF), which is required as input to existing stability lobe calculations, is determined analytically using receptance coupling substructure analysis and Euler-Bernoulli beams with step changes in cross section. The development of three-dimensional stability limit map is described, that combine the traditional dependence of allowable depth of cut on spindle speed with inherent dependence on tool overhang length, due to the corresponding changes of dynamics with overhang in the system. The stability of nonuniform pitch milling tools is predicted. Nonuniform pitch milling tool is a powerful technique to reduce the vibration level in milling when the system is unstable, while the influence of nonuniform pitch milling tools only plays an important part in period doubling lobes. Using FEM and EMA, the FRF of thin-walled workpiece depending on tool positions is obtained, and the three dimensional stability limit map of thin-walled workpiece milling process are obtained. An integrated theory of structural parameters design of solid Carbide endmill for HSM is established, which combines the milling uniformity with milling stability.
Stability citeria for HSM processes is derived by the characteristic multipliers of the transition matrix which obtained by the Floquet theory, and a method for identifying stability limit lobes is also introduced. A novel method which may simply obtain stability limits lobes of milling processes is presented. The method is based on two theories: the first is that the stability boundary has a typical 'lobed' structure, with maxima stability located at spindle speeds corresponding to the integer fractions of the eigen-frequencies of the most flexible modes of the machine-tool-workpiece system; the second is theory of semi-bandwidth for resonant region. An updated method for dynamic optimation is proposed to determine the cutting parameters and structural parameters for increasing the chtter-free MRR and suface finish through considering the self-excited vibration and forced vibration in HSM processes. The objective function of the method is chatter-free MRR, constrains are chatter stability and surface finish, and optimizing variable are cutting parameters and structural parameters. The proposed method can be used in machining processes with lower surface finish, e.g. rough machining, semifinishing. Directional cutting force factors and stability limit charts are conducted for the down- and up-milling cases of various immersion rates. An in-depth investigation of the optimal stable immersion rates for down-milling in the vicinity of where the average cutting force changes sign is presented. Stability charts and performance contour in the parametric space for HSM processes are obtained. A new stable region-optimal stable region is definited in the tranditional conditional stable region, which is divided into three parts: unconditional stable region, optimal stable region, and new conditional stable region. The optimal cutting parameters are obtained, which are suitable for precision finishing or ultraprecision machining operations.
Stable cutting conditions have been selected and the influence of forced vibrations on part geometric accuracy (Dynamic surface location error-DSLE) is investigated. The underlying theory, based on the situation of forced vibrations, is outlined. The DSLE is predicted by using the harmonic balance analyses during stable milling operations. Comparisons between the influences of system parameters (spindle speed, radial depth of cut, tooth number, helix angle, and tool overhang length) on the DSLE are included. Under the cases of stable and noresonant milling, stable and resonant milling, and unstable milling, cutting distortion, and time-dependent distortion are investigated by HSM experiments with thin-walled workpiece. Influences of vibration on machining distortion are explained in HSM monolithic component with uniform and nonuniform pitch milling tools.
考虑每齿进给量、主轴-刀柄-刀具偏心、再生效应、刀具-工件静态变形和后刀面与已加工表面间的“耕犁力”或“刃口力”等因素的影响,建立整体硬质合金立铣刀高速铣削系统四自由度(4-DOF)动力学模型;将螺旋齿立铣刀的切削过程分为三部分,研究螺旋角对刀具-工件动态切削区的影响,并从动力学角度解释,当轴向切削深度等于齿距时,螺旋齿铣刀系统稳定性极限中不出现倍周期分叉的原因;利用有限元法,建立薄壁件铣削系统的时变参数周期延迟微分方程;考虑进给量和刀具振动对延迟时间的共同影响,建立2-DOF状态再生延迟动力学模型,根据Frechet微分理论,对该模型进行周期状态延迟微分方程的线性化研究。
通过变每齿进给量试验,针对航空铝合金7050-T7451,获得切削力模型中的切削力系数,同时运用试验模态分析方法,获得七种整体超细晶粒硬质合金立铣刀系统的模态参数;并探讨铣削过程中存在的振动频率及分叉形式;研究切削参数对系统稳定性的影响规律,建立铣削系统的三维稳定性极限曲面;探讨1-DOF、2-DOF和4-DOF铣削系统稳定性极限之间的关系;另外,在精确估计变速铣削系统延迟时间的基础上,从变速的影响机理出发,研究转速的调制幅度和调制频率对系统稳定性极限的影响规律,建立变速铣削系统的三维稳定性极限曲面,并对调制幅度和调制频率进行优化选择。
研究刀具主要结构参数对铣削系统稳定性的影响规律,建立考虑刀具悬伸长度的三维稳定性极限曲面;探讨不等齿距铣刀系统的稳定性问题,并研究此种铣刀对铣削颤振的抑制作用机理;建立薄壁件铣削系统的三维稳定性极限曲面,探讨薄壁件铣削稳定性极限与刀具加工位置的关系;另外,提出并建立基于铣削均匀性和稳定性结合的高速立铣刀结构参数设计理论。
根据共振区理论和前后连续两刀齿切削过程的相位差的三种临界状态,给出六种主轴转速,并将高速铣削稳定区划分为四部分;依据Floquet理论的单值矩阵的特征乘子与单位圆的关系,推导高速铣削系统的稳定性判据,给出高速铣削系统稳定性极限图的绘制方法;利用共振区与稳定区在稳定性极限图中的位置关系,提出一种适合试验现场的简单、快速获得系统稳定性较好的极限值的方法;以最大稳定性的材料切除率为优化目标,以加工过程稳定且非共振为约束条件,以系统的结构参数和切削参数为优化变量,提出一种同时考虑自激振动和强迫振动的动态优化方法,此优化方法适合粗加工或半精加工等对加工精度要求不太高的高效加工过程;基于平均切削力理论模型,提出一种获得最优径向切削深度的研究方法;利用最优控制理论,建立一种新的稳定区一最优稳定区,将传统稳定区进行细分;结合最优径向切削深度理论和最优稳定区理论,提出一种获得最优切削参数的研究方法,所获得的最优切削参数适合精密加工、超精密加工等加工精度要求较高、加工过程要求稳定且抗外界干扰能力较强的加工过程。
在切削稳定区内,从系统响应的角度,研究动态表面位置误差的产生机理;运用谐平衡法,计算获得强迫振动在工件已加工表面产生的动态表面位置误差,并研究各种系统参数(主轴转速、径向切削深度、刀具齿数、刀具螺旋角和刀具悬伸长度等)对动态表面位置误差的影响规律;另外,通过铣削试验,对比研究稳定非共振切削、稳定且共振切削和不稳定切削三种工况对薄壁件铣削加工前后和时效前后的变形量的影响规律;最后,研究振动对航空整体框类零件加工变形的影响规律,并探讨不等齿距铣刀对航空整体结构件加工变形的改善作用。
本课题得到国家自然科学基金重点项目“大型航空整体结构件加工变形机理及精度保障技术(50435020)”的支持。
High-speed milling (HSM), which is one of the advanced manufacturing technologies, has been become the important part of modern manufacture technology in 21 century and used in many different fields, e.g. aeronautics and astronautics, automobile, die and mould, energy, and rail transit. While the material removal rate (MRR), reflecting the machining efficiency, is often limited by the occurrence of an instability phenomenon called chatter in HSM processes. In order to increase the chatter-free MRR and surface accuracy, the numerical analysis and experimental researches are carried out through underlying and systematacial investigation of the occurring sources of the different types of vibrations, influencing factors, and machining accuracy in HSM processes.
An integrated four degree-of-freedom (DOF) dynamic model for HSM processes with solid carbide endmill is developed, including feed per tooth, tool eccentricity, regenerative effect, static deflection of tool-workpiece, and plouging effect. Dividing the cutting process into three cutting processes, the influence of the helix angle on dynamic cutting zone is considered. Unstable flip islands arise in the stability lobe diagram due to the helical flutes of the tool. The analysis of the directional cutting force factor gives a clear explanation for the existence of the unstable islands. The periodic delay differential equation with variable parameters for thin-walled workpiece milling process is proposed. Considering the feed motion and tool vibration, a 2-DOF dynamic model of regenerative chatter with state dependent time delay is developed in HSM processes. Based on the Frechet derivative theory, the linearization of periodic state-dependent delay different equation is investigated. For a system with practical milling paramters, it is shown that the incorporation of the state-dependent delay into the model does not essentially affect the linear stability properties of the system.
Cutting force coefficients and tool or workpiece modal parameters are found by using experiments with variable feed rates and experimental modal analysis (EMA), respectively. The vibration frequencies and bifurcations during milling processes are described. The influences of cutting parameters on stability limits are investigated in detail. The three dimensional stability limit map for different spindle speeds, different axial depths of cut, and different radial depths of cut are obtained. Two types of instability are predicted corresponding to quasiperiodic (Hopf) and periodic (flip) chatter. The stability lobes of 1 -DOF, 2-DOF, and 4-DOF milling processes are shown. It is shown that the stability behaviour depends strongly on the flexibility of system. In this dissertation, a better delay approximation has been used in the modeling of variable spindle speed (VSS) milling processes, and the benefits of VSS milling operations are discussed by comparing the stability charts of VSS milling operations with those obtained for constant spindle speed milling operations. The three dimensional stability limit map for different frequencies and amplitudes of the cosine speed variation at the speed 12000rpm is shown. From the graph, it is possible to select variable parameters that are adequate for the cutting conditions required.
The influences of different tool structural parametes on stability limits are investigated respectively. The tool frequency response function (FRF), which is required as input to existing stability lobe calculations, is determined analytically using receptance coupling substructure analysis and Euler-Bernoulli beams with step changes in cross section. The development of three-dimensional stability limit map is described, that combine the traditional dependence of allowable depth of cut on spindle speed with inherent dependence on tool overhang length, due to the corresponding changes of dynamics with overhang in the system. The stability of nonuniform pitch milling tools is predicted. Nonuniform pitch milling tool is a powerful technique to reduce the vibration level in milling when the system is unstable, while the influence of nonuniform pitch milling tools only plays an important part in period doubling lobes. Using FEM and EMA, the FRF of thin-walled workpiece depending on tool positions is obtained, and the three dimensional stability limit map of thin-walled workpiece milling process are obtained. An integrated theory of structural parameters design of solid Carbide endmill for HSM is established, which combines the milling uniformity with milling stability.
Stability citeria for HSM processes is derived by the characteristic multipliers of the transition matrix which obtained by the Floquet theory, and a method for identifying stability limit lobes is also introduced. A novel method which may simply obtain stability limits lobes of milling processes is presented. The method is based on two theories: the first is that the stability boundary has a typical 'lobed' structure, with maxima stability located at spindle speeds corresponding to the integer fractions of the eigen-frequencies of the most flexible modes of the machine-tool-workpiece system; the second is theory of semi-bandwidth for resonant region. An updated method for dynamic optimation is proposed to determine the cutting parameters and structural parameters for increasing the chtter-free MRR and suface finish through considering the self-excited vibration and forced vibration in HSM processes. The objective function of the method is chatter-free MRR, constrains are chatter stability and surface finish, and optimizing variable are cutting parameters and structural parameters. The proposed method can be used in machining processes with lower surface finish, e.g. rough machining, semifinishing. Directional cutting force factors and stability limit charts are conducted for the down- and up-milling cases of various immersion rates. An in-depth investigation of the optimal stable immersion rates for down-milling in the vicinity of where the average cutting force changes sign is presented. Stability charts and performance contour in the parametric space for HSM processes are obtained. A new stable region-optimal stable region is definited in the tranditional conditional stable region, which is divided into three parts: unconditional stable region, optimal stable region, and new conditional stable region. The optimal cutting parameters are obtained, which are suitable for precision finishing or ultraprecision machining operations.
Stable cutting conditions have been selected and the influence of forced vibrations on part geometric accuracy (Dynamic surface location error-DSLE) is investigated. The underlying theory, based on the situation of forced vibrations, is outlined. The DSLE is predicted by using the harmonic balance analyses during stable milling operations. Comparisons between the influences of system parameters (spindle speed, radial depth of cut, tooth number, helix angle, and tool overhang length) on the DSLE are included. Under the cases of stable and noresonant milling, stable and resonant milling, and unstable milling, cutting distortion, and time-dependent distortion are investigated by HSM experiments with thin-walled workpiece. Influences of vibration on machining distortion are explained in HSM monolithic component with uniform and nonuniform pitch milling tools.
引文
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