复杂切削条件高速铣削加工动力学建模、仿真与切削参数优化研究
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摘要
本论文以复杂切削条件高速铣削加工为研究对象,深入研究了与铣削加工动力学建模与仿真相关的若干问题,进行了刀柄(主轴)-铣刀响应耦合建模研究,构建了圆角铣削、T型槽铣削动态切削力及颤振稳定域解析模型,在动力学建模与仿真研究的基础上实现了铣削加工过程切削参数优化。基于理论研究成果开发了相应的功能模块,开发的模块已得到实验验证并已成功应用于实际工程中,扩充了铣削加工动力学仿真优化系统的功能。
在立铣加工动力学建模与仿真拓展研究方面,通过使用数值方法对铣削动力学微分方程进行求解实现了铣削加工时域仿真,在此基础上综合使用时域稳定性判据对时域仿真数据进行处理,获得了颤振稳定域时域解。基于传统的颤振稳定域解析算法,通过仿真系统地分析了固有频率、阻尼比和刚度等工艺系统模态参数对颤振稳定域的影响,得到了模态参数简化的一般原则和方法。使用解析法计算铣刀子结构端部的原点响应和跨点响应,使用锤击实验测量刀柄末端的频响函数,通过构建的刀柄(主轴)-铣刀响应耦合模型快速获得机床-刀具系统的频响函数。在此基础上,利用开发的功能模块分析了铣刀直径和安装悬伸长度对机床-刀具系统频响函数及工艺系统颤振稳定域的影响,并以此作为选择切削参数的依据。使用正交多项式模态参数整体估计方法,可直接由频响函数获得工艺系统的模态参数,以供动态切削力仿真及颤振稳定域时域仿真使用。
在复杂切削条件高速铣削动力学建模与仿真方面,首先,通过借鉴圆柱立铣刀切削力建模与仿真方法,用离散方法对R刀切削刃进行处理,获得了R刀切削力模型及切削力系数辨识公式。其次,基于T型铣刀的切削刃几何建模,建立考虑再生作用的铣削动力学微分方程,通过数值方法进行求解,获得了T型槽铣削动态切削力时域解。借鉴圆柱立铣刀颤振稳定域解析算法,通过数值积分方法计算平均方向系数,获得了T型槽铣削颤振稳定域分析解。在此基础上,根据实际工程的应用需求,开发了固定轴向切深条件下用于描述主轴转速与临界径向切深关系及固定径向切深条件下用于描述主轴转速与临界轴向切深关系的两种颤振稳定域算法。T型槽铣削动态切削力验证实验及颤振稳定域验证实验分别对各自仿真模型和算法的正确性进行了证实。最后,通过构建典型的圆角铣削几何模型,对圆弧走刀轨迹进行离散化处理,利用计算得到的不同离散位置处的铣刀与工件的啮合角来求出作用在整个铣刀上的瞬时切削力,以实现对整个圆角铣削过程中切削力、切削功率和切削力矩的预测。建立了考虑再生切屑厚度的圆角铣削动力学方程,通过使用数值积分方法计算平均方向系数,推导出可将直线铣削颤振稳定域解析模型应用于圆角铣削中,前提是采用圆角铣削中最大径向啮合角来代替名义径向啮合角。在此基础上,根据圆角铣削中铣刀与工件之间的几何关系,推导出了均匀径向切深与非均匀径向切深两种圆角铣削的最大径向啮合角的计算公式。切削实验证实了圆角铣削切削力预测模型及颤振稳定域解析模型的正确性。
在铣削加工动力学建模与仿真分析的基础上,以铣削加工工艺参数为设计变量,以最小加工时间为优化目标函数,以动力学仿真结果为约束条件,将复杂的切削参数优化问题分解成若干个相对简单的条件极值问题进行处理,可方便获得优化的切削参数。针对型腔铣削和T型槽铣削两个切削参数优化实例进行的验证实验,不仅证实了本文所述的动力学建模与仿真算法的正确性,而且使加工零件的表面质量和切削效率得到了显著的提高。同时,多个工程应用实例也揭示复杂切削条件高速数控铣削动力学仿真与切削参数优化技术具有较大的应用价值。
With high speed milling under complicated cutting conditions as the research object of this paper, several problems corresponding to dynamic modeling and simulation of end milling are investigated. The dynamic cutting force model and the analytical chatter stability model for both circular corner milling and tee slot milling are setup. The receptance coupling model of a spindle-holder with a cutting tool is presented. With the result of dynamic simulation, the cutting parameters of milling process are optimizated. Based on the related researches and achievements, several functional modules are developed which are verified by cutting experiments and have some successful applications in practical engineering.
As for the further research of dynamic modeling and simulation of end milling, the time domain simulation is inplemented by applying the numerical integration algorithm to solve the dynamic differential equations, and as a result, the chatter stability lobes in the time domain are otained by applying some chatter detection criteria synthetically to the simulated data. With the traditional analytical solution for the stability limits, the influence of modal parameters, i.e frequency, damping ratio and stiffness, on the chatter stability lobes are discussed, and a general method for modal simplification is achieved.
With receptance coupling model, the end point receptances of the tool obtained by an analytical model, and the frequency response function of the spindle-holder assembly obtained by hammer tests, the receptance of spindle-holder and tool assembly is achieved. Futher more, the effects of cutter’s diameter and the overhange length on the chatter limits of the machining system have been investigated according to the developed functional module.
By applying the orthogonal polynomial global estimation approach to the FRF of the tool tip, the modal parameters of a machining system are obtained, which are indispensable to the simulation of dynamic cutting force and the chatter stability in the time domain.
As for the dynamic modeling and simulation of a milling process under complicated cutting condition, firstly, when the approach of cutting force modeling and simulation of flat end mill is used as reference and the discretiztion approach is applied to the cutting edges of a bull nose end mill, the cutting force model and the cutting force coefficients identification expressions for a bull nose end mill are obtained.
Secondly, based on the geometrical modeling for the cutting edges of a tee slot end mill, the dynamic differential equations are set up, in which the regenerative effect is taken into account. When the numerical integration approach is used for solving of these equations, the dynamic cutting forces of tee slot milling are achieved. On the basis of the above achievements, the stability lobes in terms of axial depth of cut under a given radial depth of cut and the stability lobes in terms of radial depth of cut under a given axial depth of cut are both created to meet the requirements of practical applications. The cutting experiments for both dynamic cutting forces and chatter stability of tee slot milling have approved the validation of the related simulation model and algorithm.
Lastly, when a typical geometrical model of circular corner milling is constructed and the circular cutting path is discretized, the engagement angles between the tool and the workpiece at each discretized positions are first calculated, and then the overall cutting forces acting on the cutter are obtained. As a result, the cutting forces, the power and the torque during the whole process of the circular corner milling are predicated. The dynamic equations for circular corner milling are set up, in which the regenerative effect is taken into account. When the average directional coefficients are obtained by numerical intergration, the analytical determination of chatter limits used for linear milling can be adopted for circular corner milling, the precondition is that the maximal radial engagement angle instead of the nominal radial engagement angle should be used. The expressions of the maximal radial engagement angle for circular corner milling with both uniform and non-uniform radial depth of cut are derived by the geometrical relationship between the cutter and the workpiece. The cutting force and the chatter stability models were verified by cutting experiments.
With the result of the dynamic modeling and simulation of a milling process, the optimization of the milling process is further studied. The optimization variables include the spindle speed n, the axial depth of cut ap, the radial depth of cut ae and the feedrate per flute ft. The minimal cutting time is selected as the target of the optimization and the result of dynamic simulation is selected as the constraint condition of the optimization. It is convenient to obtain the optimized cutting parameters when the complicated optimization problem is divided into several relative simple conditional extremum problems. The constraint condition of chatter stability is introduced into the optimization of the milling process. As a result, the dynamics of high speed milling can further be reflected and the optimization of cutting parameters is more scientific and effective. The verification tests conducted for the cutting parameters optimization of both pocket milling and tee slot milling have approved that when the approach of dynamic simulation and optimization presented in this paper are used the machining efficient can be improved remarkably. Meanwhile, several successful engineering applications have also revealed the significant applied value of dynamic simulation and cutting parameters optimization.
在立铣加工动力学建模与仿真拓展研究方面,通过使用数值方法对铣削动力学微分方程进行求解实现了铣削加工时域仿真,在此基础上综合使用时域稳定性判据对时域仿真数据进行处理,获得了颤振稳定域时域解。基于传统的颤振稳定域解析算法,通过仿真系统地分析了固有频率、阻尼比和刚度等工艺系统模态参数对颤振稳定域的影响,得到了模态参数简化的一般原则和方法。使用解析法计算铣刀子结构端部的原点响应和跨点响应,使用锤击实验测量刀柄末端的频响函数,通过构建的刀柄(主轴)-铣刀响应耦合模型快速获得机床-刀具系统的频响函数。在此基础上,利用开发的功能模块分析了铣刀直径和安装悬伸长度对机床-刀具系统频响函数及工艺系统颤振稳定域的影响,并以此作为选择切削参数的依据。使用正交多项式模态参数整体估计方法,可直接由频响函数获得工艺系统的模态参数,以供动态切削力仿真及颤振稳定域时域仿真使用。
在复杂切削条件高速铣削动力学建模与仿真方面,首先,通过借鉴圆柱立铣刀切削力建模与仿真方法,用离散方法对R刀切削刃进行处理,获得了R刀切削力模型及切削力系数辨识公式。其次,基于T型铣刀的切削刃几何建模,建立考虑再生作用的铣削动力学微分方程,通过数值方法进行求解,获得了T型槽铣削动态切削力时域解。借鉴圆柱立铣刀颤振稳定域解析算法,通过数值积分方法计算平均方向系数,获得了T型槽铣削颤振稳定域分析解。在此基础上,根据实际工程的应用需求,开发了固定轴向切深条件下用于描述主轴转速与临界径向切深关系及固定径向切深条件下用于描述主轴转速与临界轴向切深关系的两种颤振稳定域算法。T型槽铣削动态切削力验证实验及颤振稳定域验证实验分别对各自仿真模型和算法的正确性进行了证实。最后,通过构建典型的圆角铣削几何模型,对圆弧走刀轨迹进行离散化处理,利用计算得到的不同离散位置处的铣刀与工件的啮合角来求出作用在整个铣刀上的瞬时切削力,以实现对整个圆角铣削过程中切削力、切削功率和切削力矩的预测。建立了考虑再生切屑厚度的圆角铣削动力学方程,通过使用数值积分方法计算平均方向系数,推导出可将直线铣削颤振稳定域解析模型应用于圆角铣削中,前提是采用圆角铣削中最大径向啮合角来代替名义径向啮合角。在此基础上,根据圆角铣削中铣刀与工件之间的几何关系,推导出了均匀径向切深与非均匀径向切深两种圆角铣削的最大径向啮合角的计算公式。切削实验证实了圆角铣削切削力预测模型及颤振稳定域解析模型的正确性。
在铣削加工动力学建模与仿真分析的基础上,以铣削加工工艺参数为设计变量,以最小加工时间为优化目标函数,以动力学仿真结果为约束条件,将复杂的切削参数优化问题分解成若干个相对简单的条件极值问题进行处理,可方便获得优化的切削参数。针对型腔铣削和T型槽铣削两个切削参数优化实例进行的验证实验,不仅证实了本文所述的动力学建模与仿真算法的正确性,而且使加工零件的表面质量和切削效率得到了显著的提高。同时,多个工程应用实例也揭示复杂切削条件高速数控铣削动力学仿真与切削参数优化技术具有较大的应用价值。
With high speed milling under complicated cutting conditions as the research object of this paper, several problems corresponding to dynamic modeling and simulation of end milling are investigated. The dynamic cutting force model and the analytical chatter stability model for both circular corner milling and tee slot milling are setup. The receptance coupling model of a spindle-holder with a cutting tool is presented. With the result of dynamic simulation, the cutting parameters of milling process are optimizated. Based on the related researches and achievements, several functional modules are developed which are verified by cutting experiments and have some successful applications in practical engineering.
As for the further research of dynamic modeling and simulation of end milling, the time domain simulation is inplemented by applying the numerical integration algorithm to solve the dynamic differential equations, and as a result, the chatter stability lobes in the time domain are otained by applying some chatter detection criteria synthetically to the simulated data. With the traditional analytical solution for the stability limits, the influence of modal parameters, i.e frequency, damping ratio and stiffness, on the chatter stability lobes are discussed, and a general method for modal simplification is achieved.
With receptance coupling model, the end point receptances of the tool obtained by an analytical model, and the frequency response function of the spindle-holder assembly obtained by hammer tests, the receptance of spindle-holder and tool assembly is achieved. Futher more, the effects of cutter’s diameter and the overhange length on the chatter limits of the machining system have been investigated according to the developed functional module.
By applying the orthogonal polynomial global estimation approach to the FRF of the tool tip, the modal parameters of a machining system are obtained, which are indispensable to the simulation of dynamic cutting force and the chatter stability in the time domain.
As for the dynamic modeling and simulation of a milling process under complicated cutting condition, firstly, when the approach of cutting force modeling and simulation of flat end mill is used as reference and the discretiztion approach is applied to the cutting edges of a bull nose end mill, the cutting force model and the cutting force coefficients identification expressions for a bull nose end mill are obtained.
Secondly, based on the geometrical modeling for the cutting edges of a tee slot end mill, the dynamic differential equations are set up, in which the regenerative effect is taken into account. When the numerical integration approach is used for solving of these equations, the dynamic cutting forces of tee slot milling are achieved. On the basis of the above achievements, the stability lobes in terms of axial depth of cut under a given radial depth of cut and the stability lobes in terms of radial depth of cut under a given axial depth of cut are both created to meet the requirements of practical applications. The cutting experiments for both dynamic cutting forces and chatter stability of tee slot milling have approved the validation of the related simulation model and algorithm.
Lastly, when a typical geometrical model of circular corner milling is constructed and the circular cutting path is discretized, the engagement angles between the tool and the workpiece at each discretized positions are first calculated, and then the overall cutting forces acting on the cutter are obtained. As a result, the cutting forces, the power and the torque during the whole process of the circular corner milling are predicated. The dynamic equations for circular corner milling are set up, in which the regenerative effect is taken into account. When the average directional coefficients are obtained by numerical intergration, the analytical determination of chatter limits used for linear milling can be adopted for circular corner milling, the precondition is that the maximal radial engagement angle instead of the nominal radial engagement angle should be used. The expressions of the maximal radial engagement angle for circular corner milling with both uniform and non-uniform radial depth of cut are derived by the geometrical relationship between the cutter and the workpiece. The cutting force and the chatter stability models were verified by cutting experiments.
With the result of the dynamic modeling and simulation of a milling process, the optimization of the milling process is further studied. The optimization variables include the spindle speed n, the axial depth of cut ap, the radial depth of cut ae and the feedrate per flute ft. The minimal cutting time is selected as the target of the optimization and the result of dynamic simulation is selected as the constraint condition of the optimization. It is convenient to obtain the optimized cutting parameters when the complicated optimization problem is divided into several relative simple conditional extremum problems. The constraint condition of chatter stability is introduced into the optimization of the milling process. As a result, the dynamics of high speed milling can further be reflected and the optimization of cutting parameters is more scientific and effective. The verification tests conducted for the cutting parameters optimization of both pocket milling and tee slot milling have approved that when the approach of dynamic simulation and optimization presented in this paper are used the machining efficient can be improved remarkably. Meanwhile, several successful engineering applications have also revealed the significant applied value of dynamic simulation and cutting parameters optimization.
引文
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