CN103823945A

CN103823945A - Flutter stability domain modeling approach for face cutting process

Info

Publication number: CN103823945A
Application number: CN201410093527.3A
Authority: CN
Inventors: 李宏坤; 赵鹏仕; 丛明; 罗孟然
Original assignee: DALIAN XINYU POLYTECHNIC TECHNOLOGY DEVELOPMENT CENTER CO LTD; Dalian University of Technology
Current assignee: DALIAN XINYU POLYTECHNIC TECHNOLOGY DEVELOPMENT CENTER CO LTD; Dalian University of Technology
Priority date: 2014-03-13
Filing date: 2014-03-13
Publication date: 2014-05-28

Abstract

The invention belongs to the technical field of simulation calculation analysis and modal test, and relates to a modeling method of a flutter stable domain in a plane cutting process. After understanding the various characteristic parameters of the material, the computer simulates the machining cutting process, calculates the cutting force during the machining process and analyzes the corresponding cutting coefficient. After the cutting coefficient is obtained, the modal test is carried out on the tool system of the machine tool spindle by using the modal experiment, and the modal characteristic parameters of the tool system of the machine tool spindle are analyzed, including multi-order natural frequency, damping ratio, dynamic stiffness, etc. According to the chatter cutting theory, combined with the cutting coefficient and system characteristic parameters, the computer assembly program is used to draw the stability lobe diagram, which is used to select reasonable cutting parameters, avoid the chatter zone, improve the machining accuracy and quality, and protect the machine tool system.

Description

A Modeling Method of Chatter Stability Domain in Planar Cutting Process

技术领域technical field

本发明属于仿真计算分析与模态测试技术领域，涉及一种平面切削过程的颤振稳定域建模方法。The invention belongs to the technical field of simulation calculation analysis and modal test, and relates to a modeling method of a flutter stable domain in a plane cutting process.

背景技术Background technique

制造业是我们国家经济增长的支柱产业，作为一个比较传统的领域，它目前已经建立了比较系统的理论体系，积累了丰富的实践经验，但随着科学技术水平的提高，机械制造业面临着新的挑战，迫使机械制造技术正在朝自动化、柔性化、精密化、信息化和智能化方向发展。切削加工是应用最广泛的加工方式，随着先进制造技术的发展，对切削加工的稳定性、可靠性提出更高的要求。在实际切削加工中，加工系统颤振和刀具失效是影响切削加工效率、精度、质量以及稳定性和可靠性的重要因素。近年来加工制造高精度、高质量的零件成为难题。因此，在切削加工过程中选取合适的切削参数对于提高加工精度及质量具有重大的意义。The manufacturing industry is the pillar industry of our country's economic growth. As a relatively traditional field, it has established a relatively systematic theoretical system and accumulated rich practical experience. However, with the improvement of the level of science and technology, the machinery manufacturing industry is facing New challenges force mechanical manufacturing technology to develop in the direction of automation, flexibility, precision, informatization and intelligence. Cutting is the most widely used processing method. With the development of advanced manufacturing technology, higher requirements are put forward for the stability and reliability of cutting. In actual cutting, machining system chatter and tool failure are important factors affecting cutting efficiency, precision, quality, stability and reliability. In recent years, processing and manufacturing high-precision and high-quality parts has become a difficult problem. Therefore, selecting appropriate cutting parameters in the cutting process is of great significance for improving the machining accuracy and quality.

在机械加工中，除了切削运动以外，有时还会在刀具与被切削材料表面之间产生相对振动，这种切削振动会对机械加工系统带来不良影响，导致加工精度、表面质量及系统可靠性的降低。其中最严重的自激振动是在切削过程中，在无周期性外部激振力的作用下由于加工系统本身特征所引起的一种切削振动，通常将这种切削振动称为颤振。切削系统是一个非常复杂的动态系统，在切削过程中，切屑的厚度随切削时间变化而变化，其切削力也与切屑厚度、机床系统的固有特性成正比，因此刀具与加工工件之间除正常的切削运动外，还会产生一种十分强烈的相对振动，这种切削振动将会导致切削过程中出现不稳定切削。切削颤振是发生在切削过程中一种强烈的自激振动。如果在切削中不能有效抑制不稳定颤振，那么将会影响零部件的加工质量，同时将加剧刀具的磨损。所以为了提高机床的精度和效率，对切削系统进行切削颤振稳定性分析，避免发生颤振，这对提高生产效率，提高零部件加工质量，降低刀具磨损具有非常重要的意义，这也是国内外研究者研究的焦点。In mechanical processing, in addition to cutting motion, sometimes there will be relative vibration between the tool and the surface of the material to be cut. This cutting vibration will have a negative impact on the machining system, resulting in machining accuracy, surface quality and system reliability. decrease. The most serious self-excited vibration is a kind of cutting vibration caused by the characteristics of the processing system itself under the action of non-periodic external exciting force during the cutting process. This cutting vibration is usually called chatter. The cutting system is a very complex dynamic system. During the cutting process, the chip thickness changes with the cutting time, and its cutting force is also proportional to the chip thickness and the inherent characteristics of the machine tool system. In addition to the cutting motion, there will be a very strong relative vibration, which will lead to unstable cutting during the cutting process. Cutting chatter is a strong self-excited vibration that occurs during cutting. If the unstable chatter cannot be effectively suppressed during cutting, it will affect the processing quality of the parts and increase the wear of the tool. Therefore, in order to improve the accuracy and efficiency of the machine tool, the cutting chatter stability analysis of the cutting system is carried out to avoid chatter, which is of great significance to improve production efficiency, improve the processing quality of parts, and reduce tool wear. The focus of the researcher's research.

发明内容Contents of the invention

本发明提供一种平面切削过程的颤振稳定域建模方法，所要解决的技术问题是精确仿真切削过程并计算切削系数。The invention provides a chatter stable domain modeling method in the plane cutting process, and the technical problem to be solved is to accurately simulate the cutting process and calculate the cutting coefficient.

本发明的技术方案如下：Technical scheme of the present invention is as follows:

一种平面切削过程的颤振稳定域建模方法，包括以下步骤：A chatter stable domain modeling method for a planar cutting process, comprising the following steps:

构建二自由度的切削系统，仅考虑x,y方向的动力因素，则：Construct a two-degree-of-freedom cutting system and only consider the dynamic factors in the x and y directions, then:

$\{\begin{matrix} {m m}_{x x} \overset{\cdot \cdot \cdot \cdot}{x x} + + {c c}_{x x} \overset{\cdot \cdot}{x x} + + {k k}_{x x} x x = = {Σ Σ}_{j j = = 11}^{N N} {F f}_{xj xj} = = {F f}_{x x} ((t t)) \\ {m m}_{y the y} \overset{\cdot \cdot \cdot \cdot}{y the y} + + {c c}_{y the y} \overset{\cdot \cdot}{y the y} + + {k k}_{y the y} y the y = = {Σ Σ}_{j j = = 11}^{N N} {F f}_{yj yj} = = {F f}_{y the y} ((t t)) \end{matrix}$

式中,m_x,m_y,c_x,c_y,k_x,k_y分别为x,y方向上机床-刀具系统的质量、阻尼和刚度；F_xj和F_yj分别为作用在铣刀刀齿j上的切削力在x,y方向上的分量。In the formula, m _x , m _y , c _x , c _y , k _x , k _y are the mass, damping and stiffness of the machine tool-tool system in the x and y directions respectively; F _xj and F _yj are the The components of the cutting force on tooth j in the x, y direction.

通过对上式进行整理，并进行拉氏变换后，其传递函数可表示为：After sorting out the above formula and performing Laplace transformation, its transfer function can be expressed as:

$\{\begin{matrix} {G G}_{xx xx} ((s the s)) = = \frac{x x ((s the s))}{{F f}_{x x} ((s the s))} = = \frac{{ω ω}_{nx nx}^{22}}{{K K}_{x x} (({s the s}^{22} + + 22 {ζ ζ}_{x x} {ω ω}_{nx nx} s the s + + {ω ω}_{nx nx}^{22}))} \\ {G G}_{yy yy} ((s the s)) = = \frac{y the y ((s the s))}{{F f}_{y the y} ((s the s))} = = \frac{{ω ω}_{ny no}^{22}}{{K K}_{y the y} (({s the s}^{22} + + 22 {ζ ζ}_{y the y} {ω ω}_{ny no} s the s + + {ω ω}_{ny no}^{22}))} \end{matrix}$

其中，ζ_x,ζ_y为阻尼比，ω_nx，ω_ny为系统固有频率。Among them, ζ _x , ζ _y are the damping ratios, ω _nx , ω _ny are the natural frequencies of the system.

在切削加工中，只考虑再生颤振的动态切削厚度表达式为：In the cutting process, the dynamic cutting thickness expression considering only regenerative chatter is:

h_j(φ)＝Δxsinφ_j+Δycosφ_j h _j (φ)＝Δxsinφ _j +Δycosφ _j

其中: $Δx = (x_{c} - x_{c}^{0}) - (x_{w} - x_{w}^{0}), Δy = (y_{c} - y_{c}^{0}) - (y_{w} - y_{w}^{0}) .$ in: $Δx = (x_{c} - x_{c}^{0}) - (x_{w} - x_{w}^{0}), Δy = ({the y}_{c} - {the y}_{c}^{0}) - ({the y}_{w} - {the y}_{w}^{0}) .$

基于Tlusty的理论提出正交切削理论的模型当瞬时角位移为φ时，作用在刀齿j上的切向和径向动态切削力可以表示为：Based on the theory of Tlusty, the model of orthogonal cutting theory is proposed. When the instantaneous angular displacement is φ, the tangential and radial dynamic cutting force acting on the tooth j can be expressed as:

$\{\begin{matrix} {F f}_{tj tj} ((φ φ)) = = {K K}_{t t} {a a}_{p p} {h h}_{j j} ((φ φ)) \\ {F f}_{rj r j} ((φ φ)) = = {K K}_{r r} {F f}_{tj tj} ((φ φ)) \end{matrix}$

其中，K_r为系数比，K_r＝K_rcK_tc。将上式改写成矩阵的形式：Wherein, K _r is the coefficient ratio, K _r =K _rc K _tc . Rewrite the above formula into matrix form:

${{F f ((t t))}} = = \frac{11}{22} {a a}_{p p} {K K}_{t t} [[A A ((t t))]] {{Δ Δ ((t t))}}$

其中，A(t)为与瞬时角位移φ_j相关的周期函数，其角频率ω＝Nn60，周期T＝2πω。对A(t)进行Fourier级数展开并保留第一项，则上式可以改写成：Among them, A(t) is a periodic function related to the instantaneous angular displacement φ _j , its angular frequency ω=Nn60, and its period T=2πω. Perform Fourier series expansion on A(t) and keep the first item, then the above formula can be rewritten as:

${{F f ((t t))}} = = \frac{11}{22} {a a}_{p p} {K K}_{t t} \frac{N N}{22 π π} [\begin{matrix} {α α}_{xx xx} & {α α}_{xy xy} \\ {α α}_{yx yx} & {α α}_{yy yy} \end{matrix}] {{Δ Δ ((t t))}}$

其中，α_xx,α_xy,α_yx,α_yx为平均方向系数。Among them, α _xx , α _xy , α _yx , α _yx are the average direction coefficients.

系统稳定的充要条件是传递函数G(s)特征方程的根均具有负的实部。因此，频域中切削力可以表示为：The necessary and sufficient condition for the stability of the system is that the roots of the characteristic equation of the transfer function G(s) all have negative real parts. Therefore, the cutting force in the frequency domain can be expressed as:

${{F f}} {e e}^{i i {ω ω}_{c c} t t} = = \frac{11}{22} {a a}_{p p} {K K}_{t t} ((11 - - {e e}^{i i {ω ω}_{c c} t t})) [[{A A}_{00}]] [[G G (({iω iω}_{c c}))]] {{F f}} {e e}^{i i {ω ω}_{c c} t t}$

其中，ω_c表示颤振频率。切削再生颤振频率下的闭环反馈系统的特征方程为：Among them, ω _c represents flutter frequency. The characteristic equation of the closed-loop feedback system at the cutting regenerative chatter frequency is:

$det det [[[[I I]] - - \frac{11}{22} {a a}_{p p} {K K}_{t t} ((11 - - {e e}^{i i {ω ω}_{c c} t t})) [[{A A}_{00}]] [[G G (({iω iω}_{c c}))]]]] = = 00$

Λ为方程的特征值，其表达式为Λ is the eigenvalue of the equation, and its expression is

$Λ Λ = = - - \frac{N N}{44 π π} {a a}_{p p} {K K}_{t t} ((11 - - {e e}^{- - i i {ω ω}_{c c} t t}))$

则其特征值Λ解析法表示为：Then its eigenvalue Λ analytical method is expressed as:

$Λ Λ = = - - \frac{11}{22 {a a}_{00}} (({a a}_{11} &PlusMinus; &PlusMinus; \sqrt{{a a}_{11}^{22} - - 44 {a a}_{00}}))$

其中，a₀＝G_xx(iω_c)G_yy(iω_c)(α_xxα_yy-α_xyα_yx),a₁＝α_xxG_xx(iω_c)+α_yyG_yy(iω_c)。Wherein, a ₀ =G _xx (iω _c )G _yy (iω _c )(α _xx α _yy −α _xy α _yx ), a ₁ =α _xx G _xx (iω _c )+α _yy G _yy (iω _c ).

令虚部等于零，由颤振稳定理论其中的ZOA解析法得临界轴向切深为：Let the imaginary part be equal to zero, and the critical axial depth of cut obtained from the ZOA analytical method in the flutter stability theory is:

${a a}_{plim plim} = = - - \frac{22 π π {Λ Λ}_{R R} ((11 + + {(({Λ Λ}_{I I} / / {Λ Λ}_{R R}))}^{22}))}{{NK NK}_{tc tc}}$

主轴的转速表达式为：The expression of the spindle speed is:

$n no = = \frac{6060 {ω ω}_{c c}}{N N ((((22 k k + + 11)) π π - - 22 arctan arctan (({Λ Λ}_{I I} / / {Λ Λ}_{R R}))))}$

其中，k为叶瓣图中的叶瓣数，Λ_R和Λ_I分别为系统传递函数特征根的实部和虚部，N为刀齿数，K_tc切削系数，ω_c为特征频率。Among them, k is the number of lobes in the lobe diagram, _ΛR and _ΛI are the real part and imaginary part of the characteristic root of the system transfer function, N is the number of teeth, K _tc cutting coefficient, _ωc is the characteristic frequency.

ω_c为特征频率，通过模态试验，分析数据结果而得。为了提高模态测试精度采用多次激励然后求取平均值，并从多方向测试器不同的多阶模态，最后分析所对应的各种特征参数，包括多阶特征频率。ω _c is the characteristic frequency, which is obtained by analyzing the data results through the modal test. In order to improve the accuracy of the modal test, multiple excitations are used to calculate the average value, and from the different multi-order modes of the multi-directional tester, the corresponding various characteristic parameters, including the multi-order characteristic frequency, are finally analyzed.

K_tc为切削系数，了解刀具材料、工件材料，通过仿真机械加工切削过程，并计算加工过程中的切削力，分析数据，最后计算切削系数。在切削有限元仿真中，选择切屑分离准则：物理准则和几何准则。几何准则是求解前预先在有限元模型中设置分离线。通过判断分离线上的点与切削刃间的距离是否达到分离条件来确定切屑是否分离。物理准则是通过在求解过程中某些物理量是否达到预设临界值来判定切屑是否分离。这种失效应力准则可以表示为：K _tc is the cutting coefficient, understand the tool material and workpiece material, simulate the cutting process of machining, calculate the cutting force during the processing, analyze the data, and finally calculate the cutting coefficient. In the cutting finite element simulation, select the chip separation criterion: physical criterion and geometric criterion. The geometric criterion is to pre-set the separation line in the finite element model before solving. Whether the chips are separated is determined by judging whether the distance between the point on the separation line and the cutting edge meets the separation condition. The physical criterion is to determine whether the chips are separated by whether some physical quantities reach the preset critical value during the solution process. This failure stress criterion can be expressed as:

${((\frac{| | {σ σ}_{n no} | |}{{τ τ}_{n no}}))}^{22} + + {((\frac{| | {σ σ}_{s the s} | |}{{τ τ}_{s the s}}))}^{22} &GreaterEqual; &Greater Equal; 11$

其中，σ_n，σ_s分别表示切屑-工件分界面正应力和剪应力；τ_n表示正应力的临界值，τ_s为剪应力的临界值。基于切削分离准则，仿真切削加工的过程。并计算切削力，通过切削力系数计算理论及回归分析，可以计算出切削力系数。通常切削系数是利用切削力采集系统实时采集切削信号，并利用相应设备系统分析计算出所需结果，而计算机模拟分析切削系数大大节省了实际实验采集切削力数据并分析切削系数的时间。在切削力建模当中：Among them, σ _n and σ _s represent the normal stress and shear stress of the chip-workpiece interface respectively; τ _n represents the critical value of normal stress, and τ _s is the critical value of shear stress. Based on the cutting separation criterion, the cutting process is simulated. And calculate the cutting force, through the cutting force coefficient calculation theory and regression analysis, the cutting force coefficient can be calculated. Usually, the cutting coefficient is collected in real time by the cutting force acquisition system, and the corresponding equipment is used to analyze and calculate the required results. However, the computer simulation analysis of the cutting coefficient greatly saves the time of collecting cutting force data and analyzing the cutting coefficient in actual experiments. In cutting force modeling:

$\{\begin{matrix} {dF f}_{t t} = = {K K}_{tc tc} \cdot &Center Dot; h h \cdot \cdot dz dz + + {K K}_{te te} \cdot &Center Dot; ds ds \\ {dF f}_{r r} = = {K K}_{rc rc} \cdot &Center Dot; h h \cdot &Center Dot; dz dz + + {K K}_{re re} \cdot &Center Dot; ds ds \\ {dF f}_{a a} = = {K K}_{ac ac} \cdot \cdot h h \cdot \cdot dz dz + + {K K}_{ac ac} \cdot &Center Dot; ds ds \end{matrix}$

其中，dF_t为切向力微元，dF_r为径向力微元，dF_a为轴向力微元，ds为切削刃长度微元，dz为轴向切深微元，h为切削厚度，K_tc为切向力系数，K_rc为径向力系数，K_ac为轴向力系数，K_te为切向刃口力系数，K_re为径向刃口力系数，K_ae为轴向刃口力系数。仿真计算各方向的切削力有效值，并通过多次不同切削参数仿真，拟合出各方向的切削系数。Among them, dF _t is the element of tangential force, dF _r is the element of radial force, dF _a is the element of axial force, ds is the element of length of cutting edge, dz is the element of axial cutting depth, h is the element of cutting thickness , K _tc is the tangential force coefficient, K _rc is the radial force coefficient, K _ac is the axial force coefficient, K _te is the tangential edge force coefficient, K _re is the radial edge force coefficient, and K _ae is the axial force coefficient Edge force coefficient. The simulation calculates the effective value of the cutting force in each direction, and through multiple simulations of different cutting parameters, the cutting coefficient in each direction is fitted.

本发明的有益效果是对于给定的机床-刀具-工件系统，通过颤振频率（系统固有频率附近）、铣刀齿数、刀具切削系数、切削系统频率响应函数就能够计算出轴向临界切深和相对应的主轴转速，进而可以构建出颤振稳定性叶瓣图，完成颤振稳定域建模。The beneficial effect of the present invention is that for a given machine tool-tool-workpiece system, the axial critical depth of cut can be calculated through the chatter frequency (near the natural frequency of the system), the number of milling cutter teeth, the cutting coefficient of the cutter, and the frequency response function of the cutting system And the corresponding spindle speed, and then the flutter stability lobe diagram can be constructed to complete the modeling of the flutter stability domain.

附图说明Description of drawings

图1为构建稳定性切削参数选择叶瓣图的流程示意图。Fig. 1 is a schematic flow chart of constructing the leaflet diagram for selection of stability cutting parameters.

图2为主轴刀具锤击模态分析流程图。Fig. 2 is the flow chart of spindle tool hammering modal analysis.

图3为切削系统二自由度简化图。Figure 3 is a simplified diagram of the cutting system with two degrees of freedom.

图4为机床刀具系统模态示意图。Fig. 4 is a modal schematic diagram of the tool system of the machine tool.

图中：1机床刀具系统；2信号传感器；3激振力锤；4信号采集卡；5PC。In the figure: 1 machine tool tool system; 2 signal sensor; 3 exciting hammer; 4 signal acquisition card; 5PC.

图5切削参数转速1000r/min、切深0.2mm、进给速度200mm/min在Y方向切削力仿真曲线。Fig. 5 Cutting parameters simulation curve of cutting force in Y direction with speed of 1000r/min, depth of cut of 0.2mm, and feed rate of 200mm/min.

图6切削参数转速1000r/min、切深0.2mm、进给速度200mm/min在Y方向切削力实测曲线。Fig. 6 Cutting parameters of speed 1000r/min, depth of cut 0.2mm, feed rate 200mm/min measured cutting force curve in Y direction.

图7为已构建的某种材料的稳定性叶瓣图。Figure 7 is a diagram of the stability lobe of a constructed material.

具体实施方式Detailed ways

以下结合技术方案和附图详细叙述本发明的实施例。Embodiments of the present invention will be described in detail below in conjunction with technical solutions and accompanying drawings.

如图1和图2所示，其中，材料特性参数包括工件和刀具的材料，计算其切削过程总的切削力，并利用回归拟合出切削系数。结合模态实验得出的特征参数，画出稳定性叶瓣图，用来选择切削参数，包括转数、切深等等。As shown in Figure 1 and Figure 2, the material characteristic parameters include the material of the workpiece and the tool, the total cutting force of the cutting process is calculated, and the cutting coefficient is obtained by regression fitting. Combined with the characteristic parameters obtained from the modal experiment, the stability lobe diagram is drawn, which is used to select the cutting parameters, including the number of revolutions, depth of cut and so on.

利用激振器（力锤或者激振器）对机床主轴刀具系统进行激励，将激励信号和采集到的响应信号经处理后采集到信号采集设备，利用FFT变换及模态拟合，由计算机分析系统的特性参数，包括多阶固有频率、所对应的阻尼比、动刚度等。Use the exciter (hammer or exciter) to excite the tool system of the machine tool spindle, process the excitation signal and the collected response signal to the signal acquisition device, use FFT transformation and model fitting, and analyze it by computer The characteristic parameters of the system, including multi-order natural frequency, corresponding damping ratio, dynamic stiffness, etc.

具体步骤为：The specific steps are:

第一步：针对机床-刀具进行模态测试实验，分析数据，得出相应各阶固有频率、动刚度、阻尼比等。Step 1: Carry out modal test experiments for the machine tool-tool, analyze the data, and obtain the corresponding natural frequency, dynamic stiffness, damping ratio, etc. of each order.

第二步：了解所用刀具材料与工件材料，查询资料知道刀具材料和加工材料的特征参数，如杨氏模量，泊松比等。The second step: understand the tool material and workpiece material used, query the information to know the characteristic parameters of the tool material and processing material, such as Young's modulus, Poisson's ratio, etc.

第三步：仿真计算加工过程，并计算相对应的切削力，通过切削力建模理论拟合计算出切削系数。The third step: simulate and calculate the machining process, and calculate the corresponding cutting force, and calculate the cutting coefficient through the theoretical fitting of cutting force modeling.

第四步：结合第一步中的固有特性及第三步的切削系数，编程绘制稳定性叶瓣图，用来选择最佳切削参数，提高加工质量和效率。The fourth step: Combining the inherent characteristics in the first step and the cutting coefficient in the third step, program and draw the stability lobe diagram to select the best cutting parameters and improve the processing quality and efficiency.

实施例的加工材料为常见叶轮的材料。首先在机床刀具系统进行模态测试试验，仪器为激振力锤，信号采集卡。The processing material of the embodiment is the material of a common impeller. Firstly, the modal test is carried out on the tool system of the machine tool. The instrument is an exciting hammer and a signal acquisition card.

如图4所示，获取刀具材料与加工件材料的特征参数，通过计算机仿真切削过程，并计算其各方向的切削力有效值。为对比仿真精确度，采用仿真结果与实际结果相对比。As shown in Figure 4, the characteristic parameters of the tool material and workpiece material are obtained, the cutting process is simulated by computer, and the effective value of cutting force in each direction is calculated. In order to compare the simulation accuracy, the simulation results are compared with the actual results.

如图5和图6所示，通过计算机仿真曲线Y方向切削力有效值为65.88N，实测数据有效值为66.2N，误差在允许范围内。并在各方向、不同切削参数进行仿真，将结果结合切削力建模理论，回归模拟出该材料的切削系数。该材料的切削系数如下表1：As shown in Figure 5 and Figure 6, the effective value of the cutting force in the Y direction of the computer simulation curve is 65.88N, and the effective value of the measured data is 66.2N, and the error is within the allowable range. The simulation is carried out in various directions and with different cutting parameters, and the results are combined with the cutting force modeling theory to regression simulate the cutting coefficient of the material. The cutting coefficient of the material is shown in Table 1:

K_tc _k K_rc _K K_ac K _ac K_re k _re K_te K _te K_ae _Kae 40744074 19181918 47874787 95.595.5 155155 268268

结合所得固有频率和切削系数，再通过计算机编程绘制稳定性叶瓣图，用来选择最佳切削参数，提高加工质量和效率。Combining the obtained natural frequency and cutting coefficient, the stability lobe diagram is drawn by computer programming, which is used to select the best cutting parameters and improve the processing quality and efficiency.

如图7所示，从叶瓣图可知，对于该种材料的切削加工，选择800r/min左右的转数、0.6mm左右的切深的加工参数进行切削，既可以提高加工效率和能源利用，又可以提高加工质量和精度。As shown in Figure 7, it can be seen from the lobe diagram that for the cutting of this kind of material, the processing parameters of the rotation speed of about 800r/min and the depth of cut of about 0.6mm can be selected for cutting, which can improve the processing efficiency and energy utilization. It can also improve the processing quality and precision.

Claims

1. A chatter stability domain modeling method in the planar cutting process. For a given machine tool-tool-workpiece system, the axial The critical depth of cut and the corresponding spindle speed are used to construct the chatter stability lobe diagram to complete the modeling of the chatter stability domain; it is characterized in that

The critical axial depth of cut obtained by ZOA analysis method is:

{a a}_{plim plim} = = - - \frac{22 π π {Λ Λ}_{R R} ((11 + + {(({Λ Λ}_{I I} / / {Λ Λ}_{R R}))}^{22}))}{{NK NK}_{tc tc}}

The expression of the spindle speed is:

n no = = \frac{6060 {ω ω}_{c c}}{N N ((((22 k k 11)) π π - - 22 arctan arctan (({Λ Λ}_{I I} / / {Λ Λ}_{R R}))))}

Among them, k is the number of lobes in the lobe diagram, _ΛR and _ΛI are the real part and imaginary part of the characteristic root of the system transfer function, N is the number of teeth, K _tc cutting coefficient, _ωc is the characteristic frequency.

2. flutter stability region modeling method according to claim 1, is characterized in that, the calculation process of described cutting coefficient _K is as follows:

By simulating the cutting process of machining, calculate the cutting force in the process, analyze the data, and finally get the cutting coefficient; in the cutting finite element simulation, select the chip separation criterion: physical criterion and geometric criterion; the failure stress criterion is expressed as:

{((\frac{| | {σ σ}_{n no} | |}{{τ τ}_{n no}}))}^{22} + + {((\frac{| | {σ σ}_{s the s} | |}{{τ τ}_{s the s}}))}^{22} &GreaterEqual; &Greater Equal; 11

Among them, σ _n and σ _s represent the normal stress and shear stress of the chip-workpiece interface respectively; τ _n represents the critical value of the normal stress, and τ _s is the critical value of the shear stress; in the milling force modeling:

\{\begin{matrix} {dF f}_{t t} = = {K K}_{tc tc} \cdot \cdot h h \cdot &Center Dot; dz dz + + {K K}_{te te} \cdot \cdot ds ds \\ {dF f}_{r r} = = {K K}_{rc rc} \cdot \cdot h h \cdot &Center Dot; dz dz + + {K K}_{re re} \cdot \cdot ds ds \\ {dF f}_{a a} = = {K K}_{ac ac} \cdot &Center Dot; h h \cdot &Center Dot; dz dz + + {K K}_{ac ac} \cdot &Center Dot; ds ds \end{matrix}

Among them, dF _t is the element of tangential force, dF _r is the element of radial force, dF _a is the element of axial force, ds is the element of length of cutting edge, dz is the element of axial cutting depth, h is the element of cutting thickness , K _tc is the tangential force coefficient, K _rc is the radial force coefficient, K _ac is the axial force coefficient, K _te is the tangential edge force coefficient, K _re is the radial edge force coefficient, and K _ae is the axial force coefficient Edge force coefficient.

3. according to claim 1 and 2 described flutter stability region modeling methods, it is characterized in that, described eigenfrequency ω _c acquisition process is: by modal test, adopts multiple excitations to obtain average value then, and From the different multi-order modes of the multi-directional tester, finally through FFT and mode fitting, analyze the corresponding various characteristic parameters, including multi-order characteristic frequencies, and analyze the data results.