CN103559550A

CN103559550A - Milling stability domain prediction method under multi-modal coupling

Info

Publication number: CN103559550A
Application number: CN201310409076.5A
Authority: CN
Inventors: 万敏; 马颖超; 张卫红; 杨昀
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2013-09-09
Filing date: 2013-09-09
Publication date: 2014-02-05
Anticipated expiration: 2033-09-09
Also published as: CN103559550B

Abstract

The invention discloses a milling stability domain prediction method under multi-modal coupling to solve a technical problem that the efficiency of an existing milling stability domain prediction method is low. The technical scheme is that firstly the transmission function of a process system is determined through a modal test experiment, then modal parameters are extracted from the transmission function and two orthogonal direction modal parameters are paired and combined, a milling test is carried out to calibrate a milling force coefficient, based on the milling force coefficient and each scale of modal parameters, an improved semi discrete method is employed to obtain a stability lobe diagram under each scale of modals, and finally lobe diagrams under obtained from each scale of modals are drawn in a same coordinate system to obtain a stable domain under multi modal coupling. Through a test, when a cutting cycle is divided into 40 sections, 80 sections and 120 sections, compared with a background technology method, the method can save time for 4949.6 seconds, 74200.4 seconds and 344699.5 seconds, and the efficiency is increased by 85.9%, 92% and 88.5%.

Description

Prediction method of milling stable region under multi-modal coupling

技术领域technical field

本发明涉及一种铣削稳定域预测方法，特别涉及一种多模态耦合下的铣削稳定域预测方法。The invention relates to a milling stable region prediction method, in particular to a milling stable region prediction method under multi-modal coupling.

背景技术Background technique

参照图1-2。铣削加工是最常用的金属材料成型工艺方法之一，广泛应用于各种模具、汽车零件及其航空航天零件的生产制造中。铣削过程中由于切削参数选取不合理而导致的再生颤振现象将严重影响加工精度和刀具寿命，甚至导致机床过早破坏。为了合理选取切削参数，避免颤振现象的发生，需要建立一套行之有效的稳定域预测方法。考虑实际工艺系统的复杂性，为准确表征其动力学行为，需要建立多自由度模型来预测铣削过程稳定域，从而建立多模态耦合下的稳定性预测方法。Refer to Figure 1-2. Milling is one of the most commonly used metal forming processes, and it is widely used in the production and manufacture of various molds, auto parts and aerospace parts. Regenerative chatter caused by unreasonable selection of cutting parameters during milling will seriously affect machining accuracy and tool life, and even lead to premature failure of the machine tool. In order to select the cutting parameters reasonably and avoid the occurrence of chatter, it is necessary to establish an effective stable region prediction method. Considering the complexity of the actual process system, in order to accurately characterize its dynamic behavior, it is necessary to establish a multi-degree-of-freedom model to predict the stability domain of the milling process, so as to establish a stability prediction method under multi-modal coupling.

文献1“T.Insperger,G.Stepan,Updated semi-discretization method for periodic delaydifferential equations with discrete delay,International Journal for Numerical Methods inEngineering 61(2004)117-141.”公开了一种在时域内采用半离散方法预测铣削稳定域的方法，该方法只适用于单延时系统，无法考虑刀具螺旋角、刀具偏心等因素对稳定域的影响。Document 1 "T.Insperger, G.Stepan, Updated semi-discretization method for periodic delay differential equations with discrete delay, International Journal for Numerical Methods in Engineering 61(2004) 117-141." discloses a semi-discretization method in the time domain The method of predicting the stable region of milling is only suitable for single-delay systems, and cannot consider the influence of factors such as tool helix angle and tool eccentricity on the stable region.

文献2“M.Wan,W.H.Zhang,J.W.Dang,Y.Yang,A unified stability predictionmethod for milling process with multiple delays,International Journal of Machine Tools&Manufacture 50(2010)29-41.”公开了一种在时域内采用改进半离散方法预测多延时铣削系统稳定域（即稳定性叶瓣图）的方法，该方法可系统考虑刀具偏心、不等距齿等现象对铣削稳定域的影响。Document 2 "M.Wan, W.H.Zhang, J.W.Dang, Y.Yang, A unified stability prediction method for milling process with multiple delays, International Journal of Machine Tools&Manufacture 50(2010) 29-41." The semi-discrete method is improved to predict the stable domain of multi-delay milling system (that is, the stability lobe diagram). This method can systematically consider the influence of tool eccentricity and unequal teeth on the stable domain of milling.

以上关于在时域内预测铣削稳定域的文献的典型特点是：在建模过程中，为了缩短计算时间，只选取了刚性最差的单阶模态参数进行求解，没有考虑多模态耦合的影响，造成在某些转速范围内预测失真。The typical characteristics of the above literatures on predicting the stability domain of milling in the time domain are: in the modeling process, in order to shorten the calculation time, only the single-order modal parameters with the worst rigidity are selected for solution, and the influence of multi-modal coupling is not considered , causing prediction distortion in certain speed ranges.

发明内容Contents of the invention

为了克服现有铣削稳定域预测方法效率低的不足，本发明提供一种多模态耦合下的铣削稳定域预测方法。该方法首先通过模态测试实验测定工艺系统的传递函数，再从传递函数中提取模态参数并将其两个正交方向的模态参数按阶数进行配对组合，然后进行切削实验标定铣削力系数，之后基于铣削力系数和各阶模态参数采用改进半离散法得到各阶模态下的稳定性叶瓣图，最后由各阶模态得到的叶瓣图绘制在同一坐标系中取其最低包络线即可得到多模态耦合下的稳定域，可以提高铣削稳定域预测效率。In order to overcome the low efficiency of the existing milling stable region prediction method, the present invention provides a milling stable region prediction method under multi-modal coupling. In this method, the transfer function of the process system is first determined through the modal test experiment, and then the modal parameters are extracted from the transfer function, and the modal parameters in the two orthogonal directions are paired and combined according to the order, and then the cutting experiment is carried out to calibrate the milling force coefficient, and then based on the milling force coefficient and the parameters of each order mode, the improved semi-discrete method is used to obtain the stability lobe diagrams of each order mode, and finally the lobe diagrams obtained by each order mode are drawn in the same coordinate system, whichever is the best The lowest envelope can get the stable domain under multi-modal coupling, which can improve the efficiency of milling stable domain prediction.

本发明解决其技术问题所采用的技术方案是：一种多模态耦合下的铣削稳定域预测方法，其特点是包括以下步骤：The technical solution adopted by the present invention to solve the technical problem is: a method for predicting the stable region of milling under multimodal coupling, which is characterized in that it includes the following steps:

步骤一、将铣刀与刀柄安装于机床主轴系统，然后采用标准冲击试验测试铣刀-刀柄-机床主轴系统的模态参数，测试得到的第j阶模态参数记为m_X,j、c_X,j、k_X,j，m_Y,j、c_Y,j和k_Y,j，下标X和Y表示在X和Y方向的测试结果，下标j表示第j阶模态参数，符号m、c与k分别表示模态质量、阻尼系数以及模态刚度。Step 1. Install the milling cutter and tool holder on the machine tool spindle system, and then use the standard impact test to test the modal parameters of the milling cutter-tool holder-machine tool spindle system. The jth order modal parameters obtained from the test are denoted as m _X,j , c _X,j , k _X,j , m _Y,j , c _Y,j and k _Y,j , the subscripts X and Y represent the test results in the X and Y directions, and the subscript j represents the jth order mode Parameters, the symbols m, c and k represent the modal mass, damping coefficient and modal stiffness, respectively.

步骤二、将步骤一测得的X方向的第j阶模态参数与Y方向第j阶模态参数组成一个组合，把该组合记为模态j；Step 2, forming a combination of the jth order modal parameter in the X direction measured in step 1 and the jth order modal parameter in the Y direction, and denoting the combination as modal j;

步骤三、通过铣削实验测试铣削力，标定切向铣削力系数K_t、径向铣削力系数K_r、刀具偏心参数ρ和λ。ρ表示刀具旋转中心与刀具几何中心的偏移量，λ表示刀具偏心产生的方向与相邻最近的刀齿头部之间的夹角。Step 3: Test the milling force through a milling experiment, and calibrate the tangential milling force coefficient K _t , the radial milling force coefficient K _r , and the tool eccentricity parameters ρ and λ. ρ represents the offset between the center of rotation of the tool and the geometric center of the tool, and λ represents the angle between the direction of tool eccentricity and the head of the nearest adjacent tooth.

步骤四、根据铣刀几何参数以及步骤三得到的偏心参数ρ和λ，分析确定铣削系统可能出现的延时量的大小和个数，将延时量按从小到达的顺序记为

N_M表示延时量的个数。Step 4. According to the geometric parameters of the milling cutter and the eccentric parameters ρ and λ obtained in Step 3, analyze and determine the size and number of delays that may occur in the milling system, and record the delays in the order of arrival from small to small as

N _M represents the number of delays.

步骤五、将铣削系统在模态j下的动力学控制方程表示为：Step 5. Express the dynamic control equation of the milling system under mode j as:

${M m}_{j j} \overset{\cdot \cdot \cdot &Center Dot;}{X x} ((t t)) + + {C C}_{j j} \overset{\cdot \cdot}{X x} ((t t)) + + {K K}_{j j} X x ((t t)) = = {Σ Σ}_{l l = = 11}^{{N N}_{M m}} [[{H h}_{j j,, l l} ((t t)) ((X x ((t t - - {τ τ}_{l l})) - - X x ((t t))))]]$

其中，in,

${M m}_{j j} = = [\begin{matrix} {m m}_{X x,, j j} & 00 \\ 00 & {m m}_{Y Y,, j j} \end{matrix}]$

${C C}_{j j} = = [\begin{matrix} {c c}_{X x,, j j} & 00 \\ 00 & {C C}_{Y Y,, j j} \end{matrix}]$

${K K}_{j j} = = [\begin{matrix} {k k}_{X x,, j j} & 00 \\ 00 & {k k}_{Y Y,, j j} \end{matrix}]$

X(t)表示刀具动态变形向量， $H_{l} (t) = [\begin{matrix} H_{l, XX} & H_{l, YY} \\ H_{l, YX} & H_{l, YY} \end{matrix}]$ 表示方向系数矩阵，其各元素X(t) represents the tool dynamic deformation vector, $h_{l} (t) = [\begin{matrix} h_{l, XX} & h_{l, YY} \\ h_{l, YX} & h_{l, YY} \end{matrix}]$ Represents the direction coefficient matrix, each element of which

表达式如下：The expression is as follows:

H_l,XX(t)＝∑[z_l,p,qsinθ_l,p,q(t)(K_tcosθ_l,p,q(t)+K_rsinθ_l,p,q(t))]H _l,XX (t)＝∑[z _l,p,q sinθ _l,p,q (t)(K _t cosθ _l,p,q (t)+K _r sinθ _l,p,q (t)) ]

H_l,XY(t)＝∑[z_l,p,qcosθ_l,p,q(t)(K_tcosθ_l,p,q(t)+K_rsinθ_l,p,q(t))]H _l,XY (t)＝∑[z _l,p,q cosθ _l,p,q (t)(K _t cosθ _l,p,q (t)+K _r sinθ _l,p,q (t)) ]

H_l,YX(t)＝∑[z_l,p,qsinθ_l,p,q(t)(-K_tsinθ_l,p,q(t)+K_rcosθ_l,p,q(t))]H _l,YX (t)＝∑[z _l,p,q sinθ _l,p,q (t)(-K _t sinθ _l,p,q (t)+K _r cosθ _l,p,q (t) )]

H_l,YY(t)＝∑[z_l,p,qcosθ_l,p,q(t)(-K_tsinθ_l,p,q(t)+K_rcosθ_l,p,q(t))]H _l,YY (t)＝∑[z _l,p,q cosθ _l,p,q (t)(-K _t sinθ _l,p,q (t)+K _r cosθ _l,p,q (t) )]

式中，每一刀齿沿轴向被离散成若干个等长的刀齿片，z_l,p,q和θ_l,p,q(t)表示第p个刀齿上第q个单元所对应的轴向长度和切削角度；下标l表示在时间t与第p个刀齿上第q个单元对应的延时量为τ_l。In the formula, each tooth is discretized into several blades of equal length along the axial direction, z _{l, p, q} and θ _{l, p, q} (t) represent the corresponding The axial length and cutting angle of ; the subscript l indicates that the time delay corresponding to the qth unit on the pth tooth at time t is τ _l .

步骤六、对由步骤五得到的控制方程进行稳定性分析，求解与模态j对应的稳定性叶瓣图。Step 6: Perform stability analysis on the control equation obtained in Step 5, and solve the stability lobe diagram corresponding to mode j.

步骤七、从j=1到j=n，重复执行步骤五与步骤六，直到得到与各阶模态对应的稳定性叶瓣图，n表示测得的最大模态数。Step 7. From j=1 to j=n, repeat steps 5 and 6 until the stability lobe diagram corresponding to each mode is obtained, and n represents the maximum number of modes measured.

步骤八、将由各个单阶模态得到的叶瓣图绘制在同一坐标系下，取所有叶瓣图最下缘连接成连续曲线，即做最低包络线，即可得到多模态耦合下多延时铣削系统的稳定性叶瓣图。Step 8. Draw the lobe diagrams obtained from each single-order mode in the same coordinate system, take the bottom edge of all the lobe diagrams and connect them into a continuous curve, that is, make the lowest envelope, and you can get the multi-mode coupling. Stability lobe diagram of a time-lapse milling system.

本发明的有益效果是：该方法首先通过模态测试实验测定工艺系统的传递函数，再从传递函数中提取模态参数并将其两个正交方向的模态参数按阶数进行配对组合，然后进行切削实验标定铣削力系数，之后基于铣削力系数和各阶模态参数采用改进半离散法得到各阶模态下的稳定性叶瓣图，最后由各阶模态得到的叶瓣图绘制在同一坐标系中取其最低包络线即可得到多模态耦合下的稳定域，提高了铣削稳定域预测效率。经测试，当切削周期被离散为40段时，本发明方法比背景技术方法节省时间为4949.6秒，效率提高了85.9%；当切削周期被离散为80段时，本发明方法比背景技术方法节省时间为74200.4秒，效率提高了92.0%；当切削周期被离散为120段时，本发明方法比背景技术方法节省时间为344699.5秒，效率提高了88.5%；不难看出，对于精度要求越高的多模态多延时稳定域的预测，本发明方法的高效性体现得越明显。The beneficial effects of the present invention are: the method first measures the transfer function of the process system through a modal test experiment, then extracts the modal parameters from the transfer function and pairs and combines the modal parameters in two orthogonal directions according to the order, Then the cutting experiment is carried out to calibrate the milling force coefficient, and then based on the milling force coefficient and the modal parameters of each order, the stability lobe diagram of each order mode is obtained by using the improved semi-discrete method, and finally the lobe diagram obtained by each order mode is drawn The stable domain under multi-modal coupling can be obtained by taking the lowest envelope in the same coordinate system, which improves the efficiency of milling stable domain prediction. After testing, when the cutting cycle is discretized into 40 segments, the method of the present invention saves 4949.6 seconds compared with the method of the background technology, and the efficiency is increased by 85.9%; The time is 74200.4 seconds, and the efficiency is increased by 92.0%; when the cutting cycle is discretized into 120 segments, the time saving of the method of the present invention is 344699.5 seconds compared with the method of the background technology, and the efficiency is increased by 88.5%; it is not difficult to see that the higher precision requirements For the prediction of multi-modal and multi-delay stable domains, the efficiency of the method of the present invention is more obvious.

下面结合附图和实施例对本发明作详细说明。The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

附图说明Description of drawings

图1是背景技术方法中多模态模型示意图。Fig. 1 is a schematic diagram of a multimodal model in the method of the background technology.

图2是背景技术方法中各单阶模态下的稳定性叶瓣图。Fig. 2 is a diagram of the stability lobe in each single-order mode in the method of the background technology.

图3是本发明方法求得的多模态叶瓣图。Fig. 3 is a multimodal lobe diagram obtained by the method of the present invention.

图中，m_X,1、c_X,1、k_X,1和m_Y,n、c_Y,n、k_Y,n分别表示第一阶模态质量、模态阻尼、模态刚度和第n阶模态质量、模态阻尼、模态刚度；θ_l,p,q表示第p个刀齿上第q个单元所对应的切削角度。1-是按照第一阶模态参数计算得到的叶瓣图，2-是第二阶模态参数计算得到的叶瓣图，3-是按照第三阶模态参数计算得到的叶瓣图；A,B,C,D,E,F,G,H表示不同阶模态参数计算得到的叶瓣图的交点。黑色实心正方形代表实际实验测定的稳定切削过程，空心圆代表实测不稳定切削过程。In the figure, m _X,1 , c _X,1 , k _X,1 and m _Y,n , c _Y,n , k _Y,n represent the first-order modal mass, modal damping, modal stiffness and the first-order modal mass, respectively. n-order modal mass, modal damping, and modal stiffness; θ _{l, p, q} represent the cutting angle corresponding to the qth unit on the pth tooth. 1- is the lobe diagram calculated according to the first-order modal parameters, 2- is the lobe diagram calculated according to the second-order modal parameters, and 3- is the lobe diagram calculated according to the third-order modal parameters; A, B, C, D, E, F, G, H represent the intersection points of the lobe diagrams obtained by calculating the modal parameters of different orders. The black solid squares represent the stable cutting process measured by the actual experiment, and the open circles represent the measured unstable cutting process.

具体实施方式Detailed ways

本发明多模态耦合下的铣削稳定域预测方法的具体步骤如下。The specific steps of the milling stable region prediction method under multi-modal coupling in the present invention are as follows.

1）将半径为12mm、螺旋角为30°、刀齿数N为3的铣刀安装于刀柄然后安装于机床主轴系统，接着采用标准冲击试验测试铣刀-刀柄-机床主轴系统的模态参数，测试得到的各阶模态参数，如下表：1) Install a milling cutter with a radius of 12mm, a helix angle of 30°, and a number of teeth N of 3 on the tool holder and then on the machine tool spindle system, and then use the standard impact test to test the modal of the milling cutter-tool holder-machine tool spindle system Parameters, the modal parameters of each order obtained from the test, as shown in the following table:

表1.模态参数Table 1. Modal parameters

2）将步骤1）中测得的X方向和Y方向的模态参数进行配对组合，即将X方向的第一阶模态参数与和Y方向的第一阶模态组合为一组记成模态1；同理，即将X方向的第二阶模态参数与和Y方向的第二阶模态组合为一组记成模态2；即将X方向的第三阶模态参数与和Y方向的第三阶模态组合为一组记成模态3。2) Combine the modal parameters in the X direction and Y direction measured in step 1), that is, the first-order modal parameters in the X direction and the first-order modal parameters in the Y direction are combined into a group and recorded as a model State 1; Similarly, the second-order modal parameters in the X direction and the second-order mode in the Y direction are combined into a group and recorded as mode 2; the third-order modal parameters in the X direction and the Y direction The combination of the third-order modes of is denoted as mode 3 as a group.

3）将测力仪安装于机床工作台，再将铝合金7050安装于测力仪上，然后利用步骤1）的铣刀-刀柄-机床主轴系统对铝合金7050进行加工，并测试加工过程中的铣削铣削力，根据测试得到的铣削力利用文献3“W.A.Kline，R.E.DeVor,J.R.Lindberg,Theprediction of cutting forces in end milling with application to cornering cuts.InternationalJournal of Machine Tool Design and Research,22(1982),7-22”公开的方法标定切向铣削力系数K_t和径向铣削力系数K_r，采用文献4“M.Wan，M.S.LU，W.H.Zhang，Y.Yang,Y.Li,A new method for identifying the cutter runout parameters in flat milling process,Materials Science Forum,697-698(2011),71-74”公开的方法标定刀具偏心参数ρ和λ。ρ表示刀具旋转中心与刀具几何中心的偏移量，λ表示刀具偏心产生的方向与相邻最近的刀齿头部之间的夹角。该例中标定结果如下：K_t为1110.6MPa,K_r为554.45MPa，ρ,λ分别为13.5μm和-17.51°。3) Install the dynamometer on the machine table, then install the aluminum alloy 7050 on the dynamometer, and then use the milling cutter-knife handle-machine spindle system in step 1) to process the aluminum alloy 7050, and test the processing process The milling force in milling, according to the milling force obtained by the test using literature 3 "WAKline, REDeVor, JRLindberg, The prediction of cutting forces in end milling with application to cornering cuts.InternationalJournal of Machine Tool Design and Research, 22(1982), 7- 22" public method to calibrate tangential milling force coefficient K _t and radial milling force coefficient K _r , using literature 4 "M.Wan, MSLU, WH Zhang, Y.Yang, Y.Li, A new method for identifying the cutter runout Parameters in flat milling process, Materials Science Forum, 697-698 (2011), 71-74 "Disclosed method to calibrate tool eccentricity parameters ρ and λ. ρ represents the offset between the center of rotation of the tool and the geometric center of the tool, and λ represents the angle between the direction of tool eccentricity and the head of the nearest adjacent tooth. The calibration results in this example are as follows: K _t is 1110.6MPa, K _r is 554.45MPa, ρ and λ are 13.5μm and -17.51° respectively.

4）根据铣刀几何参数以及步骤3）得到的偏心参数ρ和λ，分析确定铣削系统可能出现的延时量总数为3，其大小分别为T/3、2T/3、T，T为刀具旋转周期。4) According to the geometric parameters of the milling cutter and the eccentric parameters ρ and λ obtained in step 3), analyze and determine that the total amount of delay that may occur in the milling system is 3, and their sizes are T/3, 2T/3, T respectively, and T is the tool rotation period.

5）将铣削系统在模态j下的动力学控制方程表示为：5) Express the dynamic control equation of the milling system under mode j as:

${M m}_{j j} \overset{\cdot &Center Dot; \cdot &Center Dot;}{X x} ((t t)) + + {C C}_{j j} \overset{\cdot &Center Dot;}{X x} ((t t)) + + {K K}_{j j} X x ((t t)) = = {Σ Σ}_{l l = = 11}^{33} [[{H h}_{j j,, l l} ((t t)) ((X x ((t t - - {τ τ}_{l l})) - - X x ((t t))))]]$

其中，in,

X(t)表示刀具动态变形向量， $H_{l} (t) = [\begin{matrix} H_{l, XX} & H_{l, XY} \\ H_{l, YX} & H_{l, YY} \end{matrix}]$ 表示方向系数矩阵，其各元素表达式如下：X(t) represents the tool dynamic deformation vector, $h_{l} (t) = [\begin{matrix} h_{l, XX} & h_{l, X Y} \\ h_{l, YX} & h_{l, YY} \end{matrix}]$ Indicates the direction coefficient matrix, and the expression of each element is as follows:

在上式计算过程中，每一刀齿沿轴向被离散成若干个等长的刀齿片，z_l,p,q和θ_l,p,q(t)表示第p个刀齿上第q个单元所对应的轴向长度和切削角度；下标l表示在时间t与第p个刀齿上第q个单元对应的延时量为τ_l。In the calculation process of the above formula, each tooth is discretized into several equal-length blades along the axial direction, z _{l, p, q} and θ _{l, p, q} (t) represent the The axial length and cutting angle corresponding to each unit; the subscript l indicates that the time delay corresponding to the qth unit on the pth tooth at time t is τ _l .

6）按照文献2“M.Wan,W.H.Zhang,J.W.Dang,Y.Yang,A unified stabilityprediction method for milling process with multiple delays,International Journal ofMachine Tools&Manufacture 50(2010)29-41.”公开的改进半离散方法对由步骤5）得到的控制方程进行稳定性分析，求解与模态j对应的稳定性叶瓣图；6) According to the improved semi-discrete method disclosed in document 2 "M.Wan, W.H.Zhang, J.W.Dang, Y.Yang, A unified stability prediction method for milling process with multiple delays, International Journal of Machine Tools & Manufacture 50(2010) 29-41." Perform stability analysis on the control equation obtained in step 5), and solve the stability lobe diagram corresponding to mode j;

7）从j=1到j=n，重复执行步骤5）与步骤6），直到得到与各阶模态对应的稳定性叶瓣图，n表示测得的最大模态数,此处n的取值为3。7) From j=1 to j=n, repeat step 5) and step 6) until the stability lobe diagram corresponding to each mode is obtained, n represents the maximum number of modes measured, where n The value is 3.

8）将各个单阶模态计算得到的叶瓣图绘制在同一坐标系下，参见附图2，图中A,B,C,D,E,F表示不同阶模态参数得到的叶瓣图的交点。取所有叶瓣图最下缘连接成连续曲线，即依次取图中一阶模态参数的AB段，三阶模态的BC段，一阶模态的CD段，三阶模态的DE段，一阶模态的EF段，三阶模态的FG段及一阶模态的GH段，将其连接成的曲线绘制在同一坐标系下，即可得到多模态耦合下多延时铣削系统的稳定性叶瓣图，参见附图3；为验证所给方法的有效性，特设计四组切削验证实验，实验结果已在图3中给出：图3中黑色实心正方形代表实际实验测定的稳定切削过程，空心圆代表实测不稳定切削过程。验证实验的结果与铣削稳定域预测结果吻合，表明所给方法可行有效。8) Draw the lobe diagrams calculated by each single-order mode in the same coordinate system, see Figure 2, A, B, C, D, E, F in the figure represent the lobe diagrams obtained by different order modal parameters intersection point. Take the bottom edge of all lobe diagrams and connect them into a continuous curve, that is, take the AB section of the first-order mode parameters in the figure, the BC section of the third-order mode, the CD section of the first-order mode, and the DE section of the third-order mode in the figure. , the EF section of the first-order mode, the FG section of the third-order mode and the GH section of the first-order mode, and the curves formed by connecting them are drawn in the same coordinate system, and the multi-delay milling under multi-mode coupling can be obtained For the stability lobe diagram of the system, see attached drawing 3; in order to verify the effectiveness of the given method, four sets of cutting verification experiments are specially designed, and the experimental results are shown in Figure 3: the black solid squares in Figure 3 represent the actual experimental measurements The stable cutting process of , and the hollow circle represents the measured unstable cutting process. The results of the verification experiment are consistent with the prediction results of the milling stable region, which shows that the proposed method is feasible and effective.

从图2、图3对比可以看出，在实际铣削过程中，由于多阶模态的存在，其稳定域是多个模态耦合的结果，如果只取某阶模态参数求解，预测结果必然存在误差。比如取第一阶仿真，得到的叶瓣图即为模态1的叶瓣图，参见附图2，则该稳定域在转速范围为15000至21000转/分时，预测结果将不准确。From the comparison of Figure 2 and Figure 3, it can be seen that in the actual milling process, due to the existence of multi-order modes, its stable domain is the result of multi-mode coupling. There is an error. For example, taking the first-order simulation, the lobe diagram obtained is the lobe diagram of mode 1, see Figure 2, then the prediction result will be inaccurate when the speed range of the stability domain is 15,000 to 21,000 rpm.

另一方面，包络线法计算时间与在求解动力学方程过程中考虑多模态计算时间对比如表2。表2中由于文献2“M.Wan,W.H.Zhang,J.W.Dang,Y.Yang,A unified stabilityprediction method for milling process with multiple delays,International Journal ofMachine Tools&Manufacture 50(2010)29-41.”公开的改进半离散方法在计算叶瓣图时需要将转速，轴向切深以及切削周期进行分段处理，其分段段数将对计算时间产生影响。本例中将轴向切深40mm分为100段，即每段0.4mm，转速计算范围5000至50000转/分离散为100段,即每段450转/分，将刀齿切削周期分别离散为40、80、120段求解，对比其计算时间。On the other hand, the calculation time of the envelope method is compared with the calculation time of considering multi-modality in the process of solving the dynamic equation, as shown in Table 2. In Table 2, due to the document 2 "M.Wan, W.H.Zhang, J.W.Dang, Y.Yang, A unified stability prediction method for milling process with multiple delays, International Journal of Machine Tools & Manufacture 50 (2010) 29-41." The improved semi-discrete In the method, the rotation speed, axial depth of cut and cutting cycle need to be processed in segments when calculating the lobe diagram, and the number of segments will affect the calculation time. In this example, the axial depth of cut of 40mm is divided into 100 sections, that is, each section is 0.4mm, and the rotational speed calculation range is 5000 to 50,000 rpm, which is divided into 100 sections, that is, each section is 450 rpm. 40, 80, and 120 segments are solved, and the calculation time is compared.

表2.计算时间对比Table 2. Computational time comparison

从表中可以看出，本发明方法提高了铣削稳定域预测效率，且随着延时时间离散段数的增长，效率提高越明显。当切削周期被离散为40段时，本发明方法比背景技术方法节省时间为4949.6秒，效率提高了85.9%；当切削周期被离散为80段时，本发明方法比背景技术方法节省时间为74200.4秒，效率提高了92.0%；当切削周期被离散为120段时，本发明方法比背景技术方法节省时间为344699.5秒，效率提高了88.5%；不难看出，对于精度要求越高的多模态多延时稳定域的预测，本发明方法的高效性体现得越明显。It can be seen from the table that the method of the present invention improves the efficiency of milling stable domain prediction, and the efficiency is improved more obviously with the increase of the number of discrete segments of the delay time. When the cutting cycle is discretized into 40 segments, the method of the present invention saves 4949.6 seconds of time compared with the method of the background technology, and the efficiency is increased by 85.9%; when the cutting cycle is discretized into 80 segments, the method of the present invention saves 74200.4 seconds compared with the method of the background technology seconds, the efficiency has been improved by 92.0%; when the cutting cycle is discretized into 120 segments, the method of the present invention saves 344699.5 seconds compared with the background technology method, and the efficiency has been increased by 88.5%; it is not difficult to see that for multi-modal For the prediction of multi-delay stable domains, the efficiency of the method of the present invention is more obvious.

Claims

1. A milling stability domain prediction method under multimodal coupling, is characterized in that comprising the following steps:

Step 1. Install the milling cutter and tool holder on the machine tool spindle system, and then use the standard impact test to test the modal parameters of the milling cutter-tool holder-machine tool spindle system. The jth order modal parameters obtained from the test are denoted as m _X,j , c _X,j , k _X,j , m _Y,j , c _Y,j and k _Y,j , the subscripts X and Y represent the test results in the X and Y directions, and the subscript j represents the jth order mode Parameters, the symbols m, c and k represent the modal mass, damping coefficient and modal stiffness respectively;

Step 2, forming a combination of the jth order modal parameter in the X direction measured in step 1 and the jth order modal parameter in the Y direction, and denoting the combination as modal j;

Step 3. Test the milling force through the milling experiment, calibrate the tangential milling force coefficient K _t , the radial milling force coefficient K _r , the tool eccentricity parameters ρ and λ; ρ represents the offset between the tool rotation center and the tool geometric center, and λ represents The angle between the direction generated by tool eccentricity and the head of the nearest adjacent cutter tooth;

Step 4. According to the geometric parameters of the milling cutter and the eccentric parameters ρ and λ obtained in Step 3, analyze and determine the size and number of delays that may occur in the milling system, and record the delays in the order of arrival from small to small as

N _M represents the number of delays;

Step 5. Express the dynamic control equation of the milling system under mode j as:

{M m}_{j j} \overset{\cdot &Center Dot; \cdot &Center Dot;}{X x} ((t t)) + + {C C}_{j j} \overset{\cdot \cdot}{X x} ((t t)) + + {K K}_{j j} X x ((t t)) = = {Σ Σ}_{l l = = 11}^{{N N}_{M m}} [[{H h}_{j j,, l l} ((t t)) ((X x ((t t - - {τ τ}_{l l})) - - X x ((t t))))]]

in,

{M m}_{j j} = = [\begin{matrix} {m m}_{X x,, j j} & 00 \\ 00 & {m m}_{Y Y,, j j} \end{matrix}]

{C C}_{j j} = = [\begin{matrix} {c c}_{X x,, j j} & 00 \\ 00 & {c c}_{Y Y,, j j} \end{matrix}]

{K K}_{j j} = = [\begin{matrix} {k k}_{X x,, j j} & 00 \\ 00 & {k k}_{Y Y,, j j} \end{matrix}]

X(t) represents the tool dynamic deformation vector,

h_{l} (t) = [\begin{matrix} h_{l, XX} & h_{l, X Y} \\ h_{l, YX} & h_{l, YY} \end{matrix}]

Indicates the direction coefficient matrix, and the expression of each element is as follows:

H _l,XX (t)＝∑[z _l,p,q sinθ _l,p,q (t)(K _t cosθ _l,p,q (t)+K _r sinθ _l,p,q (t)) ]

H _l,XY (t)＝∑[z _l,p,q cosθ _l,p,q (t)(K _t cosθ _l,p,q (t)+K _r sinθ _l,p,q (t)) ]

H _l,YX (t)＝∑[z _l,p,q sinθ _l,p,q (t)(-K _t sinθ _l,p,q (t)+K _r cosθ _l,p,q (t) )]

H _l,YY (t)＝∑[z _l,p,q cosθ _l,p,q (t)(-K _t sinθ _l,p,q (t)+K _r cosθ _l,p,q (t) )]

In the formula, each tooth is discretized into several blades of equal length along the axial direction, z _{l, p, q} and θ _{l, p, q} (t) represent the corresponding The axial length and cutting angle of ; the subscript l indicates that the time delay corresponding to the qth unit on the pth tooth at time t is τ _l ;

Step 6, carry out stability analysis to the governing equation obtained by step 5, and solve the stability lobe diagram corresponding to mode j;

Step 7. From j=1 to j=n, repeat steps 5 and 6 until the stability lobe diagram corresponding to each mode is obtained, and n represents the maximum number of modes measured;

Step 8. Draw the lobe diagrams obtained from each single-order mode in the same coordinate system, take the bottom edge of all the lobe diagrams and connect them into a continuous curve, that is, make the lowest envelope, and you can get the multi-mode coupling. Stability lobe diagram of a time-lapse milling system.