CN106965032A - Thin-wall part milling parameter suppressing method - Google Patents
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Abstract
本发明公开了一种薄壁件铣削颤振抑制方法，用于解决现有铣削稳定性预测方法实用性差的技术问题。技术方案是通过附加质量对薄壁零件动力学参数的局部修改，建立一种高效的加工工艺方法来提高铣削加工的稳定域，为薄壁件高速铣削加工提供可靠的参数选择范围；最终利用优化算法选取可以实现无颤振、高效率的加工参数，实现薄壁件的高速无颤振铣削加工。本发明通过对薄壁零件动力学参数的局部修改，建立一种高效的加工工艺方法来提高铣削加工的稳定域，较好的解决了工件起始和终止位置两端刚性差，稳定域范围小，严重制约铣削过程加工参数的选取的问题；为薄壁件高速铣削加工提供可靠的参数选择范围，实现了薄壁件的高速无颤振铣削加工，实用性好。
The invention discloses a chatter suppressing method for milling thin-walled parts, which is used to solve the technical problem that the existing milling stability prediction method is poor in practicability. The technical solution is to locally modify the dynamic parameters of thin-walled parts through additional mass, establish an efficient processing method to improve the stability region of milling, and provide a reliable parameter selection range for high-speed milling of thin-walled parts; the final use of optimization Algorithm selection can realize chatter-free and high-efficiency machining parameters, and realize high-speed chatter-free milling of thin-walled parts. The present invention establishes an efficient processing method to improve the stable region of milling by partially modifying the dynamic parameters of the thin-walled parts, and better solves the problem of poor rigidity at both ends of the starting and ending positions of the workpiece and the small range of the stable region , which seriously restricts the selection of processing parameters in the milling process; it provides a reliable parameter selection range for high-speed milling of thin-walled parts, realizes high-speed chatter-free milling of thin-walled parts, and has good practicability.
Description
技术领域technical field
本发明属于薄壁件制造领域，特别涉及一种薄壁件铣削颤振抑制方法。The invention belongs to the field of manufacturing thin-walled parts, in particular to a thin-walled part milling chatter suppressing method.
背景技术Background technique
文献1“Song Q,Liu Z,Wan Y,et al.Application of Sherman-Morrison-Woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component[J].International Journal of Mechanical Sciences,2015,96-97:79-90.”公开了一种利用Sherman-Morrison-Woodbury公式来考虑铣削过程中材料去除对薄壁件动力学参数影响的铣削稳定性预测方法。该方法将铣削过程离散，通过Sherman-Morrison-Woodbury公式得到离散后的薄壁件在铣削过程中动力学参数随着材料去除的变化规律进而得到相应的动力学参数，然后利用稳定性求解方程得到每个离散过程中轴转速和轴向切深的关系，最后得到铣削过程材料去除对稳定性影响的预测三维图。Document 1 "Song Q, Liu Z, Wan Y, et al. Application of Sherman-Morrison-Woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component [J]. International Journal of Mechanical Sciences, 2015, 96-97: 79-90." discloses a milling stability prediction method using the Sherman-Morrison-Woodbury formula to consider the effect of material removal on the dynamic parameters of thin-walled parts during milling. This method discretizes the milling process, and uses the Sherman-Morrison-Woodbury formula to obtain the dynamic parameters of the discretized thin-walled parts during the milling process with the change law of material removal to obtain the corresponding dynamic parameters, and then use the stability to solve the equation to get The relationship between the shaft speed and the axial depth of cut in each discrete process, and finally a three-dimensional plot of the prediction of the effect of material removal on the stability of the milling process.
文献2“Yang Y,Zhang WH,Ma YC,et al.Chatter prediction for peripheralmilling of thin-walled workpieces with curved surfaces[J].InternationalJournal of Machine Tools and Manufacture,2016,109:36-48.”公开了一种同时考虑工件在不同刀具铣削位置和轴向高度动力学参数变化的铣削稳定性预测方法。该方法先将刀具和工件沿轴向离散，得到各个离散的处的动力学方程。然后将铣削过程离散，得到每个铣削过程的动力学方程。通过动力学参数修改的方法得到每个动力学方程的参数，最后求解动力学方程得到考虑铣削位置和轴向高度动力学参数变化的铣削稳定性预测方法。Document 2 "Yang Y, Zhang WH, Ma YC, et al. Chatter prediction for peripheral milling of thin-walled workpieces with curved surfaces [J]. International Journal of Machine Tools and Manufacture, 2016, 109:36-48." A milling stability prediction method that simultaneously considers the variation of dynamic parameters of the workpiece at different milling positions and axial heights of the tool. In this method, the tool and the workpiece are discretized along the axial direction first, and the dynamic equations of each discretized position are obtained. Then the milling process is discretized to obtain the dynamic equation of each milling process. The parameters of each dynamic equation are obtained by modifying the dynamic parameters, and finally the dynamic equation is solved to obtain a milling stability prediction method considering the change of the dynamic parameters of the milling position and axial height.
以上文献都考虑了铣削过程中材料去除对工件动力学参数的影响，预测了不同刀具位置处的稳定域；但是对于铣削过程起始和终止位置处工件刚性差，铣削稳定域低的问题都没有有效解决，造成了铣削过程参数可选择范围小，加工效率无法提高。The above literatures have considered the impact of material removal on the dynamic parameters of the workpiece during the milling process, and predicted the stability domain at different tool positions; but for the poor rigidity of the workpiece at the start and end positions of the milling process, the milling stability domain is low. Effectively solved, resulting in a small selection range of milling process parameters, and processing efficiency cannot be improved.
发明内容Contents of the invention
为了克服现有铣削稳定性预测方法实用性差的不足，本发明提供一种薄壁件铣削颤振抑制方法。该方法通过附加质量对薄壁零件动力学参数的局部修改，建立一种高效的加工工艺方法来提高铣削加工的稳定域，为薄壁件高速铣削加工提供可靠的参数选择范围；最终利用优化算法选取可以实现无颤振、高效率的加工参数，实现薄壁件的高速无颤振铣削加工。本发明通过对薄壁零件动力学参数的局部修改，建立一种高效的加工工艺方法来提高铣削加工的稳定域，较好的解决了工件起始和终止位置两端刚性差，稳定域范围小，严重制约铣削过程加工参数的选取的问题；为薄壁件高速铣削加工提供可靠的参数选择范围，实现了薄壁件的高速无颤振铣削加工。In order to overcome the disadvantage of poor practicability of the existing milling stability prediction method, the invention provides a thin-walled part milling chatter suppression method. This method locally modifies the dynamic parameters of thin-walled parts through the addition of mass, establishes an efficient processing method to improve the stability region of milling, and provides a reliable parameter selection range for high-speed milling of thin-walled parts; finally, the optimization algorithm is used Select processing parameters that can achieve chatter-free and high-efficiency, and realize high-speed chatter-free milling of thin-walled parts. The present invention establishes an efficient processing method to improve the stable region of milling by partially modifying the dynamic parameters of the thin-walled parts, and better solves the problem of poor rigidity at both ends of the starting and ending positions of the workpiece and the small range of the stable region , which seriously restricts the selection of processing parameters in the milling process; it provides a reliable parameter selection range for high-speed milling of thin-walled parts, and realizes high-speed chatter-free milling of thin-walled parts.
本发明解决其技术问题所采用的技术方案：一种薄壁件铣削颤振抑制方法，其特点是包括以下步骤：The technical solution adopted by the present invention to solve the technical problem: a thin-walled part milling chatter suppression method, which is characterized in that it includes the following steps:
步骤一、建立多点接触的同时考虑刀具和工件变形的铣削动力学模型；铣削系统的运动方程为：Step 1. Establish a milling dynamics model that considers the deformation of the tool and workpiece while multi-point contact is established; the equation of motion of the milling system is:
其中，Γt(t)是表示刀具的模态位移的向量；Γwp(t)是表示工件的模态位移的向量；ζt表示刀具阻尼比的对角矩阵，ζwp表示工件阻尼比的对角矩阵；ωt表示刀具固有频率的对角阵；ωwp表示工件固有频率的对角阵；Ut表示质量归一化后刀具的模态振型，Uwp表示质量归一化后工件的模态振型；q表示将刀具与工件沿轴向微分所用的节点数；F(t)表示在每个接触点处铣削力组成的矩阵；Among them, Γ t (t) is a vector representing the modal displacement of the tool; Γ wp (t) is a vector representing the modal displacement of the workpiece; ζ t represents the diagonal matrix of the tool damping ratio, and ζ wp represents the damping ratio of the workpiece Diagonal matrix; ω t represents the diagonal matrix of the natural frequency of the tool; ω wp represents the diagonal matrix of the natural frequency of the workpiece; U t represents the mode shape of the tool after mass normalization, and U wp represents the workpiece after mass normalization modal shape; q represents the number of nodes used to differentiate the tool and workpiece along the axial direction; F(t) represents the matrix formed by the milling force at each contact point;
步骤二、将选定的铣刀安装到机床主轴后，采用多点敲击试验法和线性插值的方法测定刀具进给方向和垂直于进给方向的模态参数；ζm,t,x，ζm,t,y表示第m阶的阻尼比；ωm,t,x，ωm,t,y表示第m阶的系统固有频率；Um,t,x，Um,t,y是q×1维的矩阵，表示系统质量归一化的第m阶的模态振型；Step 2. After the selected milling cutter is installed on the machine tool spindle, the multi-point percussion test method and linear interpolation method are used to measure the feed direction of the cutter and the modal parameters perpendicular to the feed direction; ζ m,t,x , ζ m,t,y represents the damping ratio of the mth order; ω m,t,x , ω m,t,y represent the system natural frequency of the mth order; U m,t,x , U m,t,y are A q×1-dimensional matrix, representing the mode shape of the mth order normalized by the system mass;
步骤三、建立薄壁工件的有限元模型；在建立模型的过程中，分别建立去除材料，最终工件，附加质量的集合；给模型赋予相应的材料属性并给工件添加与实际加工相符合的约束与载荷后进行有限元分析，得到整体工件的固有频率并提取出各个单元的质量矩阵和刚度矩阵，最后组装得到整体工件模型和附加质量的质量矩阵和刚度矩阵,进而得到整体工件模型的各阶固有频率ωwp和模态振型Uwp；Step 3. Establish the finite element model of the thin-walled workpiece; in the process of establishing the model, respectively establish the collection of removed material, final workpiece, and additional mass; assign corresponding material properties to the model and add constraints that match the actual processing to the workpiece The finite element analysis is carried out after loading and the natural frequency of the overall workpiece is obtained, and the mass matrix and stiffness matrix of each unit are extracted. Finally, the mass matrix and stiffness matrix of the overall workpiece model and additional mass are obtained by assembling, and then the order of the overall workpiece model is obtained. Natural frequency ω wp and mode shape U wp ;
步骤四、假定阻尼比不变，利用锤击法模态实验提取工件的阻尼特性；通过测量工件不同点的频响函数，并对其拟合确定工件的阻尼比矩阵ζwp；Step 4, assuming that the damping ratio is constant, the damping characteristics of the workpiece are extracted by hammering method modal experiments; the damping ratio matrix ζ wp of the workpiece is determined by fitting the frequency response functions of different points of the workpiece;
步骤五、利用步骤二测试得到的模态参数和步骤三、四得到的整体工件模型的各阶固有频率ωwp，模态振型Uwp和工件的阻尼比矩阵ζwp，代入步骤一中，利用半离散法分别求解刀具在铣削初始位置和终止位置的状态方程，得到以轴向切深ap和主轴转速n为变量的铣削初始位置和终止位置的稳定性叶瓣图；Step 5. Use the modal parameters obtained from the test in step 2 and the natural frequencies ω wp of each order of the overall workpiece model obtained in steps 3 and 4, the mode shapes U wp and the damping ratio matrix ζ wp of the workpiece, and substitute them into step 1. Using the semi-discrete method to solve the state equations of the cutter at the milling initial position and the final position respectively, the stability lobe diagrams of the milling initial position and the final position with the axial depth of cut a p and the spindle speed n as variables are obtained;
步骤六、以材料去除率MRR最大为目标函数，MRR＝ap×ae×n×N×f；ap表示轴向切深，ae表示径向切深，n表示主轴转速，N表示刀具刀齿数，f表示每齿进给量；在铣削过程中径向切深ae，刀具刀齿数N，每齿进给量f事先已经确定；以轴向切深ap和主轴转速n变量，分别以步骤五中得到的铣削初始位置和终止位置的稳定性叶瓣图为约束，设定种群大小、随机种子产生概率、变异概率、交叉概率和遗传代数参数，利用遗传算法分别得到优化的铣削初始位置和终止位置轴向切深ap和主轴转速n；选取初始位置和终止位置对应的ap中的最小的为所选择的加工参数；Step 6. Take the maximum material removal rate MRR as the objective function, MRR=a p ×a e ×n×N×f; a p represents the axial depth of cut, a e represents the radial depth of cut, n represents the spindle speed, and N represents The number of tool teeth, f represents the feed per tooth; in the milling process, the radial depth of cut a e , the number of tool teeth N, and the feed per tooth f have been determined in advance; the axial depth of cut a p and the spindle speed n are variables , taking the stability lobe diagrams of the milling initial position and end position obtained in step 5 as constraints, set the population size, random seed generation probability, mutation probability, crossover probability and genetic algebraic parameters, and use the genetic algorithm to obtain optimized Milling initial position and end position axial depth of cut a p and spindle speed n; select the minimum of a p corresponding to the initial position and end position as the selected processing parameters;
步骤七、修改材料属性中材料密度ρ和杨氏模量E来改变附加质量的质量矩阵和刚度矩阵，利用田口法正交试验修改材料属性中材料密度ρ和杨氏模量E来改变附加质量的质量矩阵和刚度矩阵，然后再组装得到修改后的工件的动力学参数；将新的动力学参数代入步骤五中，得到与正交试验对应的稳定性叶瓣图；通过步骤六，得到与田口法正交实验对应的MRR及与之对应的轴向切深ap和主轴转速n；最后通过对田口试验得到的数据进行分析，选择得到能够使MRR最大的最优附加质量组合及与之对应的轴向切深ap和主轴转速n。Step 7. Modify the material density ρ and Young's modulus E in the material properties to change the mass matrix and stiffness matrix of the additional mass, and use the Taguchi method to modify the material density ρ and Young's modulus E in the material properties to change the additional mass mass matrix and stiffness matrix, and then assembled to obtain the dynamic parameters of the modified workpiece; put the new dynamic parameters into step 5, and obtain the stability lobe diagram corresponding to the orthogonal test; through step 6, obtain the corresponding The MRR corresponding to the Taguchi method orthogonal experiment and the corresponding axial depth of cut a p and the spindle speed n; finally, by analyzing the data obtained from the Taguchi test, the optimal additional mass combination that can maximize the MRR and its Corresponding axial depth of cut a p and spindle speed n.
本发明的有益效果是：该方法通过附加质量对薄壁零件动力学参数的局部修改，建立一种高效的加工工艺方法来提高铣削加工的稳定域，为薄壁件高速铣削加工提供可靠的参数选择范围；最终利用优化算法选取可以实现无颤振、高效率的加工参数，实现薄壁件的高速无颤振铣削加工。本发明通过对薄壁零件动力学参数的局部修改，建立一种高效的加工工艺方法来提高铣削加工的稳定域，较好的解决了工件起始和终止位置两端刚性差，稳定域范围小，严重制约铣削过程加工参数的选取的问题；为薄壁件高速铣削加工提供可靠的参数选择范围，实现了薄壁件的高速无颤振铣削加工。The beneficial effects of the present invention are: the method establishes an efficient processing method to improve the stability region of milling by locally modifying the dynamic parameters of thin-walled parts through additional mass, and provides reliable parameters for high-speed milling of thin-walled parts Selection range; finally, the optimization algorithm is used to select the processing parameters that can achieve chatter-free and high-efficiency, and realize high-speed chatter-free milling of thin-walled parts. The present invention establishes an efficient processing method to improve the stable region of milling by partially modifying the dynamic parameters of the thin-walled parts, and better solves the problem of poor rigidity at both ends of the starting and ending positions of the workpiece and the small range of the stable region , which seriously restricts the selection of processing parameters in the milling process; it provides a reliable parameter selection range for high-speed milling of thin-walled parts, and realizes high-speed chatter-free milling of thin-walled parts.
下面结合附图和具体实施方式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 specific embodiments.
附图说明Description of drawings
图1是本发明方法中考虑刀具和工件变形的薄壁件铣削动力学模型示意图，刀具和工件沿轴向各微分成q个微元；Fig. 1 is a schematic diagram of a thin-walled part milling dynamics model considering the deformation of the cutter and the workpiece in the method of the present invention, and the cutter and the workpiece are divided into q microelements along the axial direction;
图2是多点敲击试验法测试刀具频响函数示意图，PX1，PX2，PX3，PX4是刀具进给方向的四个测量点，PY1，PY2，PY3，PY4是垂直于刀具进给方向的四个测量点；Figure 2 is a schematic diagram of the frequency response function of the tool tested by the multi-point percussion test method. PX1, PX2, PX3, and PX4 are the four measurement points in the tool feed direction, and PY1, PY2, PY3, and PY4 are the four measurement points perpendicular to the tool feed direction. a measuring point;
图3是本发明方法实施例中验证的薄板及附加质量模型；Fig. 3 is the thin plate and the additional mass model verified in the method embodiment of the present invention;
图4是本发明方法实施例中铣削初始位置和终止位置的稳定性叶瓣图。Fig. 4 is a diagram of the stability lobe of the milling initial position and end position in the embodiment of the method of the present invention.
具体实施方式detailed description
以下实施例参照图1-4。The following examples refer to Figures 1-4.
实施例1：薄板尺寸为115mm×36mm×3.5mm，材料为铝合金7075，弹性模量为71GPa，密度为2810kg/m3，泊松比为0.33；刀具选用的是刀刃数为2，直径为15.875mm，螺旋角为30度的硬质合金铣刀，刀具伸出长度为78mm。Example 1: The size of the thin plate is 115mm×36mm×3.5mm, the material is aluminum alloy 7075, the modulus of elasticity is 71GPa, the density is 2810kg/m 3 , and the Poisson’s ratio is 0.33; 15.875mm, a carbide milling cutter with a helix angle of 30 degrees, and a tool extension of 78mm.
一、利用刀具和工件变形的薄壁件铣削动力学模型，将刀具和工件沿轴向各微分成40个微元，即q＝41；分别建立每个微元处的铣削动力学方程，并求出动态铣削力:1. Utilize the milling dynamics model of the thin-walled parts deformed by the cutting tool and the workpiece, divide the cutting tool and the workpiece into 40 microelements along the axial direction, that is, q=41; establish the milling kinetic equation at each microelement respectively, and Find the dynamic milling force:
二、将刀具安装到机床主轴后，采用多点敲击试验法和线性插值的方法测定刀具进给方向和垂直于进给方向的模态参数；ζm,t,x，ζm,t,y表示第m阶的阻尼比；ωm,t,x，ωm,t,y表示第m阶的系统固有频率；Um,t,x，Um,t,y是q×1维的矩阵，表示系统质量归一化的第m阶的模态振型；在模态敲击实验中，因为加速度计尺寸的影响，选取4个点利用加速度计测量得到模态振型，其余微元点处的模态位移利用线性插值的方法得到；刀具进给方向的四个测量点PX1，PX2，PX3，PX4分别位于距离刀尖点5、23、50、72mm处，垂直于刀具进给方向的四个测量点PY1，PY2，PY3，PY4分别位于距离刀尖点0、29、43、72mm处；选取最易变形的前三阶模态(m＝1,2,3)，下面给出了模态分析识别模态参数；利用U'm,t,x，U'm,t,y(四个点测试得到的刀具系统质量归一化的第m阶的模态振型)进行线性插值得到Um,t,x，Um,t,y，最终得到Ut；2. After installing the tool to the spindle of the machine tool, use the multi-point percussion test method and linear interpolation method to measure the tool feed direction and the modal parameters perpendicular to the feed direction; ζ m,t,x ，ζ m,t, y represents the damping ratio of the m-th order; ω m,t,x , ω m,t,y represent the natural frequency of the m-th order system; U m,t,x , U m,t,y are q×1-dimensional Matrix, which represents the mode shape of the mth order normalized by the system mass; in the modal knocking experiment, due to the influence of the size of the accelerometer, four points were selected to measure the mode shape using the accelerometer, and the remaining microelements The modal displacement at the point is obtained by linear interpolation; the four measurement points PX1, PX2, PX3, and PX4 in the tool feed direction are respectively located at 5, 23, 50, and 72mm away from the tool tip point, perpendicular to the tool feed direction The four measurement points PY1, PY2, PY3, and PY4 are respectively located at 0, 29, 43, and 72mm away from the tool tip point; select the most easily deformable first three-order mode (m=1,2,3), and the following is given The modal analysis is carried out to identify the modal parameters; use U' m,t,x , U' m,t,y (the mode shape of the mth order normalized by the quality of the tool system obtained from the four-point test) to perform linear Interpolation to get U m,t,x , U m,t,y , and finally U t ;
Ut＝[U1,t…U1,m,t] U t ＝[U 1,t ... U 1,m,t ]
三、建立薄壁工件的有限元模型；在建立模型的过程中，分别建立去除材料(尺寸都为115×36×0.5mm),最终工件(尺寸都为115×36×3mm)，三块附加质量(尺寸都为18×18×3mm)的集合；给模型赋予相应的材料属性并给工件添加与实际加工相符合的约束与载荷后进行有限元分析，得到整体工件的固有频率并提取出各个单元的质量矩阵和刚度矩阵，最后组装得到整体工件模型和附加质量的质量矩阵和刚度矩阵,进而得到整体工件模型的各阶固有频率ωwp和模态振型Uwp；3. Establish the finite element model of the thin-walled workpiece; in the process of establishing the model, respectively establish the removal material (the size is 115×36×0.5mm), the final workpiece (the size is 115×36×3mm), and three additional pieces A collection of mass (all sizes are 18×18×3mm); after assigning corresponding material properties to the model and adding constraints and loads consistent with the actual processing to the workpiece, the finite element analysis is performed to obtain the natural frequency of the overall workpiece and extract each The mass matrix and stiffness matrix of the unit are finally assembled to obtain the mass matrix and stiffness matrix of the overall workpiece model and additional mass, and then the natural frequencies ω wp and mode shapes U wp of each order of the overall workpiece model are obtained;
四、假定阻尼比不变，利用锤击法模态实验提取工件的阻尼特性；通过测量工件不同点的频响函数，并对其拟合确定工件的阻尼比矩阵ζwp；4. Assuming that the damping ratio is constant, the damping characteristics of the workpiece are extracted by hammering method modal experiments; the damping ratio matrix ζ wp of the workpiece is determined by measuring the frequency response functions of different points of the workpiece and fitting them;
五、利用步骤二测试得到的模态参数和步骤三、四得到的整体工件模型的各阶固有频率ωwp，模态振型Uwp和工件的阻尼比矩阵ζwp，代入步骤一中，利用半离散法分别求解刀具在铣削初始位置和终止位置的状态方程，得到以轴向切深ap(mm)和主轴转速n(rpm)为变量的铣削初始位置(实线1)和终止位置(虚线2)的稳定性叶瓣图；5. Use the modal parameters obtained from the test in step 2 and the natural frequencies ω wp of each order of the overall workpiece model obtained in steps 3 and 4, the mode shape U wp and the damping ratio matrix ζ wp of the workpiece to be substituted into step 1, using The semi-discrete method solves the state equations of the cutter at the initial position and end position of milling respectively, and obtains the initial milling position (solid line 1) and end position ( Stability lobe diagram of dotted line 2);
六、以材料去除率MRR最大为目标函数，MRR＝ap×ae×n×N×f，ap表示轴向切深，ae表示径向切深，n表示主轴转速，N表示刀具刀齿数，f表示每齿进给量；在铣削过程中径向切深ae＝0.5mm，刀具刀齿数N＝2，每齿进给量f＝0.1mm/转·齿；这些参数事先已经确定；以轴向切深ap和主轴转速n变量，分别以步骤五中得到的铣削初始位置和终止位置的稳定性叶瓣图为约束，根据实际加工参数设定轴向切深的范围为7000≤ap≤12000；并且设定种群大小为20、随机种子产生概率为0.12221、变异概率为0.7、交叉概率为0.8和遗传代数参数为30，利用遗传算法分别得到优化的铣削初始位置和终止位置轴向切深ap和主轴转速n；选取初始位置和终止位置对应的ap中的最小的为所选择的加工参数；Sixth, the maximum material removal rate MRR is the objective function, MRR = a p × a e × n × N × f, a p represents the axial depth of cut, a e represents the radial depth of cut, n represents the spindle speed, N represents the tool The number of teeth, f represents the feed per tooth; in the milling process, the radial depth of cut a e = 0.5mm, the number of cutter teeth N = 2, the feed per tooth f = 0.1mm/revolution · tooth; these parameters have been set in advance Determine; with the variables of the axial depth of cut a p and the spindle speed n, and the stability lobe diagrams of the milling initial position and end position obtained in step 5 respectively, the range of the axial depth of cut is set according to the actual processing parameters as 7000≤a p ≤12000; and set the population size to 20, the random seed generation probability to 0.12221, the mutation probability to 0.7, the crossover probability to 0.8 and the genetic algebra parameter to 30, and use the genetic algorithm to obtain the optimized milling initial position and termination Position, axial depth of cut a p and spindle speed n; select the smallest of a p corresponding to the initial position and the end position as the selected processing parameter;
起始位置：ap＝1.852 n＝12000 终止位置：ap＝1.675 n＝12000Start position: a p = 1.852 n = 12000 End position: a p = 1.675 n = 12000
最终选取的参数为：ap＝1.675 n＝12000 MRR＝2010The final selected parameters are: a p =1.675 n=12000 MRR=2010
七、通过在薄板上附加不同质量的质量块来局部修改工件的质量矩阵和刚度矩阵；依据表一给出的几种常见材料的材料参数，利用“田口法”L16(44)正交试验修改材料属性中材料密度ρ和杨氏模量E来改变三块附加质量的质量矩阵和刚度矩阵，然后再组装得到修改后的工件的动力学参数；将新的动力学参数代入步骤五中，得到与正交试验对应的稳定性叶瓣图；通过步骤六，得到与“田口法”L16(44)正交实验对应的表三数据；最终得到三块附加质量在不同材料属性下的质量矩阵和刚度矩阵和对应的MRR及与之对应的轴向切深ap和主轴转速n；K1,K2,K3,K4表示各个因素对水平试验的指标的影响，据此得到最优的附加质量块粘贴方式是343组合即起始处质量块1用材料45#钢，中间处质量块2用材料铜，终止处质量块3用材料45#钢；得到的加工参数为：轴向切深ap＝3.247和主轴转速n＝12000，材料去除率MRR＝3896.4；对比不粘贴质量块所得到的加工参数及材料去除率，可以看出材料去除效率提高了93.8％；证明该方法达到了很好的预期效果，具有很好的实用性。7. Locally modify the mass matrix and stiffness matrix of the workpiece by attaching mass blocks of different masses on the thin plate; according to the material parameters of several common materials given in Table 1, use the "Taguchi method" L 16 (4 4 ) orthogonal Experiment to modify the material density ρ and Young's modulus E in the material properties to change the mass matrix and stiffness matrix of the three additional masses, and then assemble the dynamic parameters of the modified workpiece; substitute the new dynamic parameters into step 5 , to obtain the stability lobe diagram corresponding to the orthogonal test; through step 6, to obtain the data in Table 3 corresponding to the "Taguchi method" L 16 (4 4 ) orthogonal test; finally get three additional masses under different material properties The mass matrix and stiffness matrix and the corresponding MRR and the corresponding axial depth of cut a p and spindle speed n; K 1 , K 2 , K 3 , K 4 represent the influence of each factor on the index of the horizontal test, according to The best way to paste the additional masses is 343 combinations, that is, the material 45 # steel is used for the mass block 1 at the beginning, the copper material is used for the mass block 2 at the middle part, and the material 45# steel is used for the mass block 3 at the end point; the obtained processing parameters are : Axial depth of cut a p = 3.247 and spindle speed n = 12000, material removal rate MRR = 3896.4; compared with the processing parameters and material removal rate obtained without pasting the mass block, it can be seen that the material removal efficiency has increased by 93.8%; prove This method has achieved good expected effect and has good practicability.
表一：几种常见材料的材料参数Table 1: Material parameters of several common materials
表二：利用田口L16(44)正交实验所得数据Table 2: Data obtained by using Taguchi L 16 (4 4 ) orthogonal experiment
实施例2：薄板尺寸为100mm×40mm×4.5mm，材料为铝合金7075，弹性模量为71GPa，密度为2810kg/m3，泊松比为0.33；刀具选用的是刀刃数为2，直径为15.875mm，螺旋角为30度的硬质合金铣刀，刀具伸出长度为78mm。Example 2: The size of the thin plate is 100mm×40mm×4.5mm, the material is aluminum alloy 7075, the elastic modulus is 71GPa, the density is 2810kg/m 3 , and the Poisson’s ratio is 0.33; 15.875mm, a carbide milling cutter with a helix angle of 30 degrees, and a tool extension of 78mm.
一、利用刀具和工件变形的薄壁件铣削动力学模型，将刀具和工件沿轴向各微分成30个微元，即q＝31；分别建立每个微元处的铣削动力学方程，并求出动态铣削力:1. Utilize the milling dynamics model of the thin-walled parts deformed by the cutting tool and the workpiece, divide the cutting tool and the workpiece into 30 microelements along the axial direction, that is, q=31; establish the milling dynamic equation at each microelement respectively, and Find the dynamic milling force:
二、将刀具安装到机床主轴后，采用多点敲击试验法和线性插值的方法测定刀具进给方向和垂直于进给方向的模态参数；ζm,t,x，ζm,t,y表示第m阶的阻尼比；ωm,t,x，ωm,t,y表示第m阶的系统固有频率；Um,t,x，Um,t,y是q×1维的矩阵，表示系统质量归一化的第m阶的模态振型；在模态敲击实验中，因为加速度计尺寸的影响，选取4个点利用加速度计测量得到模态振型，其余微元点处的模态位移利用线性插值的方法得到；刀具进给方向的四个测量点PX1，PX2，PX3，PX4分别位于距离刀尖点5、23、50、72mm处，垂直于刀具进给方向的四个测量点PY1，PY2，PY3，PY4分别位于距离刀尖点0、29、43、72mm处；选取最易变形的前三阶模态(m＝1,2,3)，下面给出了模态分析识别模态参数；利用U'm,t,x，U'm,t,y(四个点测试得到的刀具系统质量归一化的第m阶的模态振型)进行线性插值得到Um,t,x，Um,t,y，最终得到Ut；2. After installing the tool to the spindle of the machine tool, use the multi-point percussion test method and linear interpolation method to measure the tool feed direction and the modal parameters perpendicular to the feed direction; ζ m,t,x ，ζ m,t, y represents the damping ratio of the m-th order; ω m,t,x , ω m,t,y represent the natural frequency of the m-th order system; U m,t,x , U m,t,y are q×1-dimensional Matrix, which represents the mode shape of the mth order normalized by the system mass; in the modal knocking experiment, due to the influence of the size of the accelerometer, four points were selected to measure the mode shape using the accelerometer, and the remaining microelements The modal displacement at the point is obtained by linear interpolation; the four measurement points PX1, PX2, PX3, and PX4 in the tool feed direction are respectively located at 5, 23, 50, and 72mm away from the tool tip point, perpendicular to the tool feed direction The four measurement points PY1, PY2, PY3, and PY4 are respectively located at 0, 29, 43, and 72mm away from the tool tip point; select the most easily deformable first three-order mode (m=1,2,3), and the following is given The modal analysis is carried out to identify the modal parameters; use U' m,t,x , U' m,t,y (the mode shape of the mth order normalized by the quality of the tool system obtained from the four-point test) to perform linear Interpolation to get U m,t,x , U m,t,y , and finally U t ;
Ut＝[U1,t…U1,m,t] U t ＝[U 1,t ... U 1,m,t ]
三、建立薄壁工件的有限元模型；在建立模型的过程中，分别建立去除材料(100mm×40mm×0.5mm),最终工件(100mm×40mm×4mm)三块附加质量(尺寸都为20×20×4mm)的集合；给模型赋予相应的材料属性并给工件添加与实际加工相符合的约束与载荷后进行有限元分析，得到整体工件的固有频率并提取出各个单元的质量矩阵和刚度矩阵，最后组装得到整体工件模型和附加质量的质量矩阵和刚度矩阵,进而得到整体工件模型的各阶固有频率ωwp和模态振型Uwp；3. Establish the finite element model of the thin-walled workpiece; in the process of establishing the model, respectively establish three additional masses (the size is 20× 20×4mm) set; assign corresponding material properties to the model and add constraints and loads that are consistent with actual processing to the workpiece, and then perform finite element analysis to obtain the natural frequency of the overall workpiece and extract the mass matrix and stiffness matrix of each unit , and finally assemble the mass matrix and stiffness matrix of the overall workpiece model and additional mass, and then obtain the natural frequency ω wp of each order and the mode shape U wp of the overall workpiece model;
四、假定阻尼比不变，利用锤击法模态实验提取工件的阻尼特性；通过测量工件不同点的频响函数，并对其拟合确定工件的阻尼比矩阵ζwp；4. Assuming that the damping ratio is constant, the damping characteristics of the workpiece are extracted by hammering method modal experiments; the damping ratio matrix ζ wp of the workpiece is determined by measuring the frequency response functions of different points of the workpiece and fitting them;
五、利用步骤二测试得到的模态参数和步骤三、四得到的整体工件模型的各阶固有频率ωwp，模态振型Uwp和工件的阻尼比矩阵ζwp，代入步骤一中，利用半离散法分别求解刀具在铣削初始位置和终止位置的状态方程，得到以轴向切深ap(mm)和主轴转速n(rpm)为变量的铣削初始位置(实线1)和终止位置(虚线2)的稳定性叶瓣图；5. Use the modal parameters obtained from the test in step 2 and the natural frequencies ω wp of each order of the overall workpiece model obtained in steps 3 and 4, the mode shape U wp and the damping ratio matrix ζ wp of the workpiece to be substituted into step 1, using The semi-discrete method solves the state equations of the cutter at the initial position and end position of milling respectively, and obtains the initial milling position (solid line 1) and end position ( Stability lobe diagram of dotted line 2);
六、以材料去除率MRR最大为目标函数，MRR＝ap×ae×n×N×f；ap表示轴向切深，ae表示径向切深，n表示主轴转速，N表示刀具刀齿数，f表示每齿进给量；在铣削过程中径向切深ae＝0.5mm，刀具刀齿数N＝2，每齿进给量f＝0.1mm/转·齿；这些参数事先已经确定，以轴向切深ap和主轴转速n变量，分别以步骤五中得到的铣削初始位置和终止位置的稳定性叶瓣图为约束，根据实际加工参数设定轴向切深的范围为7000≤ap≤12000；并且设定种群大小为20、随机种子产生概率为0.12221、变异概率为0.7、交叉概率为0.8和遗传代数参数为30，利用遗传算法分别得到优化的铣削初始位置和终止位置轴向切深ap和主轴转速n；选取初始位置和终止位置对应的ap中的最小的为所选择的加工参数；6. Take the maximum material removal rate MRR as the objective function, MRR = a p × a e × n × N × f; a p represents the axial depth of cut, a e represents the radial depth of cut, n represents the spindle speed, and N represents the tool The number of teeth, f represents the feed per tooth; in the milling process, the radial depth of cut a e = 0.5mm, the number of cutter teeth N = 2, the feed per tooth f = 0.1mm/revolution · tooth; these parameters have been set in advance Determined, with the variables of axial depth of cut a p and spindle speed n, respectively constrained by the stability lobe diagrams of the milling initial position and end position obtained in step 5, the range of axial depth of cut is set according to the actual processing parameters as 7000≤a p ≤12000; and set the population size to 20, the random seed generation probability to 0.12221, the mutation probability to 0.7, the crossover probability to 0.8 and the genetic algebra parameter to 30, and use the genetic algorithm to obtain the optimized milling initial position and termination Position, axial depth of cut a p and spindle speed n; select the smallest of a p corresponding to the initial position and the end position as the selected processing parameter;
起始位置：ap＝2.833 n＝11200 终止位置：ap＝2.763 n＝11400Start position: a p = 2.833 n = 11200 End position: a p = 2.763 n = 11400
最终选取的参数为：ap＝2.763 n＝11400 MRR＝3149.82The final selected parameters are: a p =2.763 n=11400 MRR=3149.82
七、通过在薄板上附加不同质量的质量块来局部修改工件的质量矩阵和刚度矩阵；依据表一给出的几种常见材料的材料参数，利用“田口法”L16(44)正交试验修改材料属性中材料密度ρ和杨氏模量E来改变三块附加质量的质量矩阵和刚度矩阵，然后再组装得到修改后的工件的动力学参数；将新的动力学参数代入步骤五中，得到与正交试验对应的稳定性叶瓣图；通过步骤六，得到与“田口法”L16(44)正交实验对应的表三数据；最终得到三块附加质量在不同材料属性下的质量矩阵和刚度矩阵和对应的MRR及与之对应的轴向切深ap和主轴转速n；K1,K2,K3,K4表示各个因素对水平试验的指标的影响，据此可以得到最优的附加质量块粘贴方式是423组合即起始处质量块1用材料铜，中间处质量块2用材料铝合金，终止处质量块3用材料45#钢；得到的加工参数为：轴向切深ap＝5.098和主轴转速n＝10950，材料去除率MRR＝5582.31；对比不粘贴质量块所得到的加工参数及材料去除率，可以看出材料去除效率提高了77.2％；证明该方法达到了很好的预期效果，具有很好的实用性。7. Locally modify the mass matrix and stiffness matrix of the workpiece by attaching mass blocks of different masses on the thin plate; according to the material parameters of several common materials given in Table 1, use the "Taguchi method" L 16 (4 4 ) orthogonal Experiment to modify the material density ρ and Young's modulus E in the material properties to change the mass matrix and stiffness matrix of the three additional masses, and then assemble the dynamic parameters of the modified workpiece; substitute the new dynamic parameters into step 5 , to obtain the stability lobe diagram corresponding to the orthogonal test; through step 6, to obtain the data in Table 3 corresponding to the "Taguchi method" L 16 (4 4 ) orthogonal test; finally get three additional masses under different material properties The mass matrix and stiffness matrix and the corresponding MRR and the corresponding axial depth of cut a p and spindle speed n; K 1 , K 2 , K 3 , K 4 represent the influence of each factor on the index of the horizontal test, according to It can be obtained that the optimal method of pasting the additional masses is 423 combinations, that is, the starting mass 1 is made of copper, the middle mass 2 is made of aluminum alloy, and the ending mass 3 is made of 45 # steel; the obtained processing parameters are : Axial depth of cut a p = 5.098 and spindle speed n = 10950, material removal rate MRR = 5582.31; compared with the processing parameters and material removal rate obtained without pasting the mass block, it can be seen that the material removal efficiency has increased by 77.2%; prove This method has achieved good expected effect and has good practicability.
表三：利用田口L16(44)正交实验所得数据Table 3: Data obtained by using Taguchi L 16 (4 4 ) orthogonal experiment
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| CN107479499A (en) * | 2017-09-29 | 2017-12-15 | 西北工业大学 | Thin-wall part cuts interface mismachining tolerance compensating Modeling and penalty coefficient learning control method |
| CN107807526A (en) * | 2017-10-31 | 2018-03-16 | 上海交通大学 | A kind of method for intelligently suppressing processing flutter based on Simulation of stability |
| CN107914183A (en) * | 2017-12-05 | 2018-04-17 | 上海复合材料科技有限公司 | The flutter stability Forecasting Methodology of milling carbon fiber layer plywood |
| CN108595874A (en) * | 2018-05-07 | 2018-09-28 | 西南石油大学 | A kind of large thin-wall slewing parts Milling Process vibration mechanical model construction method |
| CN108732995A (en) * | 2018-04-25 | 2018-11-02 | 西北工业大学 | The fast acquiring method of milling process workpiece kinetic parameter |
| CN108846242A (en) * | 2018-07-09 | 2018-11-20 | 西北工业大学 | The thin-wall part milling parameter suppressing method applied based on pre-tensile stress |
| CN109093130A (en) * | 2018-08-08 | 2018-12-28 | 西北工业大学 | Annular thin-wall parts roughing technique optimization method based on subregion processing |
| CN110153781A (en) * | 2019-05-24 | 2019-08-23 | 西北工业大学 | Vibration suppression device and method for thin-walled parts processing based on bending actuator |
| CN110245402A (en) * | 2019-05-31 | 2019-09-17 | 西安交通大学 | A Calculation Method of Structural Parts Machining Parameters Based on Combined Machining Features |
| CN110516340A (en) * | 2019-08-21 | 2019-11-29 | 西北工业大学 | A Unified Modeling Method for Process Damping Based on Stiffness Variation of Milling System |
| CN113059221A (en) * | 2021-03-10 | 2021-07-02 | 华中科技大学 | Method and device for improving machining stability of thin-wall part based on mirror image magnetic adsorption of tool nose |
| CN113894333A (en) * | 2021-09-26 | 2022-01-07 | 西北工业大学 | Robust process control method of surface state for precision milling of titanium alloy thin-walled structures |
| CN114895566A (en) * | 2022-05-24 | 2022-08-12 | 西北工业大学 | Chatter prediction method for milling process by adopting transfer matrix reduction technology |
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| CN118123097A (en) * | 2024-05-08 | 2024-06-04 | 南京航空航天大学 | Thin-wall part milling flutter suppression method based on magneto-rheological damper |
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| CN107479499A (en) * | 2017-09-29 | 2017-12-15 | 西北工业大学 | Thin-wall part cuts interface mismachining tolerance compensating Modeling and penalty coefficient learning control method |
| CN107479499B (en) * | 2017-09-29 | 2019-07-19 | 西北工业大学 | Machining Error Compensation Modeling and Compensation Coefficient Learning Control Method for Cutting Interface of Thin-walled Parts |
| CN107807526A (en) * | 2017-10-31 | 2018-03-16 | 上海交通大学 | A kind of method for intelligently suppressing processing flutter based on Simulation of stability |
| CN107914183A (en) * | 2017-12-05 | 2018-04-17 | 上海复合材料科技有限公司 | The flutter stability Forecasting Methodology of milling carbon fiber layer plywood |
| CN107914183B (en) * | 2017-12-05 | 2020-04-07 | 上海复合材料科技有限公司 | Chatter stability prediction method for milling carbon fiber laminated plate |
| CN108732995B (en) * | 2018-04-25 | 2019-05-31 | 西北工业大学 | The fast acquiring method of milling process workpiece kinetic parameter |
| CN108732995A (en) * | 2018-04-25 | 2018-11-02 | 西北工业大学 | The fast acquiring method of milling process workpiece kinetic parameter |
| CN108595874A (en) * | 2018-05-07 | 2018-09-28 | 西南石油大学 | A kind of large thin-wall slewing parts Milling Process vibration mechanical model construction method |
| CN108846242B (en) * | 2018-07-09 | 2019-05-07 | 西北工业大学 | Chatter suppression method for milling thin-walled parts based on pretensioning stress |
| CN108846242A (en) * | 2018-07-09 | 2018-11-20 | 西北工业大学 | The thin-wall part milling parameter suppressing method applied based on pre-tensile stress |
| CN109093130A (en) * | 2018-08-08 | 2018-12-28 | 西北工业大学 | Annular thin-wall parts roughing technique optimization method based on subregion processing |
| CN110153781A (en) * | 2019-05-24 | 2019-08-23 | 西北工业大学 | Vibration suppression device and method for thin-walled parts processing based on bending actuator |
| CN110153781B (en) * | 2019-05-24 | 2020-11-20 | 西北工业大学 | Device and method for suppressing vibration of thin-walled parts machining based on bending type actuator |
| CN110245402A (en) * | 2019-05-31 | 2019-09-17 | 西安交通大学 | A Calculation Method of Structural Parts Machining Parameters Based on Combined Machining Features |
| CN110516340A (en) * | 2019-08-21 | 2019-11-29 | 西北工业大学 | A Unified Modeling Method for Process Damping Based on Stiffness Variation of Milling System |
| CN110516340B (en) * | 2019-08-21 | 2022-04-12 | 西北工业大学 | Process damping unified model modeling method based on milling system rigidity change |
| CN113059221A (en) * | 2021-03-10 | 2021-07-02 | 华中科技大学 | Method and device for improving machining stability of thin-wall part based on mirror image magnetic adsorption of tool nose |
| CN113894333A (en) * | 2021-09-26 | 2022-01-07 | 西北工业大学 | Robust process control method of surface state for precision milling of titanium alloy thin-walled structures |
| CN113894333B (en) * | 2021-09-26 | 2022-07-22 | 西北工业大学 | Robust process control method of surface state for precision milling of titanium alloy thin-walled structures |
| CN114895566A (en) * | 2022-05-24 | 2022-08-12 | 西北工业大学 | Chatter prediction method for milling process by adopting transfer matrix reduction technology |
| CN114895566B (en) * | 2022-05-24 | 2023-11-10 | 西北工业大学 | Chatter prediction method for milling process by adopting transmission matrix reduction technology |
| CN117103280A (en) * | 2023-10-19 | 2023-11-24 | 中国长江电力股份有限公司 | Material reduction processing method and system for large-sized water turbine top cover on-site robot |
| CN117103280B (en) * | 2023-10-19 | 2023-12-22 | 中国长江电力股份有限公司 | Material reduction processing method and system for large-sized water turbine top cover on-site robot |
| CN118123097A (en) * | 2024-05-08 | 2024-06-04 | 南京航空航天大学 | Thin-wall part milling flutter suppression method based on magneto-rheological damper |
| CN118123097B (en) * | 2024-05-08 | 2024-09-20 | 南京航空航天大学 | Thin-wall part milling flutter suppression method based on magneto-rheological damper |
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