CN103196643B

CN103196643B - Main shaft-knife handle joint surface nonlinear dynamic characteristic parameter identification method

Info

Publication number: CN103196643B
Application number: CN201310068050.9A
Authority: CN
Inventors: 刘雪梅; 李爱平; 张正旺; 罗建伟
Original assignee: Tongji University
Current assignee: Tongji University
Priority date: 2013-03-04
Filing date: 2013-03-04
Publication date: 2015-08-19
Anticipated expiration: 2033-03-04
Also published as: CN103196643A

Abstract

A method for identifying the dynamic characteristic parameters of the spindle-tool holder joint surface is based on the non-parametric method combined with the finite element analysis technology to identify the nonlinear dynamic characteristic parameters of the spindle-tool holder joint surface. Specifically, firstly, the finite element analysis model of the spindle-tool holder system is established, and the nonlinear transient response analysis is performed on the model to obtain the transient response of displacement, velocity, and acceleration at the joint surface, and then deduced according to Newton's second law of motion The time history data of the nonlinear contact force at the joint surface was obtained, and the sample data was regression analyzed using the least square method and Chebyshev polynomial based on the non-parametric method, and finally the radial and tangential non-linear contact force between the spindle-toolholder joint surface was obtained. Analytical expression model of linear contact force. This nonlinear contact force model can be directly applied to the dynamic modeling of the spindle-HSK tool holder system, which provides a necessary condition for further research on the overall dynamic characteristics of the spindle-HSK tool holder system.

Description

Identification Method of Nonlinear Dynamic Characteristic Parameters of Spindle-Tool Holder Joint Surface

技术领域technical field

本发明属于机械结构的结合面技术领域，尤其涉及一种主轴-刀柄结合面非线性动态特性参数识别方法。The invention belongs to the technical field of joint surfaces of mechanical structures, and in particular relates to a method for identifying nonlinear dynamic characteristic parameters of a spindle-knife handle joint surface.

背景技术Background technique

主轴-刀柄系统是数控机床的核心部件之一，其动力学特性直接影响切削稳定性、加工精度、表面粗糙度和生产效率。在主轴-刀柄系统动力学分析中，通常是通过测试及参数辨识以识别结合面动力学参数，进而进行主轴-刀柄系统动态特性分析。主轴-刀柄结合面对主轴系统动力学特性有着非常显著的影响，目前普遍采用线性分析模型进行近似模拟。随着机床性能向高转速、高精度方向发展，这种近似模拟的方法存在较大的分析误差，难以满足高速高性能主轴-刀柄系统动力学分析要求。主轴与刀柄的设计通常采用了非对称结构，比如HSKA型刀柄锥柄端面设有两个深度不一致的驱动键槽、拉杆机构中的螺纹联接结构、单刃刀片结构、侧边紧固螺钉结构等，以及制造、装配过程产生的加工误差，主轴-刀柄系统中存在不可避免的偏心质量。当主轴高速旋转时，偏心质量成为主要的激振源，使整个主轴-刀柄系统产生振动，从而导致主轴和刀柄的弹性结合面处呈现出非常复杂的非线性特性。主轴-刀柄结合面等弹性连接导致的非线性特性是高速切削时产生颤振的一个主要来源，为了准确分析主轴-刀柄系统的动态性能，尽量避免颤振的产生，需要建立主轴-刀柄系统的动力学模型，而主轴-刀柄结合面的参数识别是主轴-刀柄系统动力学精确建模的关键问题。The spindle-tool holder system is one of the core components of CNC machine tools, and its dynamic characteristics directly affect cutting stability, machining accuracy, surface roughness and production efficiency. In the dynamic analysis of the spindle-tool holder system, the dynamic characteristics of the spindle-tool holder system are usually analyzed by testing and parameter identification to identify the dynamic parameters of the joint surface. The spindle-tool holder combination surface has a very significant impact on the dynamic characteristics of the spindle system, and the linear analysis model is generally used for approximate simulation at present. With the development of machine tool performance towards high speed and high precision, this approximate simulation method has large analysis errors, and it is difficult to meet the dynamic analysis requirements of high-speed and high-performance spindle-tool holder system. The design of the spindle and the tool holder usually adopts an asymmetric structure, such as the end surface of the HSKA tool holder taper handle with two driving keyways with different depths, the thread connection structure in the pull rod mechanism, the single-edged blade structure, and the side fastening screw structure Etc., as well as the machining errors generated in the manufacturing and assembly process, there is an inevitable eccentric mass in the spindle-tool holder system. When the spindle rotates at a high speed, the eccentric mass becomes the main excitation source, causing the entire spindle-tool holder system to vibrate, resulting in very complex nonlinear characteristics at the elastic joint surface of the spindle and tool holder. The nonlinear characteristics caused by the elastic connection of the spindle-tool holder joint surface is a main source of chatter during high-speed cutting. In order to accurately analyze the dynamic performance of the spindle-tool holder system and avoid chatter as much as possible, it is necessary to establish a spindle-tool The dynamic model of the shank system, and the parameter identification of the spindle-toolholder joint surface is a key issue in the accurate modeling of the spindle-toolholder system dynamics.

现有的技术中，只提出了适用于识别问题主轴与刀柄结合面的线性动态特性参数的解决办法，例如中国专利申请号为：201110061668.3，发明名称为：主轴与刀柄结合面静动态特性试验装置及试验方法，该专利申请提出了一种主轴与刀柄结合面静动态特性的试验方法，该方法可识别主轴与刀柄结合面的线性刚度及线性阻尼，但该发明仅适用于识别主轴与刀柄结合面的线性动态特性参数；中国专利申请号为：201010298969.3，发明名称为：滚动导轨结合面动态特性参数识别系统及识别方法，该专利申请提出了一种滚动导轨结合面动态特性参数识别系统及控制方法，可完成法向和切向结合面参数的识别，该发明也仅适用于识别结合面的线性动态特性参数。以上的方案都未能有效的解决由于主轴-刀柄系统的非线性问题所造成的问题。In the existing technology, only a solution for identifying the linear dynamic characteristic parameters of the joint surface of the spindle and the tool holder is proposed. For example, the Chinese patent application number is: 201110061668.3, and the name of the invention is: static and dynamic characteristics of the joint surface of the spindle and the tool holder Test device and test method. This patent application proposes a test method for the static and dynamic characteristics of the joint surface of the spindle and the tool holder. This method can identify the linear stiffness and linear damping of the joint surface of the spindle and the tool holder, but the invention is only suitable for identifying The linear dynamic characteristic parameters of the joint surface of the spindle and the tool holder; the Chinese patent application number is: 201010298969.3, and the title of the invention is: the identification system and identification method of the dynamic characteristic parameters of the joint surface of the rolling guide rail. The patent application proposes a dynamic characteristic of the joint surface of the rolling guide rail The parameter identification system and control method can complete the identification of normal and tangential joint surface parameters, and the invention is only applicable to the identification of linear dynamic characteristic parameters of the joint surface. None of the above solutions can effectively solve the problems caused by the nonlinear problem of the spindle-tool holder system.

发明内容Contents of the invention

本发明的目的在于提供一种可识别主轴-刀柄结合面非线性动态特性参数的方法。The purpose of the present invention is to provide a method that can identify the nonlinear dynamic characteristic parameters of the spindle-knife handle joint surface.

为达到上述目的，本发明的解决方案是：To achieve the above object, the solution of the present invention is:

一种主轴-刀柄结合面非线性动态特性参数识别方法，包括以下步骤，A method for identifying nonlinear dynamic characteristic parameters of a spindle-tool holder joint surface, comprising the following steps,

（1）建立主轴-刀柄的有限元分析模型；(1) Establish the finite element analysis model of the spindle-tool holder;

（2）检验主轴-刀柄有限元分析模型是否正确，若确认无误，转入步骤（4），若确认存在差异，转入步骤（3）；(2) Check whether the spindle-tool holder finite element analysis model is correct, if it is confirmed, go to step (4), if it is confirmed that there is a difference, go to step (3);

（3）修正所述主轴-刀柄有限元分析模型，并转入步骤（2）继续检测；(3) Correct the finite element analysis model of the spindle-knife holder, and transfer to step (2) to continue testing;

（4）对检验后的主轴-刀柄系统有限元模型进行非线性瞬态响应分析处理，以获取主轴-刀柄结合面处的相对瞬态位移、相对瞬态速度以及径向非线性接触力、切向非线性接触力的历程数据的样本数据；(4) Perform nonlinear transient response analysis on the finite element model of the spindle-tool holder system after inspection to obtain the relative transient displacement, relative transient velocity and radial nonlinear contact force at the joint surface of the spindle-tool holder , Tangential nonlinear contact force The sample data of the history data;

（5）依据非线性振动系统中一般表达式，采用非参数化方法对所述样本数据进行回归分析，建立主轴-刀柄结合面非线性接触力的解析表达模型。(5) According to the nonlinear vibration system The general expression, using the non-parametric method to perform regression analysis on the sample data, and establish the nonlinear contact force of the spindle-tool holder joint surface The analytical expression model of .

所述步骤（2）中，包括以下步骤，In the step (2), the following steps are included,

（a）对所述主轴-刀柄的有限元分析模型进行自由模态分析，计算有限元分析模型的固有频率；(a) performing free modal analysis on the finite element analysis model of the spindle-knife holder, and calculating the natural frequency of the finite element analysis model;

（b）将有限元分析模型的固有频率与自由模态实验得到主轴-刀柄系统的固有频率进行对比，如存在差异转入步骤（3）；若确认无误，转入步骤（4）。(b) Compare the natural frequency of the finite element analysis model with the natural frequency of the spindle-tool holder system obtained from the free mode experiment, if there is a difference, go to step (3); if confirmed, go to step (4).

所述步骤（b）中，采用弹性绳悬挂主轴-刀柄的实验模型，使用锤击法进行自由模态实验，以获取自由模态实验下的主轴-刀柄系统的固有频率。In the step (b), the elastic rope is used to hang the experimental model of the spindle-tool holder, and the hammering method is used to conduct the free mode experiment, so as to obtain the natural frequency of the spindle-tool holder system under the free mode experiment.

步骤（3）中，通过调整有限元模型网格大小和结合面的摩擦系数参数修正所述有限元模型。In step (3), the finite element model is corrected by adjusting the grid size of the finite element model and the friction coefficient parameters of the joint surface.

步骤（4）中，所述历程数据的取得包括以下步骤，In step (4), the acquisition of the history data includes the following steps,

（Ⅰ）对修正后的主轴-刀柄系统有限元模型进行非线性瞬态响应分析，得到主轴-刀柄结合面相对瞬态位移、相对瞬态速度及相对瞬态加速度的时间历程数据；(I) Perform nonlinear transient response analysis on the revised finite element model of the spindle-tool holder system, and obtain the time history data of the relative transient displacement, relative transient velocity and relative transient acceleration of the spindle-tool holder joint surface;

（Ⅱ）结合相对瞬态加速度的历程数据分析主轴-刀柄简化非线性振动系统中刀柄的运动方程，以获得和的时间历程数据。(II) Combined with the history data of the relative transient acceleration, the equation of motion of the toolholder in the spindle-toolholder simplified nonlinear vibration system is analyzed to obtain and time history data.

所述步骤（Ⅱ）中，取刀柄质量块M₁为受力分析对象，根据牛顿第二运动定律，所述主轴-刀柄简化非线性振动系统中刀柄的运动方程变形为 _In the step (II), the tool holder mass M1 is taken as the force analysis object, and according to Newton’s second law of motion, the kinematic equation of the tool holder in the spindle-tool holder simplified nonlinear vibration system is deformed as

$f f ((x x,, \overset{\cdot &Center Dot;}{x x})) = = {F f}_{r r} ((t t)) + + {F f}_{r r} - - {M m}_{11} \overset{\cdot \cdot \cdot &Center Dot;}{x x} ((t t))$

$f f ((y the y,, \overset{\cdot &Center Dot;}{y the y})) = = {F f}_{t t} ((t t)) + + {F f}_{t t} - - {M m}_{11} \overset{\cdot &Center Dot; \cdot &Center Dot;}{y the y} ((t t))$

其中，F_r、F_t分别为刀柄锁紧机构通过夹紧锥向刀柄施加的径向和切向夹紧力，F_r(t)、F_t(t)分别为偏心质量引起的径向和切向外部激励力，分别为径向和切向相对瞬态加速度。Among them, F _r , F _t are the radial and tangential clamping forces exerted by the tool holder locking mechanism on the tool holder through the clamping cone, respectively, F _r (t), F _t (t) are the radial force caused by the eccentric mass, respectively directional and tangential external incentives, are the radial and tangential relative transient accelerations, respectively.

所述步骤（4）中，以一定的时间间距从所述相对瞬态位移、相对瞬态速度、以及的时间历程数据中取出一定数量的样本数据，即In the step (4), from the relative transient displacement, relative transient velocity, as well as Take a certain number of sample data from the time history data of

${x x}_{k k} = = x x (({t t}_{k k})),, {\overset{\cdot &Center Dot;}{x x}}_{k k} = = \overset{\cdot \cdot}{x x} (({t t}_{k k})),, {f f}_{k k} ((x x,, \overset{\cdot \cdot}{x x})) = = f f ((x x (({t t}_{k k})),, \overset{\cdot \cdot}{x x} (({t t}_{k k}))))$

${y the y}_{k k} = = x x (({t t}_{k k})),, {\overset{\cdot \cdot}{y the y}}_{k k} = = \overset{\cdot &Center Dot;}{y the y} (({t t}_{k k})),, {f f}_{k k} ((y the y,, \overset{\cdot &Center Dot;}{y the y})) = = f f ((y the y (({t t}_{k k})),, \overset{\cdot &Center Dot;}{y the y} (({t t}_{k k}))))$

其中，t_k为时间间距，x_k、y_k为位移样本点，为速度样本点，为非线性接触力样本点。Among them, t _k is the time interval, x _k and y _k are the displacement sample points, is the velocity sample point, is the sample point of the nonlinear contact force.

所述步骤（5）中，非线性振动系统中一般表达式为，In the step (5), in the nonlinear vibration system The general expression is,

$f f ((x x,, \overset{\cdot &Center Dot;}{x x})) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{11 i i} {x x}^{i i} + + {Σ Σ}_{i i = = 11}^{n no} {c c}_{11 i i} {\overset{\cdot &Center Dot;}{x x}}^{i i} + + {Σ Σ}_{i i,, j j = = 11}^{n no} {l l}_{11 i i} {x x}^{i i} {\overset{\cdot &Center Dot;}{x x}}^{j j}$

$f f ((y the y,, \overset{\cdot &Center Dot;}{y the y})) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{22 i i} {y the y}^{i i} + + {Σ Σ}_{i i = = 11}^{n no} {c c}_{22 i i} {\overset{\cdot &Center Dot;}{y the y}}^{i i} + + {Σ Σ}_{i i,, j j = = 11}^{n no} {l l}_{22 i i} {y the y}^{i i} {\overset{\cdot &Center Dot;}{y the y}}^{j j}$

其中，x、分别为结合面的径向相对位移和径向相对速度，y、分别为结合面的切向相对位移和切向相对速度，k₁₁、c₁₁分别为结合面的线性径向刚度和线性径向阻尼，k₂₁、c₂₁分别为结合面的线性切向刚度和线性切向阻尼，l_1i、l_2i分别为结合面的径向刚度和径向阻尼非线性项。Among them, x, are the radial relative displacement and radial relative velocity of the combined surface, respectively, y, are the tangential relative displacement and tangential relative velocity of the joint surface respectively, k ₁₁ and c ₁₁ are the linear radial stiffness and linear radial damping of the joint surface respectively, k ₂₁ and c ₂₁ are the linear tangential stiffness and Linear tangential damping, l _1i and l _2i are the radial stiffness and radial damping nonlinear terms of the combined surface, respectively.

步骤（5）中，依据一般表达式，基于最小二乘法及切比雪夫多项式的非参数化方法分析所述样本数据，建立主轴-刀柄结合面非线性接触力及的解析表达模型，即In step (5), according to General expression, based on the least squares method and the non-parametric method of Chebyshev polynomials to analyze the sample data, and establish the nonlinear contact force of the spindle-tool holder joint surface and The analytical expression model of

$f f ((x x,, \overset{\cdot \cdot}{x x})) \approx \approx {Σ Σ}_{i i = = 00}^{m m} {Σ Σ}_{j j = = 00}^{n no} {c c}_{ij ij} {T T}_{i i} ((x x)) {T T}_{j j} ((\overset{\cdot &Center Dot;}{x x}))$

$f f ((y the y,, \overset{\cdot &Center Dot;}{y the y})) \approx \approx {Σ Σ}_{i i = = 00}^{m m} {Σ Σ}_{j j = = 00}^{n no} {d d}_{ij ij} {T T}_{i i} ((y the y)) {T T}_{j j} ((\overset{\cdot &Center Dot;}{y the y}))$

其中，c_ij、d_ij为切比雪夫多项式系数，T_n(ζ)为切比雪夫多项式。Among them, c _ij and d _ij are Chebyshev polynomial coefficients, and T _n (ζ) is Chebyshev polynomial.

所述步骤（1）中采用Hyper Works有限元分析软件建立所述主轴-刀柄的有限元分析模型。In the step (1), Hyper Works finite element analysis software is used to establish the finite element analysis model of the spindle-tool holder.

由于采用上述方案，本发明的有益效果是：本发明基于非参数化方法结合有限元分析技术识别主轴-刀柄结合面非线性动态特性参数。具体的，首先建立主轴-刀柄系统的有限元分析模型，对该模型进行非线性瞬态响应分析，得到结合面处位移、速度、加速度的瞬态响应，再根据牛顿第二运动定律推导得出结合面处非线性接触力的时间历程数据，基于非参数化方法利用最小二乘法及切比雪夫多项式对样本数据进行回归分析，最终得到主轴-刀柄结合面之间径向和切向非线性接触力的解析表达模型。此非线性接触力模型可直接应用于主轴-刀柄系统的动力学建模中，能够方便的识别出主轴-刀柄结合面的非线性动态特征参数，为完整、准确分析主轴-刀柄系统的动力学特性提供基础条件。Due to the adoption of the above solution, the beneficial effect of the present invention is that the present invention identifies the nonlinear dynamic characteristic parameters of the spindle-knife handle joint surface based on the non-parametric method combined with the finite element analysis technology. Specifically, firstly, the finite element analysis model of the spindle-tool holder system is established, and the nonlinear transient response analysis is performed on the model to obtain the transient response of displacement, velocity, and acceleration at the joint surface, and then deduced according to Newton's second law of motion The time history data of the nonlinear contact force at the joint surface was obtained, and the sample data was regression analyzed using the least square method and Chebyshev polynomial based on the non-parametric method, and finally the radial and tangential non-linear contact force between the spindle-toolholder joint surface was obtained. Analytical expression model of linear contact force. This nonlinear contact force model can be directly applied to the dynamic modeling of the spindle-toolholder system, and can easily identify the nonlinear dynamic characteristic parameters of the spindle-toolholder joint surface. The dynamic characteristics provide the basic conditions.

附图说明Description of drawings

图1是本发明主轴-刀柄结合面非线性动态特征参数识别流程图；Fig. 1 is the flow chart of identifying the nonlinear dynamic characteristic parameters of the spindle-knife handle joint surface of the present invention;

图2是本发明主轴-刀柄简化非线性振动系统图；Fig. 2 is the simplified nonlinear vibration system diagram of the spindle-knife handle of the present invention;

图3为本发明一实施例主轴-刀柄系统的结构图。Fig. 3 is a structural diagram of a spindle-tool holder system according to an embodiment of the present invention.

具体实施方式Detailed ways

以下结合附图所示实施例对本发明作进一步的说明。The present invention will be further described below in conjunction with the embodiments shown in the accompanying drawings.

如图1所示，一种主轴-刀柄结合面非线性动态特性参数识别方法，包括以下步骤：As shown in Figure 1, a method for identifying the nonlinear dynamic characteristic parameters of the spindle-tool holder joint surface includes the following steps:

（1）采用有限元分析软件建立主轴-刀柄的有限元分析模型；本实施例中，采用HyperWorks有限元分析软件建立主轴-刀柄的有限元分析模型。(1) The finite element analysis model of the spindle-knife holder is established by using the finite element analysis software; in this embodiment, the finite element analysis model of the spindle-knife holder is established by using the HyperWorks finite element analysis software.

本实施例中，步骤（2）具体包括以下步骤：In this embodiment, step (2) specifically includes the following steps:

（a）对主轴-刀柄的有限元分析模型进行自由模态分析，计算有限元分析模型的固有频率；(a) Perform free modal analysis on the finite element analysis model of the spindle-tool holder, and calculate the natural frequency of the finite element analysis model;

（b）将有限元分析模型的固有频率与自由模态实验得到主轴-刀柄系统的固有频率进行对比，如存在差异转入步骤（3）；若确认无误，转入步骤（4）；(b) Compare the natural frequency of the finite element analysis model with the natural frequency of the spindle-tool holder system obtained from the free mode experiment, if there is a difference, go to step (3); if it is confirmed, go to step (4);

在有限元分析软件中建立主轴-刀柄系统的有限元模型后，为保证该有限元模型的正确性，需要对主轴-刀柄系统有限元模型进行自由模态分析，并将得到的固有频率与自由模态实验得到主轴-刀柄系统的固有频率进行对比，如存在差异则修正有限元模型。After establishing the finite element model of the spindle-tool holder system in the finite element analysis software, in order to ensure the correctness of the finite element model, it is necessary to conduct free modal analysis on the finite element model of the spindle-tool holder system, and the obtained natural frequency Compared with the natural frequency of the spindle-tool holder system obtained from the free mode experiment, if there is a difference, the finite element model is corrected.

本实施例中，步骤（b）采用弹性绳悬挂主轴-刀柄的实验模型，使用锤击法进行自由模态实验，以获取自由模态实验下的主轴-刀柄系统的固有频率。In this embodiment, step (b) adopts an experimental model in which the main shaft-tool holder is suspended by an elastic rope, and performs a free modal experiment using the hammering method, so as to obtain the natural frequency of the main shaft-tool holder system under the free modal experiment.

（3）修正主轴-刀柄有限元分析模型，并转入步骤（2）继续检测；本实施例中，通过调整有限元模型网格大小和结合面的摩擦系数参数修正有限元模型。(3) Correct the spindle-toolholder finite element analysis model, and turn to step (2) to continue detection; in this embodiment, the finite element model is corrected by adjusting the grid size of the finite element model and the friction coefficient parameters of the joint surface.

步骤（4）中，通过对主轴-刀柄有限元分析模型进行非线性瞬态响应分析，得到结合面处位移、速度、加速度的瞬态响应，再根据牛顿第二运动定律推导得出结合面处非线性接触力的时间历程数据，具体步骤如下，In step (4), through the nonlinear transient response analysis of the spindle-tool holder finite element analysis model, the transient response of displacement, velocity, and acceleration at the joint surface is obtained, and then the joint surface is derived according to Newton's second law of motion. The time history data of the nonlinear contact force, the specific steps are as follows,

（Ⅱ）结合相对瞬态加速度的历程数据分析主轴-刀柄简化非线性振动系统中刀柄的运动方程，以获得和的时间历程数据；(II) Combined with the history data of the relative transient acceleration, the equation of motion of the toolholder in the spindle-toolholder simplified nonlinear vibration system is analyzed to obtain and time history data;

将主轴-刀柄系统中的刀柄与主轴分别看成质量块M₁、M₂，主轴-刀柄端面和锥面结合面看作可以用系统状态变量（相对位移、相对速度）描述的非线性单元，得到如图2所示的主轴-刀柄简化非线性振动系统。取刀柄质量块M₁为受力分析对象，根据牛顿第二运动定律，主轴-刀柄简化非线性振动系统中刀柄的运动方程为：The tool holder and the main shaft in the spindle-tool holder system are regarded as mass blocks M ₁ and M ₂ respectively, and the joint surface of the main shaft-tool holder and the taper surface are regarded as non- Linear unit, the spindle-tool holder simplified nonlinear vibration system shown in Fig. 2 is obtained. Taking the mass block M1 _of the tool handle as the force analysis object, according to Newton's second law of motion, the motion equation of the tool handle in the spindle-tool handle simplified nonlinear vibration system is:

$\begin{matrix} {M m}_{11} \overset{\cdot &Center Dot; \cdot &Center Dot;}{x x} ((t t)) + + f f ((x x,, \overset{\cdot &Center Dot;}{x x})) = = {F f}_{r r} ((t t)) + + {F f}_{r r} \\ {M m}_{11} \overset{\cdot &Center Dot; \cdot \cdot}{y the y} ((t t)) + + f f ((y the y,, \overset{\cdot &Center Dot;}{y the y})) = = {F f}_{t t} ((t t)) + + {F f}_{t t} \end{matrix} - - - - - - ((11))$

即 $\begin{matrix} f (x, \overset{\cdot}{x}) = F_{r} (t) + F_{r} - M_{1} \overset{\cdot \cdot}{x} (t) \\ f (y, \overset{\cdot}{y}) = F_{t} (t) + F_{t} - M_{1} \overset{\cdot \cdot}{y} (t) \end{matrix} - - - (2)$ Right now $\begin{matrix} f (x, \overset{\cdot}{x}) = f_{r} (t) + f_{r} - m_{1} \overset{\cdot \cdot}{x} (t) \\ f (the y, \overset{\cdot}{the y}) = f_{t} (t) + f_{t} - m_{1} \overset{&Center Dot; &Center Dot;}{the y} (t) \end{matrix} - - - (2)$

其中，F_r、F_t分别为刀柄锁紧机构通过夹紧锥向刀柄施加的径向和切向夹紧力；F_r(t)、F_t(t)分别为偏心质量引起的径向和切向外部激励力，当主轴-刀柄系统工作频率为ω，偏心量为e时，F_r(t)、F_t(t)大小分别为：Among them, F _r , F _t are the radial and tangential clamping forces exerted by the tool holder locking mechanism on the tool holder through the clamping cone; F _r (t), F _t (t) are the radial force caused by the eccentric mass, respectively When the spindle-toolholder system operating frequency is ω and the eccentricity is e, the values of F _r (t) and F _t (t) are respectively:

$\begin{matrix} {F f}_{r r} ((t t)) = = {M m}_{11} {eω eω}^{22} cos cos ((ωt ωt)) \\ {F f}_{t t} ((t t)) = = {M m}_{11} {eω eω}^{22} sin sin ((ωt ωt)) \end{matrix} - - - - - - ((33))$

分别为径向和切向相对瞬态加速度，其数值大小可由步骤（Ⅰ）中的非线性瞬态响应分析获得。 are the radial and tangential relative transient accelerations respectively, and their values can be obtained from the nonlinear transient response analysis in step (I).

由于，F_r、F_t、F_r(t)、F_t(t)以及均可求得，因此代入式（2）中可得知、和的时间历程数据。Since, F _r , F _t , F _r (t), F _t (t) and can be obtained, so it can be obtained by substituting into formula (2) ,and time history data.

（Ⅲ）采样相对瞬态位移、相对瞬态速度、以及的历程数据。本实施例中，以一定的时间间距从相对瞬态位移、相对瞬态速度、以及的时间历程数据中取出一定数量的样本数据，即(Ⅲ) Sampling relative transient displacement, relative transient velocity, as well as history data. In this embodiment, the relative transient displacement, relative transient velocity, as well as Take a certain number of sample data from the time history data of

$\begin{matrix} {x x}_{k k} = = x x (({t t}_{k k})),, {\overset{\cdot \cdot}{x x}}_{k k} = = \overset{\cdot \cdot}{x x} (({t t}_{k k})),, {f f}_{k k} ((x x,, \overset{\cdot \cdot}{x x})) = = f f ((x x (({t t}_{k k})),, \overset{\cdot &Center Dot;}{x x} (({t t}_{k k})))) \\ {y the y}_{k k} = = y the y (({t t}_{k k})),, {\overset{\cdot &Center Dot;}{y the y}}_{k k} = = \overset{\cdot &Center Dot;}{y the y} (({t t}_{k k})),, {f f}_{k k} ((y the y,, \overset{\cdot &Center Dot;}{y the y})) = = f f ((y the y (({t t}_{k k})),, \overset{\cdot &Center Dot;}{y the y} (({t t}_{k k})))) \end{matrix} - - - - - - ((44))$

（5）依据非线性振动系统中一般表达式，采用非参数化方法分析样本数据，获得主轴-刀柄结合面非线性接触力的解析表达模型。(5) According to the nonlinear vibration system General expression, using non-parametric method to analyze the sample data, to obtain the nonlinear contact force of the spindle-toolholder joint surface The analytical expression model of .

步骤（5）中，非线性振动系统中一般表达式为，In step (5), in the nonlinear vibration system The general expression is,

$\begin{matrix} f f ((x x,, \overset{\cdot &Center Dot;}{x x})) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{11 i i} {x x}^{i i} + + {Σ Σ}_{i i = = 11}^{n no} {c c}_{11 i i} {\overset{\cdot &Center Dot;}{x x}}^{i i} + + {Σ Σ}_{i i,, j j = = 11}^{n no} {l l}_{11 i i} {x x}^{i i} {\overset{\cdot &Center Dot;}{x x}}^{j j} \\ f f ((y the y,, \overset{. .}{y the y})) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{22 i i} {y the y}^{i i} + + {Σ Σ}_{i i = = 11}^{n no} {c c}_{22 i i} {\overset{\cdot &Center Dot;}{y the y}}^{i i} + + {Σ Σ}_{i i,, j j = = 11}^{n no} {l l}_{22 i i} {y the y}^{i i} {\overset{\cdot \cdot}{y the y}}^{j j} \end{matrix} - - - - - - ((55))$

其中，分别为结合面的径向相对位移和径向相对速度，分别为结合面的切向相对位移和切向相对速度，k_1i、c_1i、l_1i、k_2i、c_2i、l_2i为未知系数，k₁₁、c₁₁分别为结合面的线性径向刚度和线性径向阻尼，k21、c21分别为结合面的线性切向刚度和线性切向阻尼，l_1i、l_2i分别为结合面的径向刚度和径向阻尼非线性项。in, are the radial relative displacement and radial relative velocity of the joint surface, respectively, are the tangential relative displacement and tangential relative velocity of the bonding surface, k _1i , c _1i , l _1i , k _2i , c _2i , l _2i are unknown coefficients, k ₁₁ and c ₁₁ are the linear radial stiffness of the bonding surface, respectively and linear radial damping, k21 and c21 are the linear tangential stiffness and linear tangential damping of the joint surface, respectively, l _1i and l _2i are the radial stiffness and radial damping nonlinear terms of the joint surface, respectively.

步骤（5）中的非参数化方法是基于最小二乘法及切比雪夫多项式对有限元分析得到的样本数据进行分析，用于确定非线性振动系统中一般表达式中的未知系数，最终得到结合面非线性接触力的解析表达模型，即The non-parametric method in step (5) is to analyze the sample data obtained from the finite element analysis based on the least square method and Chebyshev polynomials, and is used to determine the Unknown coefficients in the general expression, and finally get the nonlinear contact force of the joint surface The analytical expression model of

$\begin{matrix} f f ((x x,, \overset{\cdot \cdot}{x x})) \approx \approx {Σ Σ}_{i i = = 00}^{m m} {Σ Σ}_{j j = = 00}^{n no} {c c}_{ij ij} {T T}_{i i} ((x x)) {T T}_{j j} ((\overset{\cdot &Center Dot;}{x x})) \\ f f ((y the y,, \overset{\cdot \cdot}{y the y})) \approx \approx {Σ Σ}_{i i = = 00}^{m m} {Σ Σ}_{j j = = 00}^{n no} {d d}_{ij ij} {T T}_{i i} ((y the y)) {T T}_{j j} ((\overset{\cdot &Center Dot;}{y the y})) \end{matrix} - - - - - - ((11))$

切比雪夫多项式是在区间[-1，1]上权函数为的正交多项式，具有较高的拟合精度，且不易产生病态矩阵。The Chebyshev polynomial is the weight function on the interval [-1, 1] as The orthogonal polynomial has high fitting accuracy and is not easy to produce ill-conditioned matrices.

T_n(ζ)=cos(narccosζ)-1≤ζ≤1(2)T _n (ζ)=cos(narccosζ)-1≤ζ≤1(2)

切比雪夫多项式具有正交性，即Chebyshev polynomials are orthogonal, that is,

$(({T T}_{n no},, {T T}_{m m})) = = {&Integral; &Integral;}_{- - 11}^{11} \frac{{T T}_{n no} ((ζ ζ)) {T T}_{m m} ((ζ ζ))}{\sqrt{11 - - {ζ ζ}^{22}}} dζ dζ = = \{\begin{matrix} 00,, m m &NotEqual; &NotEqual; n no \\ \frac{π π}{22},, m m = = n no &NotEqual; &NotEqual; 00 \\ π π,, m m = = n no = = 00 \end{matrix} - - - - - - ((33))$

以下结合HSK63A主轴-刀柄系统为实施例对本发明的内容加以说明。The content of the present invention will be described below in conjunction with the HSK63A spindle-knife handle system as an example.

如图3所示，HSK63A刀柄是在高速切削加工中得到广泛应用的一款刀柄，其形状尺寸及相应的主轴内孔锥面的尺寸可根据德国标准DIN69893-1:1996-01确定。As shown in Figure 3, the HSK63A tool holder is a tool holder widely used in high-speed cutting. Its shape and size and the size of the corresponding spindle inner hole taper surface can be determined according to the German standard DIN69893-1:1996-01.

设主轴-刀柄系统的工作转速为n=24000rpm，系统不平衡质量产生的偏心量为e=0.02mm，通过拉杆的夹紧锥作用在刀柄内孔30°斜面上的夹紧力沿主轴轴向方向的大小为F=18KN。Suppose the working speed of the spindle-tool holder system is n=24000rpm, the eccentricity generated by the unbalanced mass of the system is e=0.02mm, and the clamping force acting on the 30° inclined surface of the inner hole of the tool holder through the clamping cone of the pull rod is along the main axis The size of the axial direction is F=18KN.

建立主轴-HSK63A刀柄系统的三维模型，并将其导入商业有限元分析软件中，建立有限元分析模型。模型由刀柄、主轴以及它们之间的结合面组成。Establish the three-dimensional model of the spindle-HSK63A tool holder system, and import it into the commercial finite element analysis software to establish the finite element analysis model. The model consists of the tool holder, the main shaft and the interface between them.

施加好所需的约束及载荷条件后，利用商业有限元分析软件进行模态分析，得到主轴-刀柄系统的固有频率，同时，对主轴-刀柄系统进行自由模态实验，测得主轴-刀柄系统的固有频率，根据两种方法得到的固有频率对比结果，对有限元模型进行修正。After applying the required constraints and load conditions, use commercial finite element analysis software to conduct modal analysis to obtain the natural frequency of the spindle-tool holder system. At the same time, conduct free modal experiments on the spindle-tool holder system to measure the spindle- For the natural frequency of the tool holder system, the finite element model is corrected according to the natural frequency comparison results obtained by the two methods.

对修正后的主轴-刀柄系统有限元模型进行非线性瞬态响应分析，可得到主轴-刀柄结合面处在转速为24000rpm时的相对瞬态位移、相对瞬态速度及相对瞬态加速度。The nonlinear transient response analysis is carried out on the revised finite element model of the spindle-tool holder system, and the relative transient displacement, relative transient velocity and relative transient acceleration of the spindle-tool holder joint surface at a rotational speed of 24000rpm can be obtained.

以相同的时间间距从各个瞬态响应值中取出50对相对应的数据作为样本点，即样本点为Take 50 pairs of corresponding data from each transient response value at the same time interval as sample points, that is, the sample points are

$\begin{matrix} {y the y}_{k k} = = y the y (({t t}_{k k})),, {\overset{\cdot &Center Dot;}{y the y}}_{k k} = = \overset{\cdot &Center Dot;}{y the y} (({t t}_{k k})),, {f f}_{k k} ((y the y,, \overset{\cdot &Center Dot;}{y the y})) = = f f ((y the y (({t t}_{k k})),, \overset{\cdot \cdot}{y the y} (({t t}_{k k})))) \\ k k = = 0,1 0,1,, . . . . . .,, 4949 \end{matrix} - - - - - - ((44))$

应用切比雪夫多项式对样本点进行最小二乘法拟合，最终得到主轴-刀柄结合面切向非线性接触力的表达式为Using the Chebyshev polynomial to fit the sample points with the least squares method, the expression of the tangential nonlinear contact force on the spindle-toolholder joint surface is finally obtained as

$\begin{matrix} f f ((y the y,, \overset{\cdot \cdot}{y the y})) \approx \approx 1.43 1.43 \times \times 1010^{88} y the y - - 6.75 6.75 \times \times 1010^{1010} y the y \overset{\cdot \cdot}{y the y} \\ + + 9.29 9.29 \times \times 1010^{1515} {y the y}^{33} + + 201.63 201.63 \overset{\cdot \cdot}{y the y} \end{matrix} - - - - - - ((1010))$

主轴-刀柄结合面径向非线性接触力的表达式为The expression of the radial nonlinear contact force on the spindle-toolholder joint surface is

$\begin{matrix} f f ((x x,, \overset{\cdot \cdot}{x x})) \approx \approx 8.52 8.52 \times \times 1010^{1010} x x - - 2.37 2.37 \times \times 1010^{1313} x x \overset{\cdot \cdot}{x x} \\ + + 4.64 4.64 \times \times 1010^{1818} {x x}^{33} + + 3725.88 3725.88 \overset{\cdot \cdot}{x x} \end{matrix} - - - - - - ((1111))$

为了验证前面得到的主轴-刀柄结合面非线性接触力计算模型的正确性，在商业有限元分析软件中采用非线性单元模拟刀柄承受的如式(10)及式(11)所示的非线性接触力，对刀柄有限元模型进行直接频响分析，然后对整个主轴-刀柄系统的有限元模型进行直接频响分析，分别得到刀柄前端中心部位的频响函数，发现两种频响曲线较为一致，说明采用本非线性接触力计算模型进行主轴-刀柄系统的动态特性分析能够得到比较正确的分析结果。In order to verify the correctness of the nonlinear contact force calculation model obtained above on the spindle-toolholder joint surface, the nonlinear element is used in the commercial finite element analysis software to simulate the bearing of the toolholder, as shown in formula (10) and formula (11). Non-linear contact force, conduct direct frequency response analysis on the finite element model of the tool holder, and then conduct direct frequency response analysis on the finite element model of the entire spindle-tool holder system, and obtain the frequency response function of the center of the front end of the tool holder respectively, and find two The frequency response curves are relatively consistent, which shows that using this nonlinear contact force calculation model to analyze the dynamic characteristics of the spindle-tool holder system can obtain relatively correct analysis results.

上述的对实施例的描述是为便于该技术领域的普通技术人员能理解和应用本发明。熟悉本领域技术的人员显然可以容易地对这些实施例做出各种修改，并把在此说明的一般原理应用到其他实施例中而不必经过创造性的劳动。因此，本发明不限于这里的实施例，本领域技术人员根据本发明的揭示，不脱离本发明范畴所做出的改进和修改都应该在本发明的保护范围之内。The above description of the embodiments is for those of ordinary skill in the art to understand and apply the present invention. It is obvious that those skilled in the art can easily make various modifications to these embodiments, and apply the general principles described here to other embodiments without creative efforts. Therefore, the present invention is not limited to the embodiments herein. Improvements and modifications made by those skilled in the art according to the disclosure of the present invention without departing from the scope of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for identifying nonlinear dynamic characteristic parameters of a main shaft-cutter handle combined surface is characterized by comprising the following steps: comprises the following steps of (a) carrying out,

(1) establishing a finite element analysis model of the spindle-tool handle;

(2) checking whether the spindle-tool shank finite element analysis model is correct, if so, turning to the step (4), and if so, turning to the step (3);

(3) correcting the spindle-tool shank finite element analysis model, and turning to the step (2) to continue detection;

(4) for the spindle-knife handle after inspectionThe finite element model of the system is subjected to nonlinear transient response analysis processing to obtain the relative transient displacement, the relative transient speed and the radial nonlinear contact force at the joint surface of the spindle and the tool shankTangential nonlinear contact forceSample data of the history data of (1);

(5) in systems based on non-linear vibrationThe general expression is that the non-parametric method is adopted to carry out regression analysis on the sample data to establish the nonlinear contact force of the main shaft-tool handle joint surfaceThe analytical expression model of (2);

wherein x is,The radial relative displacement and the radial relative speed of the joint surface, y,Respectively the tangential relative displacement and the tangential relative speed of the joint surface;

the step (2) comprises the following steps,

(a) carrying out free mode analysis on the finite element analysis model of the spindle-tool handle, and calculating the natural frequency of the finite element analysis model;

(b) comparing the natural frequency of the finite element analysis model with the natural frequency of the spindle-tool shank system obtained by the free mode experiment, and if the difference exists, switching to the step (3); and (4) if the result is correct, switching to the step (4).

2. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 1, wherein the method comprises the following steps: in the step (b), an experiment model of the spindle-knife handle is suspended by an elastic rope, and a free mode experiment is performed by using a hammering method to obtain the natural frequency of the spindle-knife handle system in the free mode experiment.

3. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 1, wherein the method comprises the following steps: and (3) correcting the finite element model by adjusting the mesh size of the finite element model and the friction coefficient parameter of the joint surface.

4. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 1, wherein the method comprises the following steps: in the step (4), the acquisition of the history data includes the steps of,

carrying out nonlinear transient response analysis on the corrected finite element model of the spindle-tool handle system to obtain time history data of relative transient displacement, relative transient speed and relative transient acceleration of the joint surface of the spindle and the tool handle;

(II) analyzing the motion equation of the tool shank in the simplified nonlinear vibration system of the spindle and the tool shank by combining the history data of the relative transient acceleration to obtainAndtime history data of;

wherein x is,The radial relative displacement and the radial relative speed of the joint surface, y,Respectively the tangential relative displacement and the tangential relative velocity of the joint surface.

5. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 4, wherein the method comprises the following steps: in the step (II), a mass block M of the tool shank is taken₁For a stress analysis object, according to Newton's second motion law, the motion equation of the tool holder in the spindle-tool holder simplified nonlinear vibration system is transformed into

f (x, \dot{x}) = F_{r} (t) + F_{r} - M_{1} \overset{. .}{x} (t)

f (y, \dot{y}) = F_{t} (t) + F_{t} - M_{1} \overset{. .}{y} (t)

Wherein, F_r、F_tRespectively, radial sum of shank locking mechanism applied to shank by clamping coneTangential clamping force, F_r(t)、F_t(t) radial and tangential external excitation forces respectively due to the eccentric mass,radial and tangential relative transient accelerations, respectively.

6. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 1, wherein the method comprises the following steps: in the step (4), the relative transient displacement, the relative transient speed and the relative transient speed are measured at a certain time interval,Andtakes a certain amount of sample data from the time history data, i.e.

x_{k} = x (t_{k}), {\dot{x}}_{k} = \dot{x} (t_{k}), f_{k} (x, \dot{x}) = f (x (t_{k}), \dot{x} (t_{k}))

y_{k} = y (t_{k}), {\dot{y}}_{k} = \dot{y} (t_{k}), f_{k} (y, \dot{y}) = f (y (t_{k}), \dot{y} (t_{k}))

Wherein, t_kIs a time interval, x_k、y_kIn order to displace the sample point(s),in order to be a point of the speed sample,is a non-linear contact force sampleThis point.

7. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 1, wherein the method comprises the following steps: in the step (5), in a nonlinear vibration systemThe general expression is as follows,

wherein x is,The radial relative displacement and the radial relative speed of the joint surface, y,Tangential relative displacement and tangential relative velocity, k, of the faying surface_1i、c_1i、l_1i、k_2i、c_2i、l_2iFor unknown coefficients, k₁₁、c₁₁Linear radial stiffness and linear radial of the faying surface respectivelyDamping, k₂₁、c₂₁Linear tangential stiffness and linear tangential damping, respectively, of the joint surface_1i、l_2iThe radial stiffness and radial damping nonlinear terms of the joint surface are respectively.

8. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 1, wherein the method comprises the following steps: in step (5), according toA general expression is adopted, the sample data is analyzed based on a least square method and a non-parametric method of the Chebyshev polynomial, and the nonlinear contact force of the joint surface of the spindle and the tool holder is establishedAndan analytical expression model of (i), i.e.

Wherein, c_ij、d_ijIs the coefficient of Chebyshev polynomial, T_nAnd (ζ) is a chebyshev polynomial.

9. The method for identifying the nonlinear dynamic characteristic parameters of the combined surface of the spindle and the tool holder as recited in claim 1, wherein the method comprises the following steps: and (2) establishing a finite element analysis model of the spindle-tool handle by adopting Hyper Works finite element analysis software in the step (1).