CN103203670B

CN103203670B - Grinding chatter prediction method based on maximum information entropy and directional divergence

Info

Publication number: CN103203670B
Application number: CN201310113873.9A
Authority: CN
Inventors: 董新峰; 张为民
Original assignee: Tongji University
Current assignee: Tongji University
Priority date: 2013-04-03
Filing date: 2013-04-03
Publication date: 2015-04-15
Anticipated expiration: 2033-04-03
Also published as: CN103203670A

Abstract

A grinding chatter prediction method based on maximum information entropy and directional divergence, which mainly takes the acceleration vibration signal of the worktable during the surface grinding process as the research object, through an unsupervised data processing method, that is, based on the maximum information The chatter prediction method of entropy and direction divergence can predict the state of grinding chatter. The present invention first uses the principle of maximum information entropy in information theory to accurately estimate the probability density distribution of the vibration signal of the workbench, and then uses the direction divergence to quantify the maximum entropy probability density distribution, and the surface grinding process is controlled by the change of the direction divergence value. The state is observed, and then the purpose of surface grinding chatter prediction is achieved. Through the method of the invention, the grinding state can be monitored in real time, thereby achieving the purpose of avoiding chatter. Compared with other flutter prediction methods, the method of the invention has the advantages of no need for training data, fast calculation speed, strong anti-interference ability of processing results, high recognition rate and the like.

Description

Grinding chatter prediction method based on maximum information entropy and directional divergence

技术领域technical field

本发明属于零部件磨削加工领域，具体涉及一种平面磨削加工颤振预测方法。The invention belongs to the field of parts grinding, and in particular relates to a chatter prediction method for surface grinding.

背景技术Background technique

颤振是机械加工中一种常见的有害现象，主要是由刀具与工件之间的自激振动引起。在加工过程中，颤振会降低加工表面的加工质量、加剧刀具磨损、产生过大噪声、降低加工效率、加速机床破坏。因此，在加工过程中，如果能够对颤振进行预测，并观察其变化规律，就可以有效地对颤振进行控制，从而消除颤振引起的不良影响。Chatter is a common harmful phenomenon in machining, which is mainly caused by the self-excited vibration between the tool and the workpiece. During the machining process, chatter will reduce the machining quality of the machined surface, increase tool wear, generate excessive noise, reduce machining efficiency, and accelerate machine tool damage. Therefore, in the process of processing, if the chatter vibration can be predicted and its change law can be observed, the chatter vibration can be effectively controlled, thereby eliminating the adverse effects caused by the chatter vibration.

在磨削加工中，由于运动部件的非线性特征(例如运动部件摩擦力、负载和阻尼变化所引起的非线性)，加工过程中的振动信号呈非平稳、非线性特征。传统的时域、频域分析方法，如FFT分析、Wigner-Ville分析、小波分析等方法基于线性假设提出，它们的分析过程不能自适应，属于监督式学习方法，即其模型的建立需要颤振特征值对模型进行训练，当训练样本无法获得时，模型无法进行建立。In the grinding process, due to the nonlinear characteristics of the moving parts (such as the nonlinearity caused by the friction force, load and damping changes of the moving parts), the vibration signal during the processing is non-stationary and nonlinear. Traditional time-domain and frequency-domain analysis methods, such as FFT analysis, Wigner-Ville analysis, and wavelet analysis, are proposed based on linear assumptions. Their analysis process cannot be adaptive, and they belong to supervised learning methods, that is, the establishment of their models requires chatter The eigenvalues train the model, and when the training samples are not available, the model cannot be established.

发明内容Contents of the invention

本发明的目的在于提供一种平面磨削颤振预测方法，通过安装在工作台部位的加速度传感器对磨削过程中的振动信号进行采集，根据本发明中的方法对测量的离散时间序列信号进行处理与分析，从而达到磨削颤振预测的目的。The purpose of the present invention is to provide a method for predicting chatter in surface grinding, which collects the vibration signal during the grinding process through the acceleration sensor installed on the workbench, and performs the discrete time series signal measurement according to the method of the present invention. Processing and analysis, so as to achieve the purpose of grinding chatter prediction.

本发明根据平面磨削加工中振动信号的特点，提出一种非监督式颤振预测方法，即基于最大信息熵与方向散度的磨削颤振预测方法，并通过趋于颤振的平面磨削加工对该方法的有效性进行了验证。According to the characteristics of the vibration signal in the surface grinding process, the present invention proposes a non-supervised chatter prediction method, that is, a grinding chatter prediction method based on maximum information entropy and direction Machining validates the effectiveness of this method.

基于此，本发明给出的技术方案为：Based on this, the technical scheme that the present invention provides is:

一种基于最大信息熵与方向散度的磨削颤振预测方法，其特征在于，以平面磨削加工过程中工作台部位的加速度振动信号为采集对象，实施方法包括如下步骤：A grinding chatter prediction method based on maximum information entropy and directional divergence, characterized in that the acceleration vibration signal of the workbench during the surface grinding process is used as the acquisition object, and the implementation method includes the following steps:

1)、磨削过程振动信号采集硬件系统的构建，该硬件系统主要由三向加速度传感器5、电荷放大器6、数据采集卡7和计算机8构成；加速度传感器5通过信号线与电荷放大器连接，振动信号经过电荷放大器6放大后，通过信号线与数据采集卡7相连，采集卡7对信号进行采集后，输入到计算机8进行存储、处理与分析；所述三向加速度传感器5将工作台的振动物理量转换成可以量化的电信号；所述电荷放大器6为将电荷量进行放大；所述数据采集卡7将放大的电信号进行二进制量化，供计算机存储以及后续对采集信息的处理与分析；1), the construction of grinding process vibration signal acquisition hardware system, this hardware system is mainly made of three-way acceleration sensor 5, charge amplifier 6, data acquisition card 7 and computer 8; Acceleration sensor 5 is connected with charge amplifier by signal line, vibration After the signal is amplified by the charge amplifier 6, it is connected to the data acquisition card 7 through the signal line. After the acquisition card 7 collects the signal, it is input to the computer 8 for storage, processing and analysis; The physical quantity is converted into a quantifiable electrical signal; the charge amplifier 6 is to amplify the amount of charge; the data acquisition card 7 performs binary quantization on the amplified electrical signal for computer storage and subsequent processing and analysis of the collected information;

2)、磨削过程振动信号采集软件系统的构建，在所述计算机8安装有对采集信号进行处理与分析的算法软件模块，以及经过算法软件模块分析后对获得的颤振预测结果进行必要的输出显示模块；2), the construction of the vibration signal acquisition software system in the grinding process, the algorithm software module that the acquisition signal is processed and analyzed is installed in the computer 8, and the flutter prediction result obtained after the analysis of the algorithm software module is necessary. output display module;

3)、加速度振动信号概率密度的最大信息熵估计，采用最大信息熵原理对有限长时间序列进行估计，从而获得实际磨削加工状态的加速度振动信号概率密度分布的精确估计，即：3), the maximum information entropy estimation of the probability density of the acceleration vibration signal, the maximum information entropy principle is used to estimate the finite time sequence, thereby obtaining the accurate estimation of the probability density distribution of the acceleration vibration signal of the actual grinding process state, namely:

设采集卡实时送入计算机的加速度振动信号为离散值随机变量X，加速度振动信号概率值p(x_i)，随机变量X的信息熵表示为：Assuming that the acceleration vibration signal sent to the computer by the acquisition card in real time is a discrete value random variable X, the probability value of the acceleration vibration signal is p(xi ₎ , and the information entropy of the random variable X is expressed as:

$((X x)) = = - - {Σ Σ}_{i i = = 11}^{N N} p p (({x x}_{i i})) Inp Inp (({x x}_{i i}))$

通过软件算法模块可获得加速度振动信号的最大信息熵概率密度分布；The maximum information entropy probability density distribution of the acceleration vibration signal can be obtained through the software algorithm module;

4)、采用方向散度原理对步骤3)获得的最大信息熵概率密度分布的变化进行量化，即：将初始正常磨削加工时振动信号的概率密度分布作为基准，通过软件算法模块计算不同磨削状态的振动信号相对于基准的方向散度，通过方向散度值对加工状态的变化进行量化；4) Use the principle of directional divergence to quantify the change in the probability density distribution of the maximum information entropy obtained in step 3), that is: take the probability density distribution of the vibration signal during the initial normal grinding process as a benchmark, and use the software algorithm module to calculate the probability density distribution of different grinding processes. The vibration signal of the cutting state is relative to the direction divergence of the reference, and the change of the processing state is quantified by the direction divergence value;

5)、通过方向散度值的变化对平面磨削的加工状态进行观察，进而对磨削状态进行预测。5) Observing the processing state of the surface grinding through the change of the directional divergence value, and then predicting the grinding state.

其特征在于，所述采集卡为：分布式系统结构，双DSP并行处理技术，低噪声硬件设计技术，滤波技术和24位分辨率的ADC/DAC，采样频率可达192kHz。It is characterized in that the acquisition card is: distributed system structure, dual DSP parallel processing technology, low-noise hardware design technology, filtering technology and 24-bit resolution ADC/DAC, and the sampling frequency can reach 192kHz.

其特征在于，在实际磨削过程中，可以仅对y方向的振动信号进行测量，然后通过本发明方法对测量的数据进行分析，就能对磨削状态进行检测，从而达到颤振预测的目的。It is characterized in that in the actual grinding process, only the vibration signal in the y direction can be measured, and then the measured data can be analyzed by the method of the present invention to detect the grinding state, thereby achieving the purpose of chatter prediction .

其特征在于，本发明采用变磨削深度的方式趋于颤振。The characteristic lies in that the present invention tends to flutter by adopting the mode of variable grinding depth.

本发明主要针对平面磨削颤振进行预测，通过本发明方法可对磨削状态进行实时监测，进而达到避免颤振的目的。本发明从磨削颤振机理研究中获得，不仅适用于平面磨削颤振预测，也适用于其他磨削加工，如外圆磨削等。本发明方法与其他颤振预测方法相比，具有无需训练数据、计算速度快、处理结果抗干扰能力强、识别率高等优点。The invention mainly predicts the chatter vibration of plane grinding, and the grinding state can be monitored in real time through the method of the invention, thereby achieving the purpose of avoiding chatter vibration. The invention is obtained from the research on the mechanism of grinding chatter, and is not only applicable to the prediction of plane grinding chatter, but also applicable to other grinding processes, such as cylindrical grinding and the like. Compared with other flutter prediction methods, the method of the invention has the advantages of no need for training data, fast calculation speed, strong anti-interference ability of processing results, high recognition rate and the like.

附图说明Description of drawings

图1为平面磨削加工以及硬件检测系统图。标记说明：主轴箱1，砂轮2，工作台3，工件4，加速度传感器5，放大器6，数据采集卡7，计算机8。Figure 1 is a diagram of the surface grinding process and hardware detection system. Marking description: headstock 1, grinding wheel 2, workbench 3, workpiece 4, acceleration sensor 5, amplifier 6, data acquisition card 7, computer 8.

图2为磨削深度为O.09mm顺磨时工作台y方向的振动信号图。Figure 2 is the vibration signal diagram of the table in the y direction when the grinding depth is 0.09 mm along the grinding.

图3为顺磨时工作台y方向最大熵概率密度图。Figure 3 is the probability density map of the maximum entropy in the y direction of the workbench during grinding.

图4为逆磨时工作台y方向最大熵概率密度图。Figure 4 is the probability density map of the maximum entropy in the y direction of the workbench during reverse grinding.

图5为混合磨工作台y方向最大熵概率密度图。Fig. 5 is the maximum entropy probability density map in the y direction of the mixing mill workbench.

图6为y方向振动信号的方向散度变化图。Fig. 6 is a diagram of the directional divergence variation of the vibration signal in the y direction.

具体实施方式Detailed ways

实施例一(理论依据)Embodiment one (theoretical basis)

本发明以平面磨削加工过程中工作台部位的加速度振动信号为研究对象，通过无监督式的数据处理方法，即基于最大信息熵与方向散度的颤振预测方法，对磨削颤振状态进行预测。本发明首先采用信息论中最大信息熵原理对工作台振动信号的概率密度分布进行精确估计，然后采用方向散度对最大熵概率密度分布进行量化，通过方向散度值的变化对平面磨削的加工状态进行观察，进而达到平面磨削颤振预测的目的。The present invention takes the acceleration vibration signal of the workbench during the surface grinding process as the research object, and uses an unsupervised data processing method, that is, a chatter prediction method based on maximum information entropy and direction divergence, to analyze the grinding chatter state Make predictions. The present invention first uses the principle of maximum information entropy in information theory to accurately estimate the probability density distribution of the vibration signal of the workbench, and then uses the direction divergence to quantify the maximum entropy probability density distribution, and the surface grinding process is controlled by the change of the direction divergence value. The state is observed, and then the purpose of surface grinding chatter prediction is achieved.

本发明需要考虑的两个方面：Two aspects that the present invention needs to consider:

1、颤振预测系统的构建。1. Construction of flutter prediction system.

1.1颤振预测硬件系统的构建。1.1 Construction of flutter prediction hardware system.

该硬件系统主要由三向加速度传感器5、电荷放大器6、数据采集卡7、以及计算机8构成；加速度传感器5通过信号线与电荷放大器连接，振动信号经过电荷放大器6放大后，通过信号线与数据采集卡7相连，采集卡7对信号进行采集后，输入到计算机8进行存储、处理与分析。This hardware system is mainly made up of three-way acceleration sensor 5, charge amplifier 6, data acquisition card 7, and computer 8; The acquisition card 7 is connected, and after the acquisition card 7 collects the signal, it is input to the computer 8 for storage, processing and analysis.

所述三向加速度传感器5为将工作台的振动物理量转换成可以量化的电信号，该振动传感器为电荷型，即将振动物理量转换成电荷信号。The three-way acceleration sensor 5 converts the vibration physical quantity of the workbench into a quantifiable electrical signal. The vibration sensor is a charge type, that is, the vibration physical quantity is converted into a charge signal.

所述电荷放大器6为将电荷量进行放大，传感器输出的电荷信号较微弱，为便于信号采集以及提高信号的抗干扰能力，需要电荷放大器6对信号进行放大。The charge amplifier 6 is to amplify the amount of charge, and the charge signal output by the sensor is relatively weak. In order to facilitate signal collection and improve the anti-interference ability of the signal, the charge amplifier 6 is required to amplify the signal.

所述数据采集卡7为将放大的电信号进行采集量化。为便于计算机存储、处理与分析需要对信号进行二进制量化，采集卡7能完成该目的。The data acquisition card 7 collects and quantifies the amplified electrical signal. In order to facilitate computer storage, processing and analysis, it is necessary to perform binary quantization on the signal, and the acquisition card 7 can accomplish this purpose.

所述计算机8为对信号进行存储、处理与分析。The computer 8 stores, processes and analyzes the signals.

1.2颤振预测软件系统的构建。1.2 Construction of flutter prediction software system.

采集的信号通过本发明方法算法对信号进行处理，从而获得颤振预测结果。The collected signal is processed by the algorithm of the method of the present invention, so as to obtain the flutter prediction result.

2、信息论中的最大信息熵与方向散度方法。2. The method of maximum information entropy and directional divergence in information theory.

2.1最大信息熵原理2.1 The principle of maximum information entropy

最大信息熵原理是信息论中一个重要理论，是一种从不完全信息中进行预测和推断的方法，该方法在1957年由E.T.Jaynes提出。E.T.Jaynes指出：对一个未知的概率分布进行估计，其最优的概率分布估计是在满足未知概率分布的某种约束条件下，使熵值达到最大时所对应的概率分布。这一准则被称为最大熵原理。The principle of maximum information entropy is an important theory in information theory. It is a method of prediction and inference from incomplete information. This method was proposed by E.T.Jaynes in 1957. E.T. Jaynes pointed out: To estimate an unknown probability distribution, the optimal probability distribution estimate is the corresponding probability distribution when the entropy value reaches the maximum under certain constraints of the unknown probability distribution. This criterion is known as the principle of maximum entropy.

目前最大熵原理在不同的领域得到了应用，如在天文学、投资组合优化、图像重构、统计物理、物种分布、信号处理以及概率密度分布估计等领域中都得到了应用。本发明采用最大熵原理对平面磨削加工过程中振动信号的概率密度值进行估计，从而获得磨削过程中振动信号概率密度的最优估计。下面对随机变量X的最大熵概率分布进行介绍：At present, the principle of maximum entropy has been applied in different fields, such as astronomy, portfolio optimization, image reconstruction, statistical physics, species distribution, signal processing, and probability density distribution estimation. The invention adopts the principle of maximum entropy to estimate the probability density value of the vibration signal during the surface grinding process, so as to obtain the optimal estimation of the probability density of the vibration signal during the grinding process. The following is an introduction to the maximum entropy probability distribution of a random variable X:

设有一个离散随机变量X，其概率值p(x_i)未知，随机变量X的信息熵可表示为：Assuming a discrete random variable X, whose probability value p( _xi ) is unknown, the information entropy of the random variable X can be expressed as:

$H h ((X x)) = = - - {Σ Σ}_{i i = = 11}^{N N} p p (({x x}_{i i})) Inp Inp (({x x}_{i i})) - - - - - - ((11))$

式(1)在约束条件式(2)、式(3)和式(4)下，求得的p(x_i)就是随机变量X的最大熵概率密度值，根据最大熵原理可以知道求得的p(x_i)是信号最优的概率密度值，能够反应信号的真实分布。Equation (1) under the constraints of Equation (2), Equation (3) and Equation (4), the obtained p( _xi ) is the maximum entropy probability density value of the random variable X, which can be obtained according to the principle of maximum entropy The p( _xi ) is the optimal probability density value of the signal, which can reflect the true distribution of the signal.

${Σ Σ}_{i i = = 11}^{N N} p p (({x x}_{i i})) = = 11 - - - - - - ((22))$

${Σ Σ}_{i i = = 11}^{N N} p p (({x x}_{i i})) {f f}_{m m} (({x x}_{i i})) = = {c c}_{m m} - - - - - - ((33))$

${f f}_{m m} = = {x x}_{i i}^{m m} m m = = 1,2 1,2,, K K,, c c - - - - - - ((44))$

其中p(x_i)是随机变量x_i的概率值，x_i是随机变量X的取值，f_m(x_i)是随机变量X在不同区域平均值的m次方，c_m是随机变量m次方的均值。Where p( _xi ) is the probability value of the random variable x _i , x _i is the value of the random variable X, f _m ( _xi ) is the m power of the average value of the random variable X in different regions, c _m is the random variable The mean of the mth power.

一般情况下，求目标函数式(1)在约束条件式(2)、(3)和(4)的最优概率密度值p(x_i)时，需要构造Lagrange函数，如式(5)所示：In general, when finding the optimal probability density value p( _xi ) of the objective function (1) under the constraint conditions (2), (3) and (4), it is necessary to construct a Lagrange function, as shown in formula (5) Show:

$F f (({p p}_{i i},, β β,, {α α}_{m m})) = = H h ((x x)) - - β β (({Σ Σ}_{i i = = 11}^{N N} p p (({x x}_{i i})) - - 11)) - - {Σ Σ}_{m m = = 11}^{c c} {α α}_{m m} (({Σ Σ}_{i i = = 11}^{N N} p p (({x x}_{i i})) {f f}_{m m} ((x x)) - - {c c}_{m m})) - - - - - - ((55))$

分别对式(5)求偏微分：Calculate the partial differential of formula (5):

$\frac{&PartialD; &PartialD; F f}{&PartialD; &PartialD; {p p}_{i i}} = = 00,, \frac{&PartialD; &PartialD; F f}{&PartialD; &PartialD; {α α}_{m m}} = = 00,, \frac{&PartialD; &PartialD; F f}{&PartialD; &PartialD; β β} = = 00$

求解式(6)可得到最优的概率密度值p(x_i)。The optimal probability density value p( _xi ) can be obtained by solving formula (6).

2.2方向散度2.2 Directional Divergence

方向散度的概念由I.J.Good和I.J.Savage等人发展而来。Kullback在1959年以著作的形式详细地解释了方向散度的概念。在20世纪70年代J.E.Shore和R.W.Johnson在方向散度方面做了大量的工作，随后使方向散度在数据处理中得到了发展，使方向散度得到广泛的认可，使方向散度成为现代信息论中重要的内容。下面简要介绍随机变量X在离散数据情况下的方向散度：The concept of directional divergence was developed by I.J.Good and I.J.Savage et al. Kullback explained the concept of directional divergence in detail in a book in 1959. In the 1970s, J.E.Shore and R.W.Johnson did a lot of work on direction divergence, and then made direction divergence develop in data processing, making direction divergence widely recognized and making direction divergence a modern information theory. important content. The following briefly describes the directional divergence of a random variable X in the case of discrete data:

设随机变量X可能出现的值为(a₁，a₂，...，a_k)，其中X的概率分布(实际中将某个值出现的频率密度值近似代替该值概率密度值)和H₁和H₂这2种假设有关联。Let the possible value of random variable X be (a ₁ , a ₂ ,..., a _k ), where the probability distribution of X (in practice, the frequency density value of a certain value is approximately replaced by the probability density value of the value) and The 2 hypotheses _H1 and _H2 are related.

设在H₁状态时，X的概率密度分布为：Assuming that in the H ₁ state, the probability density distribution of X is:

$[\begin{matrix} X x \\ {p p}_{11} ((x x)) \end{matrix}] = = [\begin{matrix} {a a}_{11} & {a a}_{22} & L L & {a a}_{K K} \\ {p p}_{11} (({a a}_{11})) & {p p}_{11} (({a a}_{22})) & L L & {p p}_{11} (({a a}_{K K})) \end{matrix}]$

在H₂状态时，X的概率密度分布为：In the _H2 state, the probability density distribution of X is:

$[\begin{matrix} X x \\ {p p}_{22} ((x x)) \end{matrix}] = = [\begin{matrix} {a a}_{11} & {a a}_{22} & L L & {a a}_{K K} \\ {p p}_{22} (({a a}_{11})) & {p p}_{22} (({a a}_{22})) & L L & {p p}_{22} (({a a}_{K K})) \end{matrix}]$

设H₁成立时概率为p(H₁)，H₂成立时概率为p(H₂)，根据概率论中条件概率和全概率定理，可得到下面的式子：Suppose the probability of H ₁ is p(H ₁ ), and the probability of H ₂ is p(H ₂ ), according to the conditional probability and total probability theorem in probability theory, the following formula can be obtained:

$p p (({H h}_{11} | | {a a}_{k k})) = = \frac{p p (({H h}_{11})) {p p}_{11} (({a a}_{k k}))}{p p (({H h}_{11})) {p p}_{11} (({a a}_{k k})) + + p p (({H h}_{22})) {p p}_{22} (({a a}_{k k}))}$

$p p (({H h}_{22} | | {a a}_{k k})) = = \frac{p p (({H h}_{22})) {p p}_{22} (({a a}_{k k}))}{p p (({H h}_{11})) {p p}_{11} (({a a}_{k k})) + + p p (({H h}_{22})) {p p}_{22} (({a a}_{k k}))}$

根据H₁和H₂状态下X的概率分布，可以得到：According to the probability distribution of X in states _H1 and _H2 , we can get:

p₁(a_k)＝p(a_k|H₁)p ₁ (a _k )=p(a _k |H ₁ )

p₂(a_k)＝p(a_k|H₂)p ₂ (a _k )=p(a _k |H ₂ )

由上式可得到：It can be obtained from the above formula:

$log log \frac{{p p}_{11} (({a a}_{k k}))}{{p p}_{22} (({a a}_{k k}))} = = log log \frac{{p p}_{11} (({H h}_{11} | | {a a}_{k k}))}{{P P}_{22} (({H h}_{22} | | {a a}_{k k}))} - - log log \frac{p p (({H h}_{11}))}{p p (({H h}_{22}))} - - - - - - ((77))$

定义在假设H₁时，式(7)的数学期望称为两个概率分布{p₁(x)}和{p₂(x)}之间的鉴别信息，如式(8)所示。Definition When assuming H ₁ , the mathematical expectation of formula (7) is called the discriminative information between two probability distributions {p ₁ (x)} and {p ₂ (x)}, as shown in formula (8).

$D D. (({p p}_{11},, {p p}_{22})) = = {Σ Σ}_{i i = = 11}^{K K} {p p}_{11} (({a a}_{i i})) log log \frac{{p p}_{11} (({a a}_{i i}))}{{p p}_{22} (({a a}_{i i}))} - - - - - - ((88))$

本发明实施步骤解析：The implementation steps of the present invention are analyzed:

1.磨削过程振动信号采集系统的构建。本实施例已详述之。1. The construction of the vibration signal acquisition system in the grinding process. This embodiment has been described in detail.

2.加速度振动传感器安装位置的选择。加速度振动传感器的安装位置对数据的处理结果具有重要的影响，在研究中发现工作台部位振动信号的抗干扰能力强，即在非磨削状态时，磨床的空载运行对工作台的振动信号影响较小，本发明选择工作台部位的振动加速度信号进行分析。2. Selection of the installation position of the acceleration vibration sensor. The installation position of the acceleration vibration sensor has an important influence on the data processing results. In the research, it was found that the vibration signal of the workbench has strong anti-interference ability, that is, in the non-grinding state, the no-load operation of the grinding machine has a great influence on the vibration signal of the workbench. The influence is small, and the present invention selects the vibration acceleration signal of the workbench for analysis.

3.加速度振动信号概率密度的最大信息熵估计。当磨削加工的状态发生变化时，加速度传感器测量的振动信号的概率密度分布会发生变化，因此采用振动信号的概率密度分布能真实的反映加工状态，但振动信号的数据长度对概率密度分布的影响较大，理论认为当数据长度趋于无穷大时，获得的概率密度分布才能够准确的反映信号的真实分布，在实际加工过程中是不可行的，因此本发明采用信息论中最大信息熵的概念对有限长时间序列进行估计，从而获得实际磨削状态的精确估计。3. The maximum information entropy estimation of the probability density of the acceleration vibration signal. When the state of the grinding process changes, the probability density distribution of the vibration signal measured by the acceleration sensor will change, so the probability density distribution of the vibration signal can truly reflect the processing state, but the data length of the vibration signal has a great influence on the probability density distribution. The influence is relatively large. The theory believes that when the data length tends to infinity, the probability density distribution obtained can accurately reflect the real distribution of the signal, which is not feasible in the actual processing process. Therefore, the present invention adopts the concept of maximum information entropy in information theory Estimates are made on a finite time series to obtain an accurate estimate of the actual grinding state.

4.基于方向散度的最大信息熵概率密度变化的度量。通过步骤3可以获得工作台振动信号的最接近实际的概率密度分布估计，为了定量分析磨削加工状态的变化，即振动信号概率密度分布的变化，本发明采用信息论中方向散度对最大信息熵概率密度分布的变化进行量化，即将初始正常磨削加工时振动信号的概率密度分布作为基准，不同磨削状态的振动信号与其做比较，通过方向散度值对加工状态的变化进行量化。4. The measure of the maximum information entropy probability density change based on directional divergence. The closest actual probability density distribution estimate of the vibration signal of the workbench can be obtained by step 3. In order to quantitatively analyze the change of the grinding processing state, that is, the change of the probability density distribution of the vibration signal, the present invention adopts the direction divergence in information theory to the maximum information entropy The change of probability density distribution is quantified, that is, the probability density distribution of the vibration signal during the initial normal grinding process is used as a benchmark, and the vibration signals of different grinding states are compared with it, and the change of the processing state is quantified by the directional divergence value.

实施例二(具体例)Embodiment two (specific example)

下面结合附图对本发明技术方案作进一步说明。The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.

步骤一，磨削过程振动信号采集系统的构建。Step 1, the construction of the vibration signal acquisition system in the grinding process.

根据磨削过程中振动信号的特点，振动信号测量系统主要由以下部件组成：三向加速度传感器5(灵敏度：100mV/g；频率范围：0.3～10KHz；峰值±50g)、放大器6、数据采集卡7(分布式系统结构，双DSP并行处理技术，低噪声硬件设计技术、滤波技术和24位分辨率的ADC/DAC，采样频率可达192kHz，)、计算机8。According to the characteristics of the vibration signal during the grinding process, the vibration signal measurement system is mainly composed of the following components: three-way acceleration sensor 5 (sensitivity: 100mV/g; frequency range: 0.3～10KHz; peak value ±50g), amplifier 6, and data acquisition card 7 (distributed system structure, dual DSP parallel processing technology, low-noise hardware design technology, filtering technology and 24-bit resolution ADC/DAC, sampling frequency can reach 192kHz,), computer 8.

步骤二，选择工作台部位的振动加速度信号进行分析来确定传感器的设置位置。Step 2, selecting the vibration acceleration signal of the workbench for analysis to determine the location of the sensor.

图1为平面磨削加工以及振动信号采集系统，磨削加工主要由砂轮2的旋转运动和工作台3的直线往复运动形成。为达到颤振预测的目的，按照以下磨削方式趋于颤振：砂轮2的磨削速度为35m/s，工作台3进给速度为3m/min，磨削深度分别为0.03mm、0.05mm、0.07mm、0.09mm(根据磨削颤振机理理论可知，当磨削深度逐渐增大时，磨削趋于颤振，本发明采用变磨削深度的方式趋于颤振，然后采用所提方法对趋于颤振时振动信号的变化进行观察，进而对磨削状态进行预测)。为了说明本发明方法的分析过程，以顺磨时y方向振动信号为分析对象，对本发明方法的分析过程进行说明，即完成后续步骤：Figure 1 shows the surface grinding process and the vibration signal acquisition system. The grinding process is mainly formed by the rotary motion of the grinding wheel 2 and the linear reciprocating motion of the worktable 3 . In order to achieve the purpose of flutter prediction, the following grinding methods tend to flutter: the grinding speed of grinding wheel 2 is 35m/s, the feed speed of worktable 3 is 3m/min, and the grinding depth is 0.03mm and 0.05mm respectively . The method observes the change of the vibration signal when it tends to flutter, and then predicts the grinding state). In order to illustrate the analysis process of the method of the present invention, the analysis process of the method of the present invention is described by taking the vibration signal in the y direction during smooth grinding as the analysis object, that is, to complete the following steps:

步骤三，最大信息熵概率密度估计。磨床按照以下方式运行，测量工作台y方向的振动信号：砂轮转速为35m/s、工作台3进给速度为3m/min，磨削深度为0.09mm，测量结果如图2所示。将处于(ai，a(i+1))小区间振动信号的个数记为mi，处于(a1，a1O)间数据的个数记为n，将(ai+a(i+1))/2处的频率密度值记为mi/n，通过以上的计算可以获得信号的离散频率密度值。将离散频率密度值代入式(1)-式(4)，通过式(5)、式(6)可获得振动信号的最大熵概率密度值，其中Ci＝(ai+a(i+1)/2)。通过本步骤可以获得趋于颤振时，即磨削深度分别为O.03mm、O.05mm、O.07mm和O.09mm时，工作台振动信号的最大信息熵概率密度分布，如图3所示。从图3中可以看出：随着磨削深度的增加，信号的最大熵概率密度曲线发生了变化，为了定量反映最大熵概率密度的变化，将采用步骤四中方向散度对其进行度量。Step three, the maximum information entropy probability density estimation. The grinding machine operates in the following way, and the vibration signal in the y direction of the worktable is measured: the speed of the grinding wheel is 35m/s, the feed speed of workbench 3 is 3m/min, and the grinding depth is 0.09mm. The measurement results are shown in Figure 2. The number of vibration signals between (ai, a(i+1)) cells is denoted as mi, the number of data between (a1, a10) is denoted as n, and (ai+a(i+1))/ The frequency density value at 2 is recorded as mi/n, and the discrete frequency density value of the signal can be obtained through the above calculation. Substituting the discrete frequency density value into formula (1) - formula (4), the maximum entropy probability density value of the vibration signal can be obtained through formula (5) and formula (6), where Ci=(ai+a(i+1)/ 2). Through this step, the maximum information entropy probability density distribution of the table vibration signal can be obtained when the vibration tends to chatter, that is, when the grinding depth is 0.03mm, 0.05mm, 0.07mm and 0.09mm, as shown in Figure 3 Show. It can be seen from Figure 3 that as the grinding depth increases, the maximum entropy probability density curve of the signal changes. In order to quantitatively reflect the change of the maximum entropy probability density, the direction divergence in step 4 will be used to measure it.

步骤四，方向散度的计算。以O.03mm对应的最大信息熵概率密度分布为基准，记为P1，O.05mm、O.07mm以及O.09mm对应的概率密度值记为P2、P3、P4，计算P1、P2、P3、P4相对于P1的方向散度，根据式(8)获得方向散度值，如表1所示。Step 4, calculation of directional divergence. Based on the probability density distribution of the maximum information entropy corresponding to 0.03mm, it is recorded as P1, and the probability density values corresponding to 0.05mm, 0.07mm and 0.09mm are recorded as P2, P3, and P4, and the calculation of P1, P2, P3, The directional divergence of P4 relative to P1 is obtained according to formula (8), as shown in Table 1.

表1顺磨y方向最大熵概率密度的方向散度Table 1 The directional divergence of the maximum entropy probability density along the y direction

从表1可以看出，当平面磨削趋于颤振时，y方向振动信号最大熵概率密度分布的方向散度逐渐增加，因此通过方向散度能够对顺磨磨削颤振进行预测。It can be seen from Table 1 that when the surface grinding tends to flutter, the directional divergence of the maximum entropy probability density distribution of the vibration signal in the y direction increases gradually, so the grinding chatter can be predicted through the directional divergence.

通过以上步骤可以获得顺磨时趋于颤振磨削时，磨削状态的变化。同理，也可分别得到在逆磨、混合磨削条件下y方向振动信号的最大熵概率密度分布及其对应的方向散度，如图4-图6所示。从图6中可以看出，三种磨削方式在趋于颤振时，y方向振动信号最大熵概率密度的方向散度逐渐增加，因此，在实际磨削过程中，只需对y方向的振动信号进行测量，然后通过本发明方法对测量的数据进行分析，就能对磨削状态进行检测，从而达到颤振预测的目的。Through the above steps, the change of grinding state can be obtained when down grinding tends to chatter grinding. Similarly, the maximum entropy probability density distribution and the corresponding directional divergence of vibration signals in the y direction under the conditions of inverse grinding and hybrid grinding can also be obtained, as shown in Figures 4-6. It can be seen from Figure 6 that when the three grinding methods tend to flutter, the directional divergence of the maximum entropy probability density of the vibration signal in the y direction increases gradually. Therefore, in the actual grinding process, only the y direction The vibration signal is measured, and then the measured data is analyzed by the method of the invention, so that the grinding state can be detected, so as to achieve the purpose of flutter prediction.

本发明能够在颤振发生之前、颤振发生的初始阶段对平面磨削颤振状态进行观察和预测，本发明能分析平面磨削加工所处的磨削状态以及未来磨削加工的发展趋势，当磨削加工处于颤振初试阶段时，可对磨削颤振进行控制，如更换砂轮、改变切削参数，从而使磨削过程处于无颤振加工状态。本发明能够有效减少工件的废品率，提高工件的加工质量，提高磨削效率，因此本发明在磨削加工，尤其在薄壁零件的加工中具有重要的实际意义。The present invention can observe and predict the state of plane grinding chatter before chatter occurs and at the initial stage of chatter, and the present invention can analyze the grinding state of the plane grinding process and the development trend of future grinding process, When the grinding process is in the preliminary test stage of chatter, the grinding chatter can be controlled, such as changing the grinding wheel and changing the cutting parameters, so that the grinding process is in a chatter-free processing state. The invention can effectively reduce the rejection rate of the workpiece, improve the processing quality of the workpiece, and improve the grinding efficiency, so the invention has important practical significance in grinding processing, especially in the processing of thin-walled parts.

Claims

1., based on a grinding trembling Forecasting Methodology for maximum informational entropy and divergence, it is characterized in that, with the acceleration vibration signal at workbench position in flat surface grinding process for acquisition target, implementation method comprises the steps:

1), the structure of grinding process vibration signals collecting hardware system, this hardware system is formed primarily of three-dimensional acceleration transducer (5), charge amplifier (6), data collecting card (7) and computer (8); Acceleration transducer (5) is connected with charge amplifier by holding wire, vibration signal is after charge amplifier (6) amplifies, be connected with data collecting card (7) by holding wire, after data collecting card (7) gathers signal, be input to that computer (8) carries out storing, treatment and analyses; Described three-dimensional acceleration transducer (5) converts the vibration physical quantity of workbench to can quantize the signal of telecommunication; The quantity of electric charge amplifies by described charge amplifier (6); The signal of telecommunication of amplification is carried out binary quantization by described data collecting card (7), for Computer Storage and the follow-up treatment and analyses to Information Monitoring;

2), the structure of grinding process vibration signals collecting software systems, the algorithm software module of collection signal being carried out to treatment and analyses is installed at described computer (8), and after algorithm software module analysis, the flutter obtained is predicted the outcome and carry out necessary output display module;

3), the maximum information entropy estimate of acceleration vibration signal probability density, adopt Maximum Entropy Principle Method to estimate limited long-term sequence, thus obtain the accurate estimation of the acceleration vibration signal probability density distribution of actual grinding state, that is:

If the acceleration vibration signal that data collecting card sends into computer is in real time discrete valued random variable X, acceleration vibration signal probable value p (x _i), the comentropy of stochastic variable X is expressed as:

H (X) = - Σ_{i = 1}^{N} p (x_{i}) Inp (x_{i})

The maximum informational entropy probability density distribution of acceleration vibration signal can be obtained by algorithm software module;

4) divergence principle, is adopted to step 3) change of maximum informational entropy probability density distribution that obtains quantizes, that is: using the probability density distribution of vibration signal during initial normal grinding as benchmark, calculated the divergence of vibration signal relative to benchmark of different grinding state by algorithm software module, quantized by the change of divergence value to machining state;

5), by the machining state of change to flat surface grinding of divergence value observe, and then grinding state is predicted.

2. the method for claim 1, is characterized in that, described data collecting card is: distributed system architecture, two CSTR parallel processing technique, low noise hardware design technique, the ADC/DAC of filtering technique and 24 bit resolutions, and sample frequency can reach 192kHz.

3. the method for claim 1, is characterized in that, in actual grinding process, only measures the vibration signal in y direction, then to the data analysis measured, just can detect grinding state.

4. the method for claim 1, is characterized in that, adopts the mode becoming grinding depth to be tending towards flutter.