Application of the hottest autoregressive algorith

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Application of autoregressive algorithm in the monitoring of milling cutter damage

with the improvement of production automation, people pay more and more attention to the monitoring of cutter damage in the machining process. Breakage is one of the main failure modes of cutting tools. Under mechanical impact or tool material fatigue (mechanical or thermal fatigue), if the internal stress of the tool exceeds the strength limit of the tool material, the cutting edge will break and fall off from the tool to form damage. In the process of cutting, the tool breakage will be shown by various phenomena or signals (such as cutting force, sound, etc.). Among the numerous signals, cutting force (torque) is the most commonly used and effective method to monitor tool breakage. Firstly, the waveform characteristics of cutting torque in milling process are studied; Then the autoregressive algorithm is introduced into the tool damage monitoring, and the application of autoregressive algorithm in tool damage monitoring is emphatically studied. The least mean square algorithm is introduced to estimate the parameters of autoregressive model; The step factor and order p of autoregressive model are studied in detail

the degree of tool damage varies, sometimes small cutting edges fall off, sometimes large cutting edges fall off, and even the whole tool is broken. Generally speaking, when the amount of damage is large, the change of cutting force signal is strong and easy to identify; Smaller damages are more difficult to identify. This paper only studies the damage of small cutting edges

the milling force (torque) measuring device used in this paper is a cutting force telemetry tool handle with a force sensor and an inductive power supply device. The force measuring tool handle can measure the cutting torque received by the tool during drilling and milling

1 waveform characteristics of cutting torque in the milling process

since the milling torque is used as the basis for tool damage monitoring, it is necessary to understand the change law of milling torque, so as to identify the tool damage. The milling cutter used in this experiment is high-speed steel three tooth spiral groove end milling cutter, and the workpiece material is quenched and tempered 45 steel

the force measuring tool handle collects the milling torque value every certain time, and connects these discrete points to form the torque waveform curve. The number of points collected within each revolution of the milling cutter is determined (60 data are collected per revolution in this paper), which is determined by the encoder installed at the end of the spindle of the milling machine

first, analyze the waveform characteristics of the cutting torque in the normal milling process (Fig. 1a): the torque signal is periodic, and its fundamental frequency is the rotation frequency of the milling cutter. The three peaks in each cycle represent the cutting torque of the three teeth of the milling cutter. Theoretically, the waveform (shape and amplitude) of cutting torque between two adjacent cycles (i.e. two adjacent revolutions) of each cutter tooth should be the same, that is, the amplitude of corresponding points of two adjacent revolutions (such as points A1 and A2 in Fig. 1a) should be the same. However, in the same cycle, the cutting torque waveform between each cutter tooth is not necessarily the same, which is mainly caused by the slight difference of the geometric angle and edge quality of each cutter tooth and the eccentric installation of the milling cutter

Fig. 1 three tooth end milling cutter milling torque waveform characteristics

(a) normal milling (b) simulated damage (c) simulated damage (d) through the air hole

tool damage is very accidental, which is difficult to capture and record, and brings great difficulties to the experiment. Therefore, the method of simulated damage is adopted in this paper. The specific methods are as follows: first, mill with intact cutters and record the data of cutting torque; Then stop the machine and grind the notch on the cutting edge with the manual grinding wheel without disassembling the tool and workpiece to simulate the damage; Then continue milling with the notched tool and record the cutting torque data. In this way, the torque waveform before and after the milling cutter is damaged can be obtained, but the change of torque at the moment of damage cannot be reproduced. According to the following analysis in this paper, it can be known that using autoregressive algorithm to monitor tool damage mainly needs to identify the change of milling torque before and after the damage, and the change law of the moment of damage is not the most important

generally speaking, there are two situations after the cutting edge generates a notch: one is that the positive rear angle at the notch can still be cut, but the cutting thickness at the notch will be reduced, the cutting edge at the notch will cut less or even no workpiece, and the cutting torque will be reduced. In this way, the torque waveform will be sunken, and the next tooth adjacent to the damaged tooth will cut off part of the material not cut off by the damaged tooth, Therefore, a bulge appears in the torque waveform (Fig. 1b); In the second case, the back angle at the notch becomes zero or negative. At this time, the friction between the back tool face and the workpiece increases sharply, resulting in a sudden increase in the cutting torque (Fig. 1c). It can be said that in either case, the amplitude and waveform of cutting torque before and after damage will change

just as the cutting torque waveform will change when the tool is damaged, the cutting torque waveform will also change under some special circumstances (such as milling cutter cutting in and cutting out the workpiece, there are holes, grooves, steps on the workpiece surface, uneven workpiece surface, etc.). This involves another problem of tool monitoring: how to distinguish cutting and tool damage under the condition of special J. power supply: 1 ∮ 220V 50Hz, so as to avoid wrong discrimination. Fig. 1D shows the milling torque waveform for milling the workpiece with air holes (the diameter of the air holes is about 5.2mm). It can be seen from the figure that when the milling cutter passes through the air holes, the cutting torque waveform of each cutter tooth will appear concave, forming a low-lying hump shaped waveform in the middle

cutting under all special conditions will change the waveform of milling torque between two adjacent revolutions. Through careful observation, it can be found that the change of cutting torque caused by tool breakage is a sudden change process, that is, the amplitude of torque suddenly increases between two adjacent revolutions; The change of cutting torque under special conditions is a gradual process. Taking Fig. 1D as an example, although the cutting torque has changed greatly in the whole process, the change is slow transition, that is, the milling cutter gradually cuts into the air hole and gradually cuts away from the air hole, so the torque change between two adjacent revolutions is quite small. The abrupt and slow change of cutting torque is an important feature to distinguish them, which provides an objective basis for the autoregressive algorithm to eliminate false positives

at this point, we can judge the state of the tool (whether it is damaged) with the naked eye according to the change of the cutting torque Poisson's ratio of 0.331 moment. The next step is to enable the computer to automatically identify the changes of milling torque waveform according to the cutting torque data, so as to further judge whether the tool is damaged. This is the research of monitoring algorithm

2 autoregressive model of milling process

2.1 establishment of autoregressive model

discrete dynamic milling process (as shown in Fig. 1A ~ d) can be combined and described by two models: the regular components determined in the process can be described by dynamic transfer function, and the random components in the process can be described by random model, as shown in Fig. 2. Thus, the output f (T) at any time t can be expressed as:


in the formula, the milling torque at time f (T) t

u (T) cutting conditions (such as cutting parameters, workpiece materials, etc.)

a (T) random input components that interfere with the milling process

b backward shift operator

the previous term on the right of formula (1) represents the amplitude of the milling force when there is no random interference component, which is determined by the cutting conditions, because it is periodic Stable components, so it is meaningless to identify tool breakage. This item can be filtered out by calculating the first-order difference between the corresponding points of the torque waveform of the two adjacent revolutions (see Figure 1a), that is, the first-order difference

f (T) = f (T) - f (T-T) (2)

is expanded to:

where T represents the number of milling torque points collected in each rotation cycle of the milling cutter (corresponding to the rotation cycle of the milling cutter), which is simplified to:


so as to obtain the milling process model with the first-order difference as the output. Since a (T) - A (T-T) is a random input, this model is a random model, which is called autoregressive moving average model ARMA (P, q) (where p, q are the order of the model). It consists of two parts: autoregressive term P (b) (AR) and moving average term Q (b) (MA). The low-order autoregressive model is a linear filter, which is more suitable for monitoring dynamic processes with rapid changes. Therefore, autoregressive model is usually used for real-time monitoring [3]

Figure 2 dynamic milling process model

p order autoregressive model can be expressed as:



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where f (T), f (t-1), f (T-2), f (T-P) are the first-order difference of cutting torque at t, T-1, T-2, T-P, and 1, 2, P are model parameters

in addition, the value of F (T) at time t can be estimated from the values of F (t-1), f (T-2), and f (T-P) before and including time T-1, i.e.


which represents the estimated value. In fact, it is the estimated value of the data about time t based on the previous data, so it does not include the influence of random factors that may occur in the process. The measured value f (T) is subtracted from the estimated value to obtain the random component of the influence process at time t, that is,


(T) is called residual error, which represents the difference between the experimental measured value and the estimated value

2.2 estimation of time-varying parameters of autoregressive model

the following problem is how to estimate the F value at time t by using the F value before time T-1 (including time t-1), so as to obtain the residual error. The key is how to calculate the model parameters 1, 2, P, which need to be determined adaptively. In this paper, the least mean square (LMS) algorithm is introduced to estimate the time-varying parameters of AR model. Its characteristic is that there is no need to calculate the correlation function and matrix inversion [2], so the operation is simple and can ensure the real-time monitoring

lms algorithm for time-varying parameter estimation of AR (P) model can be simply summarized as follows:

given parameter: model order P, step factor

initial condition: when t=0, the expression of p-dimensional vector initial value

lms algorithm is, T "with the newly expanded adhesive utilization and development laboratory in Bayer Shanghai polymer research and development center and the global innovation team that has been fully invested in scientific research projects = 0, 1, 2, H



(T) = [1 (T), 2 (T),, P (T)] (9)

represents the vector composed of model parameters at time t,

f (T) = [f (t-1), f (T-2),, f (T-P)] t (10)

represents the vector composed of F values before (including) T-1, which is the estimated value at time t

by using this set of recurrence formulas, the parameters of AR model can be estimated time-varying, and the residual error value (T) at any time t can be calculated

3 application of autoregressive model in tool damage monitoring

3.1 autoregressive algorithm for tool damage monitoring

from the above introduction, it can be seen that the input of random autoregressive model is a random process, and the output is residual error. If the input is a stable random process, the output residual error is a noise signal (i.e. the mean value is zero and the variance is constant), its value is very small and fluctuates around the zero point; If this random input suddenly deviates from the stable process, the AR model will be disturbed. It will be at least p (the order of the AR model) intervals (that is, processing P data)

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