METHOD FOR PREDICTING CHATTER OF A MACHINE TOOL

Abstract

The present invention is directed to a method for predicting chatter of a machine tool. The method comprises the following steps: Feeding first input data into an artificial neural network, which includes a plurality of weights; Determining first output data at the output of artificial neural network based on the first input data and the plurality of weights; Providing the first output data into a stability model to generate prediction data; Comparing the prediction data with measurement stability data and adjusting the plurality of weights of the artificial neural network.

Claims

1. A method for predicting chatter of a machine tool comprising: feeding first input data into an artificial neural network, which includes a plurality of weights; determining first output data at the output of artificial neural network based on the first input data and the plurality of weights; providing the first output data and second input data into a stability model to generate prediction data; comparing the prediction data with experiment data and adjusting the plurality of weights of the artificial neural network.

2. The method according to claim 1, wherein the neural network is trained with an evolutionary algorithm, in particular genetic algorithm.

3. The method according to claim 1, wherein the method further includes obtaining collected data from at least one machine tool when the machine tool machines the workpiece, in particular the collected data include experiment data, machining parameters set by the operator and machining parameters measured during machining.

4. The method according to claim 3, wherein a part of the first input data and/or the second input data are derived from the collected data.

5. The method according claim 3, wherein the collected data are divided into a training set and a validation set, and the evolutionary algorithm trains the neural network with the training set and verifies the accuracy of the trained neural network with the validation set.

6. The method according to claim 1, wherein at least one second artificial neural network is applied and the output data of the second neural network is fed into the stability model.

7. A chatter prediction unit is configured to perform the method according to claim 1 comprising a neural network module, a stability model module and a comparison module.

8. The chatter prediction unit according to claim 7, is further configured to establish the stability map.

9. A machine tool comprising a. a sensing unit configured to obtain the experiment data; b. a communication unit configured to send the collected data including the experiment data to a center database connected to the chatter prediction unit according to claim 7; and c. using the stability maps generated by chatter prediction unit to determine the machining parameters to machine the workpiece.

10. A system including a plurality of machine tools according to claim 9 and the chatter prediction unit according to claim 7.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to describe the manner in which advantages and features of the disclosure can be obtained, in the following a more particular description of the principles briefly described above will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. These drawings depict only exemplary embodiments of the disclosure and are not therefore to be considered to be limiting of its scope. The principles of the disclosure are described and explained with additional specificity and detail through the use of the accompanying drawings in which:

[0034] FIG. 1 illustrates the preferred embodiment of the method of the present invention;

[0035] FIG. 2 illustrates an artificial neural network;

[0036] FIG. 3 illustrates a first embodiment of the present invention;

[0037] FIG. 4 illustrates a second embodiment of the present invention;

[0038] FIG. 5 illustrates a simulated result of the second embodiment;

[0039] FIG. 6 illustrates a third embodiment of the present invention;

[0040] FIG. 7 illustrates a measurement result of the third embodiment;

[0041] FIG. 8 illustrates a system of the present invention.

EXEMPLARY EMBODIMENTS

[0042] The present invention presents a method for chatter prediction. In particular, the method aims to identify unknown stability model input parameters required to calculate the stability boundary in milling operations. The main steps of the method are shown in FIG. 1. In step 1, during machining a workpiece, the collected data including current machining parameters and experiment data of the respective machining are continuously recorded. The collected data can be stored in a center database of a chatter prediction unit 1 shown in FIG. 8. In steps 2 and 3, a part of the collected data is fed into an artificial neural network to identify the unknown parameters required to generate stability maps using a stability model. One condition for the identification of the unknown parameters is that the best possible agreement between model stability predictions and measurement results is obtained. To achieve this, a comparison module is provided to compare prediction data and the experiment data. The deviation of these data is used to train the neural network such that the deviation is optimized to a defined threshold value. In step 4, after the unknown parameters are identified, stability maps can be generated using the identified parameters. In further, with the identified parameters and relationships, stability predictions for new parameter combinations are possible.

[0043] FIG. 2 shows a basic structure of a neural network with one input layer having I inputs, one hidden layer having N nodes and one output layer having O outputs. The input and the hidden layer are connected with weights w.sub.h.sub.j,k which multiply the respective input i.sub.j (j=1 . . . I) and pass it to node n.sub.k (k=1 . . . N). At each node, the sum of all inputs multiplied with the respective weights is transformed with an activation function a.sub.k. The results are multiplied with the weights w.sub.o.sub.k,l and summed to obtain the desired outputs o.sub.l (l=1 . . . O). The hidden and output layer also have bias terms b.sub.h.sub.k and b.sub.o.sub.l which are constants added to the respective layer.

[0044] FIG. 3 illustrates a first embodiment of the present invention. First input data is fed into the neural network. First output data can be calculated based on the weighs and bias terms of the neural network. The calculated first output data is then fed into a stability model to obtain prediction data. A comparison module is provided and configured to compare the prediction data and the experiment data for the same cutting spindle speed and depth of cut. The output of comparison module is fed back to the neural network to train the neural network. The training means adjusting the weights and the bias terms of the neural network to achieve a minimum of the deviation between the prediction data and the experiment data. In this embodiment, besides the first output data set, second input data is fed into the stability model. The stability is calculated based on the Zero Order Solution. The stability model yields the prediction data including stability limit and the associated chatter frequency. The first input data comprises machining parameters for example, spindle speed, spindle bearing temperature. The second input data comprises parameters that are known to a high precision and can directly be fed into the stability model, for example the entry and exit angle. The prediction data is then compared with the actual stability state of the experiment, namely the experiment data.

[0045] FIG. 4 illustrates a second embodiment of the present invention. In this embodiment, two neural networks are applied and the first input data is divided into two groups and fed into the two neural networks, respectively. The first neural network is applied to identify the feed dependent cutting force coefficients while the second neural network aims to identify the TCP dynamics, the modal parameters. The input of the first neural network is therefore the feed rate and the workpiece material. A neural network having two output nodes is chosen which defines the cutting force coefficients. The input of the second neural network is spindle speed and the machining temperature. The second neural network has also two output nodes defining the modal parameters, which are natural frequency and damping. In this embodiment, the first output data encompasses the output of the first neural network and the second neural network.

[0046] FIG. 5 shows a simulative result of the embodiment of FIG. 4, in which four parameters are influenced by another four parameters. Without prior knowledge about the behaviour of the stability model inputs the underlying relationships are identified from the results of 50 simulative cuts. It is assumed that the dynamics of a given machine-spindle-tool combination show a strong dependency on the spindle speed and the spindle bearing temperature. A three fluted cutter is used for cuts in two different work piece materials (workpiece 1 and workpiece 2). These cuts are performed in both X- and Y-direction of the machine tool at different feed rates, spindle speeds and depths of cut. The following assumptions about the unknown parameters are made:

[0047] (1) Natural frequency f.sub.n and damping ratio .sub.n are dependent on spindle speed n and spindle bearing temperature T;

[0048] (2) TCP dynamics are equal in X- and Y-direction; and

[0049] (3) Cutting force coefficients K.sub.tc and K.sub.rc depend on nominal feed rate f and workpiece material WP.

[0050] Mathematically, these assumptions can be expressed as follows:

f.sub.n.sub.x=f.sub.n.sub.y=f.sub.n=f(n, T), .sub.n.sub.x=.sub.n.sub.y=.sub.n=f(n, T)

K.sub.tc=f(f.sub.t, WP), K.sub.rc=f(f.sub.t, WP)

[0051] where K.sub.tc.sub.1, K.sub.rc.sub.1 and K.sub.tc.sub.2, K.sub.rc.sub.2 are the tangential and radial cutting force coefficients of workpiece 1 and 2, respectively, and f.sub.n and .sub.n are the natural frequency and damping ratio, respectively. The stability of 50 different cuts is evaluated in simulations. For each simulation, the spindle speed, bearing temperature, entry and exit angle, feed per tooth as well as the direction of cut and workpiece type are sampled randomly in a defined range. The depth of cut for each simulative sample is chosen with respect to the theoretical stability limit as follows: a.sub.sim=(1+x).Math.a.sub.theoretical, where x is a random number uniformly drawn from the range 0.3 to 0.3. This approach corresponds to the idea that cuts are performed with up to 30% deviation from the theoretical stability limit with the same chance that a cut is performed above and below the theoretical boundary, respectively. The possibility to include such cuts away from the stability limit in the inverse identification is an important advantage of the present invention.

[0052] In order to identify the first output data of the neural network, the first input data is split into a training and a validation data set, containing 70% and 30% of the data, respectively. The optimization is run for a maximum of 250 generations, each with a population size, i.e. number of individuals, of 250. The number of nodes N and the weight and bias limit |w.sub.max| are chosen as hyperparameters. The number of nodes are iterated over in a range between N=2 and N=8 while the maximum weight is evaluated between |w.sub.max|=0.1 and |w.sub.max|=10 in 25 steps with logarithmic spacing.

[0053] The goal is now to identify a relationship between the inputs n and T and the outputs f.sub.n and .sub.n, as well as the inputs f.sub.t and workpiece material WP and the outputs K.sub.tc and K.sub.rc using the neural network. Network outputs are used to calculate speed dependent stability maps. The predicted stability limits are plotted against the theoretical ones in FIG. 5. For cases 1 and 2, a very good agreement of predicted and actual stability chart can be observed. The case 3 yields a less good prediction. In this case, the temperature is T=50 deg C, which is exactly the upper limit of the distribution the random samples were drawn from.

[0054] FIG. 6 illustrates a third embodiment, in which two neural networks are applied. The first input data however is only fed into one neural network. The first neural network is applied to estimate the TCP dynamics while the second network is used to identify the cutting force coefficients depending on feed and spindle speed. The first output data includes the output of the first neural network and the second neural network. Since no input data are present in the first neural network, the neural network is defined only by bias terms and the output, e.g. natural frequency, damping ratio.

[0055] For this embodiment, an experimental study is conducted to verify the approach with real cutting data. A two fluted 12 mm diameter end mill is mounted to a shrink fit holder with 64 mm stick-out length. The holder is clamped to a Mikron high-performance five-axis milling machine and slotting experiments are performed in Aluminum 7075 with feed rates of 0.03 mm/tooth, 0.05 mm/tooth and 0.12 mm/tooth.

[0056] Measurement data is acquired by performing 40 cuts (21 stable and 19 unstable) at arbitrary spindle speeds between 7000 rpm and 13000 rpm and depths of cut between 1.3 mm and 2.5 mm. Since the dominant mode is expected to be a mode of the tool-holder combination and a shrink fit holder is used, no dependency of the dynamics on the spindle speed is assumed. Besides the convenience of this approach in identifying dynamic parameters, it was also shown that this method can yield more precise results compared to regular impact testing if a thin tool is considered. On the other hand, it is well known that cutting force coefficients obtained from mechanistic calibration might be significantly different at different nominal feed rates and spindle speeds. Hence, K.sub.tc and K.sub.rc are set as functions of the spindle speed and feed rate.

[0057] Two separate networks are created. One has the purpose to identify the modal parameters and the other one the cutting force coefficients as a function of the feed rate and spindle speed. Since no input parameters are present in the first network, it is reduced to the bias terms b.sub.ol.sup.(1), l=1 . . . 4. For the second network, one hidden layer with two nodes is used for the approximation of the relationship between spindle speed and feed rate and cutting force coefficients. The data set is randomly split into a training and a validation set containing 28 and 12 samples, respectively. A population of 100 individuals is used, and the optimization is stopped after 150 generations. The optimization process is run for different values of |w.sub.max| in a range between 0.3 and 1.1. The lowest validation error is obtained for |w.sub.max|=0.7.

[0058] In a next step, speed- and feed-dependent stability lobes are constructed with the identified network parameters. The results are shown in FIG. 7. Overall, good predictions are obtained for the three feed rates of interest. The trend of an increasing stability limit with increasing feed rate can be well predicted, and the pocket locations are well matched. However, for the highest feed rate, the unconditional limit depth of cut is overestimated by approximately 15%.

[0059] FIG. 8 shows a system 1 comprising a chatter prediction unit 20, a center database 21 and three machine tools 10, 11 and 12. The number of the machine tools is just an illustration of including a plurality of machine tools and is therefore not limited to three. The experiment data is obtained by the machine tools and sent to the center database to be stored. The chatter prediction unit inquires the collected data needed from the center database to establish the stability maps. The established stability maps are stored in the center database and are accessible for the machine tools.