In the all kind of industry focused on precision, in which die and mould .... deriving from tool deflection, as proposed in Seo [11] and in Hascoet et al [18], and with ...
Using artificial neural networks for the prediction of dimensional error on inclined surfaces manufactured by ball-end milling Álvar Arnaiz-González, Asier Fernández- Valdivielso, Andrés Bustillo, Luis Norberto López de Lacalle Department of Mechanical Engineering, ETSI of Bilbao, University of the Basque Country (UPV/EHU)
Department of Civil Engineering, University of Burgos, Burgos, Spain Abstract There is a strong industrial demand of models and simulation tools that can predict dimensional errors in manufacturing task, like ball-end finishing of inclined surfaces. But this task becomes very complex due to the high amount of variables that influence the dimensional errors during a cutting process and their different nature. This work here presented analyses first the possibilities of semiempirical models to solve this problem, concluding that models cannot gather and replicate with enough accuracy results for all milling cases and slopes combinations. Second, this work analyses the possibilities of Artificial Neural Networks to overcome this limitation. Different kind of neural networks, like Multilayer Perceptron (MLP) and Radial Basis Functions (RBF), have been tested. The results show that RBFs predict better than MLPs, achieving a precision of 1.83 in RMSE and 0.897 in correlation coefficient with a 10x10 cross validation scheme with a smaller training and tuning times, in a factor higher than 2.5 in any case. Finally, the use of 3D Figures, generated from the RBF best model, to obtain industrial conclusions of interest for the process engineer is shown.
Keywords: Artificial Neural Networks, Radial Basis Functions, Tool deformation, Ball-end milling
1. Introduction In the all kind of industry focused on precision, in which die and mould manufacturing is included, a common issue is the work on complex surfaces on hardened steels. In moulds for example, tolerances and dimensional accuracy are very narrow. In the XX century the main manufacturing process was Electrical Discharge Machining (EDM) [1], but currently is highspeed milling (HSM) the technology for hardened steels (>30 HRC) and other difficult-to-cut alloys. HSM technology has to minimize the effect of various factors [2] producing dimensional errors. There are also error causes, due to the construction and stiffness of the machine tools, which are directly related with vibration in machining, inertial tool-path inaccuracy and thermal distortions. Various problems may also derive from the tool-clamping systems [3][4], or from thermal deformation [5] of the workpiece and of the tools. Tool runout brings
also a possibility of severe wear or tool breakage [6]. And finally there are important errors owing to the deflection of slender cutting tools, which is tackled in the present paper. In some preliminary tests and in real moulds manufacturing [7], errors derived from tool deflection in finishing processes exceeded 100 m. Such error is critical where tolerances in the mould industry are concerned, which are commonly in the range 0.05 - 0.1 mm. Therefore there is a strong industrial demand of models and simulation tools that can predict dimensional errors. But this task becomes very complex due to the high amount of variables that influence the dimensional errors during a cutting process and their different nature [1]. Although these errors can be partially compensated using semiempirical models, this research will outline the limitation of this solution and specially its applicability in many real industrial conditions, because many of these variables can not be properly evaluated under real industrial conditions while theoretical models are mainly developed under well-known laboratory conditions. For this reason, artificial intelligence methods might be more suitable for developing industrial tools for dimensional errors prediction. Artificial Intelligence (AI) algorithms copy the way the living beings process information and make decisions to build prediction models; the most often techniques within this category are: artificial neural networks (ANN), genetic algorithms, fuzzy logic and support vector machines. Extensive research has been conducted into the usefulness of these techniques for ball end-milling operations, mainly for roughness prediction, over the last 10 years. For example, ANNs has been extensively used for roughness prediction [8–12]. Its most common configuration is a multilayer perceptron (MLP) with a single hidden layer [2]. But other alternative approaches have also been tested with good results: neuro-fuzzy inference system [13– 17], Bayesian networks [18, 19], genetic algorithms [20, 21] and support vector machines [22]. Probably, ANNs are the most widely used classifier for this task. Unfortunately, the results depend strongly on the parameters of the neural networks [23]. The tuning process of these parameters is a high-consuming task that requires also the supervision of an expert, because there are no general rules that may be followed as a guide. For the present study a test plan was carried out by virtue of which the errors resulting from tool deflection were predicted. The test variables took into account were namely: a) cutting strategy, b) tool slenderness parameter, c) material hardness, and d) surface slope. Doing that it was then possible to determine what cutting strategies should be used to minimize errors resulting from tool deflection. Included here is a more complete study of the cutting types possible than that given in Kang et al. [3], in which cutting type, i.e. downmilling (climb milling) or upmilling (conventional milling), is not included among the test factors, and in which, furthermore, cutting speed is low in terms of HSM and the radial depth of cut ae is high for mould finishing. However, these authors provided useful information for a database relating to accuracy, roughness, and wear in the case of inclined surfaces machining. The process variables under study have been selected because comprises the main variables the process engineer can modify in the CAM program (cutting strategy and tool dimension) and the variables that the final customer fix (material hardness, and surface slope), while considering the main variables that affect tool deflection in cutting processes and, therefore, geometrical errors. Therefore the developed model can be of direct use in workshop and of easy integration in CAM software tools. The approach is compatible and can be compared with the use of semiempirical models, as it was done by authors in other works [24]. There the final aim is the same, but in the case here presented tool deflection errors are calculated by ANNs, based on a previous and systematic testing. In previous works [24] the experimental methodology and the machining test´s results were firstly presented, although without any deep analysis and correlation of input variables of
machining with the dimensional error caused by tool deflection. A utility for predicting values based on the full set of experiments performed were not proposed, but it was pointed our as an interesting further work. And an utility for predicting dimensional errors is useful for serving as a basis for developing a machining path correction procedure that will minimize the error deriving from tool deflection, as proposed in Seo [11] and in Hascoet et al [18], and with a real possibility of being integrated in the CAM programming stage of toolpaths, as it was proposed in other works [25, 26]. The rest of this paper is organized as follow: Section 2 presents the fundamentals of tool deflection, while Section 3 presents the experimental set-up realized to obtain real data for this industrial process; Section 4 introduces the ANNs models that will be used to predict this industrial data; Section 5 presents and discusses the results of the modelling using the ANNs models and their capability of creating accurate models for this industrial task; finally Section 6 sums up the main conclusions obtained from this research and the future lines of work.
2. Tool deflection Prior to the quantitative study of tool deflection, the question to be considered is what parameters affect it. As long as cutting is stable, i.e. as long as there is neither forced nor regenerative vibrations (chatter), the model approaches a static case. So, the cutting conditions (ap, ae, vc and fz) of all tests must avoid the influence of forced vibration due to the tooth passing frequencies. And it must be a stable case respect to chatter problems. We have measured the natural frequencies of the spindle-tool assembly of the three axismachining centres. A modal analysis of the high speed machine tool, following the procedure described in [14] has been done, obtaining the stability lobes of the machining operation. The value of lower frequencies is in X axis 436, 685 and 1115 Hz and in Y axis 430, 720 and 1110 Hz. These values and the small depth of cut of finishing tests, avoid the presence of dynamic problems like chatter in all the trials. An appealing model [15-17] for the study of deflection is that in which the tool is regarded as a cylindrical cantilever beam. Deflection then conforms to the equation
64 F L3 3 E D 4
(1)
It may thus be seen in Eq.2 that tool deflection in the static model is a function of the following three parameters: E:
Young's modulus for the tool material.
L3/D4 :
Tool slenderness parameter, where D is equivalent tool diameter and L is overhang length. These parameters will be looked at below.
F:
Cutting force perpendicular to the tool axis.
A
Figure 1: Relation between tool deflection and dimensional error At the view of Eq. 1 and several works [1,16], L/D or L3/D4 were used as the characteristic slenderness parameter. The latter expression was selected since, as may be seen in the cantilever beam model of Eq. 2, deflection is a linear function of this slenderness parameter. Here D is the equivalent tool diameter. The equivalent diameter will be less than the actual tool diameter, since the helicoidal shape of the two edges reduces the resistant section. In Ref. [14] an equivalent diameter of 0.8 D0 is assumed, D0 being the tool diameter. However the exact formula includes a premise that is false, the absolute clamping of the slender “bean” into toolholder and spindle nose. The modulus of elasticity (Young’s modulus) E depends on the tool material, being calculated for sintered carbide as 6 x 105 N/mm². The slenderness parameter depends on the geometry of tools that are selected. The other parameter is the component of the cutting force perpendicular to the tool axis in the plane perpendicular to surface in the maximum slope line. This cutting force component depends of the feed per tooth (fz) and the engagement conditions (ap, ae). The toolholder used was a hydraulic HSK 63 with much more stiffness [3] than tool. In [4] a complete study about the radial stiffness of HSK (Hollow Shank Kegel) is presented; its main conclusion is that radial stiffness of HSK50 shanks ranges from 19 N/m at 5,000 rpm to 17 N/m at 25,000 rpm. Comparing these values with those derived from the cantilever beam model (see Eq.1), which values are, for the author tested tools in a previous investigation [14], 0.15 N/m for 6 mm, 4.4 N/m for 12 mm and 1.6 N/m for 16 mm, it can be noted that in the best case (12 mm) tool stiffness is approximately four times lesser than the shank. Deflection errors in the free-form surface ball-end milling have not been studied very much in finishing conditions, that is to say with ap lower than 0.3 mm and radial depths of cut lower than 0.5 mm. The work in [15] provides useful information for a database relating to accuracy, roughness, and wear in the case of inclined surfaces machining. However, in this work cutting type (downmilling (climb milling) or upmilling (conventional milling)) is not included among the test factors, cutting speed is low in terms of HSM and the radial depth of cut ae is too high for mould finishing.
3. Experimental set up and analytical modelling 3.1 Experiments design A previous study [24] provides the experimental results of the effect of various factors on the dimensional error of machined planes (Fig.2); results are briefly explained as follows for an easier understanding by readers:
The workpiece materials were of 30 and 50 HRC hardness, with slopes of 15º, 30º, and 45º. Steel was a high alloyed one Cr-Mo-V, type H13, with different heat treatments.
The selected tools were solid ball-end mills of sintered tungsten carbide, coated with TiAIN and submicrograin size.
Their diameters and slenderness parameters (L3/D4) were respectively (6 mm and 541 mm-1; 12 mm and 19.9 mm-1; 16 mm and 52.33 mm-1).
2 Hardness: 30 HRC 50 HRC
3 Slopes 15,30,45º
Figure 2: Left) workpiece, Centre) workpiece clamped on the Kistler in the machine, Right) three tools, Below) machined sector with each strategy. The test plan was carried out using finishing cutting conditions. The following were selected: -
Cutting speed: for all tests, effective cutting speed at tool material contact point (point A in figure 1) was held constant at 200 m/min. Doing that, cutting speed in the nominal radius varies in all tests, because it depends on piece angle .
-
Depth of cut ap: for the Do 6 mm tool, depths of cut of 0.1 and 0.2 mm were used. For tools of Do 12 mm and of Do 16 mm, they were 0.2 mm and 0.3 mm respectively.
-
Radial depth of cut ae: this was set to ensure a good value for the maximum roughness Rt, less than 5 m in all cases. In the case of the Do 6 mm tool, a radial depth of cut of 0.1mm was used, while for those of Do 12 and of Do 16 mm, depth was 0.2 mm.
-
Feed per tooth fz: feed per tooth was the recommended one by tool manufacturer. It depends on the size and stiffness of edges, so it depends on each tool diameter, that is, for Do6 0.055 mm/tooth, for Do12 0.077mm/tooth, and for Do16 0.089mm/tooth.
-
In all cases dry machining.
-
Direction of machining: tests were carried out with upward machining, downward machining, and in transversal directions (horizontal). In these directions, downmilling (climb milling) or upmilling (conventional milling) was employed. Hence, the cutting types studied were: AV-D:
upward machining, downmilling.
AV-U:
upward machining, upmilling.
DV-D:
downward machining, downmilling.
DV-U:
downward machining, upmilling.
H-D:
z-level horizontal machining, downmilling.
H-U:
z-level horizontal machining, upmilling.
Fig. 3 shows a plant view of the test plan for the 50 HRC testpiece, similar to that of 30 HRC. The test plan in Fig. 5 indicates with S the spindle rotation speed, as well as the cutting conditions. The long arrow in each square indicates the direction of linear feed, while the short one indicates the sense of the radial depth of cut (or step). The M, L, and P indexes are the order numbers of tests, without technical meaning.
ae
Reference planes
F
T1-6 T2-12 T3-16
15 45º
Figure 5: Test plan for 50 HRC. Horizontal view.
15º
ap = ae = 0.2mm
ap = ae = 0.1mm
ap = ae = 0.2mm
Figure 3: test plan for 50 HRC. Test part, horizontal view.
ap = ae = 0.2mm
30º
3.2 Force measurement A Kistler dynamometer plate type 9255B has been used to measure the forces on the tool. The signal captured by the dynamometer is amplified by a Kistler 5017B charge amplifier and is recorded by a PC equipped with a National Instruments™ PC-MIO data acquisition card, with a sampling frequency of 1.2 MHz. The Kistler plate has 4 three dimensional piezoelectrics capable of capturing the forces in its 3 components. The signal of these 4 piezoelectrics is in the order of picoCoulombs, thus making the amplification of the signal necessary. The signal amplifier, as well as converting the measurement into values of between 10V, filters any noises that have been captured. To this end, it has a low-pass filter adjustable to 10, 100 or 1000 Hz depending on the frequency of the measured signal. This dynamometer plate has also been used for the measuring the cutting force during the machining process. This application requires a detailed study of the maximum frequency to be measured and an adaptation of the sampling frequency. This is why an acquisition card with such a high sampling frequency has been chosen. However, this fact is not relevant in the present study. Measurements of forces allow to check that tests were performed properly, eliminating those case when measured forces were 20% in excess of usual values. Therefore, a force recording was an error-proof checking for increasing the soundness of values that served for the ANN approach.
3.3 Measurement of displacements The possibility of using dial devices with a micrometer resolution of 1 m was studied before deciding on the following method. However, in preliminary experiments, the great dependence of this measuring procedure, both on the accuracy of the contact point of the probe with the tool, and on the skill of the worker given the job of performing the measurements, was observed. The use of inductive sensors has been resorted to for this reason (inductive/eddy current type) that enable the detection of the displacement of the tool during machining without having to be in contact with the tool. These sensors have a very high resolution (under one m), linearity and measurement frequency (up to 1.6 KHz) [19]. The use of other similar sensors, for example, capacitance type gap sensors, has been carried out by some authors [16] who use them to generate orbital diagrams that reflect the displacement of the tool during machining. The method employed by these authors consists in adding a collet around the tool tip where the sensors are placed. Its signal is captured during the machining tests. In any case, the capacitance sensors and the eddy current type sensors involve a similar working method. As a disadvantage, these types of sensor are only capable of measuring metallic materials, although this is not a problem in our study as the hard metal tools have a metallic cobalt binder (6-12% depending on hard metal grades). However, they have to be calibrated for each of the materials to be measured. The amplifiers output signal varies between 0 and 5V. There is a variation in distance in this range of voltage of around 2 mm, that is to say, 2,000 m. After calibration, the measuring range was reduced in some tools as it was not possible to measure more than 1.5 mm due to their small diameter. This means that a variation of 1mV represents a displacement of 0.4 m. Taking this value into account, it is extremely important to reduce as far as possible the electromagnetic noise of the measurements. After analysing all the
sources of noise, it has been possible to reduce the noise in the measurements up to 5mV, representing a value of 2 m. In order to achieve this laboratory supply source has been resorted to with a very low ripple factor. Other precautions have also been taken, such as preventing the normal electromagnetic noises of a manufacturing workshop (other machines, use of the same electrical ground, etc). A more stable data acquisition card against electromagnetic noise, than that used for the measurement of forces, has been used for the measurement of displacements, to be precise, the Lab-PC-1200 from National Instruments . The measurement of displacement by means of the inductive/eddy current sensor is performed in the measurement direction of the sensor axis. That is to say, small displacements in the measurement of the transversal axis do not affect the measurement, which is an important advantage with respect to the use of micrometer dials. The response of the sensors is in theory lineal for flat metallic bodies, but in the case of hard metal tools, and more exactly due to their cylindrical geometry, it has been observed that they are better adapted to a grade 2 polynomial function. The calibration procedure is as follows.
In the first place, the sensor is placed in contact with the tool, taking this value as absolute 0, from where on the controlled displacements have been carried out in 50 to 50 m, registering the amplifiers output values.
The output of each of the sensors has been adjusted with the displacement and voltage data. The displacements have been controlled using the high speed machine control, whose repeatability is lower than 1 m.
The 8mm hard metal tool has been the first tool to be calibrated, and is used as a reference, as the sensors output has been forced to read 0V when in contact with this tool. The rest of the calibrations have been performed without forcing the sensors output, and only the calibration curves have been measured. After calibrating the sensors, it is possible to simultaneously measure the forces and the displacements that they induce. A PC is used to do this in such a way that both measurement systems are activated and tested at the same time.
3.4 Physical results, general trends In short, the physical results of testing can be explained in the following points. -
In tests carried out with a 6 mm diameter tool at ae 0.2 mm and ar 0.1 mm, measurements of 70 and 80 m were taken on slopes of 15º (part with 50 HRC). Errors in 15º slopes were greater than those resulting from a slope 45º. As an example, the greatest error with the 16 mm tool arises in a plane of 15º, with a value of 20 m, while in the 45º error is 3 m. Upmilling produces smaller deflection errors than downmilling. While in the case of upmilling the maximum is 15 m, with downmilling values in excess of 20 m for the 6 mm tool can be produced. This is because in the upmilling case the direction of cutting forces tends to engage the tool into the workpiece, rather than to separate them.
-
A comparison is made of deflection results obtained with Eq.1, using those transversal cutting forces Fy obtained from dynamometer measuring, with experimentally measured errors, and it can be deduced that the cantilever beam model provides only a rough approximation of tool performance. Thus in the case of 16 mm tool, the error computed by formula (Eq. 1) is 7 m, while that
measured is 9 m. In the case of the 12 mm tool, that computed is 3 m and the actual is 6 m. But there are several cases where estimated errors and measured ones are large different. There are several reasons for this difference: a) with the cantilever model, one can use an effective diameter between 0.8 D and 1D. b) Young's modulus can range from 4.7 to 6x105 N/mm² for different hard metal grades . c) Also, the inherent inaccuracy to force simulation is introduced. d) On the other hand, if cutting forces are measured experimentally, for small depths ap and high cutting speeds Vc, measurement is highly problematic owing to noise and for a high sampling frequency needed. e) Another factor may be the HSK63 toolholder, whose stiffness is high but not infinite. Finally, f) machine-tool stiffness is also not infinite, as it is studied in [26]. -
In the case of very flexible tools, the force induced by the tool deflection is the same and contrary to the radial cutting force. It is not correct, therefore, to calculate the force to determine deflection, as deflection reduces the tool engagement (and thus the chip section) and therefore the value of the force. The condition to be applied is the balance between the cutting force and the resistance to deflection force. This idea was used in [16] in the case of very flexible micromills (
