Using the acoustic sound pressure level for quality prediction of surfaces created by abrasive waterjet

Transcription

1 Int J Adv Manuf Technol (21) 48: DOI 1.17/s ORIGINAL ARTICLE Using the acoustic sound pressure level for quality prediction of surfaces created by abrasive waterjet Jan Valíček & Sergej Hloch Received: 3 April 29 / Accepted: 17 August 29 / Published online: 24 September 29 # Springer-Verlag London Limited 29 Abstract The paper deals with an innovative way of cutting materials by abrasive waterjet with a view to increase its quality. In the research work, we were concerned with the search for a relationship between surface roughness and noise in the abrasive waterjet cutting process. Innovation lies in the use of negative characteristic of the technology noise, which is a carrier of information about the quality of cutting process. In this way, the noise can be positively used in the on-line control of the technological process. The final result is a project for control of the process of abrasive waterjet cutting of materials by means of feedback according to the on-line measurement of acoustic pressure level L aeq (db). Instantaneous information about the state of cut according to the instantaneous value of L aeq amplitude allows the automatic regulation of traverse speed of cutting head v p (mm.min 1 ), which is, together with the pressure p (MPa), one of the most important technological factors of control of production technology from the point of view of economic indicators and qualitative indicators of a semiproduct. The proposed model has been experimentally verified and was simulated in Matlab. J. Valíček Institute of Physics, Faculty of Mining and Geology, VŠB - Technical University of Ostrava, 17 Listopadu, Ostrava-Poruba, Czech Republic jan.valicek@vsb.cz S. Hloch (*) Department of Manufacturing Management, Faculty of Manufacturing Technologies, Technical University of Košice with a seat in Prešov, 8 1 Prešov, Slovakia hloch.sergej@fvt.sk Keywords Abrasive waterjet. Acoustic sound pressure level. Surface roughness Nomenclature v pj The unit traverse speed of cutting head (mm min 1 ) L aeqrad L aeq related topographic function Ra d (db) d a Focusing tube diameter (mm) d o Water orifice diameter (mm) E Young modulus of material (MPa) E k Kinetic energy (J) E p Potential energy (J) h Total depth of cut (mm) h i Distribution function of depth of cut (mm) h o Depth in neutral plane (mm) Quantity of material cut ability (mm) k h Material constant related to the depth ( ) K reg Regulation coefficient (db μm 1 ) k σ Material constant related to the flow stress (MPa 1 ) L aeq Acoustics sound pressure level (db) L aeq Distribution fiction of acoustic sound pressure level (db) L aeqrarado L aeq related to radial surface roughness Ra d on neutral plane (db) L aeqrarad L aeq related to the radial surface roughness Ra rad (db) L aeqc Total acoustic sound pressure level (db) L aeqopt Optimal acoustic sound pressure level (db) L aeqopto Regulated optimal acoustic sound pressure level (db) L aeqp Background noise (db) L aeqreg Regulated optimal acoustic sound pressure level (db) m a Abrasive mass flow rate (kg min 1 )

2 194 Int J Adv Manuf Technol (21) 48: m v Air mass flow (l min 1 ) m w Water mass flow (l min 1 ) p Liquid pressure (MPa) Ra Surface roughness profile parameter, roughness average Ra d Detected topographic function Ra do Detected surface roughness in radial direction Ra dreg Regulated surface roughness Ra d Ra i Distribution function of surface roughness Ra j Unit surface roughness (µm) Surface roughness in neutral plane of cut Ra rad Radial surface roughness (µm) v p Distribution function of traverse speed of cutting head (m s 1 ) v p Traverse speed of cutting head (mm min 1 ) v popt Optimal traverse speed of cutting head (mm min ) v preg Regulated traverse speed (m s 1 ) Y ret Retardation of cutting traces (mm) Y reto Retardation in neutral plane (mm) δ Abrasive waterjet technology deviation angle ( ) Ra M Measured surface roughness without regulation Ra MR Measured surface roughness with regulation Ra T Theoretical surface roughness without regulation Ra TR Theoretical surface roughness with regulation T Theoretical acoustic sound pressure level without regulation (db) M Measured acoustic sound pressure level without regulation (db) MR Measured acoustic sound pressure level with regulation (db) TR Theoretical acoustic sound pressure level with regulation (db) V poptt Theoretical optimal traverse speed of cutting head without regulation (mm min 1 ) Vpopt TR Theoretical optimal traverse speed of cutting head with regulation (mm min 1 ) Vpopt M Measured optimal traverse speed of cutting head without regulation (mm min 1 ) Vpopt MR Measured optimal traverse speed of cutting head with regulation (mm min 1 ) 1 Introduction Abrasive waterjet today represent a common cold precision machining process. Automation of abrasive waterjet technology (AWJ) is the basis of production intensification and a necessity for a flexible response to consumer demand. Automation, in connection with that progressive method of cutting, represents the highest evolution level. The numerical control device of AWJ technology is a universal device with a high degree of automation flexibly adaptable to changes in manufacturing production. Development of computer software for AWJ control and other enhancements allow the cutting of complex shapes from hard materials [1]. The newly developed hardware and software are more reliable and easier for operation. Programming development of cutting plans and surface quality control is based on the principle off-line, that is, independent of the operation of the equipment [2]. Whereas, software as well as hardware for the technology of high-speed jet machining itself is already solved to a considerable extent (with the exception of specific cases), the method of machined surface quality control in the case of continuous (on-line) control in production continues to be problem [3]. One possibility of how to improve the control of AWJ cutting is using the negative feature of the technology, the acoustic sound pressure level. The acoustic sound pressure level bears the information about the AWJ cutting process and hence the surface quality of the product. It should be noted that this phenomenon in relation to surface topography has not been a subject of any investigation. 2 Related works On the basis of study of historical and present-day development in AWJ technology in theory, experiments, and practise, we know, in accordance with the opinions of contemporary authors [4 11], that issues of physicalmechanical principle of material disintegration and new surface generation by abrasive water cutting remain, even now, unsolved and thus still open. It is a fact that neither in the latest publications [12 22] nor in papers presented at specialised conferences [23 31] we can find any quantitative solutions to such analytical questions, as discussed problems of the oscillations and rotation of abrasive particles, or AWJ as a tool, or problems of process hydrodynamics. Previous theoretical procedures processed in works [27, 32] have also dealt only little with the prediction of technical state of cut, both according to the selection of technological factors and according to the mechanical properties of material being machined; prediction calculations of instantaneous and final technical states of cut being urgently needed for the designing stage of operation, especially if the volume of contract work, is rather large. This also applies to the case of controlling the process of material cutting with ensuring the automated online check of instantaneous state of cut, including the

3 Int J Adv Manuf Technol (21) 48: quality of cut walls. The analytical mastering of the rules of distribution of values of geometric and stressdeformation parameters is a condition for the derivation of prediction equations that are, as a final consequence, of importance not only to the selection of suitable technology but also to the automated control of machining process. 3 Experiments For the experimental evaluation of acoustic sound pressure level, the method of design experiments was employed. This technique of data analysis makes it possible to describe the structure of dependence of the set of process factors that act on the noise of production system with a high-speed abrasive waterjet, i.e., the configuration of ratio of water nozzle diameter to focusing tube diameter d o /d a, abrasive mass flow rate m a, liquid pressure p, and traverse speed of cutting head v p. Mathematically, it is possible to write this function in the following implicit form for the overall level of acoustic pressure (Eq. 1): L aegc ¼ f Ra d ; v p ; p; m a ; d o =d a ; h;...l aegp ð1þ where L aeqp is the value of acoustic pressure level for the background of plant and pump. The value of acoustic pressure level L aeq generated by the cutting process itself is evaluated by the following relation (Eq. 2): L aeg ¼ L aegc L aegp ð2þ For four selected factors at two levels (+1, 1), particular experiments were conducted in 2 4, i.e., 16 various relations. Such a two-level factorial experiment was applied to a simple specification of the factors that statistically significantly influence the variability of values of acoustic pressure level L aeq. On the basis of justified selection of measurement method for the continuous detection of control signal, the physical and correlation characteristics of acoustic pressure level L aeq in db and the correlation, or calibration function L aeq =f (Ra), will be discussed in detail. Partial sources represented in Eq. 1 were studied under technological conditions where variable factors were pressure p=3 35 MPa, orifice diameter d o =.25 mm, abrasive mass flow rate m a =3 4 g min 1, focusing tube diameter d f =1 1.2 mm, and traverse speed v=1 2 mm min 1. As cutting tool, an Autoline cutting head from the Ingersoll-Rand Company was used with the standoff distance z=3 mm. The Barton Garnet was used as abrasive material with MESH 8. Surfaces of each test sample were measured by the shadow optical method using a charge-coupled device camera on 22 measurement lines with a vertical step of.364 mm. Optical signals concerning the light and shadow surface distribution were analysed by means of the Fourier transform, spectral decomposition, and frequency band filtration with the aim to obtain the root mean square (RMS) value of intensity of light reflected from the surface and the transforming equations between RMS and surface roughness parameters, above all, the roughness parameter Ra. We consider the distribution of roughness parameter n the cut wall to be the most important because it provides integrated and comprehensive information about both the mechanical effects of selection of technological parameters and the properties of material and interaction between the cutting forces and the material [33]. To acoustic sound pressure level measurement, a modular sound analyzer Investigator 226 (Brüel & Kjær) was applied; it enables the sound analysis with an adjustable, dynamic scale in 8 db range. The noise sample can be detected in a full range from 7 to 13 db at ten-step interval. Measurements were manually controlled within the period of 6 s from the moment when AWJ had hit the target material. The sound analyzer was installed 1.7 m from the working board edge at the 45 angle, at the height of 1.2 m and approximately 3 m from the cutting head. The measurement was performed with an A-weighted philtre, in the octave range of 16 12,5 Hz. 4 Results and discussion As already described above, we look for a relation between the traverse speed of cutting head and the acoustic pressure level being measured. Generally, for the relationship between the traverse speed and the acoustic pressure level, the derived Eq. 3 determined on the basis of measured values and documented by a graph in Fig. 1 is given: v p L aeqopt ¼ L aeqopto ð3þ v popt Equation 3 can be interpreted in non-regulated mode as follows: the higher is the speed of the cutting head, the higher is the level of acoustic pressure, and vice versa. This linear dependence is used in the design of the regulator for controlling the process of abrasive water cutting of materials. The description of regulating process requires the derivation of equations for the regulated traverse speed of the cutting head v preg.ifv p ¼ v preg and L aegopto ¼ L aegreg, then after modification, we shall obtain the following equation (Eq. 4): v preg ¼ L aeqreg v popt L aeq ð4þ In regulated mode, Eq. 4 expresses the dependence of the acoustic pressure level on the regulated traverse speed

4 196 Int J Adv Manuf Technol (21) 48: [db] reg vpopt vp [mm.min ] Fig. 1 Dependence of L aeq on v p opto of the cutting head. From Eq. 4, it is possible to express the regulated acoustic pressure level L aegreg described by the equation below (Eq. 5). L aeqreg ¼ L aeqv preg ð5þ v popt The required value, which is simultaneously the optimum level of acoustic pressure L aegopto, can be determined by the following equation (Eq. 6); thus we shall receive a constant value given by this calculation according to Fig. 1: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L aegopto ¼ L aeg L aegreg ð6þ On the basis of topographical function (Eq. 7), we are able to predict the development of surface roughness from the depth of material cutting: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ra d ¼ Ra j 1 log ðlog hþ 2 þðlogyret 1 Þ 2 þra 2 rad ð7þ where Ra j is the unit surface roughness (µm), h is the total depth of cut (mm), Y ret is the retardation of cutting trace (mm), and Ra rad is the radial surface roughness (µm). For the radial roughness of surface, the following relation (8) is valid: pffiffi Ra rad ¼ Ra j 1 log 13 :25 ð Y ret EÞ ; ð8þ where is the roughness of surface in the neutral plane of cut, and E is the Young modulus of material (MPa). The given topographical function Ra d contains in itself information on the radial roughness of surface that can be determined according to Eq. 8. Similarly, we look for a relationship between the topographical function Ra d and the acoustic pressure level L aeq, because the level of acoustic pressure contains in itself information on the quality of process of abrasive water cutting of material, and in this way, it informs us about the quality of surface topography in the course of this technological process. The relation for the calculation of level of acoustic pressure generated by the cutting process itself can be, on the basis of correlation and regression analyses, applied only to the deformation parameters of surface roughness Ra and the function corresponding to the Young modulus of given material E, and can be written for the considered types of roughness Ra d and Ra rad in Eqs. 9 and 1: L aeqrad ¼ L aeqj þ k h L aeqrarad ¼ L aeqj þ k h where: k h =4.521 k σ = þ k s Ra d E þ k s Ra rad E ð9þ ð1þ is the material constant related to the depth [1] is the material constant related to the flow stress (MPa 1 ). In Fig. 2, the dependences of L aegrad and L aegrarad on depth h are plotted. In Eqs. 9 and 1 and in other analogous relations, we are able to designate the augend as material depth term and the addend as material stress term. The quantity of material cut ability, which occurs in the relations discussed, means, from the technological point of view, a constant having a physical-technological informative value, into which geometry reflects itself (by means of Ra, h, and Y ret ) and also material properties (by means of E). It is the constant for the given type of material. Thus, reacts flexibly to a [db] Rad Rarad Fig. 2 Dependence of L aeqrad on h and dependence of L aeqrarad on h

5 Int J Adv Manuf Technol (21) 48: change in technological conditions factors (when a change in surface roughness is required under technological conditions set differently from reference ones). An auxiliary function Ra rad was used for the derivation of topographical function Ra d in form according to Eq. 7. For this reason, it is considered to have a direct relation to the flow stress in the cut and can also be regarded as check function for numerical and also graphical results. Values of acoustic pressure on the level of neutral plane h o will be calculated analogously to the previous procedure by inserting the values of variables valid for this plane (neutral plane is determined conventionally in the local minimum of topographical function as reference level ): Ra do E L aeqrado ¼ L aeqj þ k h þ k s ð11þ Ra rado E L aeqrarado ¼ L aeqj þ k h þ k s ð12þ On the basis of analysis of the previous equations (Eqs. 9 12), in Fig. 3, the graphical dependence of stated functional relations is given. In the publication [33], the initial that describes interaction of the abrasive waterjet in the area of penetration into the surface layer of material is characterised. The knowledge of initial is of importance not only to the understanding of mechanism of abrasive water cutting of material but also to regulation in the use of surface quality control with feedback. From the point of view of control and search for a relation for the subsequent automation of this technological process, this is a nonlinear region for the control theory. By putting the expressed relations for L aeq into Eqs. 4, 13, and 14, the regulation of traverse speed of cutting head can be derived with using the auxiliary function Ra rad (Eq. 8) and the topographical function for the prediction of surface roughness Ra d (Eq. 7): 1 L aeqopto v popt v pregrarad ¼ v A ð13þ Ra þ k h þ k rad E s 1 L aqopto v popt v pregrad ¼ v A Ra þ k h þ k d E s where: ð14þ v pj is the unit traverse speed of cutting head (mm min 1 ). In Fig. 4, the dependences of v preg Rarad and v preg Rad on depth h are presented. An integrated view of mutual and simultaneously comparable interconnection of parameters is offered in the following key Fig. 5, which shows the sought relationships between Eqs For comparison, all curves are presented as functional dependences on depth h. The depth of cut (Fig. 5) can be divided into three significant s from the point of view of regulation of abrasive water cutting of material, namely, on the basis of example given for steel AISI 39: 1. h 2 ð; 1Þ mm, which is conventionally designated as so-called initial and is regarded as nonlinear, experimentally found region. Both curves of this are delimited with the origin at point and points of local extremes I, G; Eq. 12 being corresponding to the behaviour of v pregrad with the local maximum at point I, f (x) Rad Rarad Rad hvz h Rad Rarad hlim 4 Fig. 3 Dependence of L aeq, Ra d, and Ra rad on h, where h vz =8 mm is the height of sample vpregrarad vpregrad Fig. 4 Dependence of v pregrarad on h and dependence of v pregrad on h

6 198 Int J Adv Manuf Technol (21) 48: f (x) I G o vpregrad vpregrado h vpregrad Rado = Radreg P Rad Rarad Fig. 5 Dependences of L aeqrad, L aeqrarad, v pregrad, v pregrarad on h for the regulation state in the course of regulation of required roughness Ra do hlim f (x) o h Rad Rarad Rarad [µm] Fig. 6 Dependence of L aeq on Ra rad and Eq. 9 being corresponding to the behaviour of L aegrad with the local minimum at point G. 2. h 2 ð1; 25Þ mm; this is the case of documented by a broad base of measured samples, which is delimited by points G and P; after exceeding the local minimum at point G, the level of acoustic pressure grows proportionally to the depth of cut; the dependence of the behaviour of acoustic pressure level on cut depth cannot be, however, in reality ideally smooth; fluctuations occur, e.g., due to material heterogeneity (as a consequence of defects, changes in the value of acoustic pressure level occur); the point P is the intersection of acoustic pressure level and regulated speeds and separates the linear region from the nonlinear region in the given material. For different materials, the position changes (for steel AISI 39 the point is there at the depth h=25 mm). 3. h 2 ð25; 35; 6Þ mm; for working purposes, we designate this as the limiting and evaluate it as strongly nonlinear region that is complicated from the point of view of the control process. For the thorough identification of cut, we carry out the prediction of its geometrical parameters (Ra, Y ret, δ), the prediction of the technological parameter (v p ), and parameter of importance to control (L aeq ). By prediction, we select the possible regulation of these parameters and parameters of controlling the AWJ cutting process of materials under strictly given technological conditions. In Fig. 6, there is a part of the curve of L aeq in relation to Ra rad which is valid for the region of linearity. We look for an answer to the question on how many db correspond to 1 μm Ra for the following conversion. If we know the regulated traverse speed of cutting head v preg, it is possible to express, in terms of ratio, the resultant values of regulated roughness by the following equations (Eqs. 15 and 16): Ra dreg ¼ v pregra d v popt Ra d ð15þ Ra radreg ¼ v pregra rad Ra rad ð16þ v popt For the speed v popt =148 mm min 1, L aeqopto =42 db is valid. We shall regard this value as the required value in the proposal for a regulated loop (see Fig. 8). Then, the acoustic pressure level in the course of regulation corresponds to the optimum acoustic pressure level L aeqrel = L aeqopto =42 db, the roughness parameter of corresponding neutral plane h o being regulated. After putting the values into Eqs. 6 and 7 for the neutral plane (for which the following values hold true: h o =9.66 mm, Y reto =1 mm, =3. 7 μm, and E=167 2 MPa), we shall obtain the value of Ra do =9.5 μm. The applicability and the principle of utilisation of regulation ratio (Eq. 17) can be seen in Fig. 7. At keeping the same ratio in regulated mode, the relation below is valid (Eq. 17): K reg ¼ L aeqopto Ra do ¼ 4:64 db mm 1 ð17þ then, the regulated roughness parameter can be expressed by means of the following equation (Eq. 16): Ra dreg ¼ L aeqreg 4:64 ¼ Ra do ¼ 9:5 mm ð18þ

7 Int J Adv Manuf Technol (21) 48: f (x) o = opt = reg 2 Rad Rad = Radreg Kreg Fig. 7 Derivation of regulation coefficient K reg Results are graphically illustrated in graphs according to Eqs in Fig. 7. The regulation coefficient K reg = 4.64 db μm 1 holds true for steel. For other materials, this value is different, not quantified yet (will be a subject matter of other analyses). 5 Proposal of the AWJ regulating process To ensure functionally of the automated check, the technologist has to select the most suitable direct or indirect hlim measurement of the parameter being checked, i.e., in our case, the roughness parameter Ra. What is meant is the selection of technically the most suitable principle of measurement from the point of view of methodology for input signal measurement and apparatus and from the point of view of ensuring the automation feedback for technology regulation in the conditions of operation. Designing works on automated check thus require, in addition to the knowledge of behaviour of distribution function Ra i =f (h i ) in the material being machined, also the knowledge of behaviours of calibration functions in relation to the value measured by the selected measurement method. A proposal for the control of abrasive water cutting process concerns the measurements of distribution of instantaneous values of roughness parameter Ra by means of remote detection of acoustic pressure level L aeq (db; Fig. 8). In Fig. 8, there is a diagrammatically illustrated proposal for the method of regulating process control. For this reason, from the above-mentioned facts, a possibility of utilising the check measurement of acoustic pressure level is analysed in the work. A change in parameter Ra is obtained by regulation of traverse speed of cutting head v p according to the functional relation L aeq = f (v p ). In this part, relations of selected parameters of surface topography in relation to the level of root and mean square value of acoustic pressure L aeq will be described. Owing to a whole series of advantages offered just by this solution in contrast to other methods, we propose the w e Regulator u Servo motors to ensure controlled by position and velocity CNC or PC umech Technological process z ma [g.min ] p [MPa] MESH Focusing tube x x x-motion Action member y y CNC control y-motion Information input b [mm] z [mm] L aeq Material being cut Water level Sensor use of the negative characteristics of this technology, the noise, which conveys information about the cutting quality process Measurement equipment Fig. 8 Proposal for the regulating process of on-line control of abrasive waterjet technology technology by means of the level of noise (L aeq ), which carries information on the quality of cutting process, where: u, actuating quantity; w, required value; u mech, mechanical actuating quantity; e, deviation; G R, regulator transfer; G M, motor transfer; G TP, technological process transfer; G S, measurement equipment transfer

8 2 Int J Adv Manuf Technol (21) 48: continuous remote check of roughness in the cut by the measurement of instantaneous change in the level of acoustic pressure and by the feedback control of traverse speed of cutting head. It is mainly the case of technically sufficient calibration closeness of function L aeqi =f (Ra i ) and other advantages, such as measurement simplicity in operational conditions and equipment availability. On the basis of qualitative influence of technological factors, technically, the most suitable regulating parameters are the traverse speed of cutting head and the close functional relations L aeqi =f (v pi ), Ra i =f (v pi ). In Fig. 9, there is an example of non-regulated and regulated AWJ technology processes. By means of regulation of input factors, we are able to achieve a greater depth with lower values of surface roughness parameter of profile Ra. Regulated value (measured) acoustic sound pressure level L aeg is compared with desired value L aegopto. Any deviation e is regulated by change of traverse speed v (mm min 1 ) of the cutting head (Figs. 8 and 9). Listed in Table 1 are experimentally obtained data by analytical measurement compared with theoretical values. Theoretical equations used in the paper were derived based on the measured values. Plots obtained from measured data and behaviours of the derived theoretical functions are given in Fig. 1. Figure 11 compare detailed plots before and after regulation. Regulation of abrasive waterjet cutting of AISI 39 by means of acoustic sound pressure level has been experimentally verified. As it can be seen, the experimentally observed values of surface profile parameter Ra MR after regulation fluctuate by function Ra TR. ABRASIVE HOPPER permeate solid phase air phase ABRASIVE DELIVERY SYSTEM p [MPa] AWJ Lenght Track AWJ cutting front PNEUMATIC VALVE ADAPTER ATTENAUTOR (Accumulator) surface topography α r α Smooth Rough h pconst. b) ABRASIVE TUBING ABRASIVE MANAGEMENT SYSTEM (AMS) Ep mw lenght of AWJ trace permeate solid phase air phase p [MPa] AWJ cutting front machnined surface Smooth ma, mv CATCHER TANK WORKPIECE Ek mw ma mv AWJ hx a) SLUDGE c) Fig. 9 An example of regulated and (b) non-regulated and (c) regulated process in (a) abrasive waterjet technology cutting system

9 Int J Adv Manuf Technol (21) 48: Table 1 Experimentally measured and theoretical values h (mm) Ra M Ra MR Ra T Ra TR T (db) M (db) MR (db) TR (db) Vpopt T (mm/min) Vp TR (mm/min) Vpopt M (mm/min) VpMR (mm/min) Conclusions In the paper, an analytical proposal for the control with a feedback of process of abrasive water cutting of materials according to the continuous measurement of acoustic pressure level L aeq is presented. For immediate control of surface quality in real-time, the measurement of acoustic pressure level on the basis of experimentally confirmed functional relation of L aeq to surface roughness and cut depth, which are functionally linked on traverse speed v p of cutting head, is proposed. By a regulating system with feedback, the regulation of traverse speed of cutting head v p and the regulation of parameter of surface roughness Ra d,whichisin functional relation to the traverse speed v p, is ensured. For this purpose, the original analytical solution for the regulating process will be developed and selected suitable PID regulator. The proposal and analytical solutions are verified by simulation in MATLAB. Results of this stage of work were utilised in the preparation of an original proposal for the project of measurement and control of cutting process quality. The model has been experimentally verified, and obtained results are graphically displayed on (Figs. 1 and 11).

10 22 Int J Adv Manuf Technol (21) 48: Fig. 1 An analytical simulation and verification of measurement of on-line automated control Ra (R)=f (L aegr, V pr ) 4 35 AWJ Lenght Track p [MPa] AWJ cutting front AWJ Lenght Track p [MPa] AWJ cutting front 3 surface topography Smooth hx surface topography α r b) α Smooth Rough h Ra M [µm] Ra T [µm] 25 c) Ra [µm] Ra MR [µm] Ra TR [µm] Fig. 11 Detailed plots of experimentally observed surface roughness Ra M versus predicted values of Ra T of non-regulated process and plot after regulation of surface roughness values where Ra MR is the experimentally observed regulated value and Ra TR is the regulated function

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