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Gaussian noise process as cutting force model for turning
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Procedia CIRP 00 (2018) 000–000 Procedia CIRP 00 (2017) 000–000 Procedia 77 (2018) 94–97 Procedia CIRP 00 000–000 Procedia CIRPCIRP 00 (2018) (2018) 000–000
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8th 8th CIRP CIRP Conference Conference on on High High Performance Performance Cutting Cutting (HPC (HPC 2018) 2018) 8th CIRP Conference on High Performance Cutting (HPC 2018)
Gaussian Gaussian noise noise process process as as cutting cutting force force model model for for turning turning Gaussian28th noise process as cutting force model for turning a a a CIRP Design aConference, May 2018, Nantes,Stepan France a , Gabor a Henrik T. Sykora , Daniel Bachrathy a Budapest a Budapest
Henrik T. Sykoraa , Daniel Bachrathya , Gabor Stepana Henrik T. Sykoraa , Daniel Bachrathya , Gabor Stepana
University of Technology and Economics, Department of Applied Mechanics, M˝uegyetem rkp. 5, Budapest H1111, Hungary University of Technology and Economics, Department of Applied Mechanics, M˝uegyetem rkp. 5, Budapest H1111, Hungary ∗ Corresponding aa Budapest author. Tel.: +36-1-463-1235; E-mail address: [email protected] University of Technology Technology and Economics, Economics, Department of of Applied Applied Mechanics, Mechanics, M˝ M˝u uegyetem egyetem rkp. rkp. 5, H1111, Hungary ∗ Corresponding Budapest University of and Department 5, Budapest Budapest H1111, Hungary author. Tel.: +36-1-463-1235; E-mail address: [email protected] ∗∗ Corresponding author. Tel.: +36-1-463-1235; E-mail address: [email protected] Corresponding author. Tel.: +36-1-463-1235; E-mail address: [email protected]
A new methodology to analyze the functional and physical architecture of existing products for an assembly oriented product family identification
Abstract Abstract Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat Abstract Abstract As an approximation for the cutting force the applicability of noise process is based on analysis of measured As an approximation for the cutting d’Arts force et theMétiers, applicability of aa Gaussian Gaussian noise process is investigated investigated based on the the analysis of measured cutting cutting École Nationale Supérieure Arts et Métiers ParisTech, LCFC EAthe 4495, 4 Rue Augustin Fresnel, Metz 57078, France force signals. It is shown by force measurement in orthogonal turning process, that Gaussian distribution fits well to the histograms of As an approximation for force of noise investigated based the analysis of measured force It is shown bycutting force measurement in orthogonal turning process, that theis distribution to the of the the As an signals. approximation for the the cutting force the the applicability applicability of aa Gaussian Gaussian noise process process isGaussian investigated based on onfits the well analysis of histograms measured cutting cutting measured time histories. It is also shown, that the variance of the measured force signal can be ∼ 5% of the mean value, which is orders of force signals. It is shown by force measurement in orthogonal turning process, that the Gaussian distribution fits well to the histograms of measured timeIthistories. also measurement shown, that the variance of turning the measured can be distribution ∼ 5% of thefits mean is orders of force signals. is shown Itbyisforce in orthogonal process,force that signal the Gaussian wellvalue, to thewhich histograms of the the higher than the noise of the measurement system. *magnitude Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected] measured time histories. It is also shown, that the variance of the measured force signal can be ∼ 5% of the mean value, which is orders magnitude higher than the noise of the measurement system. measured time histories. It is also shown, that the variance of the measured force signal can be ∼ 5% of the mean value, which is orders of of © 2018 The Authors. Published by Elsevier Ltd. magnitude than the of measurement system. © 2018 The Thehigher Authors. Published bythe Elsevier Ltd. magnitude higher thanPublished the noise noise by of the measurement system. © 2018 Authors. Elsevier Ltd. Peer-review under the responsibility of the International Scientific Committee © 2018 The Authors. by Ltd. Peer-review under thePublished responsibility theBY-NC-ND International Scientific Committee of of the the 8th 8th CIRP CIRP Conference Conference on on High High Performance Performance Cutting Cutting © 2018 The Authors. Published by Elsevier Elsevier Ltd. This is2018). an open access article under theofCC license (https://creativecommons.org/licenses/by-nc-nd/4.0/) (HPC Peer-review under the responsibility of the International Scientific Committee of the 8th CIRP Conference on High Cutting (HPC 2018). Peer-review the responsibility of the International Scientific Scientific Committee of the 8thofCIRP on HighonPerformance Performance Cutting Selection andunder peer-review under responsibility of the International Committee the 8thConference CIRP Conference High Performance Abstract (HPC 2018). Cutting (HPC 2018). (HPC 2018). chatter, turning, noise, cutting force model Keywords: Keywords: chatter, turning, noise, cutting force model chatter, turning, force model InKeywords: today’s business the trend chatter, environment, turning, noise, noise, cutting cutting forcetowards model more product variety and customization is unbroken. Due to this development, the need of Keywords: agile and reconfigurable production systems emerged to cope with various products and product families. To design and optimize production systems as well as to choose the optimal product matches, product analysis methods arestochastic needed. Indeed, most of plane the known methods aim to ministic 1. ministic and and stochastic [8], [8], like like shear shear plane oscillation oscillation [9], [9], local local 1. Introduction Introduction analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and inhomogeneities in the material properties, rough surface of the ministic and stochastic [8], like shear plane oscillation [9], local 1. Introduction inhomogeneities in the material properties, rough surface of the ministic and stochastic [8], like shear plane oscillation [9], local 1. Introduction nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production workpiece, etc. which also affect the time characteristics of the In the field of manufacturing science machine tool vibrainhomogeneities in the material properties, rough surface of the workpiece, etc. which also affect the time characteristics of inhomogeneities in the material properties, rough surface the In the field of manufacturing science machine tool vibrasystem. A new methodology isproblems, proposed toespecially analyze existing products in view of their functional and physical architecture. The aim the is tostationcluster cutting force. These phenomena greatly influence tions are source of many during roughworkpiece, etc. which also affect the time characteristics of In the field of manufacturing science machine tool vibracutting force. These phenomena greatly the stationworkpiece, etc. whichlines alsoand affect the timeofinfluence characteristics of the the tions are many problems, especially during Inproducts the source field ofofmanufacturing science machine tool vibrathese in new assembly oriented product families for theroughoptimization of existing assembly the creation future reconfigurable ary forced vibrations, which are important when determining ing processes [1], where a large material removal rate is recutting force. These phenomena greatly influence the stationtions are source of many problems, especially during rougharyproducts forced which aresubassemblies important when determining cutting force. These phenomena greatly influence the stationing processes [1], aproblems, large material removal ratestructure is re- of the tions aresystems. source ofwhere many especially during roughassembly Based on Datum Flow Chain, the physical isvibrations, analyzed. Functional are identified, and the quality of manufactured product and when dequired. There are two main types of tool vibrations: ary forced vibrations, which are when determining processes [1], where aa large material rate the surface surface quality of the the manufactured product and when the deary forced vibrations, which are isimportant important when determining quired. There are is two main types of machine machine toolfunctional vibrations: ing processes [1], where large material removal rate is is rereaing functional analysis performed. Moreover, a removal hybrid and physical architecture graph (HyFPAG) the output which depicts tecting chatter [10]. chatter and forced vibrations. Chatter is an unfavorable cutthe surface quality of the manufactured product and when quired. There are two main types of machine tool vibrations: similarity between families by of providing supportcutto both, the production system and product designers. tecting chatter [10].planners surface quality of the manufactured product An andillustrative when dedechatter and forced vibrations. Chatter is an design unfavorable quired. There areproduct two main types machine tool vibrations: The modeling of frequency impose ting by aa self-induced and re[10]. chatter and forced vibrations. Chatter is an unfavorable example of a nail-clipper is used explain methodology. industrial case study twohigh product families phenomena of steering columns The chatter modeling ofonthe the high frequency phenomena imposeofaa tecting chatter [10]. ting phenomenon phenomenon caused by to self-induced oscillation andcutre- An tecting chatter and forcedcaused vibrations. Chatterthe is proposed anoscillation unfavorable cutgreater challenge. the element sults in surface quality and potentially damages the The of the high phenomena impose ting caused aa carried self-induced oscillation and rethyssenkrupp France isby then out to give a first industrial the proposed approach. greater challenge. For example, the finite finite element models models ofaa Theof modeling modeling ofFor theexample, high frequency frequency phenomena imposeof sults phenomenon in poor poorPresta surface quality and potentially damages the tool. ting phenomenon caused by self-induced oscillation andtool. re- evaluation the cutting process could trace this fast variation, but these Forced vibrations caused by the time varying cutting force: the ©sults 2017 The Authors. Published by Elsevier B.V. greater challenge. For example, the finite element models of in poor surface quality and potentially damages the tool. the cutting processFor could trace this fast variation, but these greater challenge. example, the finite element models of Forced caused by the varyingdamages cutting force: the sults in vibrations poor surface quality andtime potentially the tool. are computationally intensive, very sensitive of the values of variation of the cutting force can occur due to the periodically Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. the cutting process could trace this fast variation, but these Forced vibrations caused by the time varying cutting force: the are computationally intensive, of the but values of the cutting process could tracevery thissensitive fast variation, these variation of the cutting cantime occur due tocutting the periodically Forced vibrations causedforce by the varying force: the
changing size shape of chip (e.g.: during intervariation the cutting occur to periodically changing of size and shapeforce of the thecan chip (e.g.:due during milling, intervariation of theand cutting force can occur due to the themilling, periodically changes in changing size chip (e.g.: milling, interrupted turning), butshape also of canthe the local changes in changing size and and shape of theoccur chip due (e.g.:toduring during milling, interthe material properties over time. rupted turning), but can occur the material properties over rupted turning), but also also cantime. occur due due to to the the local local changes changes in in theoretical investigations the material properties over The theoretical investigations on machine machine tool tool vibrations vibrations are are theThe material properties over time. time.on commonly conducted using differential The investigations on tool are conducted using deterministic deterministic delayed differential The theoretical theoretical investigations on machine machinedelayed tool vibrations vibrations are 1.commonly Introduction equations, in which the parameters are considered to be detercommonly conducted using deterministic delayed differential equations, in which theusing parameters are considered be detercommonly conducted deterministic delayed to differential ministic (and often constant), including the force coefequations, in which the are to be ministic (and oftenfast constant), including the cutting cutting force coefequations, in the which the parameters parameters are considered considered to be deterdeterDue to development in the domain of ficients [2–7]. During the measurements of these coefficients, ministic (and including force ficients [2–7]. During measurements ofcutting these coefficients, ministic (and often often constant), including the cutting force coefcoefcommunication andconstant), antheongoing trend the of digitization and the average of the measured signal is and the ficients [2–7]. During the of coefficients, the average ofmanufacturing the measured signal is considered considered and the varivarificients [2–7]. During the measurements measurements of these these coefficients, digitalization, enterprises are facing important ance is attributed to the quality of the measurement. However, the average of the measured signal is considered and the ance is attributed to the quality of the measurement. However, the averageinof today’s the measured signal is considereda and the varivarichallenges market environments: continuing it is easy to see from the measured force signals that the cutting ance is attributed to the quality of the measurement. However, it is easy to see from the measured force signals that the cutting ance is attributed to the quality of the measurement. However, tendency towards reduction of product development times and forces are rarely constant or changing There it is see the force signals the forces areto rarely constant or In changing deterministically. There it is easy easy to see from from the measured measured forcedeterministically. signals that the cutting cutting shortened product lifecycles. addition, there isthat an increasing are effects that influence the force coefficients like forces are rarely constant or changing There are slow slow that influence theatcutting cutting forcetime coefficients like forces are rarely constant or changing deterministically. There demand ofeffects customization, being thedeterministically. same in a global the tool wear or the change in the machining temperature. The are slow effects that influence the cutting force coefficients like the tool wear or the change in the machining temperature. The are slow effects that influence the cutting force coefficients like competition with competitors all over the world. This trend, slow change of parameters are important for longer machining the tool wear or the change in the machining temperature. The slow change of parameters are important for longer machining the tool wear or the change in the machining temperature. The which is inducing the development from macro to micro processes, when appropriate choice of parameters help to slow change of are important for machining processes, when appropriate choice parameters help to avoid avoid slow change of parameters parameters are important for longer machining markets, results in diminished lot of sizes duelonger to augmenting chatter for the whole process. However, these slow variations processes, when appropriate choice of parameters help to avoid chatter for the whole process. However, these slow variations processes, when appropriate choice of parameters help to avoid product varieties (high-volume low-volume production) [1]. are easily characterized using aato proper series of measurements. chatter for the whole process. However, these slow variations are easily characterized using proper series of measurements. chatter for the whole process. However, these slow variations To cope with this augmenting variety as well as to be able to Furthermore, there are phenomena, both deterare easily characterized using aa proper series of measurements. Furthermore, there optimization are high high frequency phenomena, deterare easilypossible characterized usingfrequency proper series of identify potentials in measurements. theboth existing Furthermore, there high phenomena, both Furthermore, thereitare are high frequency frequency phenomena, both deterdeterproduction system, is important to have a precise knowledge Keywords: Assembly;but Design Family identification rupted turning), alsomethod; can occur due to the local
the and measurable parameters and are are computationally intensive, very of of the numerous numerous and hardly hardly measurable parameters and values are often often are computationally intensive, very sensitive sensitive of the the values of compromised by numerical difficulties. A workaround is that the numerous and hardly measurable parameters and are often compromised by numerical difficulties. A workaround that the numerous and hardly measurable parameters and areisoften one these speed as compromised by A is one approximates approximates these high highdifficulties. speed phenomena phenomena as aa stochastic stochastic compromised by numerical numerical difficulties. A workaround workaround is that that noise [11]. The main advantage of the noise process is, one approximates these high speed phenomena as a stochastic noiseapproximates [11]. The main advantage of the noise process is, that that it it one these high speed phenomena as a stochastic can be[11]. described with only aa small number of parameters, The main advantage of noise is, that it can described withand only small number ofprocess parameters, but noise Therange main advantage of the the noise process is,and/or thatbut it ofnoise thebe[11]. product characteristics manufactured this approach leads to stochastic differential equations, which can be described with only a small number of parameters, but this approach leads to stochastic differential equations, which can be described with only a small number parameters, assembled in this system. In this context, the of main challengebut in are complex problems. Through the analysis this approach to differential equations, which are mathematically mathematically complex problems. the this approach leads to stochastic stochastic differential equations, which modelling and leads analysis is now not only Through to cope withanalysis single of a set of orthogonal cutting tests this paper examines, if are mathematically complex problems. Through the analysis of a set of orthogonal cutting tests this paper examines, if this this are mathematically complex problems. Through the analysis products, a limited product range or existing product families, modelling is a suitable choice for investigation of machine tool of a set of orthogonal cutting tests this paper examines, if this modelling is a suitable choice for investigation of machine tool of a set of orthogonal cutting tests this paper examines, if this but also to be able to analyze and to compare products to define vibrations. modelling is a suitable choice for investigation of machine tool vibrations. modelling is a suitable choice for investigation of machine tool new product families. It can be observed that classical existing vibrations. vibrations. product families are regrouped in function of clients or features. However, assembly oriented product families are hardly to find. Nomenclature On the product family level, products differ mainly in two Nomenclature main characteristics: Nomenclature Nomenclature (i) the number of components and (ii) the typeF mechanical, electrical, cutting component, where ii = zz i components Fof cutting force force(e.g. component, where = x, x, y, y,electronical). i ¯ mean of the cutting force component F Classical methodologies considering mainly single i F component, ii = mean offorce the cutting force where component F¯ ii2 cutting cutting force component, where = x, x, y, y, zz products variance of the cutting force component ¯ or σ solitary, already existing product families 2 mean of cutting force component F variance of the cutting force component analyze the σ mean of the the cutting force component F¯ iiF,i 22F,i structure hσ chip thickness product on a physical level (components variance of h F,i chip thickness of the the cutting cutting force force component component level) which σ F,i variance causes difficulties regarding an efficient definition and hh chip chip thickness thickness comparison of different product families. Addressing this
2212-8271 © © 2018 The TheAuthors. Authors.Published Published by Elsevier by Elsevier Ltd. Ltd. 2212-8271 2018 The Authors. Published by Elsevier Ltd. license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an © open article under theInternational CC BY-NC-ND Peer-review underaccess the responsibility of the Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018). 2212-8271 © 2018 The Authors. Published by Elsevier Ltd. Peer-review under the responsibility of the International Scientific Committee of the Committee 8th CIRP Conference onCIRP High Performance Cutting 2018). Cutting 2212-8271 © 2018 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the International Scientific of the 8th Conference on High(HPC Performance 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under the responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018). (HPC 2018). Peer-reviewunder underresponsibility the responsibility ofscientific the International Scientific Committee of the 8th CIRP Conference Peer-review of the committee of the 28th CIRP Design Conference 2018. on High Performance Cutting (HPC 2018). 10.1016/j.procir.2018.08.229
Henrik T. Sykora et al. / Procedia CIRP 77 (2018) 94–97 Author name / Procedia CIRP 00 (2018) 000–000
2. Force measurement 2.1. Goal and measurement layout The main goal of the measurements conducted in this work is to show, that from modelling perspective it is a sufficient approximation to use a Gaussian random process to model the effects of high frequency phenomena in the cutting force. A further goal is to estimate the magnitude of the noise relative to the mean.The measurement layout is shown in Fig. 1. The measurement was conducted on an NCT EmR-610Ms milling machine, where the workpiece was clamped into the spindle, and the tool was fixed on the table. The cutting force was measured with a Kistler Dynamometer 9129AA and the data were acquired using a 5080A charge amplifier and four NI-9234 Input Modules in a NI cDAQ-9178 Chassis at 51200 Hz sampling rate.
PC Spindle
Workpiece
Cutting Tool
Feed
x
NI data aquisition module
y z
Charge amplifier
Dynamometer
Fig. 1. Measurement layout
The test were performed on a AL 2024-T351 workpiece, with a custom made tool with 5◦ cutting angle. During the tests a series of chip thicknesses, different workpiece lengths and cutting speeds were used as detailed in Table 1. The workpiece was a pipe with a diameter of 16 mm and had a wall thickness of 1.5 mm. The tests were conducted using exponentially decreasing chip thickness between 0.1 and 0.0005 mm, in 14 steps. At each chip thickness the cutting force was measured for 1 s and between each measured chip thickness there was a 0.1 s stop for separating the different parameters, while avoiding the cooling of the workpiece and tool. The parameters which are individual for each measurement are summarized in Table 1. There were 6 measurements for vc = 200 m/min and 4 measurements for vc = 100 m/min, 14 measurement points each, totalling of 140 measurement sections. The pipes on which the tests were conducted, had a length Lbefore before the measurement, and Lafter after the measurement.
Meas no. 1 2 3 4 5 6 7 8 9 10
95
Lbefore (mm) 116 110 89 68 47 26 49 32 23 14
Lafter (mm) 95 89 68 47 26 5 40 23 14 5
vc (m/min) 200 200 200 200 200 200 100 100 100 100
Table 1. Technological parameters of the tests
2.2. Measured signal Each measurement was conducted starting with a larger chip thickness (0.1 mm) and proceeding towards the smaller ones (until reaching 0.0005 mm). The typical form of a measured signal is shown in Fig. 2. At higher chip thickness, an exponentially decaying force signal was observed due to some thermal effects. This slow variation was compensated by fitting an exponential function shown in Eq. (1), and only the fast dynamics is analyzed around this curve: F(t) = exp (a t) + b.
(1)
In the case of smaller chip thicknesses, the noise decreases, however a sudden change can be observed: the intensity of the noise of the forces is significantly larger. This could refer to a stability loss due to the fact, that the cutting edge radius is comparable with the chip thickness, the parameters are reaching the region which is used in micro cutting (e.g. high precision hard turning). Furthermore, the nonlinear force characteristics became important [12] because the cutting force characteristics became steeper near zero chip thickness. In this region the physics of the machining differs from the classical turning: there’s more plastic deformation of the workpiece which is as significant as the material removal – if not more. When performing the statistical evaluation of the measured data, each measured segment corresponding to different chip thicknesses was handled separately.
250
Fx Fy Fz
200 Force (N)
2
150 100 50 0 3
6
9 time (s)
12
15
Fig. 2. A typical measurement signal during the conducted measurements
Author name /etProcedia CIRP 00 (2018) 000–000 Henrik T. Sykora al. / Procedia CIRP 77 (2018) 94–97
96
Fy
Fx
Fz
200
200
150
150
150
100
0.5 0.4 0.3 0.2 0.1 0.0 0.000
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0 0.000
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50 40 30 20 10 0 0.000
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0.5 0.4 0.3 0.2 0.1 0.0 0.000
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50 0.025
0.050 0.075 h (mm)
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0 0.000
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0.050 0.075 h (mm)
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0.5 0.4 0.3 0.2 0.1 0.0 0.000
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0.050 0.075 h (mm)
0.100
σF,z (N )
0.050 0.075 h (mm)
σF,y (N )
50 40 30 20 10 0 0.000
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σF,y /F¯y
σF,x (N )
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0 0.000
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σF,z /F¯z
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F¯z (N )
200 F¯y (N )
F¯x (N )
3
0.025
0.050 0.075 h (mm)
p
2.3. Analysis of the measured force
3. Results From figures 3 and 4 it can be concluded, that the modeling of deterministic and stochastic high frequency phenomenas in the cutting forces can be approximated by a Gaussian noise process. For large chip thickness, the distribution of the measured force is Gaussian: a Gaussian stochastic process can be superimposed on the mean force. Furthermore in Fig. 3, it can be observed that the intensity of the noise process relative to the
-2
0
2
4
0.4 0.3 0.2 0.1 0.0 -4
-2
F −F¯ σF
0
2
(a) Accepted as Gaussian
(b) Accepted as Gaussian
0.6 0.5 0.4 0.3 0.2 0.1 0.0 -4
0.3 0.2 0.1 0.0 -4
-2
0
4
F −F¯ σF
p
p
In Fig. 3, the statistical evaluation of the measured force is shown: the mean F¯ i and the standard deviation σF,i of the measured force components in directions i = x, y, z, and their ratio as the functions of the chip thickness h. The bright lines with different colors show the statistical properties of individual measurements and the corresponding darker lines show the mean statistics. The green circles and red crosses denote if the measured force signal is considered to have a Gaussian- or a non-Gaussian distribution, respectively. The gaussianity of the measured signals was determined by inspecting the distribution functions for each investigated chip thickness for every measurement conducted. In Fig. 4 the main types of the distribution functions are shown. The distributions are standardized to have zero mean and one as standard deviation. In Fig. 4a a typical Gaussian distributed force signal can be seen. However, in Fig. 4b, the distribution function is not perfectly Gaussian, but in practice this is still an acceptable approximation. In Fig. 4c and 4d, the nonlinear nature of the force characteristics or some deterministic resonance phenomena distorts the probability density function in a way, that it looses its Gaussian form [13].
0.4 0.3 0.2 0.1 0.0 -4
p
Fig. 3. Summary of the statistical properties of the measured signal: (blue) vc = 100 m/min, (brown) vc = 200 m/min
2
F −F¯ σF
(c) Rejected as Gaussian
4
-2
0
2
4
F −F¯ σF
(d) Rejected as Gaussian
Fig. 4. Examples for the probability distribution functions of the measured signals: (blue) standardized force distribution, (red) probability distribution function of standard normal distribution
mean tends to a constant value above h ≈ 0.025 mm. That is for conventional chip thickness, this noise can be considered as ¯ All in all, a multiplicative noise with the intensity: σF = σF. the use of a Gaussian force model for turning operations can be used, especially during the modelling of the roughing phase, where large chip thickness is used. 4. Conclusion In the present study, a number of measurements were conducted to show the stochastic nature of the cutting force. It was shown that the cutting force can be characterized with the use of a Gaussian force model with a multiplicative intensity with respect to the mean force (σ = 5%). This can be used to further improve the existing models for machine tool vibrations.
4
Henrik T. Sykora et al. / Procedia CIRP 77 (2018) 94–97 Author name / Procedia CIRP 00 (2018) 000–000
As it is shown in [14], the use of a stochastic force model can help to understand measurement difficulties in the chatter tests and further improve chatter detection using a Gaussian white noise process, or give an approximation of the resulting surface roughness even during stable cutting. Acknowledgements The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/20072013) ERC Advanced grant agreement No340889 and it was supported by the Hungarian Scientific Research Fund (OTKA FK-124462). References [1] Tobias, S.. Machine-tool Vibration. 1965. [2] Insperger, T., Mann, B.P., Surmann, T., St´ep´an, G.. On the chatter frequencies of milling processes with runout. International Journal of Machine Tools and Manufacture 2008;48(10):1081–1089. doi:10.1016/j.ijmachtools.2008.02.002. [3] Insperger, T., St´ep´an, G., Bayly, P., Mann, B.. Multiple chatter frequencies in milling processes. Journal of Sound and Vibration 2003;262(2):333–345. doi:10.1016/S0022-460X(02)01131-8. [4] Insperger, T.. Stability analysis of periodic delay-differential equations modeling machine tool chatter. Ph.D. thesis; 2002. URL: http://galilei.mm.bme.hu/ inspi/dissert.pdf. [5] Chełminski, K., H¨omberg, D., Rott, O.. On a thermomechanical milling model. Nonlinear Analysis: Real World Applications 2011;12(1):615–632. doi:10.1016/j.nonrwa.2010.07.005. [6] Insperger, T.. Full-discretization and semi-discretization for milling stability prediction: Some comments. International Journal of Machine Tools and Manufacture 2010;50(7):658–662. doi:10.1016/j.ijmachtools.2010.03.010. [7] Khasawneh, F.A., Munch, E.. Chatter detection in turning using persistent homology. Mechanical Systems and Signal Processing 2016;70-71:527– 541. doi:10.1016/j.ymssp.2015.09.046. [8] Gradiˇsek, J., Grabec, I., Siegert, S., Friedrich, R.. Stochastic Dynamics Of Metal Cutting: Bifurcation Phenomena In Turning. Mechanical Systems and Signal Processing 2002;16(5):831–840. doi:10.1006/mssp.2001.1403. [9] P´almai, Z., Csern´ak, G.. Chip formation as an oscillator during the turning process. Journal of Sound and Vibration 2009;326(3-5):809–820. doi:10.1016/j.jsv.2009.05.028. [10] Munoa, J., Beudaert, X., Dombovari, Z., Altintas, Y., Budak, E., Brecher, C., et al. Chatter suppression techniques in metal cutting. CIRP Annals 2016;65(2):785–808. doi:10.1016/j.cirp.2016.06.004. [11] Øksendal, B.. Stochastic Differential Equations. In: Stochastic Differential Equations. ISBN 978-3-540-04758-2; 2003,doi:10.1007/978-3-64214394-6. [12] Stepan, G., Dombovari, Z., Mu˜noa, J.. Identification of cutting force characteristics based on chatter experiments. CIRP Annals 2011;60(1):113– 116. doi:10.1016/j.cirp.2011.03.100. [13] Zhu, H.T.. Non-stationary response of a van der Pol-Duffing oscillator under Gaussian white noise. Meccanica 2017;52(4-5):833–847. doi:10.1007/s11012-016-0458-3. [14] Sykora, H.T., Bachrathy, D., Stepan, G.. A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning. In: Volume 8: 29th Conference on Mechanical Vibration and Noise. ASME. ISBN 978-0-7918-5822-6; 2017, p. V008T12A054. doi:10.1115/DETC2017-67900.
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8th 8th CIRP CIRP Conference Conference on on High High Performance Performance Cutting Cutting (HPC (HPC 2018) 2018) 8th CIRP Conference on High Performance Cutting (HPC 2018)
Gaussian Gaussian noise noise process process as as cutting cutting force force model model for for turning turning Gaussian28th noise process as cutting force model for turning a a a CIRP Design aConference, May 2018, Nantes,Stepan France a , Gabor a Henrik T. Sykora , Daniel Bachrathy a Budapest a Budapest
Henrik T. Sykoraa , Daniel Bachrathya , Gabor Stepana Henrik T. Sykoraa , Daniel Bachrathya , Gabor Stepana
University of Technology and Economics, Department of Applied Mechanics, M˝uegyetem rkp. 5, Budapest H1111, Hungary University of Technology and Economics, Department of Applied Mechanics, M˝uegyetem rkp. 5, Budapest H1111, Hungary ∗ Corresponding aa Budapest author. Tel.: +36-1-463-1235; E-mail address: [email protected] University of Technology Technology and Economics, Economics, Department of of Applied Applied Mechanics, Mechanics, M˝ M˝u uegyetem egyetem rkp. rkp. 5, H1111, Hungary ∗ Corresponding Budapest University of and Department 5, Budapest Budapest H1111, Hungary author. Tel.: +36-1-463-1235; E-mail address: [email protected] ∗∗ Corresponding author. Tel.: +36-1-463-1235; E-mail address: [email protected] Corresponding author. Tel.: +36-1-463-1235; E-mail address: [email protected]
A new methodology to analyze the functional and physical architecture of existing products for an assembly oriented product family identification
Abstract Abstract Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat Abstract Abstract As an approximation for the cutting force the applicability of noise process is based on analysis of measured As an approximation for the cutting d’Arts force et theMétiers, applicability of aa Gaussian Gaussian noise process is investigated investigated based on the the analysis of measured cutting cutting École Nationale Supérieure Arts et Métiers ParisTech, LCFC EAthe 4495, 4 Rue Augustin Fresnel, Metz 57078, France force signals. It is shown by force measurement in orthogonal turning process, that Gaussian distribution fits well to the histograms of As an approximation for force of noise investigated based the analysis of measured force It is shown bycutting force measurement in orthogonal turning process, that theis distribution to the of the the As an signals. approximation for the the cutting force the the applicability applicability of aa Gaussian Gaussian noise process process isGaussian investigated based on onfits the well analysis of histograms measured cutting cutting measured time histories. It is also shown, that the variance of the measured force signal can be ∼ 5% of the mean value, which is orders of force signals. It is shown by force measurement in orthogonal turning process, that the Gaussian distribution fits well to the histograms of measured timeIthistories. also measurement shown, that the variance of turning the measured can be distribution ∼ 5% of thefits mean is orders of force signals. is shown Itbyisforce in orthogonal process,force that signal the Gaussian wellvalue, to thewhich histograms of the the higher than the noise of the measurement system. *magnitude Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected] measured time histories. It is also shown, that the variance of the measured force signal can be ∼ 5% of the mean value, which is orders magnitude higher than the noise of the measurement system. measured time histories. It is also shown, that the variance of the measured force signal can be ∼ 5% of the mean value, which is orders of of © 2018 The Authors. Published by Elsevier Ltd. magnitude than the of measurement system. © 2018 The Thehigher Authors. Published bythe Elsevier Ltd. magnitude higher thanPublished the noise noise by of the measurement system. © 2018 Authors. Elsevier Ltd. Peer-review under the responsibility of the International Scientific Committee © 2018 The Authors. by Ltd. Peer-review under thePublished responsibility theBY-NC-ND International Scientific Committee of of the the 8th 8th CIRP CIRP Conference Conference on on High High Performance Performance Cutting Cutting © 2018 The Authors. Published by Elsevier Elsevier Ltd. This is2018). an open access article under theofCC license (https://creativecommons.org/licenses/by-nc-nd/4.0/) (HPC Peer-review under the responsibility of the International Scientific Committee of the 8th CIRP Conference on High Cutting (HPC 2018). Peer-review the responsibility of the International Scientific Scientific Committee of the 8thofCIRP on HighonPerformance Performance Cutting Selection andunder peer-review under responsibility of the International Committee the 8thConference CIRP Conference High Performance Abstract (HPC 2018). Cutting (HPC 2018). (HPC 2018). chatter, turning, noise, cutting force model Keywords: Keywords: chatter, turning, noise, cutting force model chatter, turning, force model InKeywords: today’s business the trend chatter, environment, turning, noise, noise, cutting cutting forcetowards model more product variety and customization is unbroken. Due to this development, the need of Keywords: agile and reconfigurable production systems emerged to cope with various products and product families. To design and optimize production systems as well as to choose the optimal product matches, product analysis methods arestochastic needed. Indeed, most of plane the known methods aim to ministic 1. ministic and and stochastic [8], [8], like like shear shear plane oscillation oscillation [9], [9], local local 1. Introduction Introduction analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and inhomogeneities in the material properties, rough surface of the ministic and stochastic [8], like shear plane oscillation [9], local 1. Introduction inhomogeneities in the material properties, rough surface of the ministic and stochastic [8], like shear plane oscillation [9], local 1. Introduction nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production workpiece, etc. which also affect the time characteristics of the In the field of manufacturing science machine tool vibrainhomogeneities in the material properties, rough surface of the workpiece, etc. which also affect the time characteristics of inhomogeneities in the material properties, rough surface the In the field of manufacturing science machine tool vibrasystem. A new methodology isproblems, proposed toespecially analyze existing products in view of their functional and physical architecture. The aim the is tostationcluster cutting force. These phenomena greatly influence tions are source of many during roughworkpiece, etc. which also affect the time characteristics of In the field of manufacturing science machine tool vibracutting force. These phenomena greatly the stationworkpiece, etc. whichlines alsoand affect the timeofinfluence characteristics of the the tions are many problems, especially during Inproducts the source field ofofmanufacturing science machine tool vibrathese in new assembly oriented product families for theroughoptimization of existing assembly the creation future reconfigurable ary forced vibrations, which are important when determining ing processes [1], where a large material removal rate is recutting force. These phenomena greatly influence the stationtions are source of many problems, especially during rougharyproducts forced which aresubassemblies important when determining cutting force. These phenomena greatly influence the stationing processes [1], aproblems, large material removal ratestructure is re- of the tions aresystems. source ofwhere many especially during roughassembly Based on Datum Flow Chain, the physical isvibrations, analyzed. Functional are identified, and the quality of manufactured product and when dequired. There are two main types of tool vibrations: ary forced vibrations, which are when determining processes [1], where aa large material rate the surface surface quality of the the manufactured product and when the deary forced vibrations, which are isimportant important when determining quired. There are is two main types of machine machine toolfunctional vibrations: ing processes [1], where large material removal rate is is rereaing functional analysis performed. Moreover, a removal hybrid and physical architecture graph (HyFPAG) the output which depicts tecting chatter [10]. chatter and forced vibrations. Chatter is an unfavorable cutthe surface quality of the manufactured product and when quired. There are two main types of machine tool vibrations: similarity between families by of providing supportcutto both, the production system and product designers. tecting chatter [10].planners surface quality of the manufactured product An andillustrative when dedechatter and forced vibrations. Chatter is an design unfavorable quired. There areproduct two main types machine tool vibrations: The modeling of frequency impose ting by aa self-induced and re[10]. chatter and forced vibrations. Chatter is an unfavorable example of a nail-clipper is used explain methodology. industrial case study twohigh product families phenomena of steering columns The chatter modeling ofonthe the high frequency phenomena imposeofaa tecting chatter [10]. ting phenomenon phenomenon caused by to self-induced oscillation andcutre- An tecting chatter and forcedcaused vibrations. Chatterthe is proposed anoscillation unfavorable cutgreater challenge. the element sults in surface quality and potentially damages the The of the high phenomena impose ting caused aa carried self-induced oscillation and rethyssenkrupp France isby then out to give a first industrial the proposed approach. greater challenge. For example, the finite finite element models models ofaa Theof modeling modeling ofFor theexample, high frequency frequency phenomena imposeof sults phenomenon in poor poorPresta surface quality and potentially damages the tool. ting phenomenon caused by self-induced oscillation andtool. re- evaluation the cutting process could trace this fast variation, but these Forced vibrations caused by the time varying cutting force: the ©sults 2017 The Authors. Published by Elsevier B.V. greater challenge. For example, the finite element models of in poor surface quality and potentially damages the tool. the cutting processFor could trace this fast variation, but these greater challenge. example, the finite element models of Forced caused by the varyingdamages cutting force: the sults in vibrations poor surface quality andtime potentially the tool. are computationally intensive, very sensitive of the values of variation of the cutting force can occur due to the periodically Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. the cutting process could trace this fast variation, but these Forced vibrations caused by the time varying cutting force: the are computationally intensive, of the but values of the cutting process could tracevery thissensitive fast variation, these variation of the cutting cantime occur due tocutting the periodically Forced vibrations causedforce by the varying force: the
changing size shape of chip (e.g.: during intervariation the cutting occur to periodically changing of size and shapeforce of the thecan chip (e.g.:due during milling, intervariation of theand cutting force can occur due to the themilling, periodically changes in changing size chip (e.g.: milling, interrupted turning), butshape also of canthe the local changes in changing size and and shape of theoccur chip due (e.g.:toduring during milling, interthe material properties over time. rupted turning), but can occur the material properties over rupted turning), but also also cantime. occur due due to to the the local local changes changes in in theoretical investigations the material properties over The theoretical investigations on machine machine tool tool vibrations vibrations are are theThe material properties over time. time.on commonly conducted using differential The investigations on tool are conducted using deterministic deterministic delayed differential The theoretical theoretical investigations on machine machinedelayed tool vibrations vibrations are 1.commonly Introduction equations, in which the parameters are considered to be detercommonly conducted using deterministic delayed differential equations, in which theusing parameters are considered be detercommonly conducted deterministic delayed to differential ministic (and often constant), including the force coefequations, in which the are to be ministic (and oftenfast constant), including the cutting cutting force coefequations, in the which the parameters parameters are considered considered to be deterdeterDue to development in the domain of ficients [2–7]. During the measurements of these coefficients, ministic (and including force ficients [2–7]. During measurements ofcutting these coefficients, ministic (and often often constant), including the cutting force coefcoefcommunication andconstant), antheongoing trend the of digitization and the average of the measured signal is and the ficients [2–7]. During the of coefficients, the average ofmanufacturing the measured signal is considered considered and the varivarificients [2–7]. During the measurements measurements of these these coefficients, digitalization, enterprises are facing important ance is attributed to the quality of the measurement. However, the average of the measured signal is considered and the ance is attributed to the quality of the measurement. However, the averageinof today’s the measured signal is considereda and the varivarichallenges market environments: continuing it is easy to see from the measured force signals that the cutting ance is attributed to the quality of the measurement. However, it is easy to see from the measured force signals that the cutting ance is attributed to the quality of the measurement. However, tendency towards reduction of product development times and forces are rarely constant or changing There it is see the force signals the forces areto rarely constant or In changing deterministically. There it is easy easy to see from from the measured measured forcedeterministically. signals that the cutting cutting shortened product lifecycles. addition, there isthat an increasing are effects that influence the force coefficients like forces are rarely constant or changing There are slow slow that influence theatcutting cutting forcetime coefficients like forces are rarely constant or changing deterministically. There demand ofeffects customization, being thedeterministically. same in a global the tool wear or the change in the machining temperature. The are slow effects that influence the cutting force coefficients like the tool wear or the change in the machining temperature. The are slow effects that influence the cutting force coefficients like competition with competitors all over the world. This trend, slow change of parameters are important for longer machining the tool wear or the change in the machining temperature. The slow change of parameters are important for longer machining the tool wear or the change in the machining temperature. The which is inducing the development from macro to micro processes, when appropriate choice of parameters help to slow change of are important for machining processes, when appropriate choice parameters help to avoid avoid slow change of parameters parameters are important for longer machining markets, results in diminished lot of sizes duelonger to augmenting chatter for the whole process. However, these slow variations processes, when appropriate choice of parameters help to avoid chatter for the whole process. However, these slow variations processes, when appropriate choice of parameters help to avoid product varieties (high-volume low-volume production) [1]. are easily characterized using aato proper series of measurements. chatter for the whole process. However, these slow variations are easily characterized using proper series of measurements. chatter for the whole process. However, these slow variations To cope with this augmenting variety as well as to be able to Furthermore, there are phenomena, both deterare easily characterized using aa proper series of measurements. Furthermore, there optimization are high high frequency phenomena, deterare easilypossible characterized usingfrequency proper series of identify potentials in measurements. theboth existing Furthermore, there high phenomena, both Furthermore, thereitare are high frequency frequency phenomena, both deterdeterproduction system, is important to have a precise knowledge Keywords: Assembly;but Design Family identification rupted turning), alsomethod; can occur due to the local
the and measurable parameters and are are computationally intensive, very of of the numerous numerous and hardly hardly measurable parameters and values are often often are computationally intensive, very sensitive sensitive of the the values of compromised by numerical difficulties. A workaround is that the numerous and hardly measurable parameters and are often compromised by numerical difficulties. A workaround that the numerous and hardly measurable parameters and areisoften one these speed as compromised by A is one approximates approximates these high highdifficulties. speed phenomena phenomena as aa stochastic stochastic compromised by numerical numerical difficulties. A workaround workaround is that that noise [11]. The main advantage of the noise process is, one approximates these high speed phenomena as a stochastic noiseapproximates [11]. The main advantage of the noise process is, that that it it one these high speed phenomena as a stochastic can be[11]. described with only aa small number of parameters, The main advantage of noise is, that it can described withand only small number ofprocess parameters, but noise Therange main advantage of the the noise process is,and/or thatbut it ofnoise thebe[11]. product characteristics manufactured this approach leads to stochastic differential equations, which can be described with only a small number of parameters, but this approach leads to stochastic differential equations, which can be described with only a small number parameters, assembled in this system. In this context, the of main challengebut in are complex problems. Through the analysis this approach to differential equations, which are mathematically mathematically complex problems. the this approach leads to stochastic stochastic differential equations, which modelling and leads analysis is now not only Through to cope withanalysis single of a set of orthogonal cutting tests this paper examines, if are mathematically complex problems. Through the analysis of a set of orthogonal cutting tests this paper examines, if this this are mathematically complex problems. Through the analysis products, a limited product range or existing product families, modelling is a suitable choice for investigation of machine tool of a set of orthogonal cutting tests this paper examines, if this modelling is a suitable choice for investigation of machine tool of a set of orthogonal cutting tests this paper examines, if this but also to be able to analyze and to compare products to define vibrations. modelling is a suitable choice for investigation of machine tool vibrations. modelling is a suitable choice for investigation of machine tool new product families. It can be observed that classical existing vibrations. vibrations. product families are regrouped in function of clients or features. However, assembly oriented product families are hardly to find. Nomenclature On the product family level, products differ mainly in two Nomenclature main characteristics: Nomenclature Nomenclature (i) the number of components and (ii) the typeF mechanical, electrical, cutting component, where ii = zz i components Fof cutting force force(e.g. component, where = x, x, y, y,electronical). i ¯ mean of the cutting force component F Classical methodologies considering mainly single i F component, ii = mean offorce the cutting force where component F¯ ii2 cutting cutting force component, where = x, x, y, y, zz products variance of the cutting force component ¯ or σ solitary, already existing product families 2 mean of cutting force component F variance of the cutting force component analyze the σ mean of the the cutting force component F¯ iiF,i 22F,i structure hσ chip thickness product on a physical level (components variance of h F,i chip thickness of the the cutting cutting force force component component level) which σ F,i variance causes difficulties regarding an efficient definition and hh chip chip thickness thickness comparison of different product families. Addressing this
2212-8271 © © 2018 The TheAuthors. Authors.Published Published by Elsevier by Elsevier Ltd. Ltd. 2212-8271 2018 The Authors. Published by Elsevier Ltd. license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an © open article under theInternational CC BY-NC-ND Peer-review underaccess the responsibility of the Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018). 2212-8271 © 2018 The Authors. Published by Elsevier Ltd. Peer-review under the responsibility of the International Scientific Committee of the Committee 8th CIRP Conference onCIRP High Performance Cutting 2018). Cutting 2212-8271 © 2018 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the International Scientific of the 8th Conference on High(HPC Performance 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under the responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018). (HPC 2018). Peer-reviewunder underresponsibility the responsibility ofscientific the International Scientific Committee of the 8th CIRP Conference Peer-review of the committee of the 28th CIRP Design Conference 2018. on High Performance Cutting (HPC 2018). 10.1016/j.procir.2018.08.229
Henrik T. Sykora et al. / Procedia CIRP 77 (2018) 94–97 Author name / Procedia CIRP 00 (2018) 000–000
2. Force measurement 2.1. Goal and measurement layout The main goal of the measurements conducted in this work is to show, that from modelling perspective it is a sufficient approximation to use a Gaussian random process to model the effects of high frequency phenomena in the cutting force. A further goal is to estimate the magnitude of the noise relative to the mean.The measurement layout is shown in Fig. 1. The measurement was conducted on an NCT EmR-610Ms milling machine, where the workpiece was clamped into the spindle, and the tool was fixed on the table. The cutting force was measured with a Kistler Dynamometer 9129AA and the data were acquired using a 5080A charge amplifier and four NI-9234 Input Modules in a NI cDAQ-9178 Chassis at 51200 Hz sampling rate.
PC Spindle
Workpiece
Cutting Tool
Feed
x
NI data aquisition module
y z
Charge amplifier
Dynamometer
Fig. 1. Measurement layout
The test were performed on a AL 2024-T351 workpiece, with a custom made tool with 5◦ cutting angle. During the tests a series of chip thicknesses, different workpiece lengths and cutting speeds were used as detailed in Table 1. The workpiece was a pipe with a diameter of 16 mm and had a wall thickness of 1.5 mm. The tests were conducted using exponentially decreasing chip thickness between 0.1 and 0.0005 mm, in 14 steps. At each chip thickness the cutting force was measured for 1 s and between each measured chip thickness there was a 0.1 s stop for separating the different parameters, while avoiding the cooling of the workpiece and tool. The parameters which are individual for each measurement are summarized in Table 1. There were 6 measurements for vc = 200 m/min and 4 measurements for vc = 100 m/min, 14 measurement points each, totalling of 140 measurement sections. The pipes on which the tests were conducted, had a length Lbefore before the measurement, and Lafter after the measurement.
Meas no. 1 2 3 4 5 6 7 8 9 10
95
Lbefore (mm) 116 110 89 68 47 26 49 32 23 14
Lafter (mm) 95 89 68 47 26 5 40 23 14 5
vc (m/min) 200 200 200 200 200 200 100 100 100 100
Table 1. Technological parameters of the tests
2.2. Measured signal Each measurement was conducted starting with a larger chip thickness (0.1 mm) and proceeding towards the smaller ones (until reaching 0.0005 mm). The typical form of a measured signal is shown in Fig. 2. At higher chip thickness, an exponentially decaying force signal was observed due to some thermal effects. This slow variation was compensated by fitting an exponential function shown in Eq. (1), and only the fast dynamics is analyzed around this curve: F(t) = exp (a t) + b.
(1)
In the case of smaller chip thicknesses, the noise decreases, however a sudden change can be observed: the intensity of the noise of the forces is significantly larger. This could refer to a stability loss due to the fact, that the cutting edge radius is comparable with the chip thickness, the parameters are reaching the region which is used in micro cutting (e.g. high precision hard turning). Furthermore, the nonlinear force characteristics became important [12] because the cutting force characteristics became steeper near zero chip thickness. In this region the physics of the machining differs from the classical turning: there’s more plastic deformation of the workpiece which is as significant as the material removal – if not more. When performing the statistical evaluation of the measured data, each measured segment corresponding to different chip thicknesses was handled separately.
250
Fx Fy Fz
200 Force (N)
2
150 100 50 0 3
6
9 time (s)
12
15
Fig. 2. A typical measurement signal during the conducted measurements
Author name /etProcedia CIRP 00 (2018) 000–000 Henrik T. Sykora al. / Procedia CIRP 77 (2018) 94–97
96
Fy
Fx
Fz
200
200
150
150
150
100
0.5 0.4 0.3 0.2 0.1 0.0 0.000
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0 0.000
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σF,z (N )
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σF,y (N )
50 40 30 20 10 0 0.000
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σF,y /F¯y
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0 0.000
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F¯z (N )
200 F¯y (N )
F¯x (N )
3
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0.050 0.075 h (mm)
p
2.3. Analysis of the measured force
3. Results From figures 3 and 4 it can be concluded, that the modeling of deterministic and stochastic high frequency phenomenas in the cutting forces can be approximated by a Gaussian noise process. For large chip thickness, the distribution of the measured force is Gaussian: a Gaussian stochastic process can be superimposed on the mean force. Furthermore in Fig. 3, it can be observed that the intensity of the noise process relative to the
-2
0
2
4
0.4 0.3 0.2 0.1 0.0 -4
-2
F −F¯ σF
0
2
(a) Accepted as Gaussian
(b) Accepted as Gaussian
0.6 0.5 0.4 0.3 0.2 0.1 0.0 -4
0.3 0.2 0.1 0.0 -4
-2
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4
F −F¯ σF
p
p
In Fig. 3, the statistical evaluation of the measured force is shown: the mean F¯ i and the standard deviation σF,i of the measured force components in directions i = x, y, z, and their ratio as the functions of the chip thickness h. The bright lines with different colors show the statistical properties of individual measurements and the corresponding darker lines show the mean statistics. The green circles and red crosses denote if the measured force signal is considered to have a Gaussian- or a non-Gaussian distribution, respectively. The gaussianity of the measured signals was determined by inspecting the distribution functions for each investigated chip thickness for every measurement conducted. In Fig. 4 the main types of the distribution functions are shown. The distributions are standardized to have zero mean and one as standard deviation. In Fig. 4a a typical Gaussian distributed force signal can be seen. However, in Fig. 4b, the distribution function is not perfectly Gaussian, but in practice this is still an acceptable approximation. In Fig. 4c and 4d, the nonlinear nature of the force characteristics or some deterministic resonance phenomena distorts the probability density function in a way, that it looses its Gaussian form [13].
0.4 0.3 0.2 0.1 0.0 -4
p
Fig. 3. Summary of the statistical properties of the measured signal: (blue) vc = 100 m/min, (brown) vc = 200 m/min
2
F −F¯ σF
(c) Rejected as Gaussian
4
-2
0
2
4
F −F¯ σF
(d) Rejected as Gaussian
Fig. 4. Examples for the probability distribution functions of the measured signals: (blue) standardized force distribution, (red) probability distribution function of standard normal distribution
mean tends to a constant value above h ≈ 0.025 mm. That is for conventional chip thickness, this noise can be considered as ¯ All in all, a multiplicative noise with the intensity: σF = σF. the use of a Gaussian force model for turning operations can be used, especially during the modelling of the roughing phase, where large chip thickness is used. 4. Conclusion In the present study, a number of measurements were conducted to show the stochastic nature of the cutting force. It was shown that the cutting force can be characterized with the use of a Gaussian force model with a multiplicative intensity with respect to the mean force (σ = 5%). This can be used to further improve the existing models for machine tool vibrations.
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Henrik T. Sykora et al. / Procedia CIRP 77 (2018) 94–97 Author name / Procedia CIRP 00 (2018) 000–000
As it is shown in [14], the use of a stochastic force model can help to understand measurement difficulties in the chatter tests and further improve chatter detection using a Gaussian white noise process, or give an approximation of the resulting surface roughness even during stable cutting. Acknowledgements The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/20072013) ERC Advanced grant agreement No340889 and it was supported by the Hungarian Scientific Research Fund (OTKA FK-124462). References [1] Tobias, S.. Machine-tool Vibration. 1965. [2] Insperger, T., Mann, B.P., Surmann, T., St´ep´an, G.. On the chatter frequencies of milling processes with runout. International Journal of Machine Tools and Manufacture 2008;48(10):1081–1089. doi:10.1016/j.ijmachtools.2008.02.002. [3] Insperger, T., St´ep´an, G., Bayly, P., Mann, B.. Multiple chatter frequencies in milling processes. Journal of Sound and Vibration 2003;262(2):333–345. doi:10.1016/S0022-460X(02)01131-8. [4] Insperger, T.. Stability analysis of periodic delay-differential equations modeling machine tool chatter. Ph.D. thesis; 2002. URL: http://galilei.mm.bme.hu/ inspi/dissert.pdf. [5] Chełminski, K., H¨omberg, D., Rott, O.. On a thermomechanical milling model. Nonlinear Analysis: Real World Applications 2011;12(1):615–632. doi:10.1016/j.nonrwa.2010.07.005. [6] Insperger, T.. Full-discretization and semi-discretization for milling stability prediction: Some comments. International Journal of Machine Tools and Manufacture 2010;50(7):658–662. doi:10.1016/j.ijmachtools.2010.03.010. [7] Khasawneh, F.A., Munch, E.. Chatter detection in turning using persistent homology. Mechanical Systems and Signal Processing 2016;70-71:527– 541. doi:10.1016/j.ymssp.2015.09.046. [8] Gradiˇsek, J., Grabec, I., Siegert, S., Friedrich, R.. Stochastic Dynamics Of Metal Cutting: Bifurcation Phenomena In Turning. Mechanical Systems and Signal Processing 2002;16(5):831–840. doi:10.1006/mssp.2001.1403. [9] P´almai, Z., Csern´ak, G.. Chip formation as an oscillator during the turning process. Journal of Sound and Vibration 2009;326(3-5):809–820. doi:10.1016/j.jsv.2009.05.028. [10] Munoa, J., Beudaert, X., Dombovari, Z., Altintas, Y., Budak, E., Brecher, C., et al. Chatter suppression techniques in metal cutting. CIRP Annals 2016;65(2):785–808. doi:10.1016/j.cirp.2016.06.004. [11] Øksendal, B.. Stochastic Differential Equations. In: Stochastic Differential Equations. ISBN 978-3-540-04758-2; 2003,doi:10.1007/978-3-64214394-6. [12] Stepan, G., Dombovari, Z., Mu˜noa, J.. Identification of cutting force characteristics based on chatter experiments. CIRP Annals 2011;60(1):113– 116. doi:10.1016/j.cirp.2011.03.100. [13] Zhu, H.T.. Non-stationary response of a van der Pol-Duffing oscillator under Gaussian white noise. Meccanica 2017;52(4-5):833–847. doi:10.1007/s11012-016-0458-3. [14] Sykora, H.T., Bachrathy, D., Stepan, G.. A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning. In: Volume 8: 29th Conference on Mechanical Vibration and Noise. ASME. ISBN 978-0-7918-5822-6; 2017, p. V008T12A054. doi:10.1115/DETC2017-67900.
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