NOVEL WORKPIECE CLAMPING METHOD FOR INCREASED MACHINING PERFORMANCE

ISSN 330-365 UDC/UDK 62.9.04.2-229.3:65.0.4 NOVEL WORKPIECE CLAMPING METHOD FOR INCREASED MACHINING PERFORMANCE Djordje Vukeli, Branko Tadi, Dragomir Miljani, Igor Budak, Petar M. Todorovi, Sasa Randjelovi, Branislav M. Jeremi Original sientifi paper Fixtures whih balane utting fores and torques by the frition fores generated on ontat surfaes of loating, lamping elements and workpiee surfaes are widespread in industrial pratie. Among other things, these frition ontats are haraterized by a ertain amount of interfae ompliane whih is a omplex funtion of maro- and mirogeometry of ontat pairs in the workpiee-fixture system, as well as the lamping and utting fores. Workpiee mahining errors are mostly the onsequene of that interfae ompliane. This paper investigates workpiee-fixture interfae ompliane in ases where lamping is performed using a standard, and speially designed lamping element. Theoretial onsiderations are presented, followed by results of experimental investigation. Considerable advantages of the speially designed lamping element ompared to its standard ounterpart are demonstrated by experiments. The results are a good starting point for a researh into optimization of speial fixture lamping elements and their wider industrial appliation. Keywords: fixture, lamping fore, ompliane, indenting Izvorni znanstveni članak Naprave kod kojih se sile i momenti nastali u proesu rezanja uravnotežuju silama trenja, nastalim na kontaktima elemenata za baziranje i stezanje s izratkom, su vrlo zastupljene u industriji. Spomenute kontakte, pored ostalog, karakterizira određena popustljivost veza koja je složena funkija makro i mikrogeometrije kontaktnih parova u sustavu izradak-naprava, sila stezanja i sila rezanja. Pogreške obrade uvelike su posljedia upravo popustljivosti spomenutih veza. U radu se razmatra popustljivost veza između elemenata za stezanje i izratka u slučajevima stezanja uređajem za stezanje s ravnim čelom i speijalno dizajniranog elementa za stezanje. Nakon teorijskih razmatranja izloženi su rezultati eksperimentalnih istraživanja. Rezultati ukazuju na značajne prednosti speijalno dizajniranog elementa za stezanje u odnosu na standardni oblik elementa za stezanje s ravnim čelom. Dobiveni rezultati otvaraju prostor za istraživanja u smislu optimizaije elemenata naprava za stezanje i mogućnosti njihove industrijske primjene. Keywords: naprava, sila stezanja, popustljivost, utiskivanje Introdution Appliation of new sientifi approahes to improve the level of knowledge and organization in prodution preparation setors not only has a onsiderable impat upon the final produt harateristis but also indiretly affet prodution osts and times of delivery. Manufaturing ompanies whih primarily fous on tehnologial and operational preparation of prodution, i.e. those that keep up to date with the tehnologial parameters and the results of tehnologial proesses, stand the best hanes of improving the ativities in the observed setors []. One of essential harateristis of modern prodution systems is the ability to manufature a variety of high-quality produts in the shortest possible time. Short time-to-market is a key instrument in providing market domination and higher profit margins. Job and small-bath prodution often take priority as ditated by the market demand for a variety of produts. All this demands development of a flexible, agile, manufaturing system whih is apable of meeting new prodution programs [2]. Owing to stringent market demands and intensive development of siene, equipment, and novel tehnologies, the level and trend of further development of mahining proesses in the metal utting industry depend on numerous fators. The fators whih most influene the quality of mahining proess are: type of blank, mahining tehnology, operations, sub-operations, mahine tools, utting tools, fixtures, measuring devies, et. [3, 4, 5, 6, 7]. In order to bring the mahining proess to a higher level, all these elements must be optimized. Within a number of fators whih influene output effets of manufaturing proess, mahining fixtures play a prominent role [8]. Fixture design optimization has been foused on by numerous investigations in previous years. DeMeter [9] used a rigid body fixture-workpiee model and the min-max load riterion for synthesis of optimal fixture layout and minimum lamp atuation intensity. Nonlinear optimization methods were used while negleting the elasti deformation of workpiee. Jeng et al. [0] presented a searh algorithm for the instant enter of motion, based on the orrelation between the utting fores and lamping moments. Based on the property of instant enter of motion, minimum lamping fore was estimated. Wu and Chan [] used geneti algorithm (GA) to determine the most statially stable fixture layout. They used a rigid body fixture-workpiee model and ignored elasti deformation of the workpiee due to lamping and mahining fores. Meyer and Liou [2] presented a methodology to generate the onfiguration of a fixture, whih was under dynami mahining fores. Linear programming was used to determine optimal loator positions and lamping fores. Wang et al. [3] developed an intelligent fixturing system to adjust the lamping fores adaptively to ahieve minimum deformation of the workpiee aording to utting fores. Linear stati finite element analysis (FEA) was used to find the workpiee deformation. Krishnakumar and Melkote [4] presented a GA-based disrete fixture layout optimization method to minimize the deformation of the workpiee under stati onditions. Tehnički vjesnik 9, 4(202), 837-846 837

Novel workpiee lamping method for inreased mahining performane They applied the GA to 2-D fixturing problems. Hurtado and Melkote [5] formulated a multi-objetive optimization model that defines minimum lamping loads to ahieve workpiee shape onformability and fixture stiffness goals for a workpiee subjeted to quasi-stati mahining fores. Vallapuzha et al. [6] investigated the use of spatial oordinates to represent loations of fixture elements in their fixture layout optimization model solved by GA. Amaral et al. [7] employed 3-2- loating method and developed an algorithm to automatially optimize fixture support, lamp loations, and lamping fores, to minimize workpiee deformation, subsequently inreasing mahining auray. Hamedi [8] presented a fixture design system whih integrated nonlinear FEA into the artifiial neural network (ANN) and GA. The GA-based program is used to searh for the optimal value of lamping fores with small deformation/stress in the omponent. Deng and Melkote [9] presented a modelbased framework for determining the minimum required lamping fore to ensure the dynami stability of a fixtured workpiee during mahining. Kaya [20] presented a GA-based ontinuous fixture layout optimization method. The optimization objetive was to searh for a 2-D fixture layout that minimized the maximum elasti deformation at different loations of the workpiee. Qin et al. [2] foused on the mathematial modelling and design optimization of lamping sequene for a deformable workpiee-fixture system to minimize the effet of lamping sequene on the workpiee mahining quality. Sanhez et al. [22] alulated the ontat load at the fixture-workpiee interfae using a simple and diret mathematial tool along with the FEA, whih simplified the deformation minimisation problem. They also asertained the interpolating funtions whih related the lamping position with respet to the load ontat in order to define valid lamping regions. Siebenaler and Melkote [23] presented a fixtureworkpiee model using FEA to investigate the influene of various parameters on workpiee deformation, inluding the ompliane of the fixture body, ontat frition, and mesh density. Tian et al. [24] presented an approah to optimized seletion of loating positions of workpiees and identifying feasible lamping regions that meet the requirements of the form-losure priniple for fixture layout. Liu et al. [25] proposed a method to optimize the fixture layout in the peripheral milling of a low-rigidity workpiee. This paper dealt with the optimization of the number and positions of loating elements restrited to the seondary loating surfae. Prabhaharan et al. [26] presented a fixture layout optimization method that used GA and ant olony algorithm (ACA) separately. The workpiee deformation was modelled using FEA for the problems of fixture layout optimization with the objetive of minimizing the dimensional and form errors. Asante [27] presented a model that ombines ontat elastiity with FEA to predit ontat loads and pressure distribution at the ontat region in a workpiee-fixture system. Chen et al. [28] presented a fixture layout design and lamping fore optimization proedure based on the GA and FEA. The optimization proedure was multi-objetive: minimizing the maximum deformation of the mahined surfaes and maximizing the uniformity of deformation. Prabhaharan et al. [29] optimized fixture layout for 2-D workpiee geometry with an objetive of minimizing the workpiee elasti deformation using ACA-based disrete and ontinuous fixture layout optimization methods. Dou et al. [30] presented the appliation of partile swarm optimization (PSO) algorithm to minimize the workpiee deformation. A PSO based approah is developed to optimize fixture layout through integrating Ansys parametri design language (APDL) of FEA to ompute the objetive funtion for a given fixture layout. Lu et al. [3] reated a ellular GA model of lamping fore determination as a multimodal funtion with a set of geometri and performane onstraints, to solve the global optimal lamping fores. Vishnupriyan et al. [32] optimized the fixture layout in order to minimize the mahining error onsidering both geometri error of loating elements and elasti deformation of workpiee. Both of these parameters were simultaneously optimised using a GA. Elasti deformation of workpiee under mahining loads was obtained by FEA. Zuperl et al. [33] developed an intelligent fixturing system, whih adaptively adjusts variable lamping fores to ahieve minimum elasti deformation of the workpiee aording to the utter position and the dynami utting fores. Review of available literature leads to the onlusion that workpiee mahining errors are mostly the result of inadequate fixture lamping. Unreliable lamping not only auses larger workpiee/lamping element interfae ompliane, but an ultimately lead to a omplete detahment of workpiee from its loating elements with disastrous onsequenes. Optimization of loating and lamping shemes - inluding the number, type, and layout of loating and lamping elements, and lamping fore magnitude an signifiantly redue workpiee deformations and inrease mahining auray, whih is espeially important in the ase of thin-walled workpiees with omplex geometry [34]. The lamping fores required to seure workpiee loation within given toleranes often vary during mahining proess, being the funtion of tool path and utting parameters. This is most typial of the mahining of omplex geometry workpiees on mahining entres. With this in mind, fixture design optimization gains ever more relevane. Fixture design optimization boils down to finding suh fixture layout whih shall minimize the workpiee elasti deformation and ontat deformations at points of ontat between workpiee and various fixture elements (loating and lamping elements, supporting elements, and other fixture elements). Minimization of deformations diretly redues mahining errors and inreases surfae quality. However, a question is posed whether it would be possible to deform narrow zones on the workpiee in the proess of lamping, in order to inrease produtivity while remaining within the set toleranes. The authors of this paper suggest that, onsidering modern utting regimes (high utting speeds, exeeding 000 m/min, high feed rates, sometimes over 000 mm/min, large hip ross setions and utting fores) speial attention should be paid to fixture design optimization whih would allow minimization of workpiee-fixture interfae ompliane. Therefore, investigation should be aimed at theoretial and experimental solutions whih allow reliable fixture designs. Reviewed in this paper are theoretial and 838 Tehnial Gazette 9, 4(202), 837-846

experimental results of optimization of fixture lamping elements regarding the redution of ompliane and inrease of tangential load apaity of workpiee-fixture interfae. Tangential load apaity of workpiee-fixture interfae is defined as the load apaity in the diretion normal to the lamping fore vetor. 2 Theoretial bakground of the proposed lamping method To balane utting fores and torques during the mahining proess, fixtures most often employ frition fores effetive at points of ontat between workpiee and loating and lamping elements (Fig. ). elements. This means that the workpiee shall be displaed from ABCD position into A B C D position. Displaement ξ, whih is the result of ompliane of the ontat zones, diretly orresponds to workpiee mahining error e.g., the mahining error of y f dimension (ξ >T 2 ). The interfae ompliane is due to fore, F y, whih auses tangential stresses in y axis diretion at ontats in the neighbourhood of point H, along support AC, and on loating element (ABCD). The resulting deformation is diretly proportional to stress magnitude. The sum of these loal deformations equals interfae ompliane and diretly influenes the workpiee mahining error. Analytial desription of the hange of tangential, F t, and radial, F r, omponents of utting fore with time are well established and an be found in literature [35]. Frition fores, F f, F fs, F fb, are the omplex funtions of: ontat surfae maro - and mirogeometry, material harateristis of ontat pairs, lamping fore, F, and interfae ompliane, ξ. For lamping and loating fixture elements there holds the following relationship: F t = f (G, M, F n, ξ ). (3) Figure An example of balaning utting fores with frition fores Shown in Fig. is an example of milling of a omplex ontour K. The diretions of tangential, F t, and radial utting fore, F r, vary during mahining along the ontour, K. Equation of stati workpiee equilibrium in y axis diretion is: F f + F fs + F fb F t osφ - F r sinφ, () where: F f is frition fore between lamping element (neighbourhood of point H) and workpiee; F fs is frition fore between workpiee and loating element in AC diretion; F fb is frition fore between workpiee and base loating element; F t is tangential omponent of utting fore; F r is radial omponent of utting fore; φ is urrent angle of ontour whih defines tool path. If, in the general ase, at point G holds: F t osφ - F r sinφ = F y. (2) The equilibrium shall be maintained only by allowing ertain displaement of workpiee within the ontat zones between workpiee and lamping and loating where: G is the set of parameters whih define the ontat maro- and miro geometry; M is the set of parameters whih define material harateristis of the ontat pair; F n is the normal interfae load (as the funtion of lamping fore) and ξ is the interfae ompliane. Considering suh large number of parameters whih define the ontat miro geometry (surfae roughness) and parameters whih define material properties of ontat pairs (hardness, strength, hemial omposition), as well as the omplexity of frition and wear mehanisms, the authors maintain that analytial relationship, F t = f (G, M, F n, ξ ), is of little use for our purpose. For that reason, the relationships required by this investigation were established experimentally, as desribed in detail in the following setion. If the frition fores, F f, F fs, F fb, are experimentally determined under speified onditions for a wider interval of lamping fore values, then, based on a large quantity of experimental data, it is possible to form regression equations in the form of F t = f (G, M, F n, ξ ). Therefore, it is possible to form regression equations whih represent dependene of frition fores on the normal load and tangential ompliane, i.e., tangential stiffness of ontat. In this way, key prerequisites for determination of mahining error are made available. In other words, experimentally obtained funtions allow modelling of workpiee behaviour in fixture as well as realisti estimation of workpiee mahining error for partiular dimensions, prior to physial mahining. With this in mind, two types of elements were experimentally investigated whih an be used for lamping as well as for loating purposes. Shown in Fig. 2 are maro geometries of a standard lamping element and a speially designed lamping element. Standard lamping element was seleted as representative of the onventional lamping method. On the other hand, the speially designed lamping element is a stepped ylinder with a round utting tool insert mounted on its tip, and is used in this experiment to Tehnički vjesnik 9, 4(202), 837-846 839

Novel workpiee lamping method for inreased mahining performane quantify the differenes between tangential interfae omplianes using the standard and proposed lamping element. implies that the shear within the roughness profile or, eventually, full material, takes plae over the entire irumferene of the wedge-profiled ring. The lamping method proposed in this paper is based on the hypothesis that the load apaity of lamping element/workpiee interfae an be signifiantly inreased by allowing the lamping element to loally deform a narrow zone on the workpiee surfae. Considering previous disussion, suh small loal deformations, in the vast majority of ases, do not ompromise workpiee aesthetis. As proven by experiments in this investigation, loal deformations are small even in the ase of large lamping fores, and their order of magnitude is assessed at ten mirons. 3 Experimental investigation Experimental investigation inluded measurements of load apaity for tangential fore, F t, and interfae ompliane,, between the lamping element and test inserts whih represented workpiee material. Two types of lamping elements were used in experiment a standard lamping element and a speially designed, round insert lamping element. The experiment enompassed: Variations of lamping fore, F, within 400 N to 3.000 N interval, Variations of tangential load, F t, on the lamping element/test insert interfae, within 5 N to 2500 N interval, Monitoring of interfae ompliane,, expressed as displaement in the ontat zone. Figure 2 Maro geometries of a standard lamping element and a speially designed, round insert lamping element. The idea behind the proposed round insert lamping element (Fig. 2b) is that it should provide lower workpiee-fixture interfae ompliane ompared to the standard lamping element (Fig. 2a). It is supposed that, while lamping fore F is ative (Fig. 2b) the round insert indents the workpiee. The hardness of the round insert is muh higher than that of the workpiee, sine it is made of hard metal. Thus, round insert is indented into the workpiee over a wedge-profiled ring with a relatively large irumferene. The depth of indent largely depends on the magnitude of lamping fore. Compliane of round insert/workpiee interfae under tangential load is predominantly the funtion of the depth of indent of round insert into workpiee material. Depending on the lamping fore, round insert shall penetrate workpiee material to the depth of z, relative to mean entre line roughness, over the entire irumferene. The shear within the roughness profile height or regular material, under tangential fore, F t, ours in the neighbourhood of ontat ars AB and CD. Bearing in mind that the depth of indent is relatively small, there follows R R 2, whih Experiments were performed under stati interfae loads, using the following measurement equipment: Speially designed and manufatured devie whose operating sheme is shown in Fig. 3. Photo image of the devie is given in Fig. 4. The devie is mehanial, using a lever mehanism and alibrated weights to lamp test inserts with the standard and round insert lamping elements, at speified values of lamping fore, F. The devie also allows users to simulate tangential load, F t, while monitoring the orresponding interfae ompliane,. Dial indiators of displaement with auray of 0,0 mm. In order to enhane the auray of measurement, these instruments were used to monitor displaements within the lamping element/test insert interfae zone, amplified by 22,5 times. In this way, it was possible to monitor displaements as small as 0 4 mm, using geometri relations given in Fig. 3. Mirosope and surfae roughness measurement devies (Talysurf 6) were used to measure width and depth of indent marks left by the round insert lamping element (Fig. 7). Test lever is supported by a tapered roller bearing, along the axis x, whih runs through the entre of masses (Fig. 3). The tapered roller bearing allows rotation of the test lever about point O, in the x-y plane. Contat between either standard or round insert lamping element and test 840 Tehnial Gazette 9, 4(202), 837-846

insert, representing workpiee material, is maintained by a onstant fore, F. The lamping is performed at point O, i.e., lamping fore vetor runs through O. Relative to the axis of revolution of test lever, point O is displaed by e in the diretion of y axis. Clamping fore, F, is varied using a speially designed lever mehanism and alibrated weights. One lamping is established, fore F t is applied on the test lever at point A, at a distane y o from the lever pivotal point, and the resulting displaement,, is reorded. Fore, F t, is also applied by a speially designed system of levers and alibrated weights, whih allows its periodi, inremental inrease from minimum to maximum. In this way, a series of data pairs for F t and were obtained for both lamping element geometries and eah value of simulated lamping fore, F, and displaement. Fore F was used to simulate the lamping fore, fore F t represents the tangential load apaity of test insert/lamping element interfae, while the displaement,, is indiretly indiative of interfae ompliane. Based on the displaement, it is possible to alulate real interfae ompliane. Measuring devie (Fig. 4) is designed for extreme stability. All deformations (deformations of test lever, and other levers of measuring system, as well as the deformations of lamping element) an be disregarded in omparison with test insert/interfae ompliane. In addition, the following should be noted regarding the measuring devie used in this experiment: it provides lamping with various lamping fores; guiding auray of lamping element arrier (Fig. 4) is higher than 5 0 4 mm, whih, onsidering interfae ompliane values, allows reliable measurements; bearing supports of test lever and other levers are high-auray roller bearings with small rolling frition fator; the tapered roller bearing supporting the test lever features small rolling frition fator. To alulate the frition torque for this bearing, experimental data provided by the manufaturer were used. Frition torques were alulated for all other bearings and inluded into load apaity budgets. Figure 3 Operating sheme of the devie for measurement of test insert/lamping element interfae ompliane and load apaity. Based on geometri relationships (Fig. 3) and stati equilibrium onditions for the test lever, there follow the values of interfae load apaity, F t, and ompliane,, at point O, that is, interfae ompliane,, within the lamping zone. Based on this, follows: F t = (F t y 0 M t )/e, (4) = (e )/y 0, (5) where: F t interfae load apaity; F t interfae load at point A; M t frition torque in tapered roller bearing, e distane from lamping point to test lever axis of revolution; y 0 distane between point of attak of fore F t, and axis of revolution; interfae ompliane for test insert and lamping element at point O (Fig. 3); displaement of test lever along x axis, at point A. Figure 4 Photo image of the devie used for measuring load apaity and ompliane of test insert/lamping element interfae. 4 Results Experimental investigation was onduted on test inserts made of C45E annealed steel, with tensile strength of 70 MPa, hardness of 208 HB, and the following hemial omposition: 0,44 %C, 0,8 %Si, 0,27 %Mn, 0,0 %Si, and <0,00 %P. Test inserts were of the following dimensions: 25 30 50 mm. The standard lamping element was made of arburized steel 6MnCr5 with 56 HRC hardness, and hemial omposition:,5 % Mn, 0,95 %Cr, 0,035 %P, 0,035 %S, 0,6 %C, and <0,4 %Si. Speially designed round insert lamping element was made of hard steel, P20. Surfae roughness of Tehnički vjesnik 9, 4(202), 837-846 84

Novel workpiee lamping method for inreased mahining performane interfae between test insert and lamping element featured the following parameters: R a = 0,37 0,39 µm, and R max = 4,6 5,3 µm. Results of experimental investigation are presented in Tab.. Statistial analysis of experimental data resulted in regression equations whih desribe the dependene of frition fore (tangential fore) F t on lamping fore, F and interfae ompliane,, between lamping element and test insert (whih simulates workpiee material). Those regression equations and the orresponding oeffiients of orrelation R are given in Tab. 2. Statistial analysis of experimental data presented in Tab. was performed in Statistia 8. Presented in Fig. 5a and Fig. 5b are diagrams whih show dependene of frition fore (tangential fore), F t on interfae ompliane,, in ase of various lamping fores, F, using standard and round insert lamping elements. Table Results of experimental investigation for round insert lamping element F =400 N F =640 N F =800 N F =2900 N F =4500 N F =5700 N F =7000 N F =9000 N F =.000 N F =3.000 N F t F t F t F t F t F t F t F t F t F t / mm / N / mm / N / mm / N / mm / N / mm / N / mm / N / mm / N / mm / N / mm / N / mm / N 0 28, 0 59,4 0 73,3 0 5,5 0 28,7 0 23,84 0 296,9 0 257,5 0 27,9 0 78,3 0,0006 46, 0,0003 77,4 0,00 27,7 0,0003 05,9 0,0003 83, 0,000 322,6 0,000 405,8 0,000 366,3 0,000 326,7 0,000 287, 0,00 64,2 0,0006 95,4 0,0057 82, 0,0006 60,2 0,0006 237,6 0,0006 43,5 0,0006 54,5 0,0003 475, 0,0003 435,5 0,000 395,9 0,05 80,2 0,0009 3,4 0,054 236,4 0,007 24,6 0,00 292,0 0,00 540,2 0,00 623,4 0,0009 583,9 0,0006 544,4 0,0003 504,8 / / 0,00 3,5 0,0296 290,9 0,0057 269, 0,004 346,4 0,0034 649, 0,0034 732,2 0,0028 692,7 0,0009 653, 0,00 63,5 / / 0,007 49,5 0,0483 345,3 0,04 323,5 0,0097 400,7 0,0085 757,8 0,008 84,0 0,0046 80,6 0,00 76,9 0,004 722,4 / / 0,0034 67,5 0,05 346,2 0,099 377,9 0,048 455,2 0,048 866,7 0,03 949,9 0,008 90,4 0,00 870,8 0,0023 83,3 / / 0,0057 85,5 / / 0,0296 432,2 0,0227 509,6 0,0227 975,6 0,07 058,6 0,025 09,2 0,003 979,6 0,004 940,0 / / 0,0097 203,6 / / 0,0398 486,7 0,033 564,0 0,038 084,3 0,0227 67,5 0,07 28, 0,007 088,5 0,0074 048,9 / / 0,0256 22,5 / / 0,05 54, 0,0403 68,5 0,0539 93,2 0,0267 276,3 0,0222 236,8 0,0023 97,2 0,008 57,6 / / 0,05 24,3 / / / 0,05 672,8 / / 0,033 385, 0,0284 345,7 0,005 306, 0,037 266,5 / / / / / / / / / / / / 0,042 493,9 0,0324 454,5 0,0085 44,9 0,076 375,3 / / / / / / / / / / / / / / 0,0409 563,3 0,09 523,7 0,0227 484, / / / / / / / / / / / / / / 0,0494 672, 0,048 632,5 0,025 592,9 / / / / / / / / / / / / / / / / 0,076 74,3 0,0296 70,7 / / / / / / / / / / / / / / / / 0,026 850, 0,033 80,5 / / / / / / / / / / / / / / / / 0,0273 958,9 0,0369 99,4 / / / / / / / / / / / / / / / / 0,0335 2067,8 0,0403 2028,2 / / / / / / / / / / / / / / / / 0,0392 276,6 0,0454 236,9 / / / / / / / / / / / / / / / / 0,047 2285,5 0,05 2245,9 Table 2 Regression equations desribing dependeny of frition fore (tangential fore) on the lamping fore and test insert/lamping element interfae ompliane for two types of lamping elements Coeffiients of Clamping element Regression equation orrelation R Round insert F t = 94265,3 ξ + 0,04204 F + 99435,53 ξ,052493 + 82,3460 (ξ F ) /2 0,970 Standard F t = 8245,90 ξ + 0,035662 F 52,9507 ξ 0,000872 + 63,773 (ξ F ) /2 0,946 Figure 5 Dependene of frition fore (tangential fore) F t, on interfae ompliane, for various lamping fores a) standard lamping element, and b) round insert lamping element 842 Tehnial Gazette 9, 4(202), 837-846

5 Dissusion Based on theoretial onsiderations and results of experimental investigation, it is possible to onlude that load apaity and interfae ompliane of tangentially loaded ontats represent a very omplex matter. Generally, experimental results indiate that lamping by speially designed, round insert lamping elements yields higher load apaity ompared to the standard ones. Within the entire interval of load values (Fig. 5) round insert lamping element shows signifiantly higher load apaity and lower interfae ompliane ompared to its standard ounterpart. The advantage is notieable at both lower and higher loads, as learly shown in Fig. 6. Integration of regression equations (Tab. 2) over a partiular interval of lamping fore values, yields the P indiator, whih quantifies the advantage of round insert lamping element over its standard ounterpart: P F2 0, 05 F 0 f ( F, )df d F2 2 2 F F2 0, 05 F 0 2 f ( F, )df d f ( F, )df d 00 %, where: F, F 2 lamping fore intervals for whih P is determined; f (F, ξ ) - regression funtion (Tab. 2) whih defines the dependene of frition fore (tangential interfae load apaity) on the lamping fore and interfae ompliane in the ase of round insert lamping element; f 2 (F, ξ ) - regression funtion (Tab. 2) whih defines the dependene of frition fore (tangential interfae load apaity) on the lamping fore and interfae ompliane in the ase of standard lamping element. Figure 6 3D diagram showing dependene of frition fore (tangential fore) F t, on interfae ompliane, and lamping fore F, for standard and round insert lamping elements, based on regression equations from Tab. 2 (6) Aording to equation (6) there follows: For the lamping fore range F = 400 800 N, the round insert lamping element provides an average load apaity inrease of 43,5 %, due to larger frition fore on the test insert. This is espeially important bearing in mind that it is ahieved with small lamping fores and small loal deformations of workpiee. For the lamping fore range F =9000 3.000 N, the round insert lamping element provides an average load apaity inrease of 22,8 %, due to larger frition fore on the test insert. Again, this is important onsidering that the inrease is ahieved under large utting fores. Over the entire lamping fore interval, F = 400 3.000 N, the round insert lamping element provides an average load apaity inrease of 24,2 %, due to larger frition fore on the test insert. These baks up the laim that the round insert lamping element an be effiiently used regardless of the lamping fore order of magnitude. Of speial importane are indent marks left on the test insert by the round insert lamping element. Shown in Tab. 3 are depths of indent marks left by round insert lamping element for the appropriate lamping fore. Photo image and topography with samples of depth of indent marks are shown in Fig. 7. Table 3 Depths of indent marks produed by round insert lamping element and appropriate lamping fore Clamping fore F / N Depth of indent z / µm 400 3, 640 3,0 800 4,5 2900 5, 4500 7,2 5700 8,5 7000 9,0 9000 0,7.000 2,3 3.000 4,0 Based on Table 3 and Fig. 7 it an be onluded that the depths of indent marks are low. For example, lamping fore of 2900 N yields plasti deformation of just 5 µm, whih approximately equals the maximum height of the roughness profile for that sample. Similarly, the depth of indent of approximately 2 µm orresponds to the lamping fore of F =.000 N. Based on this, one onludes that high load apaity an be ahieved by allowing the round insert lamping element to penetrate workpiee approximately to the maximum depth of roughness profile. This onfirms the initial hypotheses about the pratial appliability of speially designed lamping or loating elements. In a majority of ases suh elements do not ompromise workpiee aesthetis, while providing muh larger load apaity and smaller workpiee/fixture interfae ompliane. Tehnički vjesnik 9, 4(202), 837-846 843

Novel workpiee lamping method for inreased mahining performane 6 Conlusion Figure 7 Photo image and samples of depths of indent marks left by round insert lamping element There are numerous fats whih underpin the laim that the proposed method of loating and lamping shall also perform satisfatorily under dynami utting fores. Speially designed loating and lamping elements an be made of high-quality tool materials (hard metal). It is ommon knowledge that, in real mahining onditions, modern tools are exposed to far greater relative speeds, wear, and geometry hange than the lamping and loating elements. Due to the effet of dynami utting fores, the workpiee osillates at speeds the magnitude of 00 mm/min, relative to lamping and loating elements. From the tribologial aspet onsidering the possibility of a signifiant drop in frition fator, hanges in material struture, heating, et. suh small speeds of osillation at the workpiee/fixture interfae do not represent a problem. Namely, they are aused by lowfrequeny dynami utting fores. It is also worth noting that manufaturers of modular fixtures offer ready-made lamping and loating elements whih are apable of sustaining similar dynami loads and also funtion on the similar priniple. Bearing in mind this fat, it is reasonable to suppose that ompared to the results obtained for testing under stati onditions the dynami loads will not ause any signifiant ompliane of the interfae between workpiee and the speially designed loating and lamping elements. Notwithstanding ertain deterioration of their load apaity, the results assure us that the proposed loating and lamping elements shall perform better than the standard lamping elements even under dynami loads. Based on the matter presented in this paper, the following onlusions an be drawn: Whenever a lamping element is used to balane the utting fore omponent whih ats orthogonally to the diretion of lamping fore vetor, there ours ompliane to a ertain extent. Interfae ompliane results in workpiee displaement relative to loating surfaes. Suh displaement is the ause of workpiee mahining error. Depending on the displaement, this error an exeed the designated tolerane. Workpiee is allowed a ertain amount of displaement in the fixture. The displaement depends on the magnitude, diretion, and sense of utting fore, as well as on the ompliane of interfae between workpiee and workpiee lamping and loating elements. It means that, within the fixture, workpiee maintains only a virtual balane. In the majority of ases, standard fixture elements (srew lamps, strap lamps, et.) used for lamping, balane utting fores with frition fores. Frition fores are generated at ontat surfaes - interfaes between lamping elements and workpiee. In this paper, lamping proess was simulated using two types of lamping elements the standard and the round insert lamping element. The investigation showed that the standard lamping element, whih is universally present in pratie, exhibits signifiantly lower load apaity ompared to the speially designed, round insert lamping element. Based on experimental results, it follows that, over a wide range of lamping fores, the speially designed lamping element an inrease workpiee/fixture load apaity and diminish interfae ompliane. This is espeially true for smaller lamping fores whih is essential for lamping workpiees of small stiffness. Considering small widths and depths of indent marks whih are the result of lamping, the proposed method of workpiee lamping and loating an be effiiently applied in design of lamping and loating elements. Design of lamping elements based on the proposed priniple, essentially employs hard metal inserts and standard lamping and loating elements (srew lamp, strap lamp, support element), whih is simple and feasible from the tehnial point of view. The authors think that the design and experimental testing of novel solutions of loating and lamping elements under dynami loads represents an up-to-date topi. With this in mind, future work shall inlude development and design of a speial devie to allow measurement of loads and ompliane of interfae between workpiee and differently designed loating and lamping fixture elements under various dynami loads. In this ase, real workpiee would be replaed by a test insert designed either as stiff or thin-walled omponent and made of various materials. This should provide us with the testing platform required for further investigation. 844 Tehnial Gazette 9, 4(202), 837-846

Finally, the authors maintain that there is a wide area of improvement in fixture design regarding the interfae ompliane of ontat surfaes loaded orthogonally relative to lamping fore. In that respet, this paper represents a small step towards the goal. Aknowledgement This researh was supported by the Ministry of Eduation, Siene and Tehnologial Development of the Republi of Serbia. 7 Referenes [] Simunovi, G.; Bali, J.; Sari, T.; Simunovi, K.; Luji, R; Svalina, I. Comparison of the tehnologial time predition models. // Strojarstvo. 52, 2(200), pp. 37-45. [2] Sari, T.; Simunovi, G.; Luji, R. Researhing and designing of hardware and software supports for an eduational flexible ell. // Tehniki Vjesnik - Tehnial Gazette. 5, 3(2008), pp. 2-28. [3] Vukeli, D.; Ostoji, G.; Stankovski, S.; Lazarevi, M.; Tadi, B.; Hodoli, J.; Simeunovi, N. Mahining fixture assembly/disassembly in RFID environment. // Assembly Automation. 3, (20), pp. 62-68. [4] Jurkovi, Z.; Cukor, G.; Andrejak, I. 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Deformation ontrol through fixture layout design and lamping fore optimization. // International Journal of Advaned Manufaturing Tehnology. 38, 9-0(2008), pp. 860-867. [29] Prabhaharan, G.; Padmanaban, K.P.; Krishnakumar, R. Mahining fixture layout optimization using FEM and evolutionary tehniques. // International Journal of Advaned Manufaturing Tehnology. 32, -2(2007), pp. 090-03. [30] Dou, J.; Wang, X.; Wang, L. Mahining Fixture Layout Optimization Using Partile Swarm Optimization Algorithm. // 4th International Seminar on Modern Cutting and Measurement Engineering / Editors: Xin J; Zhu L; Wang Z., Beijing, China, 0-2 Deember, 20, art. no. 79970S. Tehnički vjesnik 9, 4(202), 837-846 845

Novel workpiee lamping method for inreased mahining performane [3] Lu, Y. M.; Qin, G.H.; Li, M. A Cellular Geneti Algorithm Based Optimization of Clamping Fores for Fixture Design. // Advaned Siene Letters. 4, 6-7(20), pp. 2342-2346. [32] Vishnupriyan, S.; Majumder, M.C.; Ramahandran, K.P. Optimal fixture parameters onsidering loator errors. // International Journal of Prodution Researh, 49, 2(20), pp. 6343-636. [33] Zuperl, U.; Cus, F; Vukeli, D. Variable lamping fore ontrol for an intelligent fixturing. // Journal of Prodution Engineering. 4, (20), pp. 9-22. [34] Reibenshuh, M; Cus, F; Zuperl, U. Turning of high quality aluminium alloys with minimum osts. // Tehniki vjesnik - Tehnial Gazette. 8, 3(20), pp. 363-368. [35] Tadi, B.; Vukeli, D.; Hodoli, J.; Mitrovi, S.; Eri, M. Conservative-Fore-Controlled Feed Drive System for Down Milling. // Strojniski vestnik - Journal of Mehanial Engineering. 57, 5(20), pp. 425-439. Authors' addresses Dr. S. Djordje Vukeli University of Novi Sad Faulty of Tehnial Sienes Department for Prodution Engineering Trg Dositeja Obradovia 6 2000 Novi Sad, Serbia E-mail: vukeli@uns.a.rs Dr. S. Branko Tadi University of Kragujeva Faulty of Engineering Department for Prodution Engineering Sestre Janji 6 34000 Kragujeva, Serbia Mr. Dragomir Miljani Metalik DOO Trebješka 6/26 8400 Niksi, Montenegro Dr. S. Igor Budak University of Novi Sad Faulty of Tehnial Sienes Department for Prodution Engineering Trg Dositeja Obradovia 6 2000 Novi Sad, Serbia Dr. S. Petar M. Todorovi University of Kragujeva Faulty of Engineering Department for Prodution Engineering Sestre Janji 6 34000 Kragujeva, Serbia MS. Sasa Randjelovi University of Kragujeva Faulty of Engineering Department for Prodution Engineering Sestre Janji 6 34000 Kragujeva, Serbia Dr. S. Branislav M. Jeremi University of Kragujeva Faulty of Engineering Department for Prodution Engineering Sestre Janji 6 34000 Kragujeva, Serbia 846 Tehnial Gazette 9, 4(202), 837-846