OPTIMIZATION OF CUTTING CONDITIONS WHEN FIVE AXIS MILLING USING BALL NOSE END MILLS. THEORETICAL STUDY

Transcription

1 Proeedings in Manufaturing Systems, Vol. 5 (010), No. ISSN OPTIMIZATION OF CUTTING CONDITIONS WHEN FIVE AXIS MILLING USING BALL NOSE END MILLS. THEORETICAL STUDY Vlad DICIUC 1, Mirea LOBONŢIU, Marius COSMA 3 Abstrat: This paper takles the onept of parametri graphial design of the undeformed hip when five axis milling with ball nose end mills. Based on this model, the assessment of the utting onditions and the optimization of these onditions with respet to the ross setional area of the hip, the ontat length of the utting edge with the undeformed hip and the tool tilting angle. These ases will be studied and summarized and based on the results, experimental validation will be proposed. Key words: undeformed hip, ontat length, ross setional area, ball nose end mill. 1. INTRODUCTION 1 Modeling the metal utting proess has been a onstant onern of researhers in this field [1 5], et. Nevertheless, so far, no model has been developed to be effiient enough in order to render the onditions during the utting proess and estimate the output of the metal utting proess on aount of these. Every ase/attempt to model the metal utting proess has a ertain sope whih takes into aount ertain input variables. As for ball nose end mills, the modeling of the utting proess is more omplex than in the ase of simple end mills, as the utting speed varies along the main utting edge, laid on a hemisphere, in straight line or in spiral. These mills are used to mahine omplex sulptured surfaes, on three and five axis mahines. By tilting the tool with respet to the surfae to be mahined, the modeling proess beomes more ompliated through the range of input variables. Theoretially and pratially, these tools an be tilted depending on the possibilities of the mahine tool and the allowane of the piee onfiguration, by one or two diretions, i.e. by the feed diretion, by the pik feed diretion or by a ombination of the previous two (Fig.1). In the topi-related studies, the tilt of these tools is studied only by one diretion (either by the feed diretion, or by the pik feed diretion). Regardless the nature of the modeling type used in these studies, it is notieable that most of them takle the tool tilts at one of the angles 10, 15, 30, 45, 60 or 75 [6 10] and the list goes on. There is a workpaper whih mentions the tool tilt at an angle of 17 on the pik-feed diretion (θ n ) [11], yet, without justifying the hoie of this angle. 1 Eng, PhD Student, North University of Baia Mare, IMTeh, Vitor Babes 6 A, Tel , vlad.diiu@ubm.ro PhD, Prof., North University of Baia Mare, IMTeh, Head of Department, Vitor Babes 6 A, Tel mirea.lobontiu@ubm.ro 3 PhD, Leturer, North University of Baia Mare, IMTeh, Vitor Babes 6A, Tel , marius.osma@ubm.ro Another onlusion drawn from these studies is that there isn t a formula whih allows the alulation of the effetive utting diameter of the tool when using it tilted by both diretions. This effetive utting diameter is very important when the worker wants to maintain the utting speed reommended by the tool manufaturer for a type of material to be mahined. Based on the effetive diameter, the rotation of the tool an be assessed in order to obtain the desired utting speed representing also the effetive utting speed (V eff ). In this paper a parametri graphi model will be desribed. This model s purpose is to solve the above mentioned problems. Through parametri design one an understand the operation of inter-relating the graphial entities that ompose the model. In this way when one of the entities is modified, it will affet all the related entities as well. Parametri design is realized by means of CAD appliation CATIA V5 but it an be ahieved with all the CAD software appliations that allow these types of inter-relating and boolean operations with solids.. DESCRIPTION OF THE MODELING PROCESS.1. Modeling the utting proess In this ase a graphial model was hosen as a starting point beause these models have the advantage of a good representation of the final result as well as the possibility of identifying and orreting the mistakes as they appear while building the model. The starting model is the one proposed by Cosma M. [9] in his dotoral thesis, for the ase of three-axis milling. This model is to be implemented in parametri design for a better and quiker use, the extension for the ase of five-axis milling, the simulation of the feed movement and the optimization of utting onditions based on the desired outome of the proess. This model generates geometrially the undeformed hip based on the parameters of the utting regime i.e. the tool radius, the feed/tooth, the axial depth of ut and the radial depth of ut. The main purpose of this parametri model is to identify the optimum tool inlinations orrelated with the

2 8 V. Diiu et al. / Proeedings in Manufaturing Systems, Vol. 5 (010), No. / Fig. 1. Tool tilting by one of the two diretions (feed or pik feed diretion) (adapted by [1]). utting regime so as to obtain the desired utting onditions (desired variation of ross setional area of the undeformed hip and the ontat length of the utting edge with the undeformed hip). These utting onditions are important when designing equipments by means of the results from the utting proesses involved in their making. The first step for the making and parametri design implementation of the model for the situation of five-axis milling using ball nose end mills is to identify the entities/parameters that influene the outome of the utting proess. The identified input variables that determine the shape of the undeformed hip are the following: tool radius R; feed/tooth f z ; axial depth of ut (a p / a a ); radial depth of ut (a e / a r ). In addition to this list there are the variables that ontribute to the utting edge s onditions of entering and leaving the hip: feed diretion tilting angle θ f (Fig. 1); pik feed diretion tilting angle θ n (Fig. 1). This model is also destined to obtain the effetive utting diameter D ef, based on the parameters previously listed. This diameter will be useful when alulating the effetive utting speed V ef and onsequently when setting the proper spindle speed for a ertain type of material to be mahined. The model was reated using the Part Design module assisted by Generative Shape Design. The first step was to define the parameters R, f z, a p, a e. The next step was to assoiate these parameters with the graphial entities that ontribute to the formation of the undeformed hip. These entities are desribed by Cosma, in his paper [9] as follows: a plane (1) situated at a distane of R a p from the enter of the spherial tip of the mill, representing the initial surfae of the workpiee: x + y + z = R ; (3) a ylinder (4) representing the previous pass of the tool: ( x ae ) + z = R. (4) The undeformed hip is obtain, aording to [9], by interseting the ylinder, the two spheres and the plane. Based on this model the atual model was defined, replaing the spheres with the effetive shape of the tool, for a better visualization and for highlighting the tool inlination with respet to the surfae to be mahined (Fig. ). Assoiating the parameters desribed above to these entities, it beomes very easy to modify the geometrial harateristis of the graphial entities, as a funtion of the effetive parameters of the utting proess. Another advantage when working with parametri design is that although relations between parameters an be defined, the graphial entities an be independently positioned with respet to a global oordinate system. The representation of the utting edge through a plane and the polar multipliation of this plane around the axis Z, determines the suessive positions of the utting edge at a ertain hosen interval (5 for example), along its trajetory taken at one rotation of the tool (Fig. 3). These intervals an be hosen depending on the preision for whih the results are to be obtained. z = R a p ; (1) a sphere () representing the first rotation of the tool: x + ( y f z ) + z = R ; () a sphere (3) representing the seond rotation of the tool: Fig.. 3D representation of the solids that generate the undeformed hip.

3 V. Diiu et al. / Proeedings in Manufaturing Systems, Vol. 5 (010), No. / Fig. 3. Suessive positions of the utting edge along its trajetory for a rotation of the tool. In Fig. 5, the position of the utting edge for a tilting angle of 5 on the feed diretion (θ f ) and 15 on the pikfeed diretion (θ n ) is being presented. On the intersetion operation resulting graphial entities, whih represent the undeformed hip s ross setions, measurements an be arried out to obtain data like ross setional area of the undeformed hip and the ontat length of the utting edge with the undeformed hip. These measurements an be exported in an Exel file by means of a Visual Basi Maro espeially designed for this operation. The data one exported into the Exel file, an be used to raise variation harts and data filter. Having this model and using the methodology desribed, it is easy to optimise the utting onditions along the trajetory of the uttig edge for a rotation of the tool... Cutting fore estimation The maximum area obtained using the graphial model an be orrelated with the neessary utting fore for the utting proess by making an analogy with the alulation method proposed by Seo tool manufaturer [13]. They have devised a formula for alulating the utting fore based on the mean hip thikness, as follows: Fig. 4. Intersetions with the undeformed hip in different areas along the utting edge s trajetory. k γ h 0 = k m 1.1, (5) m where: γ 0 the effetive tilting angle; m exponent (table given based on the type of material to be mahined); k 1.1 the utting fore for a hip having the thikness of 1 mm [N/mm ] (table given based on the type of material to be mahined); h m mean hip thikness [mm]. The formula for alulating the mean hip thikness is given as follows [13]: Fig. 5. The position of the utting edge when inlining the tool differently on eah diretion. Interseting the planes distributed around the axis Z (Fig. 3) with the undeformed hip, result setions of the undeformed hip, plaed along the trajetory of the utting edge for a rotation of the tool (Fig. 4). The above presented are only valid for the situation when the tool is in a vertial position with respet to the surfae to be mahined (it has no inlination along one of the tilting diretions). To obtain similar data for the situation when the tool has a ertain inlination after one or two diretions, the plane that desribes the utting edge needs to be tilted. Beause this plane is a parametri entity, all the other planes that were obtained through polar multipliation will also beome inlined with respet to the initial plane. These inlinations are defined with respet to axes X and Y using parameters θ f and θ n inlination on the feed diretion and inlination on the pik-feed diretion respetively. h m 360 f z ae = sin k, (6) π D ω where: f z the feed/tooth [mm/tooth]; D the tool diameter; ω e engagement angle; k main lead angle. This formula, together with the table ontaining the fores an be found in the tool atalog of other tool produers as well [14], but beause for the experiments Seo tools will be used, the orrespondene with this data will be made from the tool atalog of this produer. Within the methodology previously desribed, the term of utting fore per mm is used whih is not quite orret. Aording to the International Measurement System fore applied on a surfae generates pressure and it is measured in [Pa] or [N/m ]. If it were to analyze the formula (5) one an notie that the resulting measurement unit is not [N/mm ] used in this ontext. e

4 84 V. Diiu et al. / Proeedings in Manufaturing Systems, Vol. 5 (010), No. / Probably this measurement unit is used to underline the fore neessary to remove a hip with a surfae of 1 mm. Beause the surfae onept is involved it is highly appropriate to replae the term in relation (5) that inludes the mean hip thikness and the tilting angle of the tool with the maximum area of the undeformed hip s ross setion. The alulation of the mean hip thikness is being done by taking into onsideration f z, a e, D, sin K and ω e. All these parameters an be found in the modeling proedure desribed above. Moreover, by means of the parametri model, the area/surfae on whih the fore is applied an be extrated diretly γ These two terms, m h m 0 and the undeformed hip s ross setional area, have a ommon ground: the way the utting edge enters and leaves the hip as well as the resistane enountered beause of the mahined material. It is known that the main leading angle K and the tilting angle γ 0, modify the area of the undeformed hip s ross setion and thus the neessary amount of fore to remove that hip. The simulation performed based on the desribed model takes these parameters into onsideration when it generates the setions of the undeformed hip. If the result is multiplied by the speifi utting fore, the neessary quantity of effort to remove that hip is obtained: k = A k sa max 1.1, (7) where A samax the maximum area of the ross setions of the undeformed hip. Pratially, taking into aount the maximum area of these setions, the maximum neessary utting fore an be estimated being equivalent with the neessary fore needed when the utting edge arrives at the biggest area of the hip that is being removed. On this hypothesis it is reommended to use the maximum area of the ross setions of the undeformed hip for alulating the neessary utting fore neessary to remove a ertain amount of material. The formula for alulating the mean hip thikness is no longer needed if it is to use the parametri model desribed. 3. CASE STUDY The results of this parametri graphial model are the way the utting edge enters and exits the hip, the volume of the undeformed hip, the variation of the ross setional area of the hip along the utting edge s trajetory at a rotation of the tool, the ontat angle of the utting edge with the workpiee material as well as the theoretial ontat length of the utting edge with the undeformed hip. These data obtained from the model will be orrelated in this ase study with the utting fore aording to relation (7). Beause some mahine tools do not allow big inlinations of the tool with respet to the surfae to be mahined and beause some piees have a omplex onfiguration that do not allow big tilting angles ause of the risk of ollisions, this study will take into aount tilting angles between 0 and 0. Aording to the tools aquired, the study will be performed for a surfae finish operation with a ball nose end mill having D = R = 14 mm, z = teeth and the utting regime f z = 0.1mm/tooth, a p = 0.3 mm, a e = 0.3 mm. The utting speed to be used is V = 50 m/min and it will ditate the neessary rotation when the effetive utting diameter will be measured. For this study there will be two hosen situations, for annealed C45 workipee material, situated at opposite extremities in what regards the utting onditions i.e. the ontat length of the utting edge with the tool: the utting edge enters the hip in the area of big thikness and at a small ontat length; the utting edge enters the hip in the area of big thikness and at a long ontat length. It was hosen that the utting edge should enter the hip in the area of big thikness, similar to the lassial situation of limb milling, beause of the tehnial reommendations for this type of milling. The purpose of the study is to highlight the differenes between the two situations similar from the utting regime point of view but different from the utting onditions point of view The utting edge enters the hip in the area of big thikness and at a small ontat length Based on the proposed model it was identified that the negative inlination of the tool on the feed diretion (θ f ) allows the utting edge to enter the hip in the region where the thikness is big and having a small ontat length with the hip. This negative inlination on the feed diretion ombined with the positive inlination on the pik-feed diretion (θ n ) reates a small ontat length of the utting edge with the undeformed hip. The variation of the ross setional area of the undeformed hip for this ase is presented in Fig. 6. It an be easily notied that the utting edge engagement angle is inversely proportional with the inlination value. The more the tool is being tilted, the less the tool stays in ontat with the workpiee. This way the same amount of material is being mahined but on a shorter engagement of the utting edge than when mahining with the tool in a vertial position. The variation of the ontat length on the utting edge with the hip, aording to the ases presented in Fig. 6, is illustrated in Fig. 7. Conluding the analysis for this ase, the following inlination has been hosen: 0 (θ f ) with 5 (θ n ). The maximum area of the ross setion for this ase was measured to be A samax = mm and the ontat length of the tool with the undeformed hip l = 1.77 mm. The utting fore neessary for mahining annealed C45 material (the type of material to be used for experimental validation of the model) based on relation 7 beomes: k = = N, (8)

5 V. Diiu et al. / Proeedings in Manufaturing Systems, Vol. 5 (010), No. / n Fig. 8. Suesive positions of the utting edge along it s trajetory for one rotation of the tool. The effetive utting diameter for this ase was measured to be D ef = 6.8mm. Fig. 6. Variation of ross setional area of undeformed hip. 3.. The utting edge enters the hip in the area of big thikness and at a long ontat length It was identified that the positive inlination on the pik-feed diretion (θ n ) ombined with the positive inlination on the feed diretion (θ f ) of the tool allows the utting edge to enter the hip in the region where the thikness is big and with a long ontat length with the hip. This ase is onsidered to be inappropriate for this type of working material (C45). This hypothesis will be onfirmed or infirmed by experimental data. The variation of the ross setional area of the undeformed hip for this ase is presented in Fig. 9. The variation of the ontat length of the utting edge with the hip, aording to this ase is illustrated in Fig. 10. Conluding the analysis for this ase, the following inlination has been hosen: 0 (θ f ) with 10 (θ n ). Fig. 9. Variation of ross setional area of undeformed hip. Fig. 7. Variation of ontat length of the utting edge with the undeformed hip. N where k 1.1 = 1500 for C45 [13]. mm This ase was onsidered to be the optimum hoie for this type of material beause, as one might see in Fig. 8, the utting edge enters the hip at a big thikness and on a short ontat length. Fig. 10. Variation of ontat length of the utting edge with the undeformed hip.

6 86 V. Diiu et al. / Proeedings in Manufaturing Systems, Vol. 5 (010), No. / University Researh Counil) Romania, Projet title: Contributions to the metal utting tribosystem, Projet ode: RU-PNII-TD36/008, Projet manager: Eng. Vlad Diiu. Fig. 11. Suessive positions of the utting edge along it s trajetory for one rotation of the tool. The maximum area of the ross setion for this ase was measured to be A samax = mm and the ontat length of the tool with the undeformed hip l =.0 mm. The utting fore neessary for mahining annealed C45 material (the type of material to be used for experimental validation of the model) based on relation (7) beomes: k = = 3.4 N, (9) N where k 1.1 = 1500 for C45 [13]. mm This ase was onsidered to be the worst hoie for this type of material beause, as one might see in Fig. 11, the utting edge enters the hip at a big thikness and on a long ontat length. Similar values of the utting fore were measured by [15], to be more speifi 50 5 N for a e = 0. mm, a p = 0.5 mm, f z = 0. mm/tooth, inlination of 45 (three axis milling) and utter radius R = 4 mm, when milling Inonel 718 of hardness 44 HRC. For a maximum ross setional area A samax = mm, the authors of the paper [16] have estimated a utting fore of 40 N for a e = 0.5 mm, a p = 0.5 mm, f z = 0.05 mm/tooth, inlination of 45 and tool radius R = 5 mm, without mentioning the type of material for whih the fore was alulated. The effetive utting diameter for this ase was measured to be D ef = 6.3mm whih is smaller than in the first ase. This means a bigger rotational speed in order to maintain the same utting speed as in the first ase. 4. CONCLUSIONS The model desribed in this paper is only appliable when mahining with ball nose end mills with straight utting edge, z = teeth and a rake angle γ = 0. The maximum ross setional area of the undeformed hip might be used for utting fore estimation. For the same undeformed hip the utting fore may vary aording to the inlination of the tool. This fat probably influenes the level of vibrations, noise and tool life. It is reommended to test these two situations under industrial onditions in order to onfirm or to infirm the validity of the proposed parametri model and the two hypotheses. The behavior of the utting tool when using utting fluids is important for this situation, beause of the different thermal onditions on the utting edge and onsequently beause of thermal fatigue. ACKNOWLEDGEMENTS: The urrent paper is part of a researh projet finaned by CNCSIS (National REFERENCES [1] X.W. Liu, K. Cheng, D. Webb, A.P. Longstaff, M.H. Widiyarto, Improved dynami utting fore model in peripheral milling. Part II: Experimental verifiation and predition. International Journal of Advaned Manufaturing Tehnology, Vol. 4, 004, pp [] X.-W. Liu, K. Cheng, A.P. Longstaff, M.H. Widiyarto, and D. 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