Analysis and Prediction of the Machining Force Depending on the Parameters of Trochoidal Milling of Hardened Steel

applied sciences

Article Analysis and Prediction of the Machining Force Depending on the Parameters of Trochoidal Milling of Hardened Steel

Michal Šajgalík 1 , Milena Kušnerová 2, Marta Harniˇcárová 1,2,*, Jan Valíˇcek 1,2, Andrej Czán 1, Tatiana Czánová 1,Mário Drbúl 1, Marian Borzan 3 and Ján Kmec 2 1 Department of Machining and Manufacturing Technology, Faculty of Mechanical Engineering—University of Zilina, Univerzitná 1, 010-26 Zilina, Slovakia; [email protected] (M.Š.); [email protected] (J.V.); [email protected] (A.C.); [email protected] (T.C.); [email protected] (M.D.) 2 Faculty of Technology, Institute of Technology and Business in Ceskˇ é Budˇejovice,Okružní 10, 370-01 Ceskˇ é Budˇejovice,Czech Republic; [email protected] (M.K.); [email protected] (J.K.) 3 Department of Manufacturing Engineering, Faculty of Machine Building, Technical University of Cluj-Napoca, B-dul Muncii, No. 103-105, 400641 Cluj-Napoca, Romania; [email protected] * Correspondence: [email protected]

Received: 4 February 2020; Accepted: 2 March 2020; Published: 5 March 2020

Featured Application: One of the progressive machining methods for machining of exotic alloys is trochoidal milling. The main contribution of this paper is the analysis of basic parameters of trochoidal movement for the prediction of their impacts on the machining force. Knowledge of these predictions will make it possible to decide more eﬀectively, on the selection of trochoidal parameters. Results from not only this paper, but our whole research on trochoidal milling are applied in various companies located near the city of the University of Zilina, such as IGV Technologies and LAGO instruments, but also local factories of well-known companies Volkswagen Slovakia, Schaeﬄer Kysuce, etc.

Abstract: Current demands on quality are the engine of searching for new progressive materials which should ensure enough durability in real conditions. Due to their mechanical properties, however, they cannot be applied to conventional machining methods. In respect to productivity, one of the methods is the finding of such machining technologies which allow achieving an acceptable lifetime of cutting tools with an acceptable quality of a machined surface. One of the mentioned technologies is trochoidal milling. Based on our previous research, where the effect of changing cutting conditions (cutting speed, feed per tooth, depth of cut) on tool lifetime was analysed, next, we continued with research on the influences of trochoid parameters on total machining force (step and engagement angle) as parameters adjustable in the CAM (computer-aided machining) system. The main contribution of this research was to create a mathematical-statistical model for the prediction of cutting force. This model allows setting up the trochoid parameters to optimize force load and potentially extend the lifetime of the cutting tool.

Keywords: trochoidal milling; machining forces; prediction; hardened steel; model

1. Introduction

1.1. Productive Technologies of Machining Research of the productivity issue is relevant mainly in such industry areas where it is necessary to solve the removal of a large volume of material in a short time. In connection with the continuous

Appl. Sci. 2020, 10, 1788; doi:10.3390/app10051788 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 1788 2 of 19 application of materials known to be hard-to-machine, a variety of methods known as productive technologies have been developed. In this area, research focuses mainly on cutting parameter adjustment or tool path optimization [1–3]. It also studies chip formation [4] and selected parameters of surface integrity [1,5]. Significant studies have also been carried out in this field, focusing on tool wear, machining not only steel materials but also nickel and titanium alloys [6–8]. One of the methods of productive technologies is trochoidal milling, which is increasingly finding its use for machining of materials with difficult machinability. Correct implementation of the technology also allows meeting the ever-increasing requirements for product quality with adequate productivity [5,9].

1.2. Trochoidal Milling

1.2.1. Research of Trochoidal Milling Trochoidal milling is an effective method not only for milling complex workpieces but also for milling relatively simple grooves. Compared to standard linear grooving, trochoidal grooving allows a single milling cutting tool to machine a groove of the desired width, at least a greater width than the diameter of the milling cutting tool, the production of the groove being limited only by the wear of the milling cutting tool. Multi-blade cutting tools can also be used to allow large table shift. In addition, very high cutting speeds and feeds can be applied at a relatively small radial depth of the cut [9,10]. Currently, trochoidal milling offers the most extensive opportunities with which it is possible to remove a greater volume of material in less time (compared to conventional milling). This technology can be applied for the production of deep grooves, pockets or high workpiece sides, with high process reliability and long tool life, although the workpiece material is usually hard to machine [10–12]. The evolution of knowledge and skills related to the possibilities of modern machining has taken about half a century, but the development of machining has gradually accelerated. Basic knowledge in the field of trochoidal machining in professional practice can be dated to this millennium. Materials harder to process are widely used in the aircraft, automotive, shipbuilding and energy industries for the production of complex and varied components; therefore, materials based on nickel, titanium and steels with improved mechanical properties have been investigated in order to understand the factors degrading the machining process thoroughly. In recent decades, various milling methods have been investigated and analysed to increase productivity [1,13–15], the subject of the investigation also included the following aspects: high-speed machining with respect to the removed material [2,13,14]; simulation methods aiming to implement different control models and the real behaviour of machines to eliminate machine failure and downtime [16,17]; adjusting tool feeds aiming to optimize the production cycle time; process monitoring to evaluate tool wear for titanium or nickel-based alloys [1,18]. The possibilities of the predictive model are control of the machining process in order to reduce vibrations, increase the stability of the cut and efficiency of the cutting process [19]; and trochoidal milling in connection with finish operations in machining superalloys based on nickel [20–22].

1.2.2. Analysis of Trochoidal Milling The term trochoidal milling is based on the mathematical definition which defines the trochoidal path as a curve created by point fixed to a circle rolling along a line. In the machining application, trochoidal milling is referred to as machining where the tool does not move linearly, and the cutting angle is constant. Our research is focused on the first case where the trochoid axis is primarily linear, as discussed below. A jump in technological development allowed for the precise setting of the minimum angle of cut of the cutting tool, which significantly reduces tool vibration. Reduction of the engagement angle is particularly advantageous in the side milling of grooves and pockets where the position of the milling cutting tool relative to the workpiece is easily changeable, and also when machining very hard materials, where relatively large frictional forces are produced, resulting in Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 20 milling machine rotating; a combination of both types of motion forms a curve, a cyclic spiral with a conventionally fixed name—trochoid (Figure 1) [11]. Appl. Sci. 2020, 10, 1788 3 of 19

Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 20 considerable warming. The centre of the tool moves directionally in the desired direction, with the millingmilling machinemachine rotating;rotating; aa combinationcombination ofof bothboth typestypes ofof motionmotion formsforms aa curve,curve, aa cycliccyclic spiralspiral withwith aa conventionallyconventionally ﬁxedfixed name—trochoidname—trochoid (Figure(Figure1 )[1) 11[11].].

Figure 1. Geometric representation of the tool path [11], where: RT is the radius of the milling cutting

tool; RP is the radius of the milling cutting circle.

The milling cutting tool takes the material off in relatively thin layers, but at a relatively fast feed rate; therefore, it is relatively less loaded with considerable performance. The effect of small radial cuttingFigure forces 1. Geometric increases representation the stability of thethe tool cut, path i.e., [there11], where: is a substantialRT is the radius decrease of the in milling pushing cutting the tool Figure 1. Geometric representation of the tool path [11], where: RT is the radius of the milling cutting awaytool; fromRP isto thethe radius workpiece of the millingas a response, cutting circle. and in the vibration. While increasing the cutting speed tool; RP is the radius of the milling cutting circle. and reducing chip thickness, the heat generated at the cutting point is reduced, so it is possible to The milling cutting tool takes the material off in relatively thin layers, but at a relatively fast feed increaseThe millingthe cutting cutting depth tool as takes needed. the material These positive off in relativelyly changed thin milling layers, conditionsbut at a relatively ensure fast that feed the rate; therefore, it is relatively less loaded with considerable performance. The effect of small radial rate;tool therefore,and the machine it is relatively are more less loadedwear-resistant, with considerable exhibiting performance. a much longer The serviceeffect of life, small and radial the cutting forces increases the stability of the cut, i.e., there is a substantial decrease in pushing the tool cuttingmachining forces process increases thus the becomes stability very of theeffective cut, i.e., and there desirable is a substantial in many new decrease applications in pushing [5,19]. the tool away from to the workpiece as a response, and in the vibration. While increasing the cutting speed and awayThe from essential to the workpiece knowledge, as especiallya response, on and theoretical in the vibration. issues of Whiletrochoidal increasing machining, the cutting was already speed reducing chip thickness, the heat generated at the cutting point is reduced, so it is possible to increase andapplied reducing in the chip last thickness, century. the The heat technical generated term at the“trochoidal cutting point milling” is reduced, is now so commonly it is possible used to the cutting depth as needed. These positively changed milling conditions ensure that the tool and the increaseconventionally, the cutting despite depth certain as needed. deviations These of thepositive real movemently changed of milling the millin conditionsg cutting ensure tool compared that the machine are more wear-resistant, exhibiting a much longer service life, and the machining process toolto mathematically and the machine predicted are more trochoidal wear-resistant, trajectories exhibiting [23] manifesting a much themselveslonger service mainly life, as and smaller the thus becomes very effective and desirable in many new applications [5,19]. machiningspaces at the process beginning thus becomesof the cut very and effectivemore significant and desirable gaps at in the many end new of the applications cut (Figure [5,19]. 2). The essential knowledge, especially on theoretical issues of trochoidal machining, was already TheIn Figure essential 2, the knowledge, outer edges especially of the trochoidal on theoretical trajectories issues canof trochoidal be compared machining, in smaller was and already larger applied in the last century. The technical term “trochoidal milling” is now commonly used appliedfeeds, and in thethe deviation last century. between The the technical two courses term is recor“trochoidalded. In realmilling” milling, is it now is possible commonly to get closerused conventionally, despite certain deviations of the real movement of the milling cutting tool compared to conventionally,to the continuously despite smooth certain outer deviations edge of theof the cut real by increasing movement the of rotarythe millin speedg cutting of the toolmilling compared cutting mathematically predicted trochoidal trajectories [23] manifesting themselves mainly as smaller spaces totool, mathematically reducing its feed predicted rate, taking trochoidal a very trajectories thin layer [23]of material manifesting and applyingthemselves the mainly knowledge as smaller of the at the beginning of the cut and more significant gaps at the end of the cut (Figure2). spacesdynamics at the of thebeginning machining of the process cut and [20]. more significant gaps at the end of the cut (Figure 2). In Figure 2, the outer edges of the trochoidal trajectories can be compared in smaller and larger feeds, and the deviation between the two courses is recorded. In real milling, it is possible to get closer to the continuously smooth outer edge of the cut by increasing the rotary speed of the milling cutting tool, reducing its feed rate, taking a very thin layer of material and applying the knowledge of the dynamics of the machining process [20].

FigureFigure 2.2.Geometric Geometric representationrepresentation ofof thethe trochoidtrochoid and and circular circular tool tool paths, paths, where: where:R RTTis is thethe radiusradius of of thethe milling milling cutting cutting tool; tool;R RPP isis thethe radiusradius ofof thethe trochoidtrochoid circle.circle.

InIn Figurethe analysis2, the outerof the edges trochoidal of the milling trochoidal model trajectories [23], cutting can forces be compared were predicted in smaller for and peripheral larger feeds,milling and of thecircular deviation corner between profiles the with two the courses main fo iscus recorded. on the Ingeometry real milling, of the it tool is possible and the to workpiece, get closer tothe the position continuously of the smoothtool relative outer to edge the of workpiece the cut by and increasing the material the rotary properties speed ofof the the milling workpiece. cutting In Figure 2. Geometric representation of the trochoid and circular tool paths, where: RT is the radius of tool,cooperation reducing with its feed analytical rate, taking and numerical a very thin soluti layerons, of material chip formation and applying was developed the knowledge for precise of the the milling cutting tool; RP is the radius of the trochoid circle. dynamicsdynamic modelling of the machining in circular process finishing [20]. milling, taking into account tooth movement and uneven InIn thethe analysisanalysis ofof thethe trochoidaltrochoidal millingmilling modelmodel [[23],23], cuttingcutting forcesforces werewere predictedpredicted forfor peripheralperipheral millingmilling ofof circularcircular corner corner proﬁles profiles with with the the main main focus focus on on the the geometry geometry of theof the tool tool and and the the workpiece, workpiece, the the position of the tool relative to the workpiece and the material properties of the workpiece. In cooperation with analytical and numerical solutions, chip formation was developed for precise dynamic modelling in circular finishing milling, taking into account tooth movement and uneven Appl. Sci. 2020, 10, 1788x FOR PEER REVIEW 44 of of 1920

chip thickness [24-25]. The dynamic model of circular finish milling was also determined by positionanalysing of time the tool changes relative of toinput the workpiece and output and stroke the material angles in properties various machining of the workpiece. zones [6,26], In cooperation thereby withlaying analytical the foundation and numerical for further solutions, tool stability chip formation analysis waswith developed the trochoid for precisemotion dynamicof the cutting modelling tool. inIn circularthe issue finishing of material milling, removal taking during into accountmilling, tooth the influence movement of andthe radial uneven depth chip of thickness cut on the [24, 25cut]. Thestability dynamic limit modelwas emphasized, of circular finish and these milling findings was also were determined verified byduri analysingng milling time of changesthe cavities of input [27]. andAdditionally, output stroke the basic angles analytical in various model machining of the zonescutting [6 forces,26], thereby of trochoidal laying themilling foundation was derived, for further and toolthis model stability was analysis experimentally with the trochoidverified. motionCutting of forces the cutting acting in tool. trochoidal In the issue milling of material in relation removal to the duringradial depth milling, of the the cut influence were also of the modelled radialdepth and successfully of cut on the verified cut stability in the limitstudy was of trochoidal emphasized, milling and thesemechanics findings [11,21,28]. were verified during milling of the cavities [27]. Additionally, the basic analytical model of the cutting forces of trochoidal milling was derived, and this model was experimentally verified. Cutting1.2.3. Trochoidal forces acting Milling in trochoidal in CAM (computer-aided milling in relation machining) to the radial systems depth of the cut were also modelled and successfullyThe development verified of in computer the study technology of trochoidal enabled milling a mechanicswider implementation [11,21,28]. of CAM systems. Currently, there are several major manufacturers of these systems (e.g., PTC Creo, CATIA, Delcam, 1.2.3. Trochoidal Milling in CAM (computer-aided machining) systems SolidCAM, EDGECAM, etc.) which, in addition to programming conventional machining methods, also allowThe development so-called smart of computermachining technology to reduce tool enabled load athrough wider implementationa constant angle of CAMthe feed. systems. From Currently,the user’s point there areof view, several the major solution manufacturers is realized by of theseentering systems the input (e.g., parameters PTC Creo, CATIA,of machining Delcam, or SolidCAM,cutting conditions. EDGECAM, The cutting etc.) which, parameters in addition which toaffect programming the (conventional) conventional cutting machining process are methods, cutting alsospeed, allow feed so-called rate (or feed smart per machining tooth) and to cutting reduce depth. tool load through a constant angle of the feed. From the user’sThe primary point of goal view, of thetrochoidal solution milling is realized also byreferred entering to theas constant-angle input parameters machining of machining by CAM or cuttingsystems conditions. manufacturers, The cutting is to reduce parameters tool whichloading. aff Ifect the the tool (conventional) is moving cuttingalong a process path similar are cutting to a speed,mathematical feed rate trochoid, (or feed the per feed tooth) angle and is cutting not consta depth.nt but is defined as the angle between two vectors describingThe primary the tool goal contact of trochoidal area with millingthe machined also referred material. to asLoad constant-angle size continuously machining increases byCAM from systemszero to maximum manufacturers, depending is to on reduce the tool tool movement loading. (Figure If the tool 3). If is this moving angle is along greater a path than similar the entered to a mathematicalvalue, a circular trochoid, motion the of the feed tool angle with is nota radius constant defined but isby defined the radius as the Rp angleparameter between is executed two vectors in a describingcontrolled manner the tool contactin this position. area with If the this machined angle is smaller material. than Load the size defined continuously value, then increases the circular from zeromotion to maximumis not generated depending at this on position, the tool movementand the tool (Figure moves3). to If thisthe next angle position. is greater Just than for the trochoidal entered value,milling, a circulartoday’s advanced motion of control the tool of with all aspects a radius of defined the tool by path, the radiusincludingRp parametercollision control, is executed seems in to a controlledbe very effective. manner in this position. If this angle is smaller than the defined value, then the circular motionWhen is not we generated use trochoidal at this position, milling, andthere the are tool two moves next to theparameters next position. (step Justof fortrochoid trochoidal and milling,engagement today’s angle) advanced which control define ofthe all trochoidal aspects of path. the tool Due path, to this including fact, the collision research control, of the seems trochoidal to be verypath ehasffective. been focused on the step of trochoid, the engagement angle and trochoidal radius (Figure 3).

Figure 3.3. Graphic presentation of trochoidal parameters:parameters: s—step of trochoid; RP—radius of the trochoid circle;circle; RT—radiusRT—radius ofof thethe millingmilling cuttingcutting tool;tool;α α—engagement—engagement angle.angle.

WhenThe trochoid we use trochoidalstep determines milling, the there distance are two betw nexteen parameters the centres (step of of two trochoid adjacent and engagementcircles that angle)characterize which the deﬁne tool’s the feed trochoidal by a given path. distance. Due to this The fact, engagement the research angle of the is trochoidalthe angle pathof stroke has beenthat focusedoccurs between on the step the oftwo trochoid, directions the engagementat the tool an angled material and trochoidal contact point. radius Between (Figure3 ).two mentioned parameters, there is a relationship which causes the curvature of the path. During the path generation, the CAM system continuously checks the engagement angle at each tool position defined Appl. Sci. 2020, 10, 1788 5 of 19

The trochoid step determines the distance between the centres of two adjacent circles that characterize the tool’s feed by a given distance. The engagement angle is the angle of stroke that occurs between the two directions at the tool and material contact point. Between two mentioned Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 20 parameters, there is a relationship which causes the curvature of the path. During the path generation, theby the CAM step. system If the continuouslyengagement angle checks is thegreater engagement than the specified angle at each value, tool the position cutting definedtool at this by position the step. Ifperforms the engagement a circular angle tool is greatermovement than with the specified the radius value, defined the cutting by the tool radius at this parameter. position performs If the aengagement circular tool angle movement is smaller with than the the radius specified defined valu bye, the the radius CAM parameter.system does If not the generate engagement a circular angle ismovement smaller than at this the position; specified the value, tool themoves CAM to systemthe next does position. not generate The trochoid a circular radius movement is the radius at this of position;the circle thedescribing tool moves the torolling the next motion position. of the The milling trochoid cutting radius tool, is the the centre radius of of the the tool circle as describingthe centre theof the rolling actual motion trochoid of the circle milling moving cutting along tool, a thesolid centre baseline. of the The tool walls as the of centre the formed of the actualgroove trochoid are not circleentirely moving straight; along they a solid have baseline. the shape The of walls small of circular the formed arcs; groove the surface are not quality entirely of straight; the groove they havewall theincreases shape with of small the set circular step and arcs; the the radius surface of quality the trochoid. of the grooveThe magnitudes wall increases of the with forces the acting set step on andthe themilling radius cutting of the tool trochoid. correspond The magnitudes to the magnitudes of the forces of the acting forces-responses on the milling of cuttingthe milling tool cutting correspond tool toacting the magnitudeson the machined of the material, forces-responses in accordance of the millingwith the cutting Newton’s tool third acting law on [5,9,29]. the machined The aim material, of the inresearch accordance of the with dynamics the Newton’s of the trochoidal third law mach [5,9,29ining]. The process aim of is the to researchexamine ofthe the dependence dynamics of the trochoidaltotal machining machining force process on the is trochoid to examine parameters the dependence qualitatively of the totaland machiningquantitatively. force At on thea relatively trochoid parameterssmall engagement qualitatively angle, andthe quantitatively.area of the workpiece At a relatively material small cut width engagement is reduced. angle, If the the area currently of the workpiecemachined surface material is cut theoretically width is reduced. reduced If theto a currently single point, machined the tangent surface at is this theoretically point is a reduced common to atangent single point,to the theradius tangent of the at thismilling point cutting is a common tool and tangent to the to radius the radius of the of current the milling trochoid cutting circle. tool andPractically, to the radiushowever, of theit is current never the trochoid case of circle.a single Practically, point, but however,always of ita machined is never the surface; case of therefore, a single point,it also depends but always on ofthe a ratio machined of the radius surface; oftherefore, the cutting it tool also and depends the radius on the of ratiocurvature of the of radius the trochoid of the cuttingcurve. The tool follow-up and the radius research of curvatureof the total of machinin the trochoidg force, curve. depending The follow-up on the radius research of the of thetrochoid total machiningcurve, is also force, fundamental, depending in on the the context radius of of the the dependence trochoid curve, on isthe also step fundamental, and engagement in the angle. context of the dependenceIn the presented on the paper, step and a groove engagement of the angle.desired width and depth (Figure 4) is milled using the trochoidalIn the milling presented technique paper, ato groove examine of the desiredmachining width forces, and depending depth (Figure on 4the) is change milled of using the two the trochoidalselected parameters milling technique that can be to examineset via CAM the machininginterface; namely, forces, dependingthe step and on the the engagement change of the angle. two selectedWhen examining parameters the that effect can beof setthe viaparameters CAM interface; on the namely, total machining the step and force, the engagementa simpler type angle. of Whentrochoidal examining milling the was effect selected, of the parameters which is on relatively the total machiningunloaded force,by other a simpler effects type of of non-linear trochoidal millingmovements was of selected, the centre which of the is tool. relatively The radius unloaded of the by trochoid other e isff ectsdefined of non-linear by the radius movements of each circular of the centrearc of the of the trochoidal tool. The trajectory, radius of the the trochoid number is and defined density by theof the radius circular of each arcs circular being arcdetermined of the trochoidal by the trajectory,trochoid step. the number and density of the circular arcs being determined by the trochoid step.

(a) (b)

Figure 4. DiagramDiagram of ofthe the presented presented method method of oftroc trochoidalhoidal grooving grooving according according to SolidCAM: to SolidCAM: (a) (presentationa) presentation of GUI of of GUI SolidCAM; of SolidCAM; (b) orthogonal (b) orthogonal view of trocho view ofidal trochoidal milling path, milling where: path, RT— where:radius P RofT —theradius milling of thecutting milling tool; cutting R —radius tool; ofRP the—radius trochoid of thecircle; trochoid b—width circle; of b—thewidth milled of groove; the milled s— groove;trochoids— step.trochoid step.

1.2.4. Cutting Forces in Trochoidal Milling The total machining force F is the action force the tool exerts on the workpiece and at which it is pressed into the machined material. The machined material exerts an equally large and inversely orientedAppl. Sci. 2020 resistive, 10, x FOR reaction PEER REVIEW force on the tool. The total machining force is the resultant one of the6 twoof 20 components, namely, the active component Fa and the passive component Fp, but in principle, it does notnot act in a a simplified simpliﬁed manner manner in in the the 2D 2D space; space; it ac itts acts in inthe the general general direction direction and and can canbe divided be divided into intothree three mutually mutually perpendicular perpendicular directions directions in the in 3D the space. 3D space. The feed The component feed component Ff acts inF ftheacts x axis; in the thex axis;normal the component normal component Ffn acts inF thefn acts y axis in as the a ynormalaxis as to a the normal feed tocomponent; the feed component; and the passive and thecomponent passive componentFp acts in theF pz actsaxis in(Figure the z axis 5). The (Figure active5). force The active component force component Fa can be consideredFa can be consideredthe result of the the result cutting of thecomponent cutting component Fc and its normalFc and itsFcn, normal and at Fthecn, same and at time, the same as the time, result as of the the result feed of component the feed component Ff and its Fnormalf and its Ffn normal. Ffn.

(a) (b)

FigureFigure 5. 5.Scheme Scheme ofof thethe componentscomponents forfor totaltotal machiningmachining force F: in 2D-plan ( a) and 3D-side 3D-side ( (bb)) views. views.

MachiningMachining forceforce componentscomponents cancan bebe measuredmeasured indirectly;indirectly; forfor example,example, fromfrom thethe powerpower outputoutput ofof thethe machinemachine electricelectric motormotor oror thethe torquetorque ofof thethe powerpower relativerelative toto thethe rotationrotation axisaxis [[7,30].7,30]. InIn thethe presentedpresented experiments,experiments, exact, exact, direct direct measurements measurements of theof the components components of the of totalthe total machining machining force wereforce usedwere usingused ausing stationary a stationary dynamometer, dynamometer, which measures which themeasures rectangular the rectangular projections ofprojections the components of the ofcomponents the forces Foff, Fthefn andforcesFp Finf, F thefn and 3D coordinateFp in the 3D system coordinate axes xsystem, y and axesz. x, y and z. TheThe activeactive componentcomponent ofof thethe forceforce FFaa isis thethe cuttingcutting force,force, thethe largestlargest andand mostmost importantimportant componentcomponent ofof thethe machining machining force, force, acting acting in in the the general general direction, direction, so so it cannotit canno bet be measured measured directly directly by theby the dynamometer. dynamometer. However, However, its its magnitude magnitude can can be be measured measured indirectly indirectly as as the the resultant resultant of of thethe feedfeed componentcomponent FFff (acting(acting inin thethex xaxis axis direction) direction) and and the the normal normal to to the the feed feed component componentFfn Ffn(acting (acting in in the they axisy axis direction). direction). Knowledge Knowledge of of the the active active force force component component is is a a fundamental fundamental basisbasis forfor calculatingcalculating thethe stressesstresses ofof the the milling milling cutting cutting tool tool and and the the workpiece workpiece chuck; chuck; and and the the energy energy balance balance of the of machinethe machine tool. Thetool. component The component of the of feed the force feedF forcef acts F inf acts the directionin the direction of the machineof the machine feed; its feed; magnitude its magnitude is mainly is themainly basis the for basis calculating for calculating the strength the strength of the tool. of the The tool. passive The componentpassive component of the force of theFp is force the smallestFp is the componentsmallest component of the machining of the machining power; in thepower; case ofin trochoidalthe case of milling, trochoidal the activemilling, force the component active force is oftencomponent more signiﬁcant is often more by orders signific ofant magnitude by orders than of the magnitude passive component, than the passive but the component, passive component but the haspassive a high component information has value a high from information the technological value from point the of technological view. In principle, point itof pushes view. In the principle, tool out strokeit pushes with the the tool workpiece, out stroke resulting with the in workpiece, vibration during resulting the in machining vibration process. during the The machining vibration isprocess. highly undesirable,The vibration primarily is highly because undesirable, it negatively primarily aﬀects because the accuracy it negatively of the workpiece affects the dimensions accuracy and of thethe qualityworkpiece of the dimensions machined and surface. the quality Since theof the passive machin componented surface. is Since very smallthe passive in the component case of trochoidal is very machining,small in the thecase cut of istrochoidal relatively machining, stable.The the presented cut is relatively results follow stable.The on from presented the current results research follow on of trochoidalfrom the current milling research and focus of trochoidal on the analysis milling of and the coursefocus on and the character analysis of of the the course machining and character forces in theof the formation machining of theforces trochoid in the pathformation using of CAM the tr software.ochoid path Trochoidal using CAM milling software. is a dynamic Trochoidal machining milling methodis a dynamic which, machining thanks to method the use ofwhich, the new thanks CAM to controlthe use systems,of the new allows CAM one control to not systems, only maintain allows constantone to not cutting only maintain conditions constant (feed and cutting angular conditions speed of (feed the cutting and angular tool), butspeed also of the the parameters cutting tool), of thebut also the parameters of the trochoid, the step, the engagement angle, the mean chip thickness and the surface roughness of the workpiece. For each application and each tool, the cutting conditions and parameters of the trochoid must be optimized. The use of the trochoid grooving method places high demands on machine tools that must be able to provide sufficient acceleration to ensure the prescribed workpiece trajectory and have sufficient power to provide the requested speed.

2. Materials and Methods Appl. Sci. 2020, 10, 1788 7 of 19 trochoid, the step, the engagement angle, the mean chip thickness and the surface roughness of the workpiece. For each application and each tool, the cutting conditions and parameters of the trochoid must be optimized. The use of the trochoid grooving method places high demands on machine tools that must be able to provide suﬃcient acceleration to ensure the prescribed workpiece trajectory and have suﬃcient power to provide the requested speed.

2. Materials and Methods The primary task of the experimental part of the research was trochoidal grooving of the steel by a vertical machine tool, with the setting of various parameters of the trochoidal path and continuous recording of the cutting forces by a stationary dynamometer to achieve knowledge about the inﬂuence of these parameters on a load of the cutting tool. As it was mentioned in the previous part, this research builds on previous analysis of tool wear due to cutting parameters. A summary of the research results is in Section 2.2.1.

2.1. Material and Technical Equipment Material and technical equipment was based on a machining computer-controlled centre and precision instruments for measuring machine tool components when milling grooves in investigated samples from material which are hard to process.

2.1.1. Workpiece Material The material EN X38CrMoV5-1, (commercially known as Bohler W300, Voestalpine Böhler Edelstahl GmbH & Co KG, Kabfenber, Austria) a tool steel designed for the production of forging dies, was selected for the experiments. This material was chosen because of its expansion in the manufacturing processes of cooperating partners (from practice), but also because of its widespread use in the industry dealing with forging and forming tools. Due to its high hardness of 58 HRC, this steel is usually used in professional practice for hot work due to its high resilience, high strength while hot, high strength and excellent air and vacuum hardenability. The machined sample was a forging die. Forging dies are used for dropping hammers, spindle and forging presses to make forgings from unalloyed, low alloy steels or light metal alloys. For the renovation of forging dies, diﬀerent types of technology are used, among which, based on the presented experience, trochoidal milling can be included.

2.1.2. Milling Machine and Tool For the trochoidal milling, the multifunction Hurco-VMX-30-T (Hurco Companies, Inc., Indianapolis, IN, USA) Vertical Machining Centre with Ultimax CNC control was used. The technical parameters of Hurco-VMX-30-T are listed in Table1. The maximum revolutions available for working tool movements are 12,000 RPM with an output of 13.5 kW. Depending on the tool used and the material being machined, this limit is reduced to 6000 RPM. The machine has basic sensors placed in travels and the spindle, but only for internal load control in the machine control system environment. According to the workpiece material, which exhibits a hardness of 58 HRC, the UNIFR41010xR1 milling cutting tool (5 mm radius, Figure6) was used for the experiments, which is designed for high-speed machining of hardened steels with a hardness of up to 70 HRC. The selected milling tool has four flutes with irregular helices (angles 35◦and 38◦) having a significant effect on controlling vibration when compared to standard end mills. This cutting tool fully complied with the recommended cutting conditions by the manufacturer and the experimental conditions. This end mills cutting tool uses the technology of nanocrystal coating for higher hardness, higher speed and longer tool life due to the higher coating hardness and heat resistance. During the machining of the workpiece, it has a lower coefficient of friction and prevents abnormal damage. The features of this type of coating in comparison with other types are listed in Table2. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 20

Appl. Sci. 2020, 10, 1788 coolant volume 265 L 8 of 19

According to the workpiece material, which exhibits a hardness of 58 HRC, the UNIFR41010xR1 milling cutting toolTable (5 mm 1. Technical radius, Figure parameters 6) was of theused used for machinethe experiments, Hurco VMX-30-T. which is designed for high- speed machining of hardened steels with a hardness of up to 70 HRC. The selected milling tool has Machine Parameter Description Properties four flutes with irregular helices (angles 35°and 38°) having a significant effect on controlling Table work area 1020 mm 510 mm vibration when compared to standard end mills. This cutting tool fully complied× with the maximum load 1000 kg recommendedTravels cutting conditions by the manu axisfacturerx and the experimental conditions.760 mm This end mills cutting tool uses the technologyaxis y of nanocrystal coating for higher510 mm hardness, higher speed and longer tool life due to the higheraxis coz ating hardness and heat resistance.610 mm During the machiningSpindle of the motor workpiece, it has a lower coefficie powernt of friction and prevents abnormal 13.5 kW damage. The the distance from the front to the edge of Spindle 150–760 mm features of this type of coating in comparisonthe with platen other types are listed in Table 2. revolutions per minute 10,000–12,000 rev min 1 · − Table 2. The featuresmoment of of nanocrystal force relative coating to the rotationin comparison axis with other214 types. N m · Tool changer number of milling cutting tools 24 Propertiesmaximum Nanocrystal milling cutting Coating tool diameter (Al, Ti, Si) N (Al, 80 mmTi) N Hardness maximum milling 3700 cutting HV tool length 3200 HV 2800 300 mm HV Adhesion maximum weight 100 ofN the miller 80 N 807 kg N Other parameters feed rate in x/y/z axes 37/35/30 m min 1 Oxidation temperature 2370 F 2010 F 1540 ·F − coolant volume 265 L Coefficient of friction 0.48 0.53 0.58

DC – cutting diameter 10mm RC – corner radius 1mm APMX – max cutting depth 25mm LF – total length of tool 70mm APFA – axial primary relief angle 7° ASCA – axial secondary clearance angel 10° HA1 – helix angle 1 38° HA2 – helix angle 2 35° PCA – primary clearance angle 5° SCA – secondary clearance angle 12° RRA – radial rake angle 8°

FigureFigure 6. 6.Milling Milling tool: tool: schematic schematic presentation presentation of of geometry. geometry.

2.1.3. Measurement of Cutting Forces Table 2. The features of nanocrystal coating in comparison with other types. During milling, three perpendicular machining forces were measured with the stationary dynamometerProperties mounted between Nanocrystal the chuck Coatingplaten and the (Al, workpiece. Ti, Si) N (Al, Ti) N It is a measuringHardness device designed 3700 for HV machining purposes. 3200 HV In principle, 2800 it HVoperates on the piezoelectricAdhesion effect, when a mechanical 100 load N on the piezoelectric 80 Nsensor generates 80an Nelectrical charge on the Oxidationsurface of temperature the measuring plate 2370cut Fout of a special crystal. 2010 F The dynamometer 1540 F contains four Coefficient of friction 0.48 0.53 0.58 sensors. Each force sensor is piezoelectric. It has three components; i.e., it contains three crystal discs, 2.1.3.each Measurementdisc recording of one Cutting force Forces in the given direction, namely, the pressure and tensile force in the directionDuring of milling,the z axis three (±Fz), perpendicularand the positive machining and negative forces shear were forces measured in both directions with the stationary±Fx and ±Fy, dynamometermeasuring three mounted given between orthogonal the chuckforce platencomponen and thets at workpiece. the same time. For 3-component force measurementsIt is a measuring during devicemilling, designed eight signals for machining are obtained, purposes. which are In summed principle, up it into operates a 3-wire on cable the piezoelectricand then lead eff ect,to three when charge a mechanical amplifiers. load The on the charge piezoelectric amplifier sensor includes generates a capacitor, an electrical and by charge changing on theits surfacerange, it of is the possible measuring to vary plate the cut measured out of a specialforce range. crystal. The The amplified dynamometer charge contains signal is four converted sensors. to a voltageEach force signal, sensor which is piezoelectric.is evaluated. ItThe has size three of components;the charge, or i.e., the it electrical contains threevoltage, crystal is proportional discs, each discto recordingthe magnitude one force of inthe the applied given direction, force. Software namely, thesignal pressure processing and tensile includes force invisualization the direction and of thespreadsheetz axis ( Fz calculations.), and the positive The technical and negative parameters shear forces of the in dynamometer both directions usedF xareand shownFy, measuringin Table 3. ± ± ± three given orthogonal force components at the same time. For 3-component force measurements during milling, eight signals are obtained, which are summed up into a 3-wire cable and then lead to three charge amplifiers. The charge amplifier includes a capacitor, and by changing its range, it is possible to vary the measured force range. The amplified charge signal is converted to a voltage signal, which is evaluated. The size of the charge, or the electrical voltage, is proportional to the magnitude of Appl. Sci. 2020, 10, 1788 9 of 19 the applied force. Software signal processing includes visualization and spreadsheet calculations. The technical parameters of the dynamometer used are shown in Table3.

Table 3. Basic technical data for the three-component piezoelectric dynamometer.

Property Numerical Value Measuring range in the direction of x axis 20 to + 20 kN − Measuring range in the direction of y axis 20 to + 20 kN − Measuring range in the direction of z axis 10 to 40 kN Allowed operating temperature 0 to 70 ◦C Actual frequency 3 kHz Relative measurement uncertainty 1% Measurement sensitivity 8 pC N 1 · −

The dynamometer is used for direct measurement by the three components of the force Ff, Ffn and Fp, in which their magnitudes are measured in the directions of the coordinate x, y and z axes. Because they are rectangular projections of the component of the active force Fa and the passive component Fp into the coordinate axes in 3D space, the magnitude of the total machining force F had to be measured indirectly, i.e., calculated as the magnitude of the vector sum of the measured components Ff, Ffn and Fp according to (1), namely, for the number of partial measurements i = 1, ... , 125,500 . h i q q F = F2 + F2 F = F2 + F2 (1) i ai pi ∧ ai f i f ni The stationary dynamometer was connected to a computer by an A/D converter.

2.1.4. The Hardware and Software Used The DAQ system DasyLab (version 13, Measurement Computing Corp., Norton, MA, USA, 2013) was used for computer data collection. DasyLab was as an environment suitable for laboratory measurement to enable eﬃcient use of measuring and control hardware. The acquisition rate was 500 Hz. The obtained signal data were not ﬁltered. In order to generate toolpaths for trochoidal machining, the SolidCAM program has been selected, which uses the investigated parameters (cutting angle and trochoid step) as the trochoid basic input parameters. The Excel spreadsheet was selected for processing the measurement results, and the MatLab (version R2018b, MathWorks©, Natick, MA, USA) interactive programming environment was selected for the statistical and graphical evaluation of the results.

2.2. Design of Experiments

2.2.1. Previous Research—the Basis for Actual Research The experiments presented in this article are part of the follow-up research carried out at the Department of Machining and Manufacturing Technology at the Faculty of Mechanical Engineering at the University of Zilina. This research was focused on the intensification of cutting parameters in the production and renovation of forging tools. The experiments carried out in the previous research were aimed at determining suitable cutting conditions with regard to adequate productivity. During the experiments, the effects of cutting conditions on tool life and wear on the cutting tool were primarily monitored. The distribution of individual values was based on the DoE (design of experiments) principles; 3 measurements were determined to evaluate tool wear based on our own research, available works by reputable experts [31,32] and ISO 8688 [33] (milling tool testing). In the wear analysis, the 1st measurement was the identification measurement, the 2nd measurement was a comparative measurement, and the 3rd measurement was a verification measurement. Cutting speed values are based on the tool speed setting in the machine control program. Their range is set based on Appl. Sci. 2020, 10, 1788 10 of 19 the characteristics of the machine, tool and workpiece, or real forging tools (identical to the current ones). In the table below (Table4), the speed is recalculated to the cutting speed for a D10 diameter tool and the feed rate for a 4-tooth tool. The depth of cut was chosen as constant ap = 10 mm, for all experiments, taking into account the dimensions of the milling cutter and machined samples of the forging tool.

Table 4. Three-level division of trochoidal milling experiments.

1 Experiment RPM vc (m min ) fz (mm) · − P1 1000 31 0.05 P2 1000 31 0.1 P3 1000 31 0.2 P4 3000 94 0.05 P5 3000 94 0.1 P6 3000 94 0.2 P7 5000 157 0.05 P8 5000 157 0.1 P9 5000 157 0.2

The critical wear limit (VBk – critical ﬂank wear on the cutting tool) was determined with respect to tool geometry at VBk = 0.2 mm (evaluated critical ﬂank wear on the cutting tool). Table5 gives an overview of the machining times achieved when the critical wear value was exceeded, and the productivity was evaluated by the total material remove parameter during such times (as total material removed).

Table 5. Tool life TVBk20 and material removal rate Q for experimental tests.

1 3 1 3 Experiment RPM vc (m min ) fz (mm) TVBk0.2 (min.) Q (cm min ) QT (cm ) · − · − P1 1000 31 0.05 51 2.68 136.68 P2 1000 31 0.1 51 5.36 273.36 P3 1000 31 0.2 47 10.72 503.84 P4 3000 94 0.05 50 8.04 402 P5 3000 94 0.1 40 16.08 643.2 P6 3000 94 0.2 33 32.16 1061.28 P7 5000 157 0.05 33 13.4 442.2 P8 5000 157 0.1 32 26.8 857.6 P9 5000 157 0.2 27 53.6 1608

As can be seen from the measured values (Table5), the longest machining times after reaching the critical wear value were at the lowest cutting speed experiments (Experiments P1 and P2). At the same time, these experiments also show the lowest productivity in terms of material removal when the tool has reached the critical wear value. This parameter was measured but was not primarily analysed and only had an auxiliary/support function in further analysis of the choice of suitable cutting parameters. When comparing the extremes of values, it can be stated that while the tool speed has increased 5-fold (from 1000 to 5000 RPM), tool wear has decreased to approximately 60%. Taking into account the parameter of the total amount of material taken as well, the setting of experiment P4 seems to represent suitable cutting conditions. It can be assumed that by adjusting the trochoid path itself (and thus the tool load), the machining time can be extended up to 60 min with wear below the set value, since the measured wear values up to this time only slightly exceeded the critical wear parameter (up to time of 60 min, the maximum VB wear was at 0.21 mm). The dependencies of the inﬂuences of the change in cutting speed and feed on the tool wear were created from the measured values, as shown in Figure7. For clarity, they are classiﬁed according to the size of the cutting force. Appl. Sci. 2020, 10, 1788 11 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 20

FigureFigure 7.7. The graphical course of tool wear at various cutting parameters of trochoid machiningmachining (see(see thethe Tabletable 44 withwith conditionsconditions P1–P9)—classiﬁedP1–P9)—classified byby cuttingcutting force.force.

AsAs cancan bebe seenseen from the chart,chart, the cutting parameters have a significant significant impact on on tool tool wear. wear. TheThe statisticalstatistical evaluationevaluation showsshows thatthat wearwear occursoccurs earlierearlier atat higherhigher speeds.speeds. It can be seen fromfrom thethe coursecourse ofof wearwear thatthat conditionsconditions withwith meanmean valuesvalues ofof cuttingcutting speedspeed oror revolutionsrevolutions proveprove toto bebe suitablesuitable cuttingcutting parameters.parameters. At the same time, at the highesthighest speeds (P8 and P9) and feeds, it was not possible toto successfullysuccessfully complete complete the the entire entire removal removal in allin all cases cases due due to complete to complete destruction destruction of the of cutting the cutting edge. edge.From the values obtained by repeating the tests, it can be seen that there were significant deviations betweenFrom measurements, the values obtained many ofby which repeating exceeded the tests, 10%. it Toolcan wearbe seen is significantlythat there were influenced significant not onlydeviations by the between cutting parameters,measurements, but alsomany by of tool wh clamping,ich exceeded or the 10%. rigidity Tool of wear the entire is significantly machining system.influenced However, not only the by variations the cutting found parameters, in the individual but also by experiments tool clamping, may or be the mainly rigidity due of to the material entire inhomogeneitymachining system. (the However, influence the of microstructurevariations found or in internal the individual errors resultingexperiments from may the be manufacture mainly due ofto thematerial workpiece), inhomogeneity which cannot (the influence be sufficiently of micros filteredtructure under or current internal metrological errors resulting procedures from the to makemanufacture the machined of the materialworkpiece), quasi-homogeneous. which cannot be Based sufficiently on the measuredfiltered under data andcurrent processed metrological results, itprocedures was determined to make that the further machined research material would quasi- focushomogeneous. on the determination Based on of thethe influence measured of data trochoid and parametersprocessed results, (step and it was engagement determined angle). that further Given research parameters would are focus in the on CAM the determination system as the of basic the parametersinfluence of that trochoid affect theparameters shape of trochoid(step and itself. engagement The trochoid angle). shape Given has parameters a direct effect are on in the the current CAM amountsystem as of the material basic parameters being cut by that the affect milling the cutter, shape therebyof trochoid directly itself. a ffTheecting trochoid the tool shape load, has wear a direct and ultimatelyeffect on the the current tool life. amount For the of mostmaterial accurate being determination cut by the milling of the cutter, impact thereby of the directly given parameters, affecting the it wastool specifiedload, wear that and the ultimately usual cutting the parameters,tool life. For such the most as cutting accurate speed determination and feed rate, of would the impact be constant. of the Thegiven depth parameters, of the cut it remainedwas specified unchanged that the compared usual cutting to the parameters, previous experiment. such as cutting speed and feed rate, would be constant. The depth of the cut remained unchanged compared to the previous experiment.

Appl. Sci. 2020, 10, 1788 12 of 19

2.2.2.Appl. Sci. Setup 2020, of10, Actualx FOR PEER Experiments REVIEW 12 of 20

2.2.2.At Setup the beginningof Actual Experiments of the experiments, the initial setting (in the SolidCAM program) was: 1 CuttingAt the beginning speed as theof the circumferential experiments, speedthe initial of the setting milling (in cutting the SolidCAM tool, vc = program)94 m min was:− ; • · Constant cutting conditions, namely, feed per tooth: fz = 0.1 mm; • Cutting speed as the circumferential speed of the milling cutting tool, vc = 94 m·min−1; • The depth of cut was identical to the depth of the groove; • Constant cutting conditions, namely, feed per tooth: fz = 0.1 mm; • Dimensions of the machined groove (width 20 mm, length 55 mm, depth 10 mm) (Figure8); • The depth of cut was identical to the depth of the groove; • Trochoid radius Rp = 5 mm (the same for all experiments); • Dimensions of the machined groove (width 20 mm, length 55 mm, depth 10 mm) (Figure 8); • Trochoid step s = 0.1,p 0.6 and 1 mm (the same for three triples of experiments); • Trochoid radius R = 5 mm (the same for all experiments); • EngagementTrochoid step angle s = 0.1,α α 0.6= 10and◦, 301 mm◦ and (the 60◦ same(the samefor three for threetriples triples of experiments); of experiments). • • Engagement angle α = 10°, 30° and 60° (the same for three triples of experiments).

Figure 8. An example of a finished ﬁnished groove sample: the the detail detail of one of the milled grooves with a noticeably higher surface waviness.

Selected trochoidal parameters were set accordingaccording toto DoEDoE principles—responseprinciples—response surface.surface. As a potentially suitable model, we chosechose thethe centralcentral compositecomposite planplan withwith threethree levelslevels ofof adjustment.adjustment. A total of nine grooves were milled, with two varied parameters for each partial experiment: parameter s—trochoid step, and parameter α—engagement angle. The individual experiments were divided into three levels according toto thethe 3-level3-level planplan (Table(Table6 ).6).

Table 6. Three-level division of conventional trochoidal milling experiments.

ExperimentExperiments (mm)s (mm) α (°) α (◦) 11 0.20.2 10 10 22 0.20.2 30 30 33 0.20.2 60 60 44 1.01.0 10 10 5 1.0 30 65 1.01.0 30 60 76 0.61.0 60 10 87 0.60.6 10 30 98 0.60.6 30 60 9 0.6 60 During the milling of each groove, the components of the machining forces were measured and recorded.During The the procedure milling of was each repeated groove, accordingthe componen to Tablets of6 ,the with machining the same forces chip volume were measured being taken and forrecorded. each groove. The procedure was repeated according to Table 6, with the same chip volume being taken for each groove.

3. Results and Discussion

3.1. Analysis of Results for the Computation of the Prediction Model Appl. Sci. 2020, 10, 1788 13 of 19

3. Results and Discussion

3.1. Analysis of Results for the Computation of the Prediction Model According to the 3-level plan (Table6), nine grooves were milled on a sample of the same material, when changing the step and the engagement angle. The dynamometer was placed underneath the workpiece, and the cutting forces were measured in the XYZ system, with the milling cutter performing a motion related to the mathematical definition of trochoid, as shown in Figures3 and5. The orientation of the tool relative to the reference system changed depending on the movement, which resulted in a change in the size of the cutting force components (projected into individual axes). At the same time, in the second part of the semicircle, the milling cutter was out of the engagement, which resulted in a “zero” load in the course of the components of the total cutting force. Based on the calculated path, the tool came into the engagement, which resulted in a change in the cutting force Ff (in the x axis’s direction). As the tool moved along the trochoid radius Rp, the force increased. As the tool shifted more in the y axis, the force component Ffn grew and the component Ff tended to decrease. The size of the component Fp reflected the entire toolpath in engagement. Research of cutting force, or of cutting force components realized by several experts [11,20,23,34,34–36] in the previous period, was focused mainly on the determination of the impact of tool movement on its load; the creation of mechanistic models; and, last but not least, identification of other impacts, such as machining vibrations. The detected dependencies make it possible to get an accurate idea of the current tool load. These factors were also taken into account when setting the dynamometer sensing frequency to identify the rotation of the tool and the influence of the load on the individual cutting edges of the tool in contact with the material (in engagement—in our case four teeth to four flutes) clearly. Since our research was focused on analysing the impacts of trochoid parameters on the overall tool load, the analysis was not performed using a chatter model, but through local toolmaking peaks for the individual tool passes and average values for these peaks. The data obtained from the development of the total cutting force components, as shown in Figure9, served as the basis. These graphical outputs do not provide an overview of the trends of the investigated influences at a glance, because the resulting machining force cannot be directly measured; not even its active component can be directly measured. Only rectangular projections of the active and passive force components into the coordinate axes can be directly and precisely measured with the dynamometer. The active force of the total machining force can then be measured indirectly; i.e., it must be evaluated in each partial measurement as the vector sum of the components of the forces Ff and Ffn. The total machining force F can also be measured indirectly; i.e., it can be evaluated in each partial measurement as the vector sum of the components of the forces Fa,Fp (Table7).

Table 7. Indirectly measured maximum machining force Fmax by the vector sum of experimentally measured maximum force components.

Engagement Angle α (◦) Maximum Machining Power Fmax 10◦ 20◦ 30◦ 0.2 mm 1159 1901 2658 Step s [mm] 0.6 mm 1933 2867 3792 1.0 mm 1548 2391 3042 Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 20

According to the 3-level plan (Table 6), nine grooves were milled on a sample of the same material, when changing the step and the engagement angle. The dynamometer was placed underneath the workpiece, and the cutting forces were measured in the XYZ system, with the milling cutter performing a motion related to the mathematical definition of trochoid, as shown in Figures 3 and 5. The orientation of the tool relative to the reference system changed depending on the movement, which resulted in a change in the size of the cutting force components (projected into individual axes). At the same time, in the second part of the semicircle, the milling cutter was out of the engagement, which resulted in a “zero” load in the course of the components of the total cutting force. Based on the calculated path, the tool came into the engagement, which resulted in a change in the cutting force Ff (in the x axis’s direction). As the tool moved along the trochoid radius Rp, the force increased. As the tool shifted more in the y axis, the force component Ffn grew and the component Ff tended to decrease. The size of the component Fp reflected the entire toolpath in engagement. Research of cutting force, or of cutting force components realized by several experts [11,20,34-36] [20,23,34–36] in the previous period, was focused mainly on the determination of the impact of tool movement on its load; the creation of mechanistic models; and, last but not least, identification of other impacts, such as machining vibrations. The detected dependencies make it possible to get an accurate idea of the current tool load. These factors were also taken into account when setting the dynamometer sensing frequency to identify the rotation of the tool and the influence of the load on the individual cutting edges of the tool in contact with the material (in engagement—in our case four teeth to four flutes) clearly. Since our research was focused on analysing the impacts of trochoid parameters on the overall tool load, the analysis was not performed using a chatter model, but through local toolmaking peaks for the individual tool passes and average values for these peaks. TheAppl. data Sci. 2020obtained, 10, 1788 from the development of the total cutting force components, as shown in Figure14 of 9, 19 served as the basis.

Figure 9. Time recording of the evolution of the cutting force components for selected cases (top—detail of one pass; bottom—the progress as a whole).

3.2. Mathematical-Statistical Analysis for Measured Values After the experiments and partial analyses of the measured results were ﬁnished, the experimental data were subjected to statistical analysis (Table8).

Table 8. The output from the analysis of variance for the total machining force F.

Source DF Adj SS Adj MS F-Value p-Value Contribution (%) Model 5 5,050,835 1,010,167 59.30 0.003 99.00% Linear 2 1,409,645 704,822 41.37 0.007 75.90% s (mm) 1 1,178,227 1,178,227 69.16 0.004 4.45% α (◦) 1 339,360 339,360 19.92 0.021 71.45% Square 2 1,177,729 588,864 34.57 0.008 23.08% s (mm) 1 1,113,985 1,113,985 65.39 0.004 21.83% α (◦) 1 63,743 63,743 3.74 0.149 1.25% 2-Way Interaction 1 832 832 0.05 0.839 0.02% Error 3 51,106 17,035 1.00% Total 8 100.00%

From the analysis of variance (Table8) for the total machining force F, it follows that the most significant influence is shown by the engagement angle α, which directly affects the value of the maximum width of the removed layer, reaching up to 75.9% of the linear model. This fact is manifested above all in a more pronounced inclination in the direction of the s axis. From the scattering analysis, it also follows that, within a given range of cutting conditions, the response has a quadratic character Appl. Sci. 2020, 10, 1788 15 of 19 in the direction of the s axis; i.e., approximately at the mean values of the step s, this force reaches its maximum. The response area is defined as the second-degree polynomial. The precision of the presented model reaches 99%, with a prediction coefficient of 87.02% and a 95% confidence interval setting, or 5% on both sides. In terms of the statistical significance of the individual members, this model can ± be considered correct and sufficiently accurate for further research, for simulation and verification of theAppl. machining Sci. 2020, 10 process, x FOR PEER and REVIEW for subsequent follow-up applications in professional practice. 15 of 20 The response area equation (Figure 10) shows the influence of the trochoid parameters: step s The response area equation (Figure 10) shows the influence of the trochoid parameters: step s (mm) and engagement angle α (◦), with the trochoid constant radius Rp = 5 mm; namely, the impact on the(mm) change and inengagement the total machining angle α (°), force withF (2):the trochoid constant radius Rp = 5 mm; namely, the impact on the change in the total machining force F (2): 2 2 F = 462 + 6131 s + 53.3 α 4664 s 0.3 α 1.43 s α (2) 𝐹 =− −462 + 6131· ⋅ ·𝑠− + 53.3· ⋅ 𝛼− −4664⋅𝑠 −0.3⋅𝛼· − −1.43⋅𝑠⋅𝛼· · (2)

Figure 10. Response area chart for the total machining force F. Figure 10. Response area chart for the total machining force F. 3.3. Verification of the Prediction Model 3.3. BasedVerification on the of determined the Prediction calculation Model model, verification measurements of the set-up of experiments were performedBased on (accordingthe determined to Table calculation6). A total ofmodel, 18 experiments verification were measurements performed, nine of forthe modelling set-up of andexperiments nine for verification. were performed The individual (according force to Table components 6). A total were of 18 measured experiments during were these performed, experiments nine asfor a basismodelling for evaluating and nine the for total verification. cutting force The of indi thevidual machining. force Thecomponents resulting were values measured were compared during withthese those experiments from the predictionas a basis for model evaluating (Table7). the total cutting force of the machining. The resulting valuesIn Tablewere 9compared is the comparison with those of from values the prediction from measurements model (Table (total 7). machining force Fmax was computedIn Table from 9 indirectis the comparison measurements of values of cutting from forces) measurements with predicted (total values—computed machining force F valuesmax was ofcomputedFmax. from indirect measurements of cutting forces) with predicted values—computed values of Fmax. Table 9. Comparison of statistically predicted magnitudes of the total machining force Fmax according to the predictive Equation (2) and measured the total machining Fmax. Table 9. Comparison of statistically predicted magnitudes of the total machining force Fmax according

max. to the predictiveExperiment Equations (mm) (2) and αmeasured(◦) Predicted the totalFmax machining(N) Measured F Fmax (N) Diﬀerence 1 0.2 10 1078 1153 7% Experiment2 s (mm) 0.2 α (°) 30 Predicted 1898 Fmax (N) Measured 1936 Fmax (N) 2%Difference 1 30.2 0.2 10 601078 2678 2693 1153 1% 7% 4 1.0 10 2032 2156 6% 2 50.2 1.0 30 301898 2841 2872 1936 1% 2% 3 60.2 1.0 60 602678 3604 3763 2693 4% 1% 7 0.6 10 1494 1471 2% 4 81.0 0.6 10 302032 2291 2245 2156 2% 6% 5 91.0 0.6 30 602841 3037 3135 2872 3% 1% 6 1.0 60 3604 3763 4% 7 0.6 10 1494 1471 2% 8 0.6 30 2291 2245 2% 9 0.6 60 3037 3135 3%

Figure 11 shows the processed values of Table 9. As can be seen from the comparison of the predictive model values with those obtained from the verification measurement, the smallest deviation achieved in two cases (Experiments 3 and 5) was only 1%. In two cases, the highest deviation was higher than 5%; in other cases this limit was not exceeded, and it is possible to evaluate the prediction model as sufficiently accurate. Appl. Sci. 2020, 10, 1788 16 of 19

Figure 11 shows the processed values of Table9. As can be seen from the comparison of the predictive model values with those obtained from the veriﬁcation measurement, the smallest deviation achieved in two cases (Experiments 3 and 5) was only 1%. In two cases, the highest deviation was higherAppl. Sci. than 2020, 5%;10, x inFOR other PEER cases REVIEW this limit was not exceeded, and it is possible to evaluate the prediction16 of 20 model as suﬃciently accurate.

Figure 11. GraphicalGraphical comparison of predicted and me measuredasured values of total machining force F.. 4. Conclusions (and Future Work) 4. Conclusions (and Future Work) The presented research aimed to analyse the impacts of trochoid parameters on the basis of the The presented research aimed to analyse the impacts of trochoid parameters on the basis of the findings from our previous research on the influences of cutting parameters. After determining the findings from our previous research on the influences of cutting parameters. After determining the influences, a mathematical-statistical prediction model was created and successfully verified based on influences, a mathematical-statistical prediction model was created and successfully verified based the experimental settings. on the experimental settings. On the basis of experimental results of direct measurements of the components of the machining On the basis of experimental results of direct measurements of the components of the machining forces with the dynamometer during the trochoidal milling of the groove in steel: forces with the dynamometer during the trochoidal milling of the groove in steel: • The total machining force was measured and evaluated indirectly. • The total machining force was measured and evaluated indirectly. • The results of nine experiments performed for combinations of three different trochoid step settings • The results of nine experiments performed for combinations of three different trochoid step andsettings three and diff threeerent different settingsof settings the engagement of the enga anglegement at constant angle at trochoid constant radius trochoid were radius processed were statistically,processed statistically, and the predictive and the equation predictive of theequation total machiningof the total force machining and the correspondingforce and the responsecorresponding area of response the total area machining of the total force machining were created. force were created. • Both the response area and the comparative regressionregression equation of the total machining force, • dependent on the trochoid step and on the engagementengagement angle, indicate that the influenceinfluence of the trochoid stepstep isis parabolic,parabolic, and the influenceinfluence of thethe engagement angle is linear with the constant radius ofof thethe trochoid.trochoid.

The limitations of the achieved model are mainly in the material and tools used, but they were chosen based on practical requirements. Knowledge ofof thethe predictive predictive equation equation of of the the machining machining force force will will make make it possible it possible to decide to decide more emoreffectively effectively about theabout settings the settings of the input of the parameters input parameters of the trochoidal of the milling trochoidal and themilling technological and the conditionstechnological of thisconditions setting. of The this resulting setting. The benefits resulting of the benefits presented of the results presented can be results seen incan the be creation seen in ofthe material creation forof material further predictions;for further predictions; namely, for namely, the prediction for the prediction of milling of cutting milling tool cutting wear tool and wear the predictionand the prediction of the quality of the ofquality the machined of the machined surface. surface. The novelty of the presented paper is the creationcreation of a model determining the influenceinfluence of trochoidal parameters onon tool loading. The resear researchch outputs are intended for real deployment for the setting of trochoid parameters (step and engagement angle) in order to simplify their settings in the programming phase in the environment of CAM systems. Based on the cooperation of the companies participating in the research (named in the Featured Application section), the outputs were successfully implemented in real production. Trochoidal milling is a method applicable to a wide range of materials, in particular, those with reduced machinability, and wherever major material removal is required in the shortest possible Appl. Sci. 2020, 10, 1788 17 of 19 setting of trochoid parameters (step and engagement angle) in order to simplify their settings in the programming phase in the environment of CAM systems. Based on the cooperation of the companies participating in the research (named in the Featured Application section), the outputs were successfully implemented in real production. Trochoidal milling is a method applicable to a wide range of materials, in particular, those with reduced machinability, and wherever major material removal is required in the shortest possible time. Based on the findings, it can be concluded that the prediction model obtained has the potential for further refinement for other tools and materials.

Author Contributions: Conceptualization A.C. and J.V.; data curation A.C. and M.Š.; resources M.H. and M.B.; methodology J.V., M.Š. and M.K.; investigation M.Š. and M.D.; formal analysis M.Š., M.K., T.C. and M.B.; funding acquisition A.C, T.C.; writing—original draft M.Š, M.K, M.B.; writing—review and editing J.V., M.H. and J.K.; validation M.K., J.V. and M.H. All authors have read and agreed to the published version of the manuscript. Funding: This article was funded by research project APVV 15-0405 at the University of Žilina—“Complex use of X-ray diffractometry for identification and quantification of functional properties of dynamically loaded structural elements from important technical materials.” Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature ap depth of cut (mm) APMX max cutting depth angle on the milling tool (%) ASCA axial secondary clearance angle on the milling tool (mm) b width of the milled groove (mm) CP centre of the trochoid circle (mm) CT centre of the milling cutting tool (mm) DC cutting diameter on the milling tool (mm) fz feed per tooth (mm) an active component of the total machining force F as the result of the cutting FC and the pressure component FCn in a general direction, which cannot be directly measured; also, Fa (N) this force is the resultant magnitude of the measured rectangular projections of the force components Ff and Ffn cutting force as a component of the active force Fa of the general direction, which cannot FC be directly measured, lies in a tangent perpendicular to the radius of the milling cutting (N) tool at point pressure force as a normal for cutting force, a component of the active force Fa of general F (N) Cn direction, which cannot be directly measured rectangular projection of the active component of the total machining force into the x axis F (N) f directly measured by a dynamometer rectangular projection of the active component of the total machining force into the y axis F (N) fn directly measured by a dynamometer HA1 helix primary angle on the milling tool (◦) HA2 helix secondary angle on the milling tool (◦) LF the total length of the tool on the milling tool (◦) machined surface reduced to the contact point of the milling cutting tool and the P (–) workpiece material; PCA primary clearance angle on the milling tool (◦) 3 1 Q material removal rate per time unit (cm min− ) · 3 QT the total quantity taken over time after the speciﬁed wear has been achieved (cm ) RC corner radius on the milling tool (mm) radius of the trochoid circle (part of the trochoid circle is in blue; the direction of the RP trochoid circle rotation is a blue arrow, and the direction of the feed of the trochoid circle (mm) centre is a red arrow) RRA radial rake angle on the milling tool (◦) Appl. Sci. 2020, 10, 1788 18 of 19

radius of the milling cutting tool (the milling tool circumference is in black, and the R (mm) T milling and cutting tool rotation directions are in red) s trochoid step (mm) t time (when measured tool wear) (min.) TVBk20 tool life on the basis of speciﬁed wear VBk = 20 µm (min.) SCA secondary clearance angle on the milling tool (◦) 1 vc cutting speed (m min ) · − VBk evaluated critical ﬂank wear on the cutting tool (mm) x the direction of the coordinate axis of the cutting plane (-) y the direction of the coordinate axis of the cutting plane (-) α engagement angle in computing of trochoidal path (◦) τ time (when measured cutting forces) (s) the mark at point P as a symbolic representation of the direction in the z axis N (perpendicularly below the xy plane) of the vector FP of the passive component of the (-) total machining force F

References

1. Waszczuk, K.; Skowronek, H.; Karolczak, P.; Kowalski, M.; Kolodziej, M. Influence of the Trochoidal Tool Path on Quality Surface of Groove Walls. Adv. Sci. Technol. Res. J. 2019, 13, 38–42. [CrossRef] 2. de Lacalle, L.N.; Lamikiz, A.; Munoa, J.; Salgado, M.A.; Sanchez, J.A. Improving the high-speed finishing of forming tools for advanced high-strength steels (AHSS). Int. J. Adv. Manuf. Technol. 2006, 29, 49–63. [CrossRef] 3. Ning, J.; Nguyen, V.; Liang, S.Y. Analytical modeling of machining forces of ultra-fine-grained titanium. Int. J. Adv. Manuf. Technol. 2019, 101, 627. [CrossRef] 4. Ning, J.; Nguyen, V.; Huang, Y.; Hartwig, K.T.; Liang, S.Y. Inverse determination of Johnson–Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search. Int. J. Adv. Manuf. Technol. 2018, 99, 1131–1140. [CrossRef] 5. Santhakumar, J.; Mohammed Iqbal, U. Parametric Optimization of Trochoidal Step on Surface Roughness and Dish Angle in End Milling of AISID3 Steel Using Precise Measurements. Materials 2019, 12, 1335. [CrossRef] 6. Krahmer, D.M.; Hameed, S.; Sanchez, A.J.E.; Perez, D.; Canales, J.; de Lacalle, L.N. Wear and MnS Layer Adhesion in Uncoated Cutting Tools When Dry and Wet Turning Free-Cutting Steels. Metals 2019, 9, 556. [CrossRef] 7. Liu, D.; Ying, Z.; Luo, M.; Zhang, D. Investigation of Tool Wear and Chip Morphology in Dry Trochoidal Milling of Titanium Alloy Ti–6Al–4V. Materials 2019, 12, 1937. [CrossRef][PubMed] 8. Polvorosa, R.; Suárez, A.; López de Lacalle, L.N.; Cerillo, I.; Wretland, A.; Veiga, F. Tool wear on nickel alloys with different coolant pressures: Comparison of Alloy 718 and Waspaloy. J. Manuf. Process. 2017, 26, 44–56. [CrossRef] 9. Krahmer, D.M.; Polvorosa, R.; López de Lacalle, L.; Alonso, U.; Abate, G.; Riu, F. Alternatives for Specimen Manufacturing in Tensile Testing of Steel Plates. Exp. Tech. 2016, 40, 1555–1565. [CrossRef] 10. Xu, K.; Wu, B.; Li, Z.; Tang, K. Time-Efficient Trochoidal Tool Path Generation for Milling Arbitrary Curved Slots. J. Manuf. Sci. Eng. 2019, 141, 031008. [CrossRef] 11. Pleta, A.; Ulutan, D.; Mears, L. Investigation of Trochoidal Milling in Nickel-Based Superalloy Inconel 738 and Comparison with End Milling. In ASME 2014 International Manufacturing Science and Engineering Conference Collocated with the JSME 2014, Proceedings of the International Conference on Materials and Processing and the 42nd North American Manufacturing Research Conference, Detroit, MI, USA, 9–13 June 2014; American Society of Mechanical Engineers: New York, NY, USA, 2014. 12. Bettine, F.; Ameddah, H.; Manna, R. A Neural Network Approach for Predicting Kinematic Errors Solutions for Trochoidal Machining in the Matsuura MX-330 Five-Axis Machine. FME Trans. 2018, 46, 453–462. [CrossRef] 13. Pleta, A.; Nithyanand, G.; Niaki, F.A.; Mears, L. Identification of optimal machining parameters in trochoidal milling of Inconel 718 for minimal force and tool wear and investigation of corresponding effects on machining affected zone depth. J. Manuf. Process. 2019, 43, 54–62. [CrossRef] 14. Kechagias, J.D.; Aslani, K.-E.; Fountas, N.A.; Vaxevanids, N.M.; Manolakos, D.E. A comparative investigation of Taguchi and full factorial design for machinability prediction in turning of a titanium alloy. Measurement 2020, 151, 107213. [CrossRef] Appl. Sci. 2020, 10, 1788 19 of 19

15. Li, Y.; Zheng, G.; Zhang, X.; Xu, R. Cutting force, tool wear and surface roughness in high-speed milling of high-strength steel with coated tools. J. Mech. Sci. Technol. 2019, 33, 5393. [CrossRef] 16. Djurdjanovic, D.; Mears, L.; Niaki, F.A.; Haq, A.U.; Li, L. State of the art review on process, system, and operations control in modern manufacturing. J. Manuf. Sci. Eng. 2017, 140, 061010. [CrossRef] 17. Li, Z.; Xu, K.; Tang, K. A new trochoidal pattern for slotting operation. Int. J. Adv. Manuf. Technol. 2019, 102, 1153. [CrossRef] 18. Saleem, W.; Ijaz, H.; Alzahrani, A.; Asad, M.; Zhang, J. Numerical modeling and simulation of macro- to microscale chip considering size effect for optimum milling characteristics of AA2024T351. J. Braz. Soc. Mech. Sci. Eng. 2019, 41, 337. [CrossRef] 19. Amaro, P.; Ferreira, P.; Simoes, F.C.K. Tool wear analysis during duplex stainless steel trochoidal milling. AIP Conf. Proc. 2018, 1960, 070001. [CrossRef] 20. Niaki, F.A.; Michel, M.; Mears, L. State of health monitoring in machining: Extended Kalman filter for tool wear assessment in turning of IN718 hard-to-machine alloy. J. Manuf. Process. 2016, 24, 361–369. [CrossRef] 21. Zhang, H.T.; Wu, Y.; He, D.; Zhao, H. Model predictive control to mitigate chatters in milling processes with input constraints. Int. J. Mach. Tools 2016, 91, 54–61. [CrossRef] 22. Karagiannis, S.; Stavropoulos, P.; Ziogas, C.; Kechagias, J. Prediction of surface roughness magnitude in computer numerical controlled end milling processes using neural networks, by considering a set of influence parameters: An aluminium alloy 5083 case study. J. Eng. Manuf. 2014, 228, 233–244. [CrossRef] 23. Pleta, A.; Ulutan, D.; Mears, L. An Investigation of Alternative Path Planning Strategies for Machining of Nickel-Based Superalloys. Procedia Manuf. 2015, 1, 556–566. [CrossRef] 24. Niaki, F.A.; Pleta, A.; Mears, L. Trochoidal Milling: Investigation of a New Approach on Uncut Chip Thickness Modeling and Cutting Force Simulation in an Alternative Path Planning Strategy. Int. J. Adv. Manuf. Technol. 2018, 97, 641–656. [CrossRef] 25. Pleta, A.; Mears, L. Cutting Force Investigation of Trochoidal Milling in Nickel-Based Superalloy. Procedia Manuf. 2016, 5, 1348–1356. [CrossRef] 26. Banerjee, A.; Feng, H.Y.; Bordatchev, E.V. Geometry of Chip Formation in Circular End Milling. Int. J. Adv. Manuf. Technol. 2012, 59, 21–35. [CrossRef] 27. Zhang, X.H.; Peng, F.Y.; Qiu, F.; Yan, R.; Li, B. Prediction of Cutting Force in Trochoidal Milling Based on Radial Depth of Cut. Adv. Mat. Res. 2014, 852, 457–462. [CrossRef] 28. Nguyen, H.T.; Hsu, Q.C. Surface Roughness Analysis in the Hard Milling of JIS SKD61 Alloy Steel. Appl. Sci. 2016, 6, 172. [CrossRef] 29. Yan, R.; Li, H.; Peng, F.; Tang, X.; Xu, J.; Zeng, H. Stability Prediction and Step Optimization of Trochoidal Milling. ASME J. Manuf. Sci. Eng. 2017, 139, 091006. [CrossRef] 30. Zagorski, I.; Kulisz, M.; Klonica, M.; Matuszak, J. Trochoidal Milling and Neural Networks Simulation of Magnesium Alloys. Materials 2019, 12, 2070. [CrossRef] 31. Brinksmeier, E.; Preuss, W.; Riemer, O.; Rentsch, R. Cutting forces, tool wear and surface finish in high speed diamond machining. Precis. Eng. 2017, 49, 293–304. [CrossRef] 32. Finkeldey, F.; Hess, S.; Wiederkehr, P. Tool wear-dependent process analysis by means of a statisticalonline monitoring system. Prod. Eng. Res. Devel. 2017, 11, 677–686. [CrossRef] 33. STN ISO. 8688-2 Metal-cutting tools. Tool life testing in milling. In End Milling; SUTN: Bratislava, Slovakia, 1993. 34. Urbikain, G.; Olvera, D.; López de Lacalle, L.N.; Beranoagirre, A.; Elías-Zuñiga, A. Prediction Methods and Experimental Techniques for Chatter Avoidance in Turning Systems: A Review. Appl. Sci. 2019, 9, 4718. [CrossRef] 35. Urbikain, G.; Olvera, D.; López de Lacalle, L.N.; Beranoagirre, A.; Elías-Zuñiga, A. Spindle speed variation technique in turning operations: Modeling and real implementation. J. Sound Vib. 2016, 383, 384–396. [CrossRef] 36. Altintas, Y. Critical Review of Chatter Vibration Models for Milling. In Autonome Produktion; Klocke, F., Pritschow, G., Eds.; Springer: Berlin/Heidelberg, Germany, 2004.

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