Modeling and analysis for clearance machining process of end mills

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    Modeling and analysis for clearance machining process of endmills

    Guochao Li & Jie Sun & Jianfeng Li

    Received: 2 March 2014 /Accepted: 7 July 2014 /Published online: 30 July 2014# Springer-Verlag London 2014

    Abstract Clearance of end mills has great impact on theperformance of milling, and therefore a high demand for itsmachining theory and process is put forward. Based on theanalysis of practical machining process, enveloping theory,principles of spatial geometry are introduced to establish theclearances processing model, as well as considering the ge-ometries, orientations, and locations of wheels used to ma-chine the clearances with convex, eccentric, or elliptic shapes.Accordingly, limitations of wheel geometry and location tomachine a desired clearance are discussed. A commercialcomputer aided design system with API function program-ming is used to visualize the machining process. The solidmodel is finally obtained.

    Keywords Clearance . Endmill . Process

    1 Introduction

    Clearance is one of the most important structures of end mills[1]. It influences the intensity and sharpness of cutter edges,

    the tool life as well as the quality of machined surfaces.However, the research on the end mill manufactureprocess has mainly focused on the helical groove grindingprocesses [25]. There is little analysis on clearance grindingprocess.

    In many cases, clearance was designed and calculated inthe groove design process, based on the assumption that it wasa straight line at the cross section of end mills [612]. Obvi-ously, clearance models built with this approach could notreflect the actual processing precisely. With different researchideas, Chong described the re-sharpen processes for clear-ances of end mills [13]. The principle of eccentric clearancere-shaping process was emphasized, including the re-shapingorder, the position of end mill, wheel, and tooth rest. Based ona five-axis CNC tool grinder, Chen et al. planed the grindingprocesses of clearance by using a tool grinding CAM system[14]. Translation and revolution sequences of every grinderaxis in flat, concave, and eccentric machining process wereintroduced. Uhlmann et al. machined several clearance faceswith cup-shaped grinding wheels and discussed the influenceof the diamond grain size of the used grinding wheels [15].Besides, the clearance processing technology has been men-tioned by some other researchers [1618]. However, thesestudies have not provided details of how to establish themathematical model of clearance machining process.

    In this paper, according to the practical machining process,enveloping theory and principles of spatial geometry model-ing technology, clearance machining processes are detailed.Mathematical models of wheel geometry, orientation, andlocation are calculated. Principle and problems in eccentricclearance machining process are emphasized. Accordingly,the clearance process simulation system is developed by usingUG second development technology. Furthermore, examplesof convex, eccentric, and elliptic clearance machining pro-cesses are carried out.

    G. Li : J. Sun (*) : J. LiSchool of Mechanical Engineering, Shandong University,Jinan 250061, Chinae-mail:

    G. Lie-mail:

    J. Lie-mail:

    G. Li : J. Sun : J. LiKey Laboratory of High Efficiency and Clean MechanicalManufacture, Ministry of Education, Shandong University,Jinan 250061, China

    Int J Adv Manuf Technol (2014) 75:667675DOI 10.1007/s00170-014-6154-3

  • Nomenclature

    0 Clearance angle 1 Inclination angle of wheelmachining the flat clearance

    Helical angle 2 Inclination angle ofwheel machining theeccentric clearance

    Adjacentcutter angle

    n1 Orientation of wheel machiningthe flat clearance

    P Lead of thecutting edge

    n2 Orientation of wheelmachining the eccentricclearance

    mR Radius ofend mill

    n3 Orientation of wheelmachining the convexclearance

    gR Radius ofgrindingwheel

    O1(xO1,yO1,zO1) Location of wheel machiningthe flat clearance

    gb Thickness ofgrindingwheel

    O2(xO2,yO2,zO3) Location of wheel machiningthe eccentric clearance

    O3(xO3,yO3,zO3) Location of wheel machiningthe convex clearance

    2 Clearance machining processes

    According to the difference of wheel types and grinding pro-cesses, the clearance geometry of end mill is generally dividedinto three kinds: flat, eccentric, and convex (Fig. 1). The flatclearance is the most common shape of end mills. As shown inFig. 1a, cup or cone-shaped wheel is used and the relativeposition to the end mill is shown. At the beginning, the wheelaxis (n1) is perpendicular to the end mill axis. To avoid thephenomenon of grinding burn caused by the overlarge contactarea, the wheel is then rotated. Therefore, the flat clearance ismainly ground by the wheel circumference. The eccentricclearance has a higher intensity and a longer tool life than theother two shapes. It is generally machined with a cylinderwheel, whose axis (n2) is coplanar with the axis of end mill(Fig. 1b). To grind a clearance angle, there must be a certainangle (2) between the two axes. The convex clearance has theminimum intensity. On the other hand, it has the easiest ma-chining process. Fig. 1c gives the wheel position relative to theendmill. The wheel axis (n3) is parallel to the endmill axis andits location could be deduced by the clearance angle 0.

    In practice, the grinding process of the clearance face isusually done from shank side to end teeth. In order to calculateconveniently, all of the process is beginning at the end teeth inthis paper, which will not influence the machining result.

    3 Flat clearance machining process

    As indicated in Fig. 2, coordinate system XgYgZg representsthe wheel frame while XYZ represents the stationary end mill

    frame. In this paper, the clearance is machined only after thehelical groove has been ground, the cutter tip is located atcoordinates (mR, 0, 0) and equations are expressed in the endmill frame.

    Figure 3 shows the transformation procedures of wheelcoordinate system for flat clearance machining. Assume thatthe wheel coordinate system is coincident with the end millcoordinate XYZ at the beginning, coordinate system XgY gZ gcan be deduced by two translation parameters mR and -gRfrom O along X-axis and Z-axis, respectively. Rotating theframe XgY gZ g by an angle 0 about its Zg-axis (get thecoordinate system Xg1Y g1Z g1), flat clearance angle with avalue of 0 could be machined. In order to avoid the phenom-enon of grinding burn, which is caused by too much contactarea between wheel and clearance, the wheel is then rotated tothe coordinate system Xg2Y g2Z g2 by an angle 1 (Fig. 3).Now, the initial wheel position relative to the end mill isobtained. The wheel orientation can be expressed by thefollowing vector:

    n1 cos 1 cos 0 ; cos 1 sin 0 ; sin 1 T 1

    and the wheel location can be expressed by

    xO1 mR gR sin 1 cos 0 yO1 gR sin 1 sin 0 zO1 gR cos 1



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