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Geometric modeling of single point cutting tool surfaces

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Abstract

In this paper we have established a new three-dimensional standard to specify single point cutting tool geometry. The paper models a single point cutting tool in terms of biparametric surface patches. Six new angles, called grinding angles, are proposed to define the orientation of these surface patches. Forward and inverse mappings among grinding angles (α i , β i , γ i ), conventional tool nomenclature (γ y, γ x, α y, α x , ..... ), and setting or swivel angles for grinding (θ A , θ B , θ C ) are established. The benefits of the new paradigm include ease of finite element based engineering analysis, simulation, and programming of the CNC tool cutter and grinder for tool sharpening. The proposed methodology is illustrated with a few numerical examples.

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Abbreviations

R :

Rotation matrix

T :

Translation matrix

d ij :

Displacement of i th plane in j th direction

n f :

Vector normal to rake face

n p :

Vector normal to principal flank

q ax , q ay , q az :

Transformed coordinates of any point on auxiliary flank

q px , q py , q pz :

Transformed coordinates of any point on principal flank

q rx , q ry , q rz :

Transformed coordinates of any point on rake face

q sx , q sy , q sz :

Transformed coordinates of any point on shoulder face

r:

Nose radius

u, v, w :

Parametric coefficients

α 1 :

Grinding angle for auxiliary flank about the x axis

α 2 :

Grinding angle for principal flank about the x axis

α 3 :

Grinding angle for rake face about the x axis

α n :

Normal clearance angle on the principal flank

α′1 :

Normal clearance angle on the auxiliary flank

α o :

Orthogonal clearance angle on the principal flank

α′o :

Orthogonal clearance angle on the auxiliary flank

α x :

Side clearance angle on the principal flank

α y :

End clearance angle on the principal flank

α'′x :

Side clearance angle on the auxiliary flank

α'′y :

End clearance angle on the auxiliary flank

β 1 :

Grinding angle for auxiliary flank about the y axis

β 2 :

Grinding angle for principal flank about the y axis

β 1 * :

Actual angle of the secondary cutting edge measured from the wire frame model

β 2 * :

Actual angle of the principal cutting edge measured from the wire frame model

γ 3 :

Grinding angle for rake face about the z axis

γ n :

Normal rake angle

γ o :

Orthogonal rake angle

γ x :

Side rake angle

γ y :

Back rake angle

λ :

Inclination angle

λ e :

Inclination angle of auxiliary cutting edge

θ :

Tool setting angle on a tool cutter and grinder

φ :

Principal cutting edge angle

φ e :

End cutting edge angle

φ s :

Side cutting edge angle

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Acknowledgment

The authors are thankful to the Department of Science & Technology (DST), Government of India for sponsoring a project to work on modeling of cutting tools. The authors further wish to acknowledge the work done by Mr. Tushar Rajpathak and Mr. Yogesh Deo in particular, as well as all the engineers and staff of CAD-P Laboratory, IIT Kanpur for helping in one way or another.

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Authors and Affiliations

  1. Computer Science & Engineering Department, Indian Institute of Technology Kanpur, Kanpur 208016, India

    P. Gupta

  2. Mechanical Engineering Department, Indian Institute of Technology Kanpur, Kanpur 208016, India

    Puneet Tandon & S. G. Dhande

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  1. Puneet Tandon
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  2. P. Gupta
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  3. S. G. Dhande
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Correspondence to P. Gupta.

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Tandon, P., Gupta, P. & Dhande, S.G. Geometric modeling of single point cutting tool surfaces. Int J Adv Manuf Technol 22, 101–111 (2003). https://doi.org/10.1007/s00170-002-1447-3

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