Calculation of normal curvature of rake face of th

Calculation of the normal curvature of the rake face of cylindrical milling cutter

1. foreword

for the cutters whose rake face is plane, the rake angle and other geometric angles have long been approved by FDA and can be used for medical purposes to completely determine the orientation of the rake face; For the tool with curved rake face, the geometric angle can only determine the tangent plane of the rake face at the blade, but can not determine the shape of the rake face. The shape of the rake face, especially the bending of the rake face at the blade, has a great impact on chip curling, chip breaking and chip removal. It is an important performance index for flexible operation and random tool switching. Reference [1] studies how to accurately grind the normal rake angle of cylindrical helical edge milling cutter. On this basis, this paper will further study the rake face which has guaranteed the normal rake angle, and calculate its normal curvature at the blade, especially in the direction perpendicular to the blade, so as to understand the bending condition of the rake face at the blade, and provide a theoretical basis for manufacturing milling cutters with excellent performance

2. rake face description

Figure 1 shows the grinding of cylindrical milling cutter rake face with cylindrical grinding wheel. The grinding principle and the significance of each symbol have been described in document [1]. The rake face equation is [1]

where the sum is a parametric variable, and the sum of the tangent vectors in the direction of the parameter curve is

Figure 1 the relative position of the grinding wheel and the tool

this is generally seen from above. For point m in Figure 1, the single tangent vectors in the direction of the two parameter curves of point m are still represented by R and R, and they are

(5). In the formula, P is the spiral parameter of the rake face, Is the included angle between the m point and the xoz plane

the unit normal vector n of the m point (the positive direction is from the rake face to the chip holding groove) is

3. the normal curvature k

in the direction is shown in Figure 1. The intersection line between the grinding wheel end face and the rake face (1) is a circle with radius RC, and its curvature at the m point is. Since it is a plane curve, the unit principal normal vector C of this point is (Fig. 1)

and the included angle 1 between

cos 1 =. = Nxsin cos w-nysin sin W + nzcos (10)

the normal curvature

4. the normal curvature K in the direction and the short-range torsion g

because the rake face is a cylindrical helicoid, the parameter curve is the helicoid on the cylindrical face with radius r = D/2. The curvature K and torsion at any point of the cylindrical helix are constant. They are (see example 2 of [2] p41)

the principal normal vector at any point of the helix intersects the axis of the helix vertically (see exercise 3 of [3] P59). Therefore, the unit principal normal vector of point m is

= O, - sin, - cos (14)

and the included angle between the normal vector n of the rake face 2 is

cos 2 =. = - In order to overcome the disadvantages of the construction process, the normal curvature K of the direction is

the included angle between the normal vector of the helical surface at any point along a helical line (parameter curve) on the cylindrical helical surface and the helical surface axis (x axis) is also fixed, so the intersection angle between the main normal vector of the helical line and the normal vector of the helical surface at the corresponding point is also fixed. From this, we can get (see Theorem 3 of [2] p237)

5. The normal curvature of point m and the radius of curvature of the normal section of the rake face m

Figure 2 shows the situation in the tangent plane of point M. It is also the normal section direction of the blade at point M. the normal curvature of this direction is expressed in kn, so the short-range torsion in this direction is - G

the included angle between the tangent plane

of point m in Figure 2 and

is

cos = R The normal curvature and short-range torsion in the direction of R (18)

meet the requirements of

k = k Cos2 + 2G sin cos + knsin2

so

kn = (K-K cos2-2g sin COS)/sin2 (19)

so that the curvature radius m of the normal section of point m is

after obtaining kn, The normal curvature K and short-range torsion g in any direction R (Fig. 2) can be obtained as

k = k Cos2 + 2G sin cos + knsin2 (21)

g = (kn-k) sin cos + G (cos2-sin2) (22)

so far, the problem of normal curvature at point m has been completely solved. In actual cutting, the chip flow direction is generally not in the RN direction. According to formula (21), the normal curvature of the chip flow direction can be calculated, and then the bending condition of the rake face in the chip flow profile (not necessarily the normal section) can be studied

6. calculation example and description

take the end milling cutter as an example, the milling cutter diameter d = 50mm, the helix angle = 45, the normal rake angle n = 15, the grinding depth h = 10mm, the grinding wheel radius RC = 35mm, the included angle between the grinding wheel axis and the tool axis W + 90 = 136.5, the grinding center distance h = 48.874mm, and the grinding offset e = -8.338. Obtain K ＝ 0., G ＝ 0.02, K ＝ 0., = 120., m ＝ 39.4074mm

for certain cutting conditions and specific chip curling, chip breaking and chip removal requirements, there is an ideal rake face bending condition, which can be characterized by m when designing tools. When the M calculated according to the given grinding process parameters cannot meet the requirements, some adjustable parameters can be changed, such as recalculating RC and W