Insert having sinusoidal undulations for ball nose end mill

An insert for use in a ball nose end mill is provided that includes an insert body having a top wall, a bottom wall, and at least one arcuate side wall. An arcuate cutting edge is defined at an intersection between the top and side walls that includes a plurality of sinusoidal undulations for reducing cutting forces, and vibration, and enhancing the breaking and removal of chips removed from a workpiece during a cutting operation. An end portion of the insert crosses the axis of rotation when the insert is mounted in the seat of an end mill body, and the undulations reduce the considerable shear forces applied to the cutting edge at this location. The cutting edge has a profile which follows the contour of a sphere to permit machining a rounded cut. The side wall of the insert body includes an upper relief portion disposed directly under the cutting edge, with a relief angle for preventing the undulations from making unwanted striations or tool marks in the sidewalls of the rounded cut.

BACKGROUND OF THE INVENTION 
This invention generally relates to an insert for a ball nose end mill, and 
is specifically concerned with such an insert having sinusoidal 
undulations along its cutting edge for reducing cutting forces and 
vibration and facilitating the breaking and removal of chips. 
Inserts for ball nose end mills are well known in the prior art. Such 
inserts typically comprise an integral body formed from a hard, wear 
resistant material having at least one arcuate cutting surface that may be 
quadrant-shaped. The end mill itself includes an elongated cylindrical 
body having a shank portion for attachment to a turning tool, and a 
hemispherically-shaped end having a quadrant-shaped seat for receiving and 
mounting the insert. The portion of the cutting edge nearest the tip of 
the hemispherically-shaped end crosses over the axis of rotation of the 
end mill a short distance to insure that the cutting edge of the insert 
engages the workpiece along the axis of rotation of the end mill body, 
thus allowing the end mill to perform a plunge operation in a workpiece. 
Such ball nose end mills have proven to be highly versatile machine tools 
that are capable of performing plunge-type cutting much like a drill, or 
face-type milling like a conventional milling head, or even ramp-type 
machine operations that combine the motions of both plunge and face-type 
cutting. However, the applicants have noted a number of shortcomings in 
the performance of the insert used with such end mills where performance 
could be substantially improved. For example, the applicants have noted 
that the region of the cutting edge that intersects the axis of rotation 
is subjected to large amounts of heat-generating shear forces since the 
rotational speed of the edge is zero at the axis, and very slow in the 
portion of the edge adjacent to the axis. Some insert designers have 
attempted to solve this problem by shaping the cutting edge so that it 
falls short of traversing the axis of rotation. Unfortunately, such a 
design necessarily creates a small protrusion of uncut workpiece material 
at the point where the axis of rotation of the end mill body intersects 
the workpiece. While the unwanted protrusion of uncut material is 
periodically broken off due to the forces applied to it by the cutting 
operation, a small rough spot along the axis of rotation can be created on 
the surface of the cut. 
Still other shortcomings include the relatively higher cutting forces and 
vibrations associated with the use of a prior art ball nose end mill 
versus the use of a more conventional (but unfortunately less versatile) 
milling cutter. The applicants have observed that one of the causes of 
such higher cutting forces and vibration is that all points of the cutting 
edge of the inserts used in such end mills orthogonally engage the 
workpiece at all times during the cutting operation. While it is possible 
to reduce the cutting forces and vibrations by mounting the insert at an 
angle with respect to the axis of rotation of the cutter body (thereby 
imparting an axial rake angle to the insert), such a technique requires 
the provision of relatively deep insert seats, which in turn weakens the 
body of the cutter. Additionally, such a tilted mounting of the insert can 
produce an unwanted concavity in the sidewalls of the cut made by the end 
mill, thus creating a distortion in the shape of the cut when a true 
hemispherical profile is desired. 
Finally, the applicants have noted that some inserts for such ball nose 
cutters do not effectively embrittle the metal chips that result from 
certain cutting operations. Hence, if such a cutter is used to implement a 
fine-cut plunge operation in a highly ductile material, the insert used in 
the cutter may not effectively embrittle the resulting foil like chips, 
which can interfere with their expulsion from the chip-expelling flute of 
the cutter body and thus interfere with the cutting operation. 
Clearly there is a need for an insert for use in a ball nose end mill that 
is capable of producing rounded cuts in a workpiece without the generation 
of large stresses and frictional heat where the cutting edge intersects 
the center line of the cutter. Ideally, such a cutter should be able to 
cut a workpiece with lower cutting forces and with less vibration than the 
inserts of the prior art without the need for tilting the insert at a 
substantial axial rake angle, thereby reducing power requirements while 
increasing tool longevity. Finally, it would be desirable if such an 
insert were capable of imparting substantial embrittling forces to the 
chips resulting from a cutting operation so that even very thin chips 
formed from highly ductile metals will curl and break into small pieces 
during a cutting operation. 
SUMMARY OF THE INVENTION 
The invention is an insert for use in a ball nose end mill that overcomes 
or ameliorates all of the aforementioned shortcomings associated with 
prior art inserts. 
The insert of the invention generally comprises an insert body having a top 
surface, a bottom surface, and at least one arcuate side surface, and at 
least one arcuate cutting edge defined at the intersection between the top 
and side surfaces that includes a plurality of sinusoidal undulations. The 
undulations advantageously reduce both the cutting forces and vibration 
associated with the operation of the insert without the need for canting 
the insert at an axial rake angle that would weaken the toolholder, and 
further enhance the curling, breaking, and removal of the metal chips 
produced by cutting. 
The insert is particularly adapted for use in an end mill body rotatable 
about an axis that has a shank portion at one end for attaching the mill 
body to a turning tool, and an insert seat at its other end for mounting 
the insert such that an end portion of the arcuate cutting edge rotates 
about the axis of rotation. The profile of the cutting edge is arcuate, 
and designed to make a hemispherically-shaped cut when rotated by an end 
mill body. A portion of the arcuate cutting edge crosses over the axis of 
rotation of the end mill body. The undulations further serve to 
advantageously reduce the substantial shear forces that are generated in 
the portion of the cutting edge that traverses the axis of rotation. 
The side surface of the insert includes a lower relief portion that 
terminates along the bottom surface of the insert body, and an upper 
relief portion that terminates at the undulating cutting edge. The upper 
relief portion is blended between the undulating cutting edge and the 
lower relief portion to provide at least a minimum relief angle with the 
workpiece. Such a combination allows the undulating cutting edge to make 
accurately rounded cuts whose walls are substantially free of unwanted 
striations or other undesirable tool mark patterns. 
The top surface of the insert body includes a land portion disposed behind 
the cutting edge for strengthening the edge. In the preferred embodiment, 
the land portion is inclined between 5.degree. and 10.degree. with respect 
to the plane of the top surface to impart a positive rake angle to the 
edge, which also helps to reduce cutting forces. 
The top surface of the insert body also includes a chip curling groove 
disposed behind the land portion having rounded bottom, front, and rear 
walls, the end portions of the front and rear walls being inclined between 
about 15.degree. and 30.degree. with respect to the plane of the top 
surface. The width of the chip curling groove is about five times the 
height between the lower most point of the trough and uppermost point of 
the crest of each of the undulations. Such dimensioning, in combination 
with the positive rake angle imparted to the cutting edge by the land 
portion, applies substantial curling forces to chips produced by the 
cutting edge, which in turn tends to work-harden them. Additionally, the 
crest and trough portions of each of the undulations alternately apply 
tensile and compressive forces to such chips, which tend to further 
work-harden them by pleating them. The combination of the curling and 
pleating forces results in substantial chip embrittlement, which in turn 
causes the chips to readily break into small pieces which are easily 
expelled from the vicinity of the cutting operation by the chip removing 
flutes in the mill.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
With reference to FIG. 1, wherein like numerals represent like components 
throughout all the several figures, the invention is particularly adapted 
for use in a ball nose end mill 1 having an elongated body 3 that rotates 
about an axis A when performing a cutting operation. The end mill body 3 
includes a shank portion 5 having a flat 7 which is detachably connectable 
to a turning tool (not shown). The end mill body 3 further includes a 
generally hemispherically-shaped end portion 9 having a seat 11 in the 
form of a recess that is complementary in shape to the cutting insert 15 
of the invention. The insert 15 is secured in the seat 11 by means of a 
mounting screw 17. A locking shoulder 18 interfits with an end recess 
present the insert 15 to prevent the insert from moving rotatably with 
respect to the mounting screw 17. 
With respect now to FIGS. 2 and 3, the insert 15 of the invention is 
comprised of an insert body 22 that is integrally formed from a hard, wear 
resistant material such as tungsten carbide, although any number of 
materials well known in the prior art may also be used for this purpose. 
The insert body 22 includes a top wall 24 having a planar portion 26, and 
a planar bottom wall 28. The top and bottom walls 24 and 28 are 
interconnected by means of a pair of opposing, arcuate sidewalls 30. The 
insert body 22 further includes a pair of opposing end recesses 32 that 
are complementary in shape to the locking shoulder 18 of the end mill body 
3 for securing the insert 15 in the seat 11 as previously described. 
The insert body 22 includes a pair of opposing, indexable cutting edges 34 
defined at the intersection between the arcuate sidewalls 30 and the top 
wall 24. Each cutting edge 34 includes at least two undulations 36, and 
more preferably between three and five undulations, as best seen in FIG. 
2. Each undulation includes a crest portion 38 and a trough portion 40, 
which together make up a single, sinusoidal wave. In the preferred 
embodiment, each of the undulations 36 has the same period and amplitude. 
Preferably the height h of each of the undulations 36 is no more than 40% 
of the maximum thickness T of the insert body 22. If the height h is much 
greater than 40% of the thickness T, then the insert body 22 becomes 
excessively weakened at the trough portions 40 of the undulations 36, 
which could lead to the breakage of the insert 15. 0n the other hand, if 
the height h is less than about 15% of the insert thickness T, the cutting 
force and vibration reducing advantages of the invention become 
substantially impaired. In the preferred embodiment, the height h is about 
25% of the insert thickness T. 
As shown in FIG. 2, each cutting edge 34 is arcuate along its length with 
respect to the center point C of a circle having a radius R in which the 
center point C is co-planar with the flat portion 26 of the top wall 24. 
As shown in FIG. 3, each cutting edge 34 is also arcuate along its width 
such that each edge 34 conforms with the wall of a sphere S having the 
same center point C. Such contouring advantageously allows the cutting 
edge 34 to make a hemispherical cut in a workpiece while utilizing the 
benefits provided by the undulations 36 in the edge 34. 
Each of the sidewalls 30 includes a lower relief surface 42, and an upper 
relief surface 44. The lower relief surface 42 is preferably inclined at 
an angle "a" of between about 7.degree. and 15.degree. relative to a line 
disposed orthogonally with respect to the planar portion 26 of the top 
wall 24. A smaller angle might not insure that the cutting edge 34 can 
engage a workpiece without interference from the sidewall 30, while a 
larger angle could unduly weaken the cutting edge 34. 
As is shown in FIGS. 4A through 4C, the cutting edge 34 intersects with the 
upper relief surface 44 as it ascends from the trough portion 40 to the 
crest portion 38 of the undulations 36. The upper relief surface 44 is, in 
effect, blended between the spherical cutting edge 34 and the lower relief 
surface 42 to provide a relief angle f.sub.1 -f.sub.3 between the cutting 
edge 34 and the sidewall of the insert 15 while preserving the spherical 
profile of the edge 34. FIG. 4A illustrates the case where the cutting 
edge 34 intersects the trough portion 40 of the undulations 36. In this 
case, there is almost no upper relief surface 44, and a relatively wide 
relief angle f.sub.1 is provided by the lower relief surface 42. However, 
in the case of FIG. 4B where the cutting edge 34 intersects an 
intermediate portion between the crest 38 and trough 40 portions, an upper 
relief surface 44 interconnects the bottom edge of the cutting edge 34 
with the upper edge of the lower relief surface 42, and provides a relief 
angle f.sub.2. In this figure, h.sub.1 illustrates the height of the 
spherical cutting edge 34, while h.sub.2 illustrates the height of the 
upper relief surface 44, where h.sub.1 +h.sub.2 is equal to h. FIG. 4C 
illustrates the case where the cutting edge 34 intersects the crest 
portion 38 of an undulation 36. Here, the length h.sub.2 of the upper 
relief surface 44 is maximized, and equals the height h of the undulations 
36. As is evident in the drawings, the upper relief surface 44 continues 
to provide a relief angle f.sub.3 to the cutting edge 34. In all cases, 
the relief angle is at least 3.degree.. 
With specific reference again to FIG. 3, the top wall 24 includes a narrow 
land 46 disposed immediately behind the cutting edge 34. The land 46 
advantageously strengthens the cutting edge 34, thereby increasing the 
longevity of the insert 15. In the preferred embodiment, the land 46 is 
disposed at a rake angle "b" of between about 5.degree. and 10.degree. 
with respect to the planar portion 26 of the top surface 24. Such a 
positive rake angle helps to reduce cutting forces by insuring that the 
cutting edge 34 cuts the workpiece 66 (shown in FIG. 5) by a slicing 
action, as opposed to a scraping action. 
Immediately disposed behind the land 46 is a chip curling groove 48. The 
groove 48 is essentially arcuate in cross-section, having a rounded bottom 
wall 50, a rounded front wall 52, and a rounded rear wall 54. The rounded 
rear wall 54 terminates in a straight back wall 56 that is orthogonal with 
respect to the planar portion 26 of the top wall 24. The front and rear 
walls 52, 54 of the groove 48 are disposed at angles "d" and "e" with 
respect to the planar portion 26 of the top wall 24, which encourages 
chips produced by the cutting edge 34 to curl as they slide over the top 
wall 24 of the insert 15. In the preferred embodiment, both angles d and e 
are preferably between about 20.degree. and 30.degree. from the plane of 
the top surface 24. Since these walls are arcuate, these angles are 
determined from a line tangential with the outer edges of the front and 
rear walls 52,54. 
Disposed directly in the center of the insert body 22 is a bore 58 for 
receiving the previously-mentioned mounting screw 17. The bore 58 includes 
a shank portion 60 and a head portion 62 for receiving the shank and head 
of the mounting screw 17, respectively. 
FIGS. 5 and 6 illustrate how the cutting insert 15 of the invention 
operates when mounted in the seat 11 at the hemispherical end portion 9 of 
an end mill body 3 and rotated about an axis A of rotation. A small 
segment 67 of the cutting edge extends over the axis of rotation A so that 
all portions of the rounded cut 64 are engaged by the cutting edge 34. 
While the amount of shear forces and heat generated in the vicinity of the 
edge segment 67 are higher than in other parts of the edge 34 due to the 
fact that the rotational speed of the edge is zero at this point, the 
undulations 36 reduce the shear forces and the heat by lowering the 
cutting forces all along the edge 34, and by further reducing the 
vibration associated with the cutting operation. These advantageous 
reductions in cutting forces, heat, and vibration result from the fact 
that the cutting edge 34 does not initially cut the workpiece 66 
simultaneously along the same line. Instead, the crest portion 38 of the 
undulations 36 form leading portions of the cutting edge that engage the 
workpiece 66 first, while the trough portions 40 provide trailing portions 
of the edge 34. Additionally, these undulations 36 advantageously produce 
metal chips 68 having embrittling pleats 70 therein. As is shown in FIG. 
5, such pleating is caused by the fact that the crest portion 38 of each 
undulation 36 tends to spread the chip outwardly during the cutting 
operation, thereby creating a thinned portion 71, while the trough portion 
40 of each undulation 36 tends to create compressed portion 72 in the chip 
68. The generation of such pleats 70 with alternately thinned and 
compressed portions 71 and 72, in combination with the curling forces 
applied to the chips 68 as a result of the positive rake angle of the land 
46 and the provision of the chip curling groove 48, effectively embrittle 
even very fine chips, which in turn allows them to be broken up and easily 
expelled out of the flute 19 present in the hemispherical end portion 9 of 
the end mill body 3. 
While this invention has been described with respect to a specific 
embodiment, various additions, modifications, and variations of this 
invention will become evident to persons skilled in the art. All such 
modifications, additions, and variations are within the scope of this 
invention, which is limited only by the claims appended hereto.