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2
1. Introduction
After years of grinding my tools on a bench grinder, I decided to buy a Tormek-T7
grinder in order to get better control on the sharpening and eliminate the risk of
loosing hardening by overheating
After some experimenting and grinding of the available knives, blades, scissors etc.
it became clear to me that the reproducibility of the grinding angles was rather poor
if the adjustment was done according to the procedure described in the handbook.
Good reproduction can be obtained if the bevel is coloured with a marker pen and
the support is adjusted until the stone clears the bevel.
That method however is not fast and easy. I wanted a simple method which could
be realised by measuring and adjusting the position of the universal support and the
length of the adjustable jig.
This document describes the method which I use since then, it derives the mathem-
atical background and gives tables which can be used instead of the mathematical
formulas.
Denominations
In the handbook you can read:
"In the literature on this subject, there are various denominations for the edge angle.
It is called bevel angle, cutting angle or sharpening angle. The edge angle on a tool
with bevels on both sides is called the included bevel angle, the effective bevel
angle, profile angle, total cutting angle or the combined bevel angle."
That was rather confusing, therefore I decided to use "grinding angle" which in my
opinion is unambiguous. Dutch however is the native language of the author rather
than English, so it might turn out to be "double-dutch" for the reader. The author
asks for comprehension if that might happen occasionally.
2. The cosine rule
The proposed adjustment procedure is based on the cosine rule.
In trigonometry, the cosine rule (also known as the cosine formula or law of cosines)
relates the lengths of the sides of a triangle to the cosine of the opposite angle.
Using notation as in Fig. 2.1, the cosine rule states:
2
2
2
=a
+b
!2ab"cos(" )
c
where " denotes the angle con-
tained between sides of lengths a
and b and opposite the side of
length c.
The law of cosines is useful for
computing the third side of a tri-
angle when two sides and their en-
closed angle are known, and in
computing the angles of a triangle
Fig. 2.1: A triangle. The angles ! (or A),
if all three sides are known.
Identical formulas can be given for
the other sides::
2
2
2
a
=b
+c
! 2bc"cos (#)
2
2
2
and b
=a
+c
! 2ac"cos ($)
Grinding Angle Adjustmentl
C
"
a
b
$
#
B
A
c
" (or B), and # (or C) are respec-
tively opposite the sides a, b, and c.
© 2013 Ton Nillesen
Table 9. Personal choices
Knife
15
grinding
angle
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