Abrading – Precision device or process - or with condition responsive... – With indicating
Reexamination Certificate
2000-06-23
2004-05-04
Rose, Robert A. (Department: 3723)
Abrading
Precision device or process - or with condition responsive...
With indicating
C451S049000
Reexamination Certificate
active
06729936
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to technologies for measuring dimensional errors of a cylinder of an object to be integrally rotated about a rotation axis, the cylinder being eccentric with the rotation axis as planned or not.
2. Discussion of the Related Art
Conventionally, grinding a workpiece such as a crankpin of a crankshaft used in a gasoline engine, or a cam, is effected by precisely synchronizing a rotary motion of the workpiece about a rotation axis (referred to as the “C-axis” where appropriate), and a linear motion of a tool stand such as a grindstone stand in a direction (referred to as the “X-axis direction”) perpendicular to the C-axis.
In the conventional art, by virtue of an advanced technology in the field associated with devices such as a servo-control device or a numerical control device, accuracies in the follow-up control, the synchronization or the movement of a machine has been improved.
However, it is the fact that only the improved accuracies in those areas above-mentioned, cannot adequately eliminate a profile error of a workpiece due to a change in rigidity of the workpiece, a change in a grinding force acting on the workpiece, and the like. Therefore, for a high precision in grinding, it is traditional that a workpiece is removed from a grinding machine before completion of a grinding process for the workpiece, and then geometrical errors of the workpiece (e.g., a circularity deviation of a crankpin and a profile of a cam) is measured. The measurements are used to obtain an amount of compensation for motion of the workpiece in a direction of the C- or X-axis, and subsequently the grinding for the same workpiece is initiated again under the new machining condition compensated accordingly.
In the field of measurement technology, there is generally well known a method employing a three-point contact type described in a technical paper titled “METHOD FOR MEASURING CIRCULARITY DEVIATION OF CYLINDRICAL WORKPIECE” (Japan Mechanical Engineering Association, Vol. 53, No. 376, May 1950), for example, as a method for accurately measuring a circularity deviation of a cylindrical workpiece. This technical paper explains a theoretical analysis for a case where a circularity deviation of a cylindrical workpiece is measured using a measuring device of a three-point contact method including a V-block type, a riding gauge type (wherein the V-shaped gauge is used so as to ride on the cylindrical workpiece) and a three-armed type. The paper teaches a method for quantitively obtaining an error of a cylindrical workpiece from a geometrically true circle in the manner shown by the following equations (1)-(6) and in
FIGS. 14-16
in the case of the riding type, by way of example.
Variables, symbols, functions, etc. which will be used for explanation of the content of the technical paper, are defined as followed:
(Figure Symbols)
K: cylindrical workpiece such as a crankpin (i.e., a circumference of a cross sectional profile of the workpiece)
O: original point (i.e., one arbitrary point near the center of the circumference “K”: a fixed point on the cross section of the workpiece)
C: arbitrary and stationary point defining an original line OC on a cross section of the workpiece)
M: gauge cylinder with a standard dimension of a radius am (i.e., a circumference of a cross section of the gauge cylinder)
a: point of contact of an end face of a measuring head of the measuring device of the three-point contact type (i.e., the riding gauge type) with the circumference “K”
b: one of two contact points at which two contact surfaces of the riding gauge contact the circumference “K”
c: the other of the two contact points mentioned above
d: reference or datum point of the riding gauge (i.e., a center point of an opposing angle &agr; mentioned below)
a′: foot of perpendicular pendent from the original point O to an end face of the measuring head of the measuring device
b′: foot of perpendicular pendent from the original point O to one of the two contact surfaces of the riding gauge
c′: foot of perpendicular pendent from the original point O to the other of the two contact surfaces of the riding gauge
(Variables)
&thgr;: angle relative to the original line OC
&agr;: opposing angle between the two contact surfaces of the riding gauge which are opposed to each other not in parallel
n: natural number (i.e., an index of the expansion of the Fourier series)
(Constants)
a
0
: average radius of circumferences “K”
c
n
: expansion coefficient of each term of the Fourier series for a radius r(&thgr;) as mentioned below, when the expansion thereof is performed (obtained by the harmonic analysis)
&phgr;
n
: initial phase of each term of the Fourier series for the radius r(&thgr;) when the expansion thereof is performed (obtained by a harmonic analysis)
a
m
: radius of the gauge cylinder “M”
m
y
: average of outputs y(&thgr;) of the measuring device, as mentioned below
J: upper limit of the natural number n mentioned above (practically, “J” is enough when adopts about “50.” In the technical paper mentioned above, the principle consideration is taken up to when J=12.).
N: the number of measuring times which the outputs y(&thgr;) are actually measured (i.e., the sampling number of the measuring points)
(Functions)
r(&thgr;): function for a radius of the circumference “K”, and of the angle &thgr; as an independent variable of the function
y(&thgr;): function for an output of the measuring device of the three-point contact type, and of the angle &thgr; as an independent variable of the function
&mgr;(&agr;,n): function for a magnification of each component of a spectrum shown in the output y(&thgr;), which magnification serves to magnify a value of the term “c
n
cos(n&thgr;+&phgr;
n
) ” in the equation (3) mentioned below
r
(&thgr;)=
a
0
+
n=1
&Sgr;
J
c
n
cos(
n&thgr;+&phgr;
n
(1)
a
m
{1/sin(&agr;/2)−1
}−y
(&thgr;)={
r
(&thgr;+&pgr;/2−&agr;/2)+
r
(&thgr;−&pgr;/2+&agr;/2)}/{2 sin(&agr;/2)}−
r
(&thgr;) (2)
y
(&thgr;)=(
a
0
−a
m
)·{1−1/sin(&agr;/2)}+
n=2
&Sgr;
J
{&mgr;(&agr;,
n
) c
n
cos(
n&thgr;+&phgr;
n
)} (3)
&mgr;(&agr;,
n
)=1−{cos
n
(&pgr;/2−&agr;/2)}/sin(&agr;/2) (4)
m
y
=
∫
y
(
θ
)
ⅆ
θ
/
2
π
(
interval
of
integral
:
0
≦
θ
≦
2
π
)
=
(
a
0
-
a
m
)
·
{
1
-
1
/
sin
(
α
/
2
)
}
=
(
∑
i
=
0
N
-
1
y
i
)
/
N
(
5
)
a
0
=
a
m
+
m
y
/
{
1
-
1
/
sin
(
α
/
2
)
}
(
6
)
a
0
=a
m
+m
y
/{1−1/sin(&agr;/2)} (6)
The expansion coefficients c, and initial phases &phgr;
n
for all the natural numbers n can be calculated when the outputs y(&thgr;) are measured using a suitable opposing angle &agr; or a suitable combination of opposing angles &agr; in the three-point contact method. Therefore, it will be understood from the technical paper mentioned above that an error in profile of the actual cylinder K from a geometrically true circle (represented by the gauge cylinder “M”) can be quantitively obtained as “&dgr;r=r(&thgr;)−a
m
according to the above equation (1). Wherein, the gauge cylinder “M” with a standard dimension of the radius a
m
is a desired cylinder.
It is noted that those definitions of variables, symbols, functions, etc. will be applicable to the following explanation.
The conventional technology mentioned above suffers from the following problems, and therefore, a general improvement in the art has been expected:
(Problem 1)
In a case where a workpiece is removed from a grinding machine before completion of a grinding process thereby, and where an accurate measurement of a profile of the workpiece (
Hori Nobumitsu
Naya Toshiaki
Niino Yasuo
Sasaki Yuji
Rose Robert A.
Toyoda Koki Kabushiki Kaisha
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