HP 5501A Operating And Service Manual page 71

2.35
Abbe
Error
A very important advantage of the Laser Transducer System is that the Abbe error evident in
almost
all
positioning systems is very easily reduced. Abbe error occurs when a displacement
measurement i s taken at a location which i s offset from the displacement to be measured and
the slideways which provide the displacement exhibit angular motion.
I n Figure 2-42A, the measurement axis is coincident with the leadscrew centerline and is
measuring a displacement of the carriage at the leadscrew. This figure illustrates the dis-
placement error
E which is generated at the tool tip due to angular motion 6 of the carriage.
Figure
2-42B shows the same carriage motion as Figure 2-42A but with the measurement
axis coincident with the tool path. I n this case the measurement system measures the actual
displacement and there is no Abbe offset error. This i s a general description of Abbe error
and illustrates the requirement for minimizing angular error and placement of the measure-
ment path.
ABBE OFFSET ERROR
MEASUREMENT AXIS
ABBE
OFFSET
ERROR IN MEASUREMENT
-dEh-
E
=
Ao ( s ~ n
H
' )
for small angles
(A)
r-----
-3-d-
I I
I
I
I
I
1
L-
, , , ,
1
L
TOOL
H
f
> - - -
MEASUREMENT ACTUAL
AXIS M DISTANCE OF--+
MOVEMENT
DISTANCE
zsz
OF
-4
Figure 2-42.
Abbe
Offset Error