10.2.1 General
Four parameters are generally required to specify the coaxiality error between the two axis average lines (see 3.7.2). Two of these parameters specify parallelism error between the two axes and the other two are the offsets between the two axes, all specified in two orthogonal planes (e.g. vertical and horizontal). Therefore, the methods used to measure parallelism error between two axes of rotation (see 10.1.5) may also be used to measure coaxiality error. Similarly, any method used for measuring coaxiality error, may also be used to measure parallelism error between two axes of rotation.
10.2.2 Stationary point run-out method (rim and face method)
This method is a very practical measurement method to yield both offset and parallelism error, while not requiring any precision artefacts. This measurement method requires the use of two linear displacement sensors mounted on one of the spindles (or rotary table) and a target bracket mounted on the other spindle (or rotary table) as shown in Figure 60. Displacement sensors are set to measure displacement of the target bracket in the radial (rim) and the axial (face) directions.
Copyright International Organization for Standardization
--`,,```,,,,````-`-`,,`,,`,`,,`---
74 © ISO 2012 – All rights reserved
The two axes are rotated together reading the displacement sensors at the 0°, 90°, 180° and 270° positions.
These measurements should be repeated three times to avoid thermal effects. The coaxiality error parameters of the two axes in two planes are given by Equations (11) to (14):
Vertical offset, VO:
0 180
O 2
R R
V
(11)
Vertical angle, VA:
180 0
A
F F
V D
(12)
Horizontal offset, HO:
90 270
O 2
R R
H
(13)
Horizontal angle, HA:
270 90
A
F F
H D
(14)
where
R0 is the mean radial reading at 0° angular position;
R90 is the mean radial reading at 90° angular position;
R180 is the mean radial reading at 180° angular position;
R270 is the mean radial reading at 270° angular position;
F0 is the mean axial reading at 0° angular position;
F90 is the mean axial reading at 90° angular position;
F180 is the mean axial reading at 180° angular position;
F270 is the mean axial reading at 270° angular position;
D is the diameter of the circle travelled by the face displacement sensor centreline.
NOTE The circle diameter defined by the linear displacement sensor measurement point for the face measurement corresponds to the length over which the coaxiality error is assessed.
Before commencing the test, the sag (compliance) of the brackets may be measured. This is done by attaching the brackets to a stiff mandrel supported between centres as shown in Figure 61. For spans of up to 200 mm, a steel mandrel 50 mm in diameter is considered adequate. (For very high accuracy machines, a calculation of the required mandrel diameter should be made or a correction applied for mandrel sag.) The displacement sensors are zeroed at the top position (0° position in Figure 61) and the mandrel rotated until the linear displacement sensors are at the bottom position (180° position in Figure 61). The readings of both displacement sensors indicate the effect of the sag in each direction.
When only one of the two axes is an axis of rotation, the arm carrying the measuring instrument should be fixed to the mandrel representing the axis around which rotation is effected. If the measuring instrument is required to rotate around a fixed mandrel, it should be mounted on a ring rotating with a minimum amount of
Copyright International Organization for Standardization
--`,,```,,,,````-`-`,,`,,`,`,,`---
© ISO 2012 – All rights reserved 75 play. This ring should be of sufficient length to ensure that the reading is not affected by the clearance in the ring.
The parallelism error measured by the rim and face method is affected by axial error motion of the rotating components being tested. To eliminate this source of measurement uncertainty, the measurement setup may be modified as shown in Figure 62. In this setup, a second radial displacement sensor mounted on the target spindle replaces the axial displacement sensor. Then, the horizontal and vertical angle calculations are based on the differences of the offsets measured by the sensors divided by the distance between the two sensors.
a) Side view b) Measurement positions (end view) Key
1 radial linear displacement sensor 2 axial linear displacement sensor 3 target bracket
g gravity
Figure 60 — Coaxiality error measurements using stationary point run-out method
a) Side view b) Measurement positions (end view) Key
1 radial linear displacement sensor 2 axial linear displacement sensor 3 steel mandrel
4 centre g gravity
Figure 61 — Calibration of the sag of the test rig
Copyright International Organization for Standardization
--`,,```,,,,````-`-`,,`,,`,`,,`---
76 © ISO 2012 – All rights reserved
a) Side view b) Measurement positions (end view) Key
1 radial linear displacement sensor 2 second radial linear displacement sensor 3 target bracket
g gravity
Figure 62 — Elimination of influence of axial error motion in coaxiality error measurements