Axis perpendicularity test

1. Test Objective:

Detect the perpendicularity of two orthogonal axes.

2. Test Instruments:

Photoelectric autocollimator (hereinafter referred to as optical tube), resolution not less than 0.1"; Plane mirror.

3. Test Environment Conditions

Ambient temperature: 20±2℃;

Relative humidity: ≤70%;

Vibration isolation requirements: The turntable under test shall be placed on a vibration isolation foundation, with no severe vibrations or impacts in the surrounding area.

4. Test Methods

The perpendicular error angle θ of the two orthogonal rotation axes 1 and 2 is shown in Figure 103-1a.                   

                                                         Figure 103-1

If axis 1 is rotated 180° around axis 2, axis 1 will change from position A0A0 ' to A1A1 ' . The angle between the axis before and after the rotation can be used to obtain twice the vertical error angle 2θ , as shown in Figure 103-1b.

4.1 Perpendicularity of the axis of rotation

Install a double-sided reflector (there must be an optical path through hole inside the shaft) at one end of the shaft 1 being measured, or install a plane mirror I and a plane mirror II at each end of the shaft . The light tube is in a horizontal position and aligned with one end of the shaft 1, as shown in Figure 103-2.

                                                                    Figure 103-2

Adjust mirrors I and II to be perpendicular to axis 1. First, align the light tube with mirror I and record the horizontal reading θ11. Then, rotate axis 1 360° at 45° intervals and record the readings θ12 , ..., θ18 . Next, rotate axis 2 180° and record the horizontal reading θ'11 when the light tube is aligned with mirror I (double-sided mirror) or mirror II (single-sided mirror). Then , rotate axis 1 360° at 45° intervals and record the readings θ'12 , ..., θ'18 .

4.2 Average axis perpendicularity

There are two working states for two adjacent rotation axes of the turntable: one is that one axis is vertical and the other is horizontal, and the other is that both axes are horizontal. The test methods are the same. This method is illustrated using the working state where both axes are horizontal as an example.

a. Install a double-sided plane mirror (with an optical path through hole inside the shaft) at one end of the shaft 1 being measured, or install a plane mirror at each end of shaft 1 and a plane mirror at one end of shaft 2. Install two optical tubes along the two axes, ensuring that shaft 1, shaft 2, optical tube I , and optical tube II are horizontal. Adjust the plane mirrors so that mirrors I and II are perpendicular to axis 1, and mirror III is perpendicular to axis 2, as shown in Figure 103-3.

Figure 103-3

Align light tube I with mirror 1 and light tube II with mirror III. Record the horizontal readings of light tubes I and II: θ1.1 and θ2.1. Fix axis 2 and rotate axis 1 360° at 5° intervals starting from θ1.1. Record the corresponding readings of light tube I: θ1.2, ..., θ1.72.

Rotate axis 2 by 180° so that mirror II is aligned with light tube I. Record the readings of light tube I as θ'1.1 and light tube II as θ'2.37. Fix axis 2 and rotate axis 1 360° at 5° intervals starting from θ'1.1. Record the corresponding readings of light tube I as follows: θ'1.2, ..., θ'1.72.

Rotate axis 2 by 180° so that mirror I is aligned with light tube I. Adjust axis 1 so that the reading of light tube I is θ1.1. Adjust axis 2 so that the reading of light tube II is θ2.1. Fix axis 1 and rotate axis 2 360° at intervals of 5, starting from θ2.1. Record the corresponding readings of light tube II as θ2.2, …, θ2.72.

b. When one axis is vertical and the other is horizontal, let the horizontal axis be axis 1 and the vertical axis be axis 2. When determining the tilt angle measurement direction of the axis 2 being measured, it should be noted that the tilt angle measurement direction of its optical tube should be parallel to axis 1.

5. Data Processing and Result Evaluation

5.1 Perpendicularity of the axis of rotation

5.1.1 Data Processing

Calculate the perpendicularity of axis 2 to axis 1 in four relative positions.

In the formula: V¹₁₂ — the perpendicularity of the two rotation axes of axis 2 and axis 1 at relative positions θ1.1 and θ1.5, (");

V²₁₂——Perpendicularity of the two rotation axes of axis 2 and axis 1 at relative positions θ1.2 and θ1.6, (");

V³₁₂ — Perpendicularity of the two rotation axes of axis 2 and axis 1 at relative positions θ1.3 and θ1.7, (");

V⁴₁₂ —- Perpendicularity of the two rotation axes of axis 2 and axis 1 at relative positions θ1.4 and θ1.8, (").

5.1.2 Result Evaluation

The perpendicularity error of the rotation axis is

5.2 Average axis perpendicularity

5.2.1 Data Processing

a. Calculate the average horizontal tilt angle  angle of the axis.

In the formula: — average of horizontal tilt angle of axis 2, unit: (");

—The average of horizontal tilt angle of axis 1 when axis 2 is θ2.1, (");

—The average of horizontal tilt angle of axis 1 when axis 2 is at θ2.37.

N---- Number of measurement points.

b. Calculate the horizontal tilt angle of axis 2

In the formula: a₁—— The horizontal tilt angle of axis 2 relative to the average axis when axis 2 is at position θ2.1, (");

a₂—— The horizontal tilt angle of axis 2 relative to the average axis when axis 2 is at position θ2.37, (") .

5.2.2 Result Evaluation

Average axis perpendicularity is