In the fields of aerospace and inertial navigation simulation testing, turntable rotation accuracy is a core indicator for evaluating the precision level of equipment, with tilt rotation accuracy being a key source of error affecting attitude simulation and angle calibration results. Many engineers often encounter problems such as inconsistent testing methods and unclear data processing standards when conducting turntable accuracy self-inspections. This article, based on common verification specifications in the precision testing industry, provides a complete and standardized experimental operation method for turntable tilt rotation accuracy, clearly explaining the selection of testing instruments, the testing process, and the error assessment logic, making it convenient for frontline testing and equipment R&D personnel to directly refer to and use.

1. Test Objective:

To detect the tilt error of the rotation axis at a specified working position.

2. Test Instruments:

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

Plane mirror;

Digital electronic level (hereinafter referred to as level), resolution not less than 0.2").

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

4.1 Method 1 (Optical Method)

The tilt angle rotation error of the rotation axis are measured using the principle of optical autocollimation.

                                 Figure  101-1

                              Figure  101-2

​

 Install an adjustable plane mirror on the worktable or at the location where the workpiece is to be measured. Place the optical tube and the base of the measured axis on the same foundation. Adjust the position of the optical tube to initially align the optical axis with the axis of the workpiece, as shown in Figure 101-1. Add a pentaprism when measuring the vertical axis, as shown in Figure 101-2.

Rotate the axis being measured and adjust the mirror surface to be perpendicular to the axis (i.e., minimize the change in the cross intersection of the optical tube reticle within one rotation).

The measured axis rotates one cycle at 5° intervals, and the angular position of the measured axis is θ = i × 5°. i=1,…,72 . Record the readings of the optical tube along the horizontal x-axis at each corresponding angular position of the measured axis, denoted as Wxi. Then rotate the optical tube 90° around its axis and record the readings of the optical tube along the vertical Y-axis at each corresponding angular position of the measured axis, denoted as Wyi.

4.2 Method 2 (Level Method)

Place two electronic levels perpendicular to each other, or place one level perpendicular to each other twice at a certain position on the worktable, as shown in Figure 101-3. Record the readings Wxi and Wyi of the electronic level in the two vertical coordinate directions at the corresponding angular positions of the axis being measured, according to Method 1.

                       Figure 101-3

5. Data Processing and Result Evaluation

5.1 Data Processing

The measured values Wxi and Wyi are periodic functions of the rotational position of the measured shaft.

The data processing method is to first expand the measured values Wi and W into Fourier series, and then subtract the zero-position error of the light tube and the zero and first harmonic components formed by the non-perpendicular installation of the plane mirror and the rotation axis to obtain the two rectangular coordinate components ΔWxi and Δ, which are the tilt angle rotation error. The two components are then combined to obtain Wi.

a. Fourier Analysis

Expand the periodic functions Wxi and Wyi into Fourier series

In the formula: i = 1, ..., 72;

k is the harmonic order;

The Fouché coefficients for the zero-order and first-order terms are axo , ayo and ax1, bx1, ay1, by1 , in units of (”).

b. Deduct installation errors

Subtracting the zeroth and first harmonic components caused by the optical tube's zero position and the non-perpendicularity of the plane mirror to the axis from the Fourier series yields two orthogonal components of the tilt rotation error: ΔWxi, ΔWyi .

c. Calculation of tilt angle rotation error:

5.2 Result Evaluation

The tilt angle rotation error is 

Note: ① If the measured values of the tilt angle rotation error at each sampling point are required, please refer to Appendix A;

② The tilt angle rotation error test is permitted to be conducted using the drawing method.