1. Test Objective

Detect the radial rotation error of the rotating axis at the specified working position.

2. Test Instruments

Standard steel ball

Capacitive sensor

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

Mount a standard steel ball with a base on the rotating shaft being measured, and mount a capacitance sensor on the base of the shaft being measured. Adjust the center of the ball to the axis of the shaft being measured, and align the capacitance sensor with the steel ball along the X and Y axes of a Cartesian coordinate plane perpendicular to the axis. See Figure 102-1.

                        Figure 102-1

The measured axis rotates one revolution at 5° intervals, with the rotation angle θ = i × 5°, i = 1, ..., 72. Capacitive sensors are used to read and record the measured values Xi and Yi in the X and Y directions at each corresponding angular position of the measured axis .

5. Data Processing and Evaluation Results

5.1 Data Processing

The measured values Xi and Yi are periodic functions of the angular position of the measured axis. The data processing method is to first expand Xi and Yi into Fourier series, and then subtract the zero and first harmonic components caused by the sphericity of the standard sphere and the centering error to obtain the two rectangular coordinate components △Xi and △Yi of the radial rotation error ; and synthesize the two components to obtain Li.

a. Fourier's analysis

Expand the periodic functions Xi, Yi into Fourier series

In the formula: i = 1,…, 72

K is the harmonic order.

The Fouché coefficients for the zeroth and first degree terms are axo, ayo and ax₁, bx₁, ay₁, by₁, in μm.

b. Subtract the spherical and centering errors of the steel ball.

Subtract the zeroth and first harmonic components caused by the sphericity of the standard sphere and centering error from the Fourier series.

c. Radial rotation error calculation

5.2 Result Evaluation

Radial rotation error is

Note: Radial rotation error testing may be conducted using a drawing method.