MOIRÉ MEASURING DEVICE FOR ANGULAR MOTION PARAMETERS

V. I. Lukovnikov

(Presented by the scientific and technical seminar of the Department of Instruments and Devices of Automation Systems)

Among the many existing schemes for measuring angular-motion parameters, the most promising should be considered those using photoelectric sensors built on the basis of applying a moiré pattern for “angle—phase” conversion [1].

Such sensors make it possible to achieve high measurement accuracy, since they provide averaging of errors over all marks and are easily made with large optical-reduction coefficients. However, the need to use an annular light source and annular photodetectors in their design substantially complicates and increases the cost of the sensors, which hinders the spread of the latter in science and technology.

We propose a simple photoelectric moiré measuring device for angular-motion parameters, in which ordinary illuminators and photodetectors are used, and the apertures of the raster disks are made circular; the manufacturing technology for such apertures is substantially simpler than the technology for manufacturing radial slits [2].

The optical diagram of the measuring device together with the block diagram of the electronic part is shown in Fig. 1.

Fig. 1. Diagram of the measuring device for angular-motion parameters.

The radiation from source 1 is formed by means of lens 2 into a parallel beam of light, which passes through rotating electro-optical modulator 4, driven by electric motor 3, is reflected from mirror 5, and illuminates raster disks 6, 7, 8; the latter is rigidly fixed to measuring shaft 9. Shaft 9 can rotate easily in bearings, and its end is brought out through holes in the center of raster disk 6 and mirror 5 for coupling to the object whose angular-motion parameters are being measured.

The luminous flux that has passed through raster disks 6, 7, 8 is divided, by means of mirror 10 with an elliptical opening at the center, into two parts, which are focused by lenses 11 and 12 onto photodetectors 13 and 14. One part of the luminous flux passes through the apertures of the fixed raster disks 6 and 7 and, when modulator 4 rotates, produces at the output of photodetector 13 a reference alternating-current signal. The second part of the luminous flux passes through the apertures of fixed raster disk 6 and movable disk 8 and produces at the output of photodetector 14 an alternating-current signal whose phase shift relative to the reference signal depends on the angular position of raster disk 8 and hence of measuring shaft 9.

Electronic units 15 and 16, each of which is a series connection of an emitter follower, an amplifier, and a Schmitt trigger, are intended for matching the photodetectors with the electronic part of the instrument and for signal shaping. In unit 17, made in the form of a symmetrical trigger, the phase shift of the signals from the photodetectors is converted into the width of the output pulse. Unit 18, made like an “inertia-free” filter [3], generates triangular pulses whose amplitude is proportional to the width of the rectangular pulse arriving from unit 17. Finally, the output unit generates a constant voltage \(U\) proportional either to the angle \(\varphi\) or to the rotational speed of shaft 9.

For the optomechanical part of this meter, the known relations [1] are valid for the optical reduction coefficient

\[ i = z_1 (z_1 - z_2)^{-1} \tag{1} \]

and for the overall transmission coefficient

\[ K = z_1, \tag{2} \]

where \(z_1\) is the number of apertures along one circumference on disk 6;
\(z_2\) is the number of apertures along the circumference on disk 7 (and 8).

In order to minimize distortion of the moiré pattern, the diameters of the apertures on the lower \((d_1)\) and upper \((d_1')\) concentric circumferences of disk 6, and hence also on disks 8 and 7 respectively \((d_2\) and \(d_2')\), should be chosen so that two adjacent apertures located on the same radius fit into the same central angle, equal to the central angle between apertures. Consequently, in manufacturing the raster disks it is necessary to take into account the following relations, obtained from geometrical considerations:

\[ \frac{d_1}{d_2} = \frac{d_1'}{d_2'} = \frac{\sin(\pi/2 z_1)}{\sin(\pi/2 z_2)}, \tag{3} \]

\[ \frac{D}{D'} = \frac{d_1}{d_1'} = \frac{d_2}{d_2'}. \tag{4} \]

where \(D\) and \(D'\) are the diameters of the lower and upper circles along which the raster apertures are arranged.

In accordance with the description, an experimental prototype of the meter was fabricated. In the prototype, a small flashlight bulb was used as the illuminator; the modulator had four equal sector-shaped cutouts and was rotated by a DRV-20 electric motor by means of a belt drive that ensured good smoothness of motion; the lenses had a diameter of \(40\ \text{mm}\) and a magnification of \(2.5^*\); the mirrors were made of metal; small-sized FEU photomultipliers of the FEU-26 type were used as photodetectors. The raster disks were made with the following dimensions: \(D = 28\ \text{mm}\); \(D' = 32\ \text{mm}\); \(d_1 = 1.15\ \text{mm}\); \(d_2 = 1.0\ \text{mm}\); \(d_1' = 1.25\ \text{mm}\); \(d_2' = 1.1\ \text{mm}\); \(z_1 = 44\); \(z_2 = 40\).

Fig. 2. Output characteristic of the meter.

This meter was experimentally investigated for determining the angle of rotation. The angle of rotation was set with an accuracy of \(1'\) by means of a backlash-free reducer with a transmission ratio of 360, and the output voltage was measured with a class-0.1 voltmeter. The meter showed full operability; moreover, according to the “output—input” characteristic presented in Fig. 2, it has a measurement range of more than \(9^\circ\), and an accuracy of about \(10'\).

LITERATURE

1. B. Ya. Karasik et al. Use of a moiré pattern for “angle–phase” conversion. Optiko-mekhanicheskaya promyshlennost’, 5, 24, 1968.

2. N. A. Valyus. Raster Optical Instruments. Moscow, Mashinostroenie, 1966.

3. V. V. Andrushchuk, V. N. Sharakhin. Measurement of small oscillations of angular velocity in automatic control systems. Izv. vuzov, “Priborostroenie,” 1966.