Resolver Synchros
The function of resolver synchros (RS) is to convert alternating voltages, which represent the cartesian coordinates of a point, into a shaft position and a voltage, which together represent the polar coordinates of that point. They may also be used in the reverse manner for voltage conversion from polar to cartesian coordinates. Typical applications of resolver synchros are to be found in flight director and integrated instrument systems.
A typical arrangement of an RS for conversion from polar to cartesian coordinates is shown in Figure 4.3.15 and from this it will be noted that the stator and rotor each have two windings arranged in phase quadrature, thus providing an eight-terminal synchro. An alternating voltage is applied to the rotor winding RI-R2, and the magnitude of this voltage, together with the angle through which the rotor is turned, represent the polar coordinates. In this application, the second winding is unused, and as is usual in such cases, it is short circuited to improve the accuracy of the RS and to limit spurious response.
In the position shown, the alternating flux produced by the current through rotor winding R1-R2 links with both stator windings, but since the rotor winding is aligned only with S1-S2 then maximum voltage will be induced in this winding. Winding S3-S4 is in phase quadrature so no voltage is induced in it. When the rotor is at a constant speed it will induce voltages in both stator windings, the voltages varying sinusoidally. The voltage across that stator winding which is aligned with the rotor at electrical zero will be a maximum at that position and will fall to zero after rotor displacement of 900; this voltage is therefore a measure of the cosine of the displacement. The voltage is in phase with the voltage applied to R1-R2 during the first 900 of displacement, and in anti-phase from 900 to 2700, finally rising from zero at 2700 to maximum in
phase at 3600. Any angular displacement can therefore be identified by the amplitude and phase of the induced stator voltages. At electrical zero, stator winding S3-S4 will have zero voltage induced in it, but at 900 displacement of rotor winding R1-R2, maximum in-phase voltage will be induced and will vary sinusoidally throughout 3600; thus, the S3-S4 voltage is directly proportional to the sine of the rotor displacement. The phase depends on the angle of displacement, any angle being identified by the amplitude and phase of the voltages induced in stator winding S3-S4. The sum of the outputs from both stators, i.e. rcosθ plus rsinθ, therefore defines in cartesian coordinates the input voltage and rotor rotation.
Figure 3.16 illustrates an arrangement whereby Cartesian coordinates may be converted to polar coordinates. An alternating voltage Vx = rcosθ is applied to the cosine stator winding S1-S2, while a voltage Vy = rsinθ is applied to the sine stator winding S3-S4. An alternating flux representing cartesian coordinates is therefore produced inside the complete stator. One of the rotor windings, in this case R1-R2, is connected to an amplifier, and in the position shown it will have maximum voltage induced in it, which will be applied to the amplifier. The output from the amplifier is applied to a servomotor which is mechanically coupled to a load and to the rotor. When the rotor is turned through 900 the induced voltage in winding R1-R2 reduces to zero and the servomotor will stop. The rotor winding R3-R4 will now be aligned with the stator flux, and a voltage will be
induced in it which is proportional to the amplitude of the alternating flux as represented by the vector r i.e. a voltage proportional to √( Vx 2 +Vy 2). This voltage together with the angular position of the rotor therefore represents an output in terms of the polar coordinates.
Figure 4.3.16: Conversion of cartesian coordinates to polar coordinates
