VRRs

Introduction to Variable Reluctance Resolvers (VRRs)

Lei Li 2023/11/27

Concept of and Construction of VRRs

In motors and their control systems, it is necessary to measure the position of the motor rotor and its angular speed, so as to realize the high precision control of motors. Variable reluctance resolvers (VRRs) are a type of non-contact electromagnetic sensor that can measure the position and speed of rotating machinery with high accuracy and precision. A VRR consists of a rotor and a stator. The rotor has a silicon-steel lamination core with salient poles, while the stator contains a silicon-steel lamination core and winding teeth.

‍ Mechanism and Application of VRRs

By using the salient pole effect of the rotor poles, the mutual inductance between the exciting winding, output windings (sine and cosine windings) changes with the position of the rotor. In a VRR, the stator has teeth that create air gaps with the stator core. As the rotor rotates, the number of teeth that align with the stator increases, reducing the magnetic reluctance and increasing the flux density. This change in flux density induces a voltage in the stator windings (output windings, sine and cosine windings) that is proportional to the rotor angle and can be accurately determined. Winding schematic diagram and output voltage equation are listed as follows.

Secondary winding

Primary winding

Output voltage equation:

ES1-S3 = K*ER1-R3*Cos(P*Θ)

ES2-S3 = K*ER1-R3*Sin(P*Θ)

Where K is transformation ration, P is No. of salient poles, Θ is The mechanical Angle at which the rotor deviates from the origin.

S1: Cos-(RED)

S2: Sin-(YEL)

S3: Cos+(BLK)

S4: Sin+(BLU)

S5: Ext-(WHT)

S6: Ext+(GRN)

Winding Schematic Diagram

The voltage amplitude corresponds to two angular positions of the rotating machinery if only one set of output winding is used. So that's why two sets of output windings are necessary, unique angular position of the rotator obtained by resolver digital converter (RDC) via solving the voltage of the two sets of windings. In general, more salient poles in rotors, the higher accuracy of VRR will perform. Typical accuracy values for VRRs with 4 salient poles and 2 salient poles are ±30 and ±60 minutes, respectively.

4 salient poles

Voltage Magnitude/v

Rotating Angle/°

2 salient poles

Voltage Magnitude/v

Rotating Angle/°

‍ Comparison of VRRs with Other Sensors

There are other sensor technologies available that have similar performance. By comparison with magnetic and optical encoders, VRRs have good manufacturability and environmental adaptability, extreme reliability, simple structure, low cost, light volume, high running speed.

Though general accuracy of VRRs, they still could be widely used as the conventional position and speed sensor of the main shaft of the brushless DC motor in many fields, especially in new energy vehicles, robotics, mining machinery, aerospace, military, and other fields.