A Variable Reluctance Resolver, abbreviated as VRR, is a special type of rotary transformer whose core working principle is based on the variation of magnetic circuit reluctance with the rotor position angle. It utilizes the magnetic resistance change caused by the Salient Pole structure on the rotor to induce voltage signals in the stator winding that are sine and cosine related to the rotor angle position.

The following is its detailed working principle:

1. Basic structure:

Stator: Contains multiple winding slots, usually embedded with two sets of mutually orthogonal windings (with a spatial difference of 90 degrees in electrical angle):

Exciter Winding: A set of windings used to input high-frequency AC reference signals (typically sine waves ranging from several kilohertz to several tens of kilohertz).

Output Windings: Two sets of windings (commonly referred to as sine winding Sin and cosine winding Cos) used to output induced voltage signals.

Rotor: Key component. It is a non winding salient pole structure (usually made of laminated iron cores with good magnetic conductivity, such as silicon steel sheets), designed in a shape such that its air gap magnetic resistance varies periodically (usually sinusoidally) with the rotation angle of the rotor. The most common rotor structure is a doubly salient pole (with two protruding magnetic poles) or more salient poles.

2. Working principle and process of variable reluctance resolver:

Excitation: Apply a high-frequency sinusoidal AC voltage ` V_exco=V_m * sin (ω t) ` to the excitation winding of the stator.

Establishing an alternating magnetic field: The excitation current generates a high-frequency alternating main magnetic field in the stator core. This magnetic field passes through the air gap and attempts to close through the path with the lowest magnetic resistance, that is, through the salient pole portion of the rotor.

Magnetic resistance variation: As the rotor rotates, the position of its salient poles relative to the stator teeth constantly changes. This leads to periodic changes in the length of the air gap between the stator and rotor.

When the rotor convex pole is aligned with the stator teeth, the air gap is minimized, the magnetic resistance is minimized, and the magnetic flux is easiest to pass through.

When the rotor salient pole is located in the stator slot, the air gap is maximized, the magnetic resistance is maximized, and it is difficult for the magnetic flux to pass through.

Magnetic flux modulation: The rotation of rotor salient poles spatially modulates the alternating main magnetic field generated by stator excitation. The change in air gap magnetic resistance (R (θ)) directly affects the magnetic conductivity of the magnetic circuit (∧ (θ)=1/R (θ)), and the magnetic conductivity usually varies approximately sinusoidally with the rotor angle θ: ∧ (θ) ≈ ∧ 0+∧ 1 * cos (2 θ) (for doubly salient rotors). Here θ is the mechanical angle of the rotor relative to the stator (for doubly salient poles, one electrical cycle corresponds to a mechanical rotation of 180 degrees).

Inductance variation and voltage induction:

The sine (Sin) and cosine (Cos) output windings on the stator are coupled with this modulated magnetic field.

The self inductance of the output winding and the mutual inductance with the excitation winding are both modulated by the air gap reluctance (i.e. rotor angle θ).

According to Faraday's law of electromagnetic induction, a changing main magnetic field will induce an electromotive force (EMF) in the output winding. Due to the fact that the main magnetic field itself is alternating (frequency ω) and its amplitude/coupling strength is modulated by the rotor position θ, the induced voltage signal is the carrier signal of the excitation frequency ω, whose envelope amplitude is modulated by the sine and cosine functions of the rotor angle θ.

Output signal: The final voltage signal obtained on the sine (S1-S2) and cosine (S3-S4) output windings is usually in the form of:

`V_sin = k * V_m * sin(ωt) * sin(θ)`

`V_cos = k * V_m * sin(ωt) * cos(θ)`

Among them:

`K 'is the transformation ratio (determined by factors such as winding turns ratio).

`V_m * sin (ω t) ` is the excitation voltage.

`Sin (θ) and cos (θ) are modulation envelopes that reflect the rotor angle θ (note: for a doubly salient rotor, θ is the mechanical angle, but the electrical angle is 2 θ, so the actual output envelope is sin (2 θ) and cos (2 θ), but the formula form is similar and the angle relationship is determined).

3. Angle calculation of variable reluctance resolver:

The subsequent calculation circuit (rotary transformer digital converter RDC or software algorithm) receives these two modulation signals ` V_sin ` and ` V_cos `.

By detecting the amplitude of these two signals relative to the excitation reference signal (or by demodulating and removing the carrier wave ω t, low-frequency 'sin (θ)' and 'cos (θ)' signals are obtained).

Calculate the angle using the arctangent function: θ=arctan (V_sin/V_cos). The calculation circuit can accurately calculate the current angular position θ of the rotor

The core advantages of MIC Sensors' variable reluctance resolver are:

Simple and sturdy structure: The rotor has no windings, brushes, or slip rings, eliminating contact wear points and greatly improving reliability and lifespan. It is particularly suitable for harsh industrial environments such as high speed, high vibration, high temperature, and high dust and oil pollution.

Maintenance free: No contact parts, no need for lubrication or replacement of electric brushes.

High speed capability: The rotor structure is sturdy, with low inertia, and can withstand extremely high speeds.

High anti-interference ability: The output is an amplitude modulated AC signal, which has good suppression ability for common mode noise and long-distance transmission.

High precision: capable of achieving high angle measurement accuracy.

For more product information, please visit www.micsensors.com