Application of resolver

In the phase-comparison working mode of the rotary transformer, the phase difference θ between the induction signal VB and the excitation signal VK can be detected by a dedicated phase detector circuit and expressed as a corresponding voltage signal, set as U(θ). By measuring the voltage signal, the value of θ can be indirectly obtained. However, since VB is a periodic function about θ, U(θ) is obtained by comparing the values ​​of VB and VK, so it is also a periodic function about θ, that is,

U(θ)=U(n×2π+θ) (n=1,2,3,…) (4-9)

Therefore, in practical applications, it is necessary not only to measure the size of U(θ), ​​but also to measure the number of periodic changes n of U(θ), ​​or to limit the measured angular displacement θ to within ±π.

In the amplitude detection mode of the rotary transformer, the amplitude of VB is set to VBm. From formula (4--8), we can know that

(4-10)

It is also a periodic function of θ. In practical applications, the angle θ also needs to be limited to ±π. In this case, if the angle α is limited to only take values ​​within [-π,π], the value of θ can be uniquely determined using formula (4-10). Otherwise, if θ=3π／2(＞π), then both α=3π／2 and α=-π／2 can make VBm=0, so that the angle θ cannot be uniquely determined, resulting in erroneous detection results.

From the above, we know that no matter the phase detection mode or amplitude detection mode of the rotary transformer, the measured angular displacement θ needs to be limited to ±π. As long as θ is within ±π, it can be correctly detected. In fact, for the case where the measured angular displacement is greater than π or less than -π, such as the case where the rotary transformer is used to detect the angle of the machine tool screw, although the total machine tool screw angle θ may be very large, far exceeding the limited ±π range, it is the sum of several small angles θi of the machine tool screw, that is,

(4-11)

However, θi is very small, generally not exceeding 3° on CNC machine tools, which meets the requirement of -π≤θi≤π. The rotary transformer and its signal processing circuit can detect them one by one in a timely manner and output the results. Therefore, this detection method belongs to dynamic follow-up detection and incremental detection.