# VMD order tracking technology for gear calculation of variable speed gearbox

In order to calculate the order tracking, a reference axis should be selected as the basis of calculation. The main idea is to collect the rotation speed signals of the reference axis with equal time intervals by hardware, and then obtain the order spectrum by angle domain resampling, cubic spline interpolation and Fourier transform. The order ratio refers to the multiple of the signal vibration frequency relative to the reference shaft rotation frequency, which is the first order ratio.

The steps to calculate the order tracking are as follows: firstly, assuming that its reference axis is accelerating constantly over a period of time, then its angle θ can be expressed as follows:

In the formula, to determine the polynomial coefficients B0, B1 and B2, it is necessary to collect the accurate arrival time T1, T2 and T3 of the three continuous bond phases. The phase difference between two adjacent points is Δ φ. Then the polynomial coefficients can be obtained by the following equation:

Where, θ 1, θ 2 and θ 3 are the rotation angles corresponding to equal angle sampling. The polynomial coefficients B0, B1 and B2 can be calculated by the above formula, then the time TN corresponding to each rotation angle can be obtained by the following formula:

Where, θ n is the rotation angle, and TN is the time corresponding to the rotation angle. The time of resampling point in the angle domain can be obtained by the formula, and then the resampling signal can be obtained by cubic spline interpolation. Fourier transform is performed on the resampled signal in diagonal domain to obtain the corresponding order spectrum.

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