Laser cutting machine groove cutting compensation method and system and computing terminal

The invention provides a laser cutting machine groove cutting compensation method and system and a computing terminal. A cutting head is controlled to move to the center of a chuck in the first defined direction; performing follow-up calibration on the four surfaces of the pipe; executing a four-point searching process, and detecting follow-up heights of four points in a second definition direction; calculating the compensation amount of the actual rotation center of the pipe according to the measured follow-up heights of the four points and the rotation angle of the rotating shaft; the forward follow-up height and the negative follow-up height are detected, the inclination angle of the pipe is calculated, and the cutting track of the cutting head is corrected and compensated with the preset compensation amount; and detecting a compensation value according to a difference value between the compensated follow-up height and the follow-up height during actual cutting, and judging whether the compensation value i