The invention discloses a 
numerical control relief 
grinding method for an enveloping worm hob and a 
machine tool. When relief 
grinding is carried out on 
side tooth faces of a hob, a main shaft and a rotary disk of the 
machine tool are synchronously rotated according to a worm pair 
transmission ratio, the rotation angle of the main shaft is thet0=2s / dl, the main shaft and the rotary disk are synchronously rotated to carry out the relief 
grinding on the tooth faces of the hob, the rotation angle of the main shaft satisfies the formula1, the 
transmission ratio of the main shaft and the rotary disk during the relief grinding of the right 
side tooth faces satisfies the a formula2, and the 
transmission ratio of the main shaft and the rotary disk during the relief grinding of the left 
side tooth faces satisfies the formula3, and the rotary disk is re-rotated with a compensation angle to finish the relief grinding of one tooth face, the compensation angle in the process of relief grinding of the right side tooth faces satisfies the formula 4, the compensation angle in the process of the relief grinding of the left side tooth face satisfies the formula 5; and when relief grinding is carried out on tooth backs, the main shaft and the rotary disk are firstly synchronously rotated, wherein the rotation angle of the main shaft is thet0= 2s / dl, the main shaft and the rotary disk are continuously rotated synchronously to enable a longitudinal feed 
carriage to carry out the relief grinding on the tooth backs along the longitudinal feeding, the rotation angle of the main shaft satisfies the formula 6, then the longitudinal feed 
carriage is reversely fed, the transmission ratio of the main shaft and the rotary disk is equal to the worm pair transmission ration in the whole process of the relief grinding of the tooth backs, and both the longitudinal feeding and the reverse feeding of the longitudinal feed 
carriage satisfy the formula7.