（3）resultant motion and velocityWhen the main motion and the feed motion take part in cutting simultaneously, the velocity in one point of the cutting edge relative to the workpiece is called resultant cutting motion, its size and direction can be represented with a vector ve, shown as Fig.1.3, and it equals the vector sum of the two motionsve=vc+vf(1.1)Fig.1.3 The resultant velocity in cutting
1.1.1.2 Three elements in cuttingve、f 、ap are called the three elements in cutting（1）Cutting speedMost of the main cutting motions are rotational motion.The velocity in one point of the rotating body(cutting tool or workpiece) can be calculated using the following formulavc= ?dnm/sor m/min (1.2)1000whered－the rotational diameter of one point in the workpiece or the cutting tool（mm)n－number of revolution per second or per minute (r/s or r/min). （r/s or r/min)（2）Feeding speed, feed and feed per tooth
Feeding speed vfis the feed in a unit time (m/sor m/min)
Feed is the relative displacement between the workpiece and the cutter along the direction of feeding motion per revolution or per stock (mm/r)。
For multiple teeth cutting tools, such as milling cutter, reamer, broach, gear hob etc. feed fzmay be measured in millimeters per tool tooth (mm/z). Obviously，
vf=f·n=fz·z·nmm/s or mm/min （1.3）
（3）Back engagement of the cutting edge
For turning and planing, the back engagement of the cutting edge apis equal to the normal distance between the machined surface and the workpiece surface to be cut(mm). For cylindrical turning,
ap=（dw-dm）/2 mm (1.4)
For drilling
ap=dm/2 mm (1.5)
where dm——diameter of machined surface（mm）
dw——diameter of workpiece surface to be cut（mm）