The well-known Merchant’s force circle is drawn and given in Fig. 3 to illustrate the details of cutting forces at tool-chip interface; where in the figure FC is the principal cutting force (tangential component), Ft is the feed force (along feed direction), Ff is the friction force (along tool face), R is the resultant force, and α is the back rake angle of the insert. The principal cutting force and feed force can be measured directly by a dynamometer. Their changes with cutting speed are shown in Fig. 4. With the increase of the cutting speed, the cutting temperature increases (referring to Fig. 2) and the hardness of workpiece material is decreased accordingly; As a result, both of the principal cutting force and feed force are reduced as depicted in the figure. To be more specific, the variation of principal cut- ting force is inversely proportional to the variation of cutting temperature. But the feed force does not decrease monotonically; it starts to increase at the cutting speed of 82 m/min. From the force circle given in Fig. 3, it can be readily shown [14] that the friction force is related to the measured forces and the rake angle by Eq. (1).
Ff =FC sinα+Ft cosα (1)
The computed friction force is shown in Fig. 5. The high friction force at low speed cutting is attributed to the high hardness of workpiece material owing to low cutting temperature. As cutting speed is increased (up to 82 m/min), the friction force decreases because of the decrease of cutting forces with the increase of cutting speed. When the cutting speed is further increased the saw-tooth chip forms and the friction force rises. This fact con- firms the finding of Matsumoto et al. [2] where the occurrence of saw-tooth chip caused friction force to increase. The rise of friction could be related to the tribological behavior between the tool and chip. This will be discussed in Section 3.4. Based on Eq. (1), the increase of feed force at the cutting speed beyond 82 m/min as that depicted in Fig. 4 is due to the increase of friction force.