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1、The forces acting on the tool and the workpiece are called cutting forces.,2.1.2 Cutting forces,2.1.2.1 Sources of cutting forces, resultant forces as well components of cutting forces,2.1.2.2 Measurement of cutting force and establishment of empirical formulas,2.1.2.3 Specific cutting force and spe

2、cific cutting power,2.1.2.4 Influence of various factors on cutting force,2.1.2.1 Sources of cutting forces, resultant forces as well as components of cutting forces,The forces acting on the tool come from two sources: resistance to metal elastic and plastic deformation in the deformation regions; f

3、rictions between tool and chip and between tool and machined surface.,(a) free orthogonal cutting,Fig.2.21 Resultant forces and components of cutting forces,Resistance Fny anti- plastic deformation on the rake face,Friction force Ffy tangential to the rake face,The resultant force Fr,Resistance Fna

4、anti- elastic and plastic deformation normal to the flank face,friction force Ffa tangential to the flank face,Fig.2.21 Resultant forces and components of cutting forces,（b）oblique cutting.,In order to measure, calculate cutting forces and analyze the effects of cutting forces, usually the force Fr

5、is decomposed into three components of forces:,Main cutting force Fz,Radial thrust force Fy,Axial thrust force Fx,2.1.2.1 Sources of cutting forces, resultant forces as well as components of cutting forces,（c） oblique cutting,From Fig 2.21(b) there is the relation: where, Fxy is the component of Fr

6、in the tool reference plane, Fy= Fxycosr Fx= Fxysinr,(2.11),2.1.2.1 Sources of cutting forces, resultant forces as well as components of cutting forces,Fig.2.22 strain transducer- dynamometers l一transducer ；2一circuitry；3一strain gauge；4一recording,2.1.2.2 Measurement of cutting force and establishment

7、 of empirical formulas,(1) The principle of dynamometers,A single factor method and a multi-factor method can be used to establish empirical formula for cutting force. The regular forms of empirical formula of cutting force are as follows: effect coefficients, their values are related to experiment

8、conditions; effect indices of back engagement of the cutting edge ap on the cutting force; effect indices of feed f on the cutting force; correction coefficients on the cutting force due to the difference between calculation and practice,(2) Establishment of empirical formulas for turning,2.1.2.2 Me

9、asurement of cutting force and establishment of empirical formulas,Take the building of the empirical formula of main cutting force Fz as example,Fig,2.25 Straight line in the dual-logarithm charts (a) pFz ；（b） fFz,(a),(b),With a series of experimental values for ap-Fz and f-Fz, we can connect these

10、 points in the dual-logarithm charts and obtain two straight lines shown in Fig 2.25.,2.1.2.2 Measurement of cutting force and establishment of empirical formulas,The equations for two lines are:,lgFz1gCap十xFz lgap 1gFz1gCf十yFzlgf The above equations can be changed into the following forms: Combinin

11、g equations (a) and (b) we get the empirical formula for the main cutting force the slope of straight line ap-Fz , f-Fz. the intercept of straight line ap-Fz , f-Fz the evaluation from the combination of equations (a), (b),(c),2.1.2.2 Measurement of cutting force and establishment of empirical formu

12、las,(3) The principle of piezo-electric transducer Fig 2.26 is a picture of a piezo-electric transducer for measuring forces in three orthogonal directions,Fig.2.26 piezo-electric transducer,2.1.2.2 Measurement of cutting force and establishment of empirical formulas,2.1.2.3 Unit cutting force and c

13、utting power,(1) Unit cutting force Unit cutting force p means the main cutting force required in the removal of a unit area of cutting layer. It is calculated with the following equation: The formula shows that p is not influenced by back engagement of the cutting edge ap, because when ap changes c

14、utting force Fz, and cutting lay area AD also change in the same proportion. Although AD is increased with the increase of f, Fz increases slightly. It is more straightforward to utilize the unit cutting force p for the calculation of the main cutting force Fz.,(2.15),（2）Cutting power,Cutting power

15、means the power expended in the cutting region. Usually the power expended by the main motion is calculated as. where Fz the main cutting force (N); vc the cutting speed of the main motion (m/min). The power PE required by the machine motor is: PE=Pm/ kW （2.17） where machine transmission efficiency.

16、,(2.16),2.1.2.3 Unit cutting force and cutting power,Unit cutting power Ps means the power expended in a unit time for the removal of a unit volume metal Zw. Ps=Pm/Zw kW/（ ） (2.18) The following relation can be developed : Table 2.1 lists some experimental values of unit cutting force p and unit cutting power Ps. In the experiment a carbide tool was used and feed f=0.3mm/r was fixed. If feed f is changed, the values of p and Ps in the table should be multiplied by the correctional coefficients K