The deformation of cutting layer metal is mainly the result of the force given by the tool, which is called cutting force.
Cutting force is an important physical phenomenon in the process of metal cutting.
1. Source of cutting force
During metal cutting, the cutting tool cuts into the workpiece to deform the processed material into chips, which is called cutting force.
Under the action of the cutting tool, the cutting layer metal, chip and workpiece surface layer metal will produce elastic deformation, plastic deformation and friction in the cutting process.
The cutting force comes from three aspects (see Fig. 1-18):
(1) Overcome the resistance of the processed material to elastic deformation.
(2) Overcome the resistance of the processed material to plastic deformation.
(3) Overcome the friction between the chip and the tool rake face Ff and the friction between the tool rake face transition surface and the machined surface Ffd.
Fig. 1-18 source of cutting force
2. Decomposition and synthesis of cutting force
Fig. 1-19 shows the decomposition diagram of cutting force during cylindrical longitudinal turning.
If the cutting effect of the auxiliary cutting edge and other factors causing the change of chip flow direction are not considered, the resultant force F is in the orthogonal plane of the tool.
In order to facilitate measurement and application, the resultant force F can be decomposed into three mutually perpendicular components: main cutting force Fz, radial force Fy and axial force Fx (see table 1-3).
Fig. 1-19 cutting force and component
Table 1-3 decomposition of cutting force
| Cutting parting force | Direction | Effect |
| Main cutting force Fz (cutting force or tangential force) | Perpendicular to the base surface and consistent with the direction of cutting speed V. | Calculate the strength of turning tool, design machine tool parts and determine the necessary parameters of machine tool power. |
| Radial force Fy, (back force or cutting force) | The feed direction is perpendicular to the workpiece axis. | It is used to determine the workpiece deflection related to the machining accuracy of the workpiece. The strength of computer machine parts and cutting tools is one of the factors leading to cutting vibration. |
| Axial force Fx (feed force) | It is in the base plane and parallel to the feed direction (i.e. workpiece axis direction), also known as the feed force. | Design the feed mechanism and calculate the necessary parameters of the feed direction of the turning tool. |
It can be seen from fig. 1-19 that the resultant force F is first decomposed into Fz and Fxy, and then Fxy is decomposed into Fy and Fx.
So,
The relationship between Fy, Fx and Fxy is:
In general, the main cutting force Fz is the largest and Fy and Fx are smaller.
With the difference of tool geometric parameters, grinding quality, wear condition and cutting parameters, the ratio of Fy and Fx to Fz changes in a large range:
Fy=（0.15~0.7）Fz
Fx=（0.1~0.6）Fz
3. Empirical formula of cutting force and net power
The empirical formula of cutting force can be obtained by measuring the cutting force with force measuring instrument and properly processing the experimental data.
The empirical formula of cutting force is a power function with back draft ap and feed f as variables.
The calculation formula of net power is:
Where, f– feed rate, unit: mm / r;
pc– specific cutting force, see table 1-4 and fig. 1-20, unit: n / mm ².
Table 1-4 pc reference values
| ISO P MC material No | Material | Specific cutting force PC (N / mm2) | Brinell hardness（HBW） |
| P1.1.Z.AN P1.2.ZAN P1.3.Z.AN | Unalloyed steel Wc=0.1%-0.25% Wc=0.25%-0.55% Wc=0.55%- 0.80% | 200021002200 | 125150170 |
| P2.1.Z.AN P2.1.Z.AN P2.5.ZHT P2.5.ZHT | Low alloy steel (alloy element ≤ 5%) Non hardening Bearing steel Quenching and tempering treatment Quenching and tempering treatment | 2150230025502850 | 180210275350 |
| P3.0.Z.AN P3.0.ZHT | High alloy steel (alloy element > 5%) Annealing Hardened tool steel | 25003900 | 200325 |
| P1.5.C.UT P2.6.C.UT P3.0.C.UT | Cast steel Non alloy Low alloy (alloying element ≤ 5%) High alloy (alloying element > 5%) | 200021002650 | 180200225 |
| P5.0.Z.AN P5.0.Z.PH P5.0.Z.HT | Ferritic / martensitic bar / forging Non hardening Precipitation hardening Chilled steel | 230035502850 | 200330330 |
| M1.0.Z.AQ M1.0.Z.PH M2.0.Z.AQ | Austenitic bar / forging austenite Precipitation hardening Super austenite | 230035502950 | 180330200 |
| M3.1.ZAQ M3.2.Z.AQ | AUSTENITIC FERRITIC (duplex) bar / forging Non weldable ≥ wc0 05% Weldable < wc0 05% | 25503050 | 230260 |
| P5.0.C.UT P5.0.C.HT | Ferritic / martensitic castings Non hardening Precipitation hardening Chilled steel | 210031502650 | 200330330 |
| M1.0.c.UT M2.0.C.AQ | Austenitic castingsaustenite Precipitation hardening Super austenite | 220031502700 | 180330200 |
| M3.1. C.AQ M3.2.C.AQ | AUSTENITIC FERRITIC (duplex) castings Non weldable ≥ Wc0.05% Weldable < wc0 05% | 22502750 | 230260 |
| KI.I.CNS | Malleable iron Ferrite (short cut eyebrow) Pearlite (long chip) | 9401100 | 130230 |
| K2.1.CUT K2.2.CUT | Grey cast iron Low tensile strength High tensile strength | 11001150 | 180220 |
| K3.1.CUT K3.3.C.UT K3.4.CUT | Ductile iron SG Ferrite Pearlite Martensite | 105017502700 | 160250380 |
Fig. 1-20 range of PC values of various materials
4. Other methods for calculating cutting force
Use the unit cutting force to calculate the main cutting force: the unit cutting force refers to the cutting force on the unit cutting area.
If p represents the unit cutting force and the unit cutting force is known, the main cutting force is:
Where
- p — unit cutting force, N / mm ²；
- bD — cutting width, unit: mm;
- Hd-cutting thickness, in mm;
- ap– back cutting amount, unit: mm;
- f — feed rate, unit: mm / r.
5. Main factors affecting cutting force
In the process of cutting, many factors will affect the cutting force to varying degrees, mainly including workpiece material, cutting parameters, tool geometric parameters, flank wear and so on.
The influence of these factors on cutting force is shown in Fig. 1-21, FIG. 1-22 and Fig. 1-23.
Fig. 1-21 influence of geometric parameters on cutting force
- a) Influence of front angle
- b) Influence of principal deflection angle
- c) Influence of blade inclination
- d) Influence of tool tip arc radius
Fig. 1-22 effect of cutting speed on cutting force
Fig. 1-23 effect of flank wear on cutting force