What Is Cutting Force In Metal Cutting?

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.

source of cutting force

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).

cutting force and component

Fig. 1-19 cutting force and component

Table 1-3 decomposition of cutting force

Cutting parting forceDirectionEffect
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.


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:



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.

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:

calculation formula of net power

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 NoMaterialSpecific cutting force PC (N / mm2)Brinell hardness(HBW)
Unalloyed steel Wc=0.1%-0.25%
Wc=0.55%- 0.80%
Low alloy steel (alloy element ≤ 5%)
Non hardening
Bearing steel
Quenching and tempering treatment
Quenching and tempering treatment
High alloy steel (alloy element > 5%)
Hardened tool steel
Cast steel
Non alloy
Low alloy (alloying element ≤ 5%)
High alloy (alloying element > 5%)
Ferritic / martensitic
bar / forging
Non hardening
Precipitation hardening
Chilled steel
Austenitic bar / forging
Precipitation hardening
Super austenite
AUSTENITIC FERRITIC (duplex) bar / forging
Non weldable ≥ wc0 05%
Weldable < wc0 05%
25503050 230260 
Ferritic / martensitic castings
Non hardening
Precipitation hardening
Chilled steel
Austenitic castingsaustenite Precipitation hardening
Super austenite
220031502700 180330200
M3.1. C.AQ
AUSTENITIC FERRITIC (duplex) castings
Non weldable ≥ Wc0.05%
Weldable < wc0 05%
22502750 230260
KI.I.CNSMalleable iron
Ferrite (short cut eyebrow)
Pearlite (long chip)
9401100 130230
K2.1.CUT K2.2.CUTGrey cast iron
Low tensile strength
High tensile strength
11001150 180220
K3.1.CUT K3.3.C.UT K3.4.CUTDuctile iron SG
105017502700 160250380
range of PC values of various materials

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:


  • 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.

influence of geometric parameters on cutting force

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

effect of flank wear on cutting force

Fig. 1-23 effect of flank wear on cutting force

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