Calculated Forces When Turning: Quick Guide

Quick take: Turning force estimates are most useful when they help a shop decide whether a setup has enough rigidity, spindle power, and process margin before chatter or edge failure appears. This page is strongest when it is paired with cutting-equation and thermal-growth references, not used in isolation.

Related references: Understanding Cutting Equations, Coefficient of Linear Thermal Expansion: Machining Guide, and Comprehensive Threading Calculators.

Using a new calculation for determining cutting force components and power when turning.

All images courtesy Kennametal

The cutting force when turning is a resultant force that combines tangential, feed and radial force components. These force components can be measured with a three-component force dynamometer. Metalcutting professionals consider Kistler dynamometers the most accurate.

Of the three cutting force components, the tangential force (F_Z) is the greatest, the feed force (F_Y) is less in magnitude and the radial force (F_X) is the least in magnitude. As a rule of thumb, the following relationships are used, but it is not a good practice because the results are not as accurate as they could be: F_Y = 0.50F_Z and F_X = 0.25F_Z.

A Kennametal CNMG 120408 RN insert was applied for the roughing test.

On Oct. 25, 2012, Kennametal conducted lab tests at its facility in Fürth, Germany, turning 218-HB alloy steel AISI 4140 (DIN 1.7225 42CrMo4), with the following indexable inserts (ISO specification is in the metric system):

• CNMG 120408 RN for roughing, carbide grade is KCP10;

• CNMG 120408 MN for semifinishing, carbide grade is KCP10; and

• CNMG 120408 FP for finishing, carbide grade is KCP10.

A Boehringer VDF315C CNC lathe and a Kistler quartz-crystal, three-component toolholder dynamometer, type Z15814, were used for the lab tests. The lathe has 80kW (107 hp) of power, 1,400 Nm (1,032 ft.-lbs.) of torque and a VDI 60 turret. The cutting force components (F_X, F_Y and F_Z) were recorded (Charts 1, 2 and 3 for roughing below) and tabulated (Tables 1, 2 and 3 below).

The ratios of the feed force to tangential force and the radial force to tangential force are (Table 1):

Test No. 1: FY ÷ F_Z = 2,309.42 ÷ 5,358.77 = 0.43; F_Y = 0.43F_Z; F_X ÷ F_Z = 887.13 ÷ 5358.77 = 0.17; F_X = 0.17F_Z

Test No. 2: FY ÷ F_Z = 2,219.69 ÷ 5,119.33 = 0.43; F_Y = 0.43F_Z; F_X ÷ F_Z = 919.39 ÷ 5,119.33 = 0.18; F_X = 0.18F_Z

Test No. 3: F_Y ÷ F_Z = 2,247.57 ÷ 5,113.66 = 0.44; F_Y = 0.44F_Z; F_X ÷ F_Z = 958.56 ÷ 5,113.66 = 0.19; F_X = 0.19F_Z

These ratios are 14 to 32 percent lower than those defined by the rule of thumb.

Similar ratios for the cutting force components are (Table 2):

Test No. 1: FY ÷ F_Z = 1,479.75 ÷ 3,060.21 = 0.48; F_Y = 0.48F_Z; F_X ÷ F_Z = 556.12 ÷ 3,060.21 = 0.18; F_X = 0.18F_Z

Test No. 2: F_Y ÷ F_Z = 1,482.56 ÷ 3,038.97 = 0.49; F_Y = 0.49F_Z; F_X ÷ F_Z = 576.00 ÷ 3,038.97 = 0.19; F_X = 0.19F_Z

Test No. 3: F_Y ÷ F_Z = 1,507.77 ÷ 3,063.95 = 0.49; F_Y = 0.49F_Z; FX ÷ F_Z = 600.88 ÷ 3,063.95 = 0.20; F_X = 0.20F_Z

These ratios are 4 to 28 percent lower than those defined by the rule of thumb.

The ratios of the cutting force components are (Table 3):

Test No. 1: FY ÷ F_Z = 491.08 ÷ 957.37 = 0.51; F_Y = 0.51F_Z; FX ÷ F_Z = 234.86 ÷ 957.37 = 0.25; F_X = 0.25F_Z

Test No. 2: F_Y ÷ F_Z = 483.72 ÷ 941.74 = 0.51; F_Y = 0.51F_Z; F_X ÷ F_Z = 236.17 ÷ 941.74 = 0.25; F_X = 0.25F_Z

Test No. 3: F_Y ÷ F_Z = 496.01 ÷ 957.27 = 0.52; F_Y = 0.52F_Z; F_X ÷ F_Z = 240.11 ÷ 957.27 = 0.25; F_X = 0.25F_Z

These ratios are similar to those defined by the rule of thumb.

As shown in Tables 1, 2 and 3, the formula developed by Edmund Isakov provides 96.1 to 99.0 percent accuracy when calculating tangential force. Such accuracy satisfies engineering requirements for metalcutting.

The method of calculating power requirements using tangential force (F_ZC) and cutting speed (V_C) is more accurate than the conventional, rule-of-thumb method, which is based on the unit power values (U_P) and the metal-removal rates. A comparison of these two methods of calculation illustrates the difference.

Power Requirements

Calculating the power requirement P using F_ZC and V_C is the advanced method. As an example, the calculations are performed using cutting parameters shown in Table 1 for roughing.