Measuring the Forces in Orthogonal Cutting of Metals | Metallurgy

As far as possible, the force measuring element should be attached to a stationary member which avoids using moving electrical contacts.

For simplicity of analysis, it is frequently convenient to reduce the lathe operation to a two dimensional process (orthogonal cutting). It this case, the resultant force will act in a known plane and only two force components act. Although any two force components can be considered, but it is convenient to consider the axial component (F_V) and the tangential component (F_H). A typical set up for measuring forces in metal cutting on a lathe is shown in Fig. 25.5.

The tubular specimen is held in a chuck. The specimen is so selected that the difference in outer and inner diameter of the tube should not be large so as to cause considerable change in cutting speed. The variation in cutting speed is however considered small.

It is evident that the force F_H will cause a bending moment M_H at a distance r from the cutting edge, and F_V will cause a corresponding moment M_V.

The distribution of strain at a section through A and B, caused by bending moment M_H is shown in Fig. 25.6. At the surface the strain is maximum and is equal to

where ε_H1 is the tensile strain (+ ve), ε_H2 is a compressive strain (– ve), E is the Young’s modulus of elasticity and I is the moment of inertia of the section about axis C-C. For a rectangular section such as shown in Fig. 25.6.

The moment M_H can be measured by applying two strain gauges to the top of measuring section (T₁ and T₂ as in Fig. 25.7) and applying two strain gauges directly below (C₁ and C₂). When M_H is applied, two gauges are put in tension, while two others receive an equal amount of compression, thereby satisfying the requirements for a complete Wheatstone bridge. Further the temperature effects also nullify automatically as all the four gauges are subjected to same temperature to undergo equal change in resistance due to change in temperature.

In a similar manner M_V is measured by the four gauges T₃, T₄, C₃, C₄, which are connected as shown in Fig. 25.7. It may be noted that in this system, there is no cross-sensitivity. When a moment M_V is applied, gauges T₃ and C₄ will be subjected to tension while T₄ and C₃ are subjected to comparison. However, if the gauges are symmetrically placed with respect to the axis of section, the strains will be of equal magnitude and there will be no net output from the Wheatstone bridge.

It was assumed as if the strain gauges are mounted directly on the tool. In actual practice as it is inconvenient to place the gauges directly on the tool, a tool-holder with a built-in measuring section is employed. A tool holder with a built-in measuring section is called dynamometer.