On the Center of Pressure of the Chip on the Cutting Tool
Abstract Generated abstract
This paper examines the commonly used assumption that normal stresses on a cutting tool rake face follow a triangular distribution, placing the chip pressure center at one third of the chip contact width from the tool tip. Using Zorev’s chip equilibrium relation and experimental cutting data for high speed machining without a built-up edge, the author calculates the coefficient locating the pressure center for several steels. The results indicate that the center of pressure lies substantially closer to the cutting edge than the triangular model predicts, especially for more plastic or softer steels. The paper concludes that actual normal stress distributions on the rake face are more concentrated near the cutting edge and differ markedly from a triangular law, consistent with photoelastic observations.
Full Text
ON THE CENTER OF PRESSURE OF THE CHIP ON THE CUTTING TOOL
M. F. POLETIKA
(Presented by Prof. Dr. A. M. Rozenberg)
When considering the stressed state of the cutting tool, and also when studying contact processes on the rake face, most researchers proceed from the assumption that the normal stresses on the rake face are distributed according to a triangular law [1], as is shown in Fig. 1 by the dashed line. If this is so, then the center of gravity of the diagram of normal stresses, and consequently the so-called center of pressure of the chip on the cutting tool (point \(B\) in Fig. 1), must be located
Fig. 1.
at a distance \(\dfrac{c}{3}\) from the tool tip, where \(c\) is the width of contact of the chip with the tool. Below we shall show that experiment does not confirm such a relation.
According to Zorev [2], from the third equilibrium equation for the chip element \((\Sigma M_0 = 0)\) we obtain the following expression:
\[ nC \cos \gamma = ml \sin(\beta - \gamma_1 - \gamma), \]
where \(\gamma_1 = \arc \tg \mu\), \(\gamma\) is the rake angle of the cutter, \(\beta\) is the angle of the shear plane, \(l\) is the width of the shear plane, and \(m\) and \(n\) are coefficients determining the points of application of the forces, respectively on the shear plane and on the contact surface of the cutter. Hence, by transformation, it is not difficult to obtain:
\[ n = \frac{ma\xi}{c}\left[\mu + \tg(\beta - \gamma)\right], \]
where \(a\) is the chip thickness, \(\xi\) is chip shrinkage, and \(\mu\) is the coefficient of friction of the chip on the cutter.
The distribution of normal stresses on the shear plane is unknown to us; however, it may be assumed that the center of gravity of the stress diagram (point E in Fig. 1) is also displaced somewhat toward the cutter tip, i.e., \(m < 0.5\). Taking, in the limiting case, \(m = 0.5\), we calculated the value of \(n\) for high cutting speeds, when no built-up edge is present. For this purpose we used the data of Zorev’s experiments [2] with a cutter made of T15K6 alloy at \(\gamma = 10^\circ\), \(\varphi = 60^\circ\), and \(S \times t = 0.156 \times 4.0\).
The results of the calculation are shown in Fig. 2; from it we see that the center of pressure of the chip is located significantly closer to the cutting edge than was assumed, and the more so, the more plastic the steel being machined.
Fig. 2.
If it is assumed that the value of \(m\) may be less than 0.5, then for \(n\) we obtain still lower values. This means that the actual diagram of normal stresses on the rake face differs substantially from a triangle, being characterized by a higher concentration of stresses near the cutting edge.
In this case, the deviation of the stress diagram from a triangle will be the greater, the softer the steel. Incidentally, an experimental investigation of the stressed state of a cutter by methods of photoelasticity also gives a law of distribution of normal stresses on the front face that differs substantially from a triangle [3].
References
- Klushin, M. I. Metal Cutting. Mashgiz, 1958.
- Zorev, N. N. Problems of the Mechanics of the Metal-Cutting Process. Mashgiz, 1956.
- Kaltwinkel, V. — Untersuchungen an Schneiden spanender Werkzeuge mit Hilfe der Spannungsoptik. — “Industrie-Anzeiger,” 36, 1957.