An Analytical-thermal Modeling Approach for Predicting Forces, Stresses and Temperatures in Machining with Worn Tools

In this paper, predictive modeling of cutting and ploughing forces, stress distributions on tool faces and temperature distributions in the presence of tool flank wear are presented. The analytical and thermal modeling of orthogonal cutting that is introduced in Karpat, Zeren and Özel [3] extended for worn tool case in order to study the effect of flank wear on the predictions. Work material constitutive model based formulations of tool forces and stress distributions at tool rake and worn flank faces are utilized in calculating non-uniform heat intensities and heat partition ratios induced by shearing, tool-chip interface friction and tool flank face-workpiece interface contacts. In order to model forces and stress distributions under the flank wear zone, a force model from Waldorf [4] is adapted. Model is tested and validated for temperature and force predictions in machining of AISI 1045 steel and AL 6061-T6 aluminum. FORCE AND STRESS DISTRIBUTION MODELING FOR A WORN TOOL Forces acting on the shear plane and the tool with assumed resultant stress distributions on the tool rake face are given in Fig. 1. Johnson-Cook workpiece material model [1] based formulation of modified Oxley’s parallel sided shear zone theory [2] is utilized in determining the forces on the shear plane FS, FNS, FCs, FTs as detailed by Karpat et al. [3]. When it is assumed that the worn flank face is parallel to the cutting direction, the actual (measured) cutting forces in the cutting and thrust directions FC and FT during machining are the superposition of the wear forces and the cutting forces from shearing. These forces can be expressed as in Eq. (1) as suggested by Thomsen et al. [9] for the case of zero clearance angle. C Cs C T Ts T w w F F F F F F = + = + (1) Figure 1. Forces acting on the shear plane, the rake and the worn faces of the tool. It has been observed by many researchers that flank wear does not affect the shear angle; therefore, superposition of forces due to flank wear and shearing forces is widely accepted. However, there is still doubt about the validity of this approach. Thomsen et al. [9] reported significant plastic flow below worn tool flank when a negative clearance angle exists but for zero clearance angle wear land does not affect the shearing mechanism. In contrast, Shi and Ramalingam [10] considered plastic flow conditions at the tool flank in their proposed slip-line field and concluded that flank face cannot be taken parallel to the cutting direction. Later, Waldorf [4] combined this model with the findings of Thomsen [9] related to the worn flank face may becoming parallel to the cutting direction and extended to round edge tools that form sharp-like edges after stable build up. Waldorf’s approach is used by many other researchers such as Huang and Liang [5], Smithey et al. [11] and Chou and Song [12]. Copyright © 2005 by ASME 1 In this study, we adapted Waldorf’s model to obtain stress distributions under the flank wear area which determine nonuniform heat intensities between the flank and workpiece interface. The cutting forces due to tool flank wear can be found by integrating and over the tool flank wear land as in Eq. (2). w σ w τ ( ) ( ) 0 0 . . VB Tw w VB Cw w F w x d F w x d σ τ = = ∫ ∫ x x (2) where w is width of cut; VB is length of wear land and x is the distance from tool tip. In Waldorf’s [4] model, the stresses at flank face are defined according to the length of the wear land, and for small values of flank wear, elastic contact between tool and workpiece exists. In this state, the stresses are modeled to have a polynomial shaped distribution as shown in Fig. 1. However, when the flank wear reaches critical wear land length (VB*) at which the plastic flow begins, the stress distributions take another form. Therefore, if VBVB* then plastic flow of the workpiece will be present at the front edge of the wear land, and elastic contact will be present at the back of the wear land. Determination of this critical tool wear value requires experimental observations. The tool tip stresses and required to define (x) and (x) are shown in Fig 1. 0 σ 0 τ w σ w τ For elastic contact (VB<VB*) and VB≠0, the stresses at the tool flank face are given by ( ) ( ) ( ) ( ) 2 0