A fully coupled temperature-displacement, explicit finite element model is implemented in this chapter to model the orthogonal cutting of Ti6Al4V alloys. The model employs the Johnson-Cook material model to describe the material flow and fracture behaviour so that chip separation and segmentation through element deletion is achieved. The model is thus able to predict the formation of segmental or saw-toothed chips, as ob- served in actual machining of titanium alloys.
The segmental chip shape prediction shows a close resemblance to the actual chips ob- tained and the cutting forces are well predicted, but there some discrepancies due to limitations of the model and the use of material model parameters obtained from litera- ture. The temperature prediction compares well with the values obtained in orthogonal turning tests and the model is useful in the analysis of temperature in the material and the cutting tool. The model, however, cannot predict the effects of tool edge radius and the associated forces generated.
Chapter 6
Milling force prediction model
Predictions of the components of cutting forces in machining operations are required for the determination of power requirements, geometrical errors as well as chatter and vibration characteristics. Furthermore, predictions may assist in the design of fixtures and tools in terms of strength requirements in machining setups [68]. The optimisation of cutting strategies in computer-aided process planning also requires force predic- tions. Knowledge of machining forces can assist in the selection of cutting conditions that reduce excessive cutter wear and breakage [69].
Up to the late 1990’s the traditional approach to modelling practical machining opera- tions had been an empirical approach where process parameters such as cutting speed, feed and depth of cut are related to experimentally determined, average force com- ponents through curve fitting techniques [68]. These models provide only an average value of force components and are, therefore, only applicable to operations where the forces do not vary cyclically, such as in turning and drilling operations.
For operations where forces fluctuate cyclically, such as in milling, semi-empirical or mechanistic approaches have been adopted in the past. With these techniques, force component coefficients are related to chip load through milling tests using curve fit- ting techniques. The empirically established force coefficients are used in mechanistic analyses to predict instantaneous force components and fluctuations during cutter ro- tation. The force component coefficients here, and in other empirical approaches, are valid only for a given tool-workpiece combination and a range of machining tests has to be repeated for every combination of tool and workpiece.
In contrast, the "fundamental" or "unified mechanics of cutting" approach is a non- empirical method which incorporates "edge forces" and relates the developed analyses of practical operations such as turning, drilling and milling to the "classical" oblique cutting process, together with the basic cutting quantities found from orthogonal cut- ting tests. The basic cutting quantities from orthogonal tests form a generic data bank for a tool-workpiece material combination and may be used to model any machining operation. The orthogonal data base consists of shear stress, shear and friction angle data from tests conducted at a range of cutting speeds, feeds and rake angles and Bu- dak et al. showed accurate transformation between these quantities and oblique cutting processes applied to cylindrical end mills [68]. The model incorporates all tool and cut geometrical variables, as well as cutting conditions and can, as result, be used to model any machining operation and cutter geometry.
6.1
Unified mechanics of cutting
In general, the elemental forces acting on a discrete, oblique cutting edge segment can be described by 6.1 in the tangential, axial and radial directions. Here the total force in a particular direction is separated into two components. The first component describes the edge forces, which are the forces due to rubbing and ploughing at the cutting edge, due to the radius found on practical cutting edges. The edge forces are represented by the edge force coefficients, Kte, Kre and Kae, on a unit width of cut basis. The second
part represents the cutting forces, which are due to shearing of the material in the shear zone and friction along the rake face. The coefficients Ktc, Krcand Kac, on a unit area of
cut basis, make up the cutting force component of 6.1.
Figure 6.1: Ball nose end-mill coordinate system and differential forces acting on an edge seg- ment [69]
In traditional mechanistic milling models, Kte, Kre, Kae, Ktc, Krcand Kacare referred to as
milling force coefficients and are determined through specific milling tests and mech- anistic analyses. Tests consist of a series of slot milling tests run at various speeds and feeds and are valid only for the specific cutter geometry with which the tests are con- ducted. In contrast, with the unified mechanics of cutting approach, the coefficients are identified from an orthogonal cutting database, calculated from oblique or orthogonal cutting analysis, and can thus be predicted for any cutter geometry.
CHAPTER6 — MILLING FORCE PREDICTION MODEL 66 dFt= edge KtedS+ shear Ktctndb (a) dFr=KredS+Krctndb (b) dFa =KaedS+Kactndb (c) (6.1)
The method of predicting machining forces in milling, or indeed any other type of cutting operation, using the "unified mechanics of cutting" approach is based on the formulation described in 6.1. The general procedure for modelling milling is to divide the cutter geometry into discrete cutting edge elements and to define the geometry in terms of rake angle, helix or obliquity angle i in terms of a local coordinate system, the velocity U of each edge segment and the variation of cut thickness with cutter rotation angleθ. Once this information is known the cutting and edge force coefficients for each edge segment can be calculated at each increment of cutter rotation from the orthogonal cutting data base. The forces acting on each segment can then be calculated in the local tangential radial and axial directions and transformed to a global coordinate system and integrated over all the segments to give the total cutting forces in the global coordinate system as a function of cutter rotation.