International Journal of Machine Tools and Manufacture
Analytical models for high performance milling. Part I: Cutting forces, structural deformations and tolerance integrity
Introduction
Milling is a very commonly used manufacturing process in industry due to its versatility to generate complex shapes in variety of materials at high quality. Due to the advances in machine tool, CNC, CAD/CAM, cutting tool and high speed machining technologies in last couple of decades, the volume and importance of milling have increased in key industries such as aerospace, die and mold, automotive and component manufacturing. Despite these developments, the process performance is still limited, and the full capability of the available hardware and software cannot be realized due to the limitations set by the process. The purpose of this two-part paper is to give an overview of the analytical methods that can be used to maximize the productivity in milling without violating the machine limitations and part quality requirements. The first part will focus on the milling force, deflection and form error modeling whereas the models of chatter stability and avoidance with high material removal rate will be presented in the second part.
Cutting force is the most fundamental, and in many cases the most significant parameter in machining operations. In milling processes, they also cause part and tool deflections which may result in tolerance violations. Due to the complexity of the process geometry and mechanics compared to turning, milling process models appeared later than some of the pioneering work done on the orthogonal cutting [1]. In one of the very early studies, Martelotti [2] analyzed and modeled the complex geometry and relative part-tool motion in milling. Later, Koenigsberger and Sabberwal [3] developed equations for milling forces using mechanistic modeling. The mechanistic approach has been widely used for the force predictions and also been extended to predict associated machine component deflections and form errors [4], [5], [6], [7], [8]. Another alternative is to use mechanics of cutting approach in determining milling force coefficients as used by Armarego and Whitfield [9]. In this approach, an oblique cutting force model together with an orthogonal cutting database is used to predict milling force coefficients [10]. This approach was applied to the cases of complex milling cutter geometries and multi-axis milling operations [11], [12], [13].
In this paper, milling force, structural deformation, form error prediction and control models are presented. Experimental results are also given to demonstrate the applications of these models. The models can be used to check the constraints such as available machine power or allowable form errors, and determine the high performance milling conditions.
Section snippets
Milling process geometry and force modeling
Milling forces can be modeled for given cutter geometry, cutting conditions, and work material. Two different methods will be presented for the force analysis: Mechanistic and mechanics of cutting models which differ in the way the cutting force coefficients, which relate the cut chip area to the fundamental milling force components, shown in Fig. 1 are determined.
Surface generation
In peripheral milling the work piece surface is generated as the cutting teeth intersect the finish surface. These points are called the surface generation points as shown in Fig. 3. As the cutter rotates, these points move along the axial direction due to the helical flutes, completing the surface profile at a certain feed position along the x-axis.
The surface generation points zcj corresponding to a certain angular orientation of the cutter, φ, can be determined from the following relation:
Feedrate scheduling
In machining operations, the usual practice is to use a constant feed rate for a machining cycle. In cases where there are tolerance violations due to excessive deflections, the feed may have to be reduced in the whole cycle even the maximum form error occurs only at a specific location. Feed rate scheduling method proposed by Budak and Altintas [8] can be used to constraint form errors reducing cycle times. This method is based on estimation of the maximum allowable feed rate for a specified
Conclusions
In this paper, analytical milling force, part and tool deflection, and form error models are presented, and their application in improving the performance of the process is demonstrated. The milling process is considered due to its complex geometry and mechanics, however similar modeling methodology can be applied to other machining processes such as turning. On the other hand, the models can be extended to more complex milling processes such as ball end and five-axis milling. These models
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