Finish milling dynamics simulation considering changing tool angles

The article presents the results of the dynamics simulation and analysis for five-axis milling, considering changing angles between the tool axis and the surface normal. The 3D structural dynamics model of the milling process is described based on the finite element tool and a workpiece dynamics model. Cutting forces in three directions Px, Py and Pz for different values of the tool angle are compared. Numerical simulation results enable identification of the optimal tool’s position for increasing free-form surface milling performance (chip formation, tool reliability tool, etc.).


Introduction
Currently, CNC production centers are widely used in machine building for machining complex parts used in aerospace, automobile, and shipbuilding industries. To ensure maximum flexibility of the tool of the workpiece, five-axis milling tools are used. Modern CNC centers help to orient the tool and the workpiece to the surface normal at a contact point at any angle.
One of the key indices characterizing workpiece machining with CNC units is forming performance which is calculated as a workpiece surface area value formed per unit time. The value characterizes the intensity rate of a tool impact on the workpiece and assesses the intensity rate of the forming system of the CNC center [1].
Mean forming performance is calculated by formula [1]: (1) where F -area of the nominal workpiece surface; t -forming time for the nominal workpiece surface. Instant forming performance determines performance at a current moment of time and is calculated by formula [2]: To achieve maximum performance of complex surface forming with regard to the requirements for the surface quality determined by the constant value of the residual ridge between adjacent lines of the 2 1234567890''"" tool movement path, it is necessary to ensure its minimum length, setting a maximum line width formed with a spherical cylindrical tool.
In [3], it was proven that at each point of the surface, there is a tool movement direction vector by which a maximum path width can be achieved. An instant forming performance can be calculated by formula: w -path line width measured in a direction transverse to the longitudinal feed. The method allows selection of optimal forming strategies when machining workpieces using three-axis tools with a maximum path line width.
As distinct from the end three-axis milling, the five-axis one suggests orientation of the tool at any angle to axis OZ. Describing finish five-axis milling of complex surfaces, one can prove that at a constant cut depth, an increase in an angle between a tool axis and a surface normal increases a tool path line width. Forming performance also increases. However, at a large angle value, the cutting torque and the bending moment acting upon the tool increase.
Preliminary analysis allows us to make the following conclusions: five-axis finish milling performance for complex workpieces can be achieved by dividing the finished surface into local areas depending on curvature values and optimal machining strategies maximizing a path line width and ensuring a constant residual ridge value. Figure 1 shows the algorithm for choosing an optimal finishing strategy for each area of the complex surface. implicit finite element analysis. Flexibility and use of traditional numerical calculation methods are its advantage [4].

Abaqus/CAE simulation 2.1 Tool -workpiece models:
A 3D milling dynamics model includes 3D tool-workpiece models. An end spherical cylindrical mill of 5 mm in diameter made of rapid steel R9 was used. The workpiece is a plate of 200х100х20 mm in size made of aluminum alloy D16Т (Figure 2).

Figure 2. 3D tool-workpiece models
To set mechanical properties of the tool and workpiece material in Abaqus/Explicit, Johnson-Cook models are used for milling (chip-type machining). Tool and workpiece material parameters are shown in Table 1.

Setting of contacts:
When simulating material removal in Abaqus, a surface-to-surface contact can be used. The driving surface is a surface of all tools, and the driven surface is a workpiece surface (Figure 3). Friction coefficient equals 0.35.  Through that link, the tool can rotate around the axes going through the virtual point and parallel to the coordinate axes.

Mesh formation:
For more precise calculations, it is necessary to choose certain elements. For the chip removal, let us choose 8-noded hexa-hedral elements of the first order C3D8R; for the complex model such as a tool, let us choose 10-noded tetrahedra C3D10М.

Calculation analysis
Simulation results for end spherical cylindrical milling were obtained at a cut depth of 0,3 mm. The position of the tool axis to the workpiece is determined as angle α to the surface normal measured in a plane perpendicular to a cutting direction vector. The initial position and position during milling are shown in Figures 5 and 6 at angles α=0˚ and α=30˚. In Abaqus, the cutting force is determined by maximum values of a response acting on the tool in projection onto three axes OX, OY and OZ.  As can be seen, before the tool contacts the workpiece, cutting force projections equal 0. When the tool contacts the workpiece, the contact area of the mill tooth edge and the workpiece changes with regard to the tool rotating around itself. In steady-state, cyclic changes of cutting force projections occur.
When comparing Fx, Fy and Fz at different tool angles α, one can see that increase in angles causes increase in cutting force projections. At α=30˚, maximum values in Ox and Oy directions increase 1.3fold, and in Oz direction, they change slightly. At α= 60°, Fx and Fy increase twofold, and Fz -1.3fold.

Chip removal performance analysis
Finish milling performance depends on a line width of the tool movement path and a chip volume removed per unit time. At the same residual ridge height, these parameters, determining the performance, depend on the angle of a spherical cylindrical cutting tool. To increase a line width formed on the workpiece as a tool movement mark, angle α has to achieve a value at which point C is above point B (Figure 10).
The following condition should be met: where Vc -chip volume removed in t.
In this case, the volume element is a product of the line cross-section area and its length in a cutting direction. Figure 11 shows a scheme of the mark when changing a tool angle. Operating finishing parameters were selected by standards and are shown in Table 2. At 30 0 , t = 0.3 mm, h = (1 -sin30 0 ) = 0.5 mm. It means that (4) is not met so the line width does not change. At 60 0 , the width increases. Autodesk AutoCAD was used to determine the cross-section area for the tool mark line. Calculation results are shown in Table 2. Thus, when increasing a tool angle, the tool movement path line width also increases and forming performance improves. An increase in cutting velocity causes increase in stock removal velocity.

Conclusion
Finish milling simulation allows us to conclude that: -the value of an angle between the tool axis and surface normal in the contact area acts upon the cutting force; -mathematical simulation of strengths in the tool when machining complex surfaces helps determine an optimal position of the tool to the workpiece for five-axis milling and avoid tool destruction; -when the angle is 60 0 , forming performance can be increased 1.05-fold, and chip removal performance -1.13-fold.