Virtual System to Simulate the Performance of Various Categories of Machine Tools during the Design Stage

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Figure 1. Flow chart of the virtual evaluation system

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Figure 2. A sample of the input/output panel of the designed evaluation system

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Figure 3. The logic chart of the evaluation system

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6. Comparison Investigation on Open and Closed Milling Machine Tool Categories

6.1. Case Definition

The virtual evaluation system is applied on both 3-axis milling machine tools of open and closed categories. The open frame machining center mainly consists of the column, bed, table, saddle, and spindle housing, as well as, three screws to provide the traverse motion in three axes as shown in the CAD model in Figure 4 (a), while the closed frame machining center consists of two columns, bed, table, X-guide, X-slider, Z-slider, and spindle housing as shown in the CAD model in Figure 4(b). Both two categories are within the same volumetric size 1200 mm* 1790 mm* 1920 mm. The material of the machine structural components was assigned as gray cast iron with modulus of elasticity of 89 GPa; density of 7250 kg/m³; and Poisson's ratio of 0.25. On the other hand, the cutting process is carried out on work piece material called Inconel718, with cutting conditions [radial depth of cut (a) =4 mm, axial depth of cut (b) =4 mm, feed rate (u) =100 mm/min, feed per tooth (f_z) =0.0125 mm/tooth, and cutting speed (s) =2000 rpm], using an end mill of radius (r) =10 mm, number of teeth (n) =4, and helix angle (ß) =pi/6.

Figure 4. 3D model for (a) open structure, and (b) closed structure

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6.2. Preprocessing
6.2.1. Adjusting Spindle Head Position

Before running the system, all data stated in the previous subsection are entered and transferred to each module of the designed system according to its requirements. The spindle head position is adjusted according to the specified depth of cut so the end mill lower surface is 4 mm below the work piece surface.

6.2.2. Cutting Loads Generation

According to the cutting conditions previously stated in the case definition, the cutting load generated using analytical methods is shown in Figure 5. The graph shows the cutting load values with respect to the end mill angle of rotation along one tooth interval.

6.2.3. Preprocessing of Static and Dynamic Analyses

For the static module, the TCP is subjected to static load of 1000 N in X-direction and 500 N in Y-direction. For the harmonic module, sinusoidal loads of 1N amplitude with exciting frequency ranges from 30 to 300 HZ frequency are subjected to the TCP. Finally, cutting load values are transferred in a tabulated form to the transient structure module where they are subjected to the TCP through a specified number of time steps so as to obtain the deformation of the TCP during one tooth interval.

Figure 5. Cutting forces generated along one tooth interval

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Figure 6. Tooltip deflection at different loads for open and closed structure

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6.3. Static Analysis Results

Figure 6 shows the relative total deformation between TCP and worktable at various static loads. It can be noticed that the closed structure gives much better results compared to the open one, and that the larger the load, the greater the deviation between the results of closed and open categories. The supporting columns in the closed category raises the static loop stiffness in YZ plane from 32.5 in the open category to 52.9 N/μm, and in XZ plane from 70.4 in the open category to 294N/μm, as shown in Figure 7. The closed category shows greater rigidity in YZ plane with enhancement of 62.7 % as the supporting columns greatly decreases the tilting of the spindle head that occurs in the open category due to the X component of the cutting load. However, the main advantage of the closed category appears in the increase of rigidity in XZ plane by 317 %, which gives the structure great rigidity against bending ^[5].

Figure 7. Static loop stiffness in X and Y direction for open and closed categories

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6.4. Modal Analysis Results

Table 2 shows the first six natural frequencies for each category, and the position of maximum deformation for each mode shape. The first six mode shapes of each closed and open structure are illustrated in Figure 8 (a), and (b).

The results show that the lowest natural frequency in both open and closed categories occurs at the spindle head, and hence, it can be marked as a weak point from the aspect of dynamic behavior. The first natural frequency in the closed category is slightly lower than the open one. It is also noticed that the range of natural frequencies in the open category is wider than that in the open one, i.e.: at 228 HZ, six vibration modes occurred in the closed category, while five occurred in the open one. This indicates higher sensitivity to vibration in the closed category than in the open one. The explanation of such results may be due to the increase occurred in the mass from 4555 kg in the open case to 5436 kg in the closed one, and also due to the overhang effect of the Z-slider that carries the spindle housing in the closed frame. However, in the open category, the spindle housing show the maximum deformation in the first three mode shapes and the fifth mode shape, while that occurs only on the first and third mode shapes in the closed category. That indicates lower probabilities for resonance in the spindle housing in the closed case. Besides, the table and bed shows low deformation in all mode shapes of the closed category except the fifth one, while in the open category they show high deformation in the last three mode shapes especially the forth one. That indicates higher dynamic rigidity for the bed and table in the closed category.

Table 2. First six natural frequencies for both open and closed categories and the position of maximum deformation at each mode shape

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Figure 8. First six mode shapes for the (a) Open category, and (b) Closed category

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6.5. Harmonic Analysis Results

As shown in Figure 9, for the open category, the maximum dynamic compliance of about 0.12 μm/N in X-direction and 0.05 μm/N in Y-direction occurred at 60 HZ, which corresponds to a dynamic stiffness in XZ and YZ planes of 8 N/μm, and 20 N/μm respectively. For the closed category, the maximum dynamic compliance of about 0.044 μm/N in X-direction and 0.97 μm/N in Y-direction occurred at 60 HZ and 90 HZ respectively, which corresponds to a dynamic stiffness in XZ and YZ planes of 22.7 N/μm, and 1.03 N/μm respectively. By comparing the maximum compliance and the compliance all over the frequency range for both categories, it can be concluded that the closed structure has much better dynamic performance in X-direction up to 220HZ especially at 160HZ at which it gives the least compliance, while the open category shows better performance in the Y-direction from 70 HZ to 190 HZ, especially at 180 HZ at which it shows the least compliance.

Figure 9. FRF at the TCP at (a) X-direction and (b) Y-direction

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