Optimization Design of Gantry Machining Center Beam Model Structure

Optimized Structural Design of the Beam Model for Gantry Machining Centers 1. Optimization of Beam Model Structure According to the theory of material mechanics, the shear stress generated by pure torsional deformation occurs in pairs, with large shear stress appearing in planes at 45° and 135° to the main plane. Therefore, during structural design, stiffeners are arranged in planes at 45° and 135° to the main plane to bear the effect of torsional loads, which can enhance the torsional stiffness of the structure. As shown in Figure 10, the transverse and longitudinal shear stresses acting on the diagonal stiffeners are decomposed in the direction of the stiffeners and perpendicular to the stiffeners. The two force components in the direction perpendicular to the stiffeners are equal in magnitude and opposite in direction, interacting with each other to limit the torsional deformation of the stiffeners. The force components along the stiffeners, as shown in Figure 11, manifest as tension and compression along the stiffeners. From the modal analysis results of the original structure discussed above, it is evident that improving the beam's torsional stiffness is crucial for enhancing the overall performance of the machine tool. Based on the diagonal stiffener torsional theory mentioned above, the longitudinal stiffeners inside the beam are changed to a double X shape. To fully utilize the torsional performance of the longitudinal stiffeners, their arrangement angle should be as close as possible to 45° and 135° relative to the horizontal plane. Additionally, considering that the beam's bending mode is in the fore-and-aft direction, a horizontal stiffener is placed at the midpoint of the beam to enhance the bending stiffness in that direction. The modified form of the longitudinal stiffeners in the beam is illustrated in Figure 12. According to the stiffener arrangement theory proposed above, a pair of diagonal brace stiffeners is designed inside the beam. The resulting form of the beam stiffeners is shown in Figure 13. The outer dimensions of the beam remain the same as the original structure, with the thickness of the outer wall maintained at 25mm, while the stiffener thickness is adjusted from 20mm to 15mm, and the arrangement of the transverse stiffeners is kept in its original form. 2. Performance Comparison Analysis (1) Comparison of Modal Analysis between the Original Beam and the Modified Beam. Considering the actual working frequency band of the machine tool, it can be concluded that the first two modal characteristics of the beam play a significant role in the dynamic performance of the entire structure. Table 2 compares the analysis results of the original beam structure with those of the improved beam structure. The first and second natural frequencies of the modified beam have increased compared to the original beam structure. According to (where n represents the nth natural frequency, corresponding to the modal stiffness and modal mass), it is evident that the torsional stiffness corresponding to the modes of the modified beam has significantly improved. Furthermore, the second mode of torsional vibration, which significantly affects the dynamic performance of the entire machine in the original beam structure, has become the third mode in the modified structure, with its natural frequency value increased by 13.9%. Thus, the modified structure achieves the optimization design goal of enhancing the dynamic performance of the beam. (2) Comparison of Static Analysis between the Original Machine Model and the New Beam Machine Model. By reassembling the modified beam with other original machine components, a new machine structure model with the new beam is obtained, which undergoes static and dynamic analysis. Table 3 compares the static analysis results of the original machine model with those of the new beam machine model. The analysis results indicate that with a 4.2% reduction in the beam's self-weight, the reasonable arrangement of internal stiffeners not only maintains the static performance of the entire machine but also improves it in all three directions, particularly with a 7.4% increase in Z-direction static stiffness. (3) Comparison of Harmonic Response Analysis between the Original Machine Model and the New Beam Machine Model. A harmonic response analysis is performed, and the results are compared with those of the original machine model, as shown in Figure 14. It can be observed that the new beam machine structure, after optimization, shows a decrease in amplitude under the harmonic force acting in the 40–140Hz range compared to the original machine model. However, the amplitude at the resonance points does not decrease significantly, as the amplitude at resonance points is primarily determined by the structure's damping rather than by dynamic stiffness. The harmonic response analysis also indicates that the frequencies of all resonance points for the new structure have increased compared to the original machine model, further validating the correctness of the modal analysis results. The dynamic and static analysis results above demonstrate that the new beam structure improves the dynamic performance of the entire machine. Additionally, the proposed diagonal brace stiffener structure has already been applied in the beams of other machine tools with significant positive results. 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