In the design of metal cutting machine tools, the machine tool spindle is complex and expensive, and is the most important part of the machine tool.
The main shaft is a weak link. The front end is equipped with a chuck and a workpiece, and directly participates in the cutting process. The deformation and vibration of the main shaft have the greatest influence on the machining accuracy and surface quality of the machine tool.
Therefore, the key to the success of machine tool design depends on the pros and cons of the spindle design. The spindle design mainly selects the main parameters of the spindle according to the machining conditions, machining requirements, machine configuration parameters and structure of the parts. Whether the parameter selection is appropriate will have a direct impact on the final machining accuracy of the machine and determine the machining quality and performance of the machine.
In the era of rapid development of science and technology, spindle optimization design is an effective means of spindle design in machine tool design. It not only overcomes the blindness in previous design methods, but also improves the design quality, design efficiency, scientific design of the spindle and reliability. This paper introduces the multi-objective optimization design method of the spindle, which has the advantages of simple and practical design method. The result of the main parameter optimization is more reasonable and reliable.
1 The establishment of mathematical model for optimization design 1.1 The actual working conditions of the design variable spindle are more complicated, and there are many influencing factors. This paper comprehensively optimizes the main structural parameters of the spindle. The structure diagram is shown in Figure 1. The structure is mainly determined by five parameters: 1 spindle overhang section diameter Da2 spindle support section diameter D3 spindle support section length L storage Kai, etc.: machine tool spindle main parameter optimization design 4 spindle overhang section length A5 spindle bore diameter d. In addition, the stiffness of the front support of the spindle is KA, the stiffness of the rear support is KB, and the spindle shaft end has a force F and a bending moment. Setting: 1.2 The objective function The deformation of the machine tool spindle has a great influence on the machining quality. Therefore, the requirement of the spindle property is mainly represented by the stiffness requirement, that is, the deflection (or displacement) Y of the protruding end of the spindle is as small as possible, so the spindle shaft The minimum end displacement is the goal pursued by the optimization design of the machine tool spindle.
Only consider the F force acting on the front end of the spindle, the front end of the spindle has a displacement Y, and the end of the F main shaft is subjected to a force (N) E spindle material elastic modulus 2.1 × 10 spindle overhang section diameter () D spindle support section diameter ( ) Spindle overhang section section inertia distance L front and rear support span () I spindle support section section inertia distance a spindle overhang section length () d spindle inner hole diameter () front support stiffness (N /) rear support stiffness (N /) ε front support counter moment coefficient (take ε = 0.45).
When only the moment is applied to the front end of the spindle, the displacement Y of the front end of the spindle is: the torque (N.) received by the front end of the spindle.
The displacement Y of the front end of the machine tool spindle can be regarded as the sum of Y and Y in the same plane. Therefore, the torque received by the spindle end of the machine tool spindle is caused by the cutting force F during the cutting process. For the design calculation, take =F? 2a, substituting into the formula (1), the same reason can be obtained, and reducing the quality of the main shaft is of great significance in practical work. Therefore, this paper takes the minimum mass as the goal of the optimization design of the machine tool spindle. In the formula, the Ï metal density (kg/hydraulic electric machine makes f multi-objective function is the α-weighted value (x) objective function in the formula.
1.3 Constraints (1) Spindle overhang section diameter D: According to experience, the range of values ​​is generally 8 ≤ D ≤ 18, so (2) the shaft diameter D between the front and rear bearings of the spindle: its value range is (3) Support span L: The support span L should be an appropriate value. If it is too large or too small, it will affect the deformation and quality of the spindle. The value range is 20 ≤ L ≤ 65, so (4) the length of the spindle overhang section a: Its size has an impact on the stiffness and quality of the spindle. Generally, a=8~15 (5) Spindle aperture d: The increase of the aperture will reduce the wall thickness of the spindle, affecting the normal operation of the spindle, and deformation during processing. Therefore, special attention must be paid to the shaft wall at the rear axle of the main shaft. (6) Spindle stiffness limitation: Increasing the spindle bore diameter d will weaken the spindle stiffness, and the stiffness of the spindle end is proportional to the moment of inertia of the section. In order to avoid excessively weakening the spindle stiffness, the d/D (7) spindle front and rear support stiffness is determined as follows: Figure 2, the bearing stiffness increases as the journal increases. Taking the 200 series as an example, the solution is: K and K are substituted into K (2), which can optimize the multi-objective function.
2 Optimization method and calculation example The mathematical model thus established shows that it is a constrained nonlinear problem with five design variables and 12 constraints, so it is solved by the SUT penalty function interior point method.
Now design the machine tool spindle, know that the spindle end force P = 14.7kN, the front and rear support select 200 series bearings, KA, the weight value is α12, the optimized results are shown in Table 1.
Therefore, if the pre-heat treatment is performed before quenching to make the progress of the structure and composition uniform, it will contribute to the great improvement of its toughness.
In summary, the heating process of heat treatment of wear-resistant materials is not only for the purpose of organizing austenite and controlling the austenite grain size, but also has the characteristics of its phase change process. The characteristics of these phase change processes will affect its final Organization and performance. Therefore, the heating process is the basic condition for heat treatment of the wear resistant material. (To be continued) (Continued from page 4) Parameter variable method Overhang section Straight support section Straight support span overhang section Long spindle aperture Spindle mass Spindle shaft end Single target (W) Optimized multi-objective (W.δ) optimization from the table It can be seen that the multi-objective optimization design has a significant improvement over the single-objective optimization design, especially the support span L and the overhang section diameter D and the length a. Since the single-objective optimization pursues the goal is the minimum quality, therefore, The optimization result is the lower limit value within its range. Although the spindle mass is small, the spindle shaft end displacement has exceeded the allowable range. In the multi-objective optimization, these three items take the intermediate value within the range, which reflects the The optimization results not only take into account the quality of the spindle but also the stiffness of the spindle. Although the spindle quality has increased, the shaft end displacement has reached the design requirements. Therefore, the multi-objective optimization results are more reasonable and more realistic, which can improve the reliability of the spindle.
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