Finite element model of machine tool spindle components
P120/ SD18 Series Monoblock Control Valve P120/ Sd18 Series Monoblock Control Valve,Hydraulic Monoblock Valves,Monoblock Valve Hydraulic,Monoblock Valve Jiangsu haohong hydraulic Co.Ltd , https://www.jshhhydraulic.com
The finite element model of the spindle part of the machine tool Zhang Yu (Changzhou Institute of Technology, Changzhou 001) static characteristics, automatic display of static deflection and various modes.
The spindle component is the most important component of the machine tool. The literature points out that under the action of dynamic load of different excitation frequencies, the medium-sized ordinary lathes are reflected in the comprehensive displacement of the cutting point between the tool and the workpiece, and the proportion of the main shaft components is the largest. The spindle component accounts for 30 to 40 when it is not in resonance, and 60 to 80 when it is in resonance. Undoubtedly, the performance of the spindle component is very important in the whole machine, so the design method of the spindle component has attracted the attention of engineers.
For a long time, extensive research has been carried out on the spindle components, and considerable progress has been made. In particular, mathematical models such as the finite element method, the transfer matrix method, and the lumped mass method are established to make it possible to theoretically calculate the spindle components and predict the performance. These methods can all meet the engineering precision, but they are not universally applied in the design, because there are two aspects: it has not yet established a universally applicable model, which brings difficulties to practical applications. . Second, the spindle support conditions are difficult to determine, which makes the calculation error large, so that the designer feels difficult to apply, and even less trust. Here is a finite element calculation model of a relatively complete machine tool spindle component, which can be used to calculate the dynamic and static performance of the spindle component and automatically display the static deflection curve and the vibration profile of the spindle. The model's calculation program was compiled in FORTRAN IV and BASI languages ​​and was successfully run on a computer.
1 The establishment of the finite element mathematical model of the main shaft component The basic idea of ​​the finite element method is to divide a continuous object into several tiny units, each of which establishes a mathematical model, and then combines the unit model into a system according to the force balance condition and the deformation continuous condition. Model, then solve the problem.
According to the structural characteristics of the main shaft component, a special portion such as a section change, a concentrated force action point, a support point, and a concentrated mass action point is generally used as a split node.
When the beam section of the equal section is long, the nodes can be appropriately added to improve the calculation accuracy.
The model takes the W6163 AL lathe spindle component as an example and is divided into 29 units and 30 nodes.
The dynamic characteristics of the spindle components mainly refer to lateral bending vibrations. Its torsional vibration and longitudinal vibration are not the main form of self-excited vibration, and the main shaft components are substantially isotropic in the radial direction, so the model treats the main shaft components as a planar beam. As for the static deformation under the action of the space force, it can be synthesized in the vertical direction by two plane beams.
This does not reduce the computational accuracy, but can save a lot of computer storage units. In the case of the 29 units of this example, the space beam element model will be about 9 times larger than the plane beam element model, and the increase in computation time will be quite amazing.
When the overall matrix is ​​composed of the element matrix, it is subjected to mechanical deposition and boundary condition processing (concentration parameter processing is required for the mass matrix). J and j. 1 unit is provided for the two adjacent cells, the corresponding array element immediately to [K] and j [K] j 1, unit mass matrix [] j and [] j. 1, synthesis j array when the right to four lower corner elements j 1 corresponding to the array of summing element 4 to the upper left corner, see formula (3), (4), called the stacking machine.
The moment of inertia of the axis of the shaft is I, and the modulus of elasticity is E. In the figure, Y is the generalized coordinate of the node displacement. Beam segments obtained by the elasticity element stiffness matrix in the micro-motion [K] i and the cell mass matrix [] i: Progress consider the effect of the support stiffness matrix constraint. There is provided on the first elastic support node j, and k is the stiffness coefficient k [theta], the bearing stiffness factor should be added to the corresponding element in the matrix: wherein k 'corresponding element value by means of mechanical bulk matrix obtained.
Some parts of the main shaft may be equipped with accessories such as gears, back caps, sleeves or flanges. Their mass, moment of inertia and stiffness and damping at the joint with the shaft affect the characteristics of the entire part. In view of the fact that we have known little about the stiffness of these joints so far, and in general these joint stiffnesses are high, simplifying them into a concentrated mass of rigid joints does not cause too much error. Therefore, in the model, these accessories are directly reduced to the concentrated mass and the moment of inertia to the Z axis and are equally divided at both ends of the unit. Let the gear on the pth unit be as shown in Figure 3.
Then, in the corresponding element in the mass matrix, the corresponding element value obtained by mechanically accumulating the unit matrix should be added.
If the system has n units, the total rigid array [ K] obtained by the above method and the coordinate vector of the displacement coordinate: if there is concentrated force or concentrated moment on the corresponding section, there is a force vector: system The static equilibrium equation and the differential equation of free vibration motion are: the displacement and rotation angle of each node can be solved by equation (10). Let the solution of equation (11) be that ω is the nth natural frequency of the system. Substituting equation (12) into equation (11), the characteristic equation is obtained as follows: ω equation (13) can solve the natural frequency and mode vector of each order by iterative and repeated washing.
2 Programming The GJJI software was compiled based on the above principles. Figure 4 shows the block diagram. The program is written in FORTRAN IV and BASI languages ​​and includes a main program and seven subroutines.
The model built is a more successful model. This model can be used to quantitatively distribute existing spindle components and propose an optimized solution for structural improvements.
1 Du Pingan. Structural finite element analysis modeling method. Beijing: Mechanical Industry Press, 1998.
2 Wang Zhiqin. Finite element method. World Book Publishing House, 1993.