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Optimization design of universal joint spider based on finite element analysis

using the large-scale general finite element analysis software ANSYS, based on the finite element analysis of the spider of the universal joint of 1700mm rolling mill in a hot rolling mill, the three-dimensional entity optimization analysis of the spider is carried out to meet the requirements of its strength and stiffness

ansys system contains parametric design language (APDL), which has high-level language elements such as parameters, mathematical functions, macros, judgment branches and cycles. It is an ideal program flow control language, which is very suitable for finite element calculation and optimization analysis

finite element method and optimization method are the two most important mathematical tools in engineering analysis. Combining the two organically will give full play to the accuracy of numerical calculation of finite element method and the efficiency of extreme value calculation of optimization method, which will play a great power in engineering analysis

1 finite element analysis and calculation of the outlet environment of the cross shaft

the driving shaft and the driven shaft of the cross shaft without the use of harmful solvent universal coupling apply two pairs of forces to the cross shaft through the bearing through the fork on it, which form a pair of force couples with equal size and opposite directions (Fig. 1) These two couple vectors are in the plane determined by the active axis and the passive axis. If the inclination angle of the two axes is ignored (very small, negligible), the forces constituting the two couple are in the plane of the cross axis

1.1 establishment of model

since the structure and load of the cross shaft are symmetrical to the two sections I-I and ii-ii (Fig. 1), it can be cut from the two sections I-I and ii-ii, and take 1/4 of the cross shaft as the research object (Fig. 2) As shown in Figure 1, the dimensions of the spider are as follows: l=865mm, a=327mm, b= 325mm, d = 242mm, H = 174mm, r=90mm, d=50mm, r=10mm The three-dimensional entity unit is selected to divide the cross axis into 41904 units The routine maintenance of the experimental machine with material change is completed by the operator, and the finite element model is shown in Figure 2

1.2 constrained boundary conditions

in Figure 2, the cross-sections a, B and y=0 planes in the two 45 ° directions of the calculation model are symmetrical planes of the cross axis structure and load The constraint conditions of the calculation model are taken as: X, y, Z three-dimensional constraints of each node with y=0 on the two planes a and B; Each node with y ≠ 0 on the A and B planes is constrained in X and 2 directions, and the Y direction is free

1.3 load application

as shown in Figure 3, the load is trapezoidal along the axis of the cross shaft; In the XY plane, the surface distributed load on the outer cylindrical surface of the cross axis is distributed according to the cosine law on the arc, and the arc AB is 120 °

1.4 analysis of finite element calculation results

Figure 4 is the distribution diagram of the maximum principal stress when the spider bears a torque of 240 kn · M. the stress on the loaded side of the transition section from the spider cylinder to the cone (that is, the r90 transition section on the loaded side) is the largest, and there is serious stress concentration. The maximum principal stress value is 498.15mpa

2 structural optimization design of cross shaft

2.1 selection of design variables

the selection of design variables is considered from two aspects: one is the structural optimization design of cross shaft under the condition that the main transmission system of the rolling mill already exists and the outer frame size of universal coupling has been determined These dimensions can only be used as given design parameters (such as l in Figure 1) Second, according to the above three-dimensional finite element analysis and calculation of the spider, the stress at the arc transition of the spider r90 is the largest, and it is in an alternating stress state, which is a dangerous part However, changing some dimensions does not reduce the stress concentration or has little effect (such as a, B, D and R in Figure 1)

therefore, the design variable can be taken as

x=[x1, X2, x3]=[r, D, h]

, where: R is the transition arc radius; D is the diameter of the spider; H is the width of rolling bearing

2.2 determination of objective function

the purpose of structural design of the spider is to reduce the bending fatigue stress (expressed as the maximum principal stress) at this place and make it as close as possible to or less than the bending fatigue strength Therefore, when transmitting 240KN · m torque, the objective function is to minimize the maximum principal stress borne by the spider Namely:

f (x) = s1max

where: S1 is when the transmission is 2400kn M the maximum principal stress borne by the spider when torque

2.3 determination of constraint function

because the stress at the place where fatigue failure occurs (i.e. the transition arc on the loaded side) is only considered to be reduced when designing the spider, there is no restriction of other factors, so there is no restriction of constraint function in this optimization process

for each design variable, the boundary constraints are as follows: 222mm ≤ D ≤ 264mm; 164mm≤H≤184mm.

2.4 selection of optimization methods and optimization process

ansys program provides two optimization methods: zero order method and first-order method Both of them use the penalty function (SUMT) method to transform the constrained optimization problem of domestic machinery price normalization into a non constrained problem for solution Due to the complex stress and deformation of the spider, the zero order method is used here to ensure the smooth optimization The optimization process is a series of analysis processes, that is, a series of pre-processing solution post-processing optimization cycles

3 comparison between optimized and pre optimized

through a series of iterations, the optimal design result value is obtained Figure 5 shows the process change of the objective function with the number of iterations, and the change of variables with the number of iterations

from the optimization results, when the transition arc radius r increases from 90mm to 94.20mm, the cross shaft diameter D increases from 242mm to 259.80 mm, and the rolling bearing width h decreases from 174mm to 166.43mm, when the cross shaft transmits 2400kn · m torque, the maximum principal stress it bears is small from 498.15 MPa to 416.07mpa The optimized result is 19.71% less than that before optimization (end)

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