Optimization of pre tightening parameters of the c

Optimization of pre tightening parameters of press combined frame structure

Abstract: under the assumption that the beam is the rigid body, the pre tightening design of the classic combined structure press frame gives the condition of no slit and the pre tightening design method, which is inconsistent with the real situation. In this paper, under the assumption that the beam is an elastic body, a new non slotting condition of the press combined frame structure is given, and the internal force of the frame caused by preloading is simulated by the superposition of temperature field. In this paper, the constrained variable scale method is used to establish the optimization calculation model to determine the preload and the diameter of the tie rod. The example shows that this method is feasible

key words: press; Pre tightening; Optimization

Chinese figure classification number: tg315.5

1 introduction

in order to ensure that the closed combined machine press can work normally and has a high service life, the contact surface between the pillar and the upper and lower beams must not have a gap [1]. Therefore, the frame should be pre tightened reasonably

in the classic press preloading design, the upper and lower beams are assumed to be rigid bodies. Based on this assumption, under the preload and working load, the upper and lower beams only produce axial rigid body displacement, so under the condition of no eccentric load, the strut and tie rod also only have axial deformation [2]. To determine the preload, it is only necessary to establish the stress deformation relationship between the strut and the tie rod as shown in Figure 1

Figure 1 force deformation relationship of strut and tie rod

based on this, we get the classic non slotting condition under working load: there is residual preload on the contact surface [3]. However, the actual situation is that the upper and lower beams are not rigid bodies. Regardless of the eccentric load, the beams and columns will produce the deformation shown in Figure 2. When the preload is insufficient, although there is still residual preload on the contact surface, there is a gap in the corner near the center of the press, as shown in Figure 2. This will accelerate the damage of the contact surface and affect the overall working performance of the press. In this regard, the preload calculation method shown in Figure 1 is powerless, and a new design calculation method needs to be established under a more real three-dimensional structural model

Figure 2 Schematic diagram of slotting when there is residual preload

at present, most of the press structures use large-scale three-dimensional CAE software for finite element analysis [4]. In the combined frame press according to the plastic △ vs value, the preload is the internal force. After the working load is applied, the internal force between the column, pull rod and beam will change accordingly. In a single structural finite element analysis, internal force loading conditions cannot be achieved, so we must find a method that can simulate the preload

generally, the design method of the combined press is to determine the overall structure of the press first, and then determine the diameter of the pull rod and the preload. Generally, these pre tightening parameters are determined by the designer based on experience and several trial calculations. Due to the difference of designers' level, even using the method shown in Figure 1, the pull rod is often too rigid or too soft, which makes the matching with the preload unreasonable. Some enterprises use the concept of pre tightening coefficient to verify the pre tightening parameters with a unified pre tightening coefficient, but the press is very different, which is difficult to regulate. Therefore, even experienced designers are often confused about determining the preload parameters. In view of this, it is urgent to establish a method to solve the optimal preload parameters

in order to solve the above problems, based on the large-scale analysis software i-deas9.0, the preload is applied by the superposition of temperature field, and the non slit condition is established under the three-dimensional overall finite element analysis model; Using the constrained variable metric method, the preload and the diameter of the tie rod are optimized to determine the best match

2 simulation method of preloading

2.1 principle of temperature field superposition

metal materials have obvious characteristics of thermal expansion and cold contraction. If the temperature of the beam and strut is kept constant, place the pull rod with the same length as the height of the press frame (beam and strut) in another low temperature field at normal temperature, and the length of the pull rod will be shortened. Due to the limitation of the press frame, in order to meet the relationship of deformation coordination, the pull rod is stretched by the frame. The greater the temperature difference, the greater the tension; Similarly, the press frame is also compressed by the pull rod. The greater the temperature difference, the greater the pressure; vice versa. The tension force on the pull rod is equal to the pressure on the frame, and the direction is opposite. It interacts with the force and reaction force of FH upper limit frequency (Hz). Obviously, this is equivalent to the effect of preload on the press frame and pull rod. That is, in the structural finite element analysis, the method of superposition of temperature field is used to apply a certain temperature difference to the pull rod, which can simulate the effect of preload. Under the working load condition, as long as the temperature difference remains unchanged, the internal force changes between the components of the frame can be simulated. The key is how to determine the temperature difference equivalent to the preload

2.2 definition of equivalent temperature difference

at room temperature T0, there is a straight rod with length of L and cross-sectional area of a, one end is fixed and restrained, and the other end is free

working condition 1: other conditions remain unchanged, and the axial tension f is applied at the free end. Under the action of F, the straight rod will extend △ L1, and the length will become l1=l+ △ l1

working condition 2: other conditions remain unchanged, and the straight rod will be heated to t0+ △ t. The change of temperature makes the straight rod extend △ L2, and the length becomes l2=l+ △ l2

if Δ l1= Δ l2= Δ l. Then △ t is defined as the extension of the rod Δ L axial tension f equivalent temperature difference. For the straight bar described in this section, the equivalent temperature change with working condition 1 is

2.3 the stress deformation of the press frame and pull rod under the preload working condition

for the press frame and pull rod under the preload F0, it is general, so that the axial stiffness of the frame is K1 and the stiffness of the pull rod is K2

in the natural state, the height of the press is L1, the length of the pull rod is L2

after pre tightening, the axial compression deformation of the frame is

the axial tension deformation of the pull rod is

in order to ensure the deformation coordination, there must be

that is,

formula (7) shows that in the natural state, the pull rod should be shorter than the height of the frame

2.4 the temperature change equivalent to the preload F0

is to simulate the preload state. In the natural state, set the pull rod temperature equal to the height of the press frame as t0- △ t (t0 is the ambient temperature). In this way, the pull rod will be shortened

, where K1 - the axial stiffness of the frame, which can be calculated through the overall finite element analysis

k2 - axial stiffness of pull rod, which can be directly obtained from formula (1)

the temperature change equivalent to the preload F0 is sorted out

3 finite element calculation model of preload structure

without considering the eccentric load, due to the symmetry of load and press structure, I-DEAS software is used to establish a three-dimensional solid model of quarter structure. In order to facilitate optimization, parametric modeling method is adopted

3.1 calculation of press frame stiffness

according to the analysis in the previous section, in order to simulate the preloading effect, the equivalent temperature difference △ t must be calculated first, and to determine △ T, it is necessary to know the press frame stiffness K1, which can be calculated by the following method

establish a solid model of the quarter structure of the overall frame of the press (excluding the pull rod), add a force fk1 of any size to the contact area between the pull rod nut and the upper surface of the upper beam, exert a vertical constraint on the contact area between the pull rod nut and the lower surface of the lower beam, and add a symmetric displacement constraint on the symmetrical plane

the finite element solution of the model with equal spacing between the upper grooves along the side wall of the disc is carried out to obtain the axial deformation △ LK1 of the press frame, and the stiffness of the press frame can be obtained from k1=fk1/△ LK1

3.2 pre tightening and working state calculation model

establish a three-dimensional solid model (including tie rods) of the overall frame structure of the press (as shown in Figure 3), and discrete the frame structure with three-dimensional tetrahedral elements (as shown in Figure 4); Connect the contact surface between the upper and lower beams and pillars as a whole, that is, do not treat as contact, and do not make contact judgment. The temperature difference △ t calculated according to formula (10) and lower than the ambient temperature is applied to the node of the tie rod, and the ambient temperature is applied to other parts of the frame. Therefore, by introducing the temperature field into the calculation model, the given preload is applied, and all the compressive stress is in the contact surface between the strut and the upper and lower beams

Figure 3 solid model of the overall frame figure 4 finite element analysis model of the overall frame calculation

in the above state, that is, under the condition of constant temperature field, the working load is applied at the specified position. At this time, the force on the tie rod increases, while the axial force on the frame decreases, and the normal stress at the contact surface between the pillar and the upper and lower beams will also decrease, The normal compressive stress is distributed unevenly along the contact surface due to the bending deformation of the beam and pillar

the above calculation model can better simulate the three-dimensional stress-strain state of the press frame in the pre tightening and working states

3.3 condition of no joint on the contact surface

under the working state, if there is tensile stress on the inner side of the contact surface, it indicates that the frame has been opened. Therefore, the condition of non slotting should be: the maximum normal stress of the contact surface is compressive stress

4 pre tightening parameter optimization

in order to solve the optimal pre tightening parameters, the following optimization model is established and optimized by the constrained variable scale method

where, D - diameter of pull rod, is the design variable and objective function, d[dd>, du>]

dd - the smallest possible diameter of the pull rod, selected according to experience

du - the maximum possible diameter of the pull rod. In order to avoid the contact between the pull rod and the hole diameter of the column, this value is slightly smaller than the hole diameter of the column

f0 - preload, which is a design variable

σ 0 - the absolute value of the average normal stress of the contact surface obtained after the finite element analysis of the initial design point

σ 1 - the maximum normal stress at the contact surface between the pillar and the upper and lower beams

ε—— Is a small positive number

σ 2 - axial tensile stress of pull rod

[ σ]—— Allowable axial tensile stress of pull rod

g1 (x) is the non slotted constraint function, G2 (x) is the constraint function of the axial tensile stress of the pull rod, and G3 (x) and G4 (x) are the constraint functions that limit the value range of the pull rod

the optimization model is to determine the preload and the diameter of the tie rod and minimize the diameter of the tie rod under the conditions of given frame structure, no slit and tie rod strength

5 calculation example

this paper takes 20Mn vertical plate stamping hydraulic press produced by a factory as the object, and establishes the structural analysis model of the hydraulic press. The upper beam of the press adopts a three cylinder welding structure, and the lower beam adopts a welding structure with a hydraulic stretching pad. The solid model is shown in Figure 3. The finite element model is shown in Figure 4. In order to meet the calculation accuracy, the lattice density is large in the contact area between the pillar and the upper and lower beams. The deformation of the pre tensioned frame under working load is shown in Figure 5

Figure 5

the optimization model is the same as 5. Where, DD = 100mm; Du＝320mm，[ σ]＝ 120MPa, initial value d0 ＝ 120mm, F0 ＝ 10kN. ε= 0.015。

after 7 iterations, the optimal values of preload and pull rod diameter are obtained. The optimal values f0* = 590kn, d* = 282.4mm. Table 1 shows the optimization calculation process. The pre tightening coefficient is defined as the ratio of the pre tightening force to the working load of the press. It can be seen from table 1 that the initial point is an infeasible point because the preload is too small, and the contact surface has been slotted; Zero at the best point indicates that this point is the best point, and the maximum normal stress of the contact surface is -2.25mpa

the results show that this algorithm can fully meet the requirements of engineering design. Table 1 optimization calculation process

6 conclusion

to sum up, this paper draws the following conclusions:

1) the pre tightening design of the combined frame press should not be carried out under the assumption that the beam is a rigid body

2) according to the deformation coordination relationship between multiple elastomers in the pre tightening state, it is reasonable to use the superposition of temperature field to simulate the pre tightening state under the three-dimensional model, and the calculation formula of equivalent temperature difference deduced in this paper is more accurate and practical

3) a three-dimensional overall analysis model of the combined frame is established to avoid the complexity of contact analysis of multiple elastomers. Based on this, the paper puts forward a method suitable for the overall analysis