Optimization and computer simulation of impact poi

2022-09-23
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Optimization and computer simulation of impact point of small vibratory impact pile driver

Abstract Based on the establishment of mechanical model and mechanical analysis of vibratory impact pile driver, the optimization analysis of impact point is carried out, the optimal impact conditions are given, and the computer simulation of the system is carried out. In addition, experiments are carried out on a prototype, which proves that the theoretical analysis is reasonable

key words vibration, impact, driving against automobile lightweight pile driver, computer simulation

the vibratory pile driver relies on its own weight to sink the pile into the soil layer. When the weight of the pile driver is reduced, the penetration efficiency of the pile is very poor, especially when the soil is hard, the penetration is even difficult. This greatly limits the miniaturization of pile drivers. In many pile foundation projects, small pile drivers also have broad application prospects. For example, in the water conservancy construction site of flood control and rescue, there is an urgent need for a small pile driver to replace manual piling to improve efficiency. This problem can be effectively solved by using vibratory impact pile driver. This pile driver vibrates the pile and impacts it rapidly, which greatly increases the penetration effect of the pile. The theoretical analysis of vibratory pile drivers generally adopts the single free vibration theory [1 ~ 3] proposed by Professor Barkan, which is relatively mature. However, it is extremely difficult for the vibratory impact pile driver to achieve optimal coordination in different soils and working conditions. Therefore, the development of its theory and practice is much more difficult and slow than that of vibratory pile driver [4]. According to the author's understanding, the theoretical research and products of small vibratory impact pile drivers have not been reported so far. Therefore, an in-depth and systematic study on the vibration and impact mechanism of small vibratory pile drivers will undoubtedly help to develop the products of small vibratory pile drivers and fill the gap in this field in theory and practice. At the same time, this research will also greatly promote the development of large-scale vibratory impact pile drivers. Based on the three-stage mechanical model, this paper analyzes the vibration and impact characteristics of the two degree of freedom vibration system, discusses the conditions for the optimal coordination of vibration and impact, and carries out computer simulation and prototype test

1 mechanical model analysis

1.1 mechanical model

vibration impact pile driver can be simplified to the mechanical model shown in Figure 1. Among them, the mass of pile driver frame and pile body is M1; The soil stiffness supporting the vibrating body is K1; Soil viscosity resistance is C; The mass of the exciter (including the hammer) is m2; The dynamic spring constant is K2; The amplitude of exciting force is f; The circular frequency of the exciting force is p; The preload of dynamic spring constant K2 is l.

Figure 1 mechanical model of vibratory impact pile driver

1.2 basic assumption of motion process under certain conditions, the vibrator M2 will impact the pile M1 once in each cycle of vibration. And the period of forced vibration of the two is the same, so the position of each impact remains the same. Now suppose that the motion of M1 and M2 in a cycle can be divided into three stages. ① The motion of M1 and M2 is not synchronous, and the motion of the whole system is described by two degrees of freedom vibration; ② By carefully selecting the spring stiffness K2 and the vibration frequency P of the exciter, the amplitude of M2 is greater than that of M1, and M2 impacts M1 at a position where M1 moves downward. At this time, the velocity of M2 is greater than that of M1 and in the same direction. In addition, it is assumed that this impact is plastic collision; ③ After M2 impacts M1, the two move synchronously until they separate and then start the movement of the first stage of the next cycle. In this stage, the whole system movement is described by single free vibration

1.3 dynamic analysis

1.3.1 the first stage - the whole system is described by the mechanics when moving with two degrees of freedom. In the coordinate system shown in Figure 1, the motion differential equation with the equilibrium position of the vibrating body under the action of gravity as the origin of the coordinate axis is solved by

, where B1 is the amplitude of the frame and pile; B2 is the amplitude of the exciter; θ 1 is the initial phase of the frame and pile; θ 2 is the initial phase of the exciter. Then the solution of equation (1) is

x1=b1cos (PT+ θ 1),x2=B2cos(Pt+ θ 2) (6)

if considering the damped attenuation motion of the system, see literature [5]

1.3.2 the second stage - mechanical description of the impact process figure 2 shows the movement of the exciter of the pile in three stages in a cycle when the dynamic spring K2 has a certain preload L. Where, X1 is the pile displacement; X2 is the displacement of the exciter

Figure 2 Schematic diagram of impact point

as shown in Figure 2, when impact, x2=x1-l, that is,

b2cos (PT+ θ 2)=B1cos(Pt+ θ 1) -l (7)

note that t satisfying equation (7) is T1, and at this time, the displacements of M1 and M2 are equal. The common velocity of the frame and the exciter after the collision is obtained when the production efficiency is improved by the centripetal collision

v0=[-m1B1Psin(Pt1+ θ 1)-m2B2Psin(Pt1+ θ 2) ] · M-1 (8)

because of the short impact time, the position of the impact two objects has hardly changed, but the speed has changed significantly. Since the impact is assumed to be plastic collision, the hammer (and vibrator) m2 and pile M1 will move synchronously after the collision

1.3.3 the third stage - mechanical description of the synchronous motion of M1 and M2. The synchronous motion of M1 and M2 can be described by single degree of freedom vibration. M is the sum of the masses of M1 and M2, and X is its displacement

that is (9)

when the initial condition of motion is t=t1, the displacement is X1 | t=t1 is recorded as x0; The speed is V0, and the general solution of equation (9) of

is

2 optimization analysis of impact point

2.1 optimal impact conditions to make full use of impact energy and achieve optimal coordination between impact and vibration, it is necessary to select a suitable working point. Obviously, the impact will occur in the process of both the exciter and the pile moving downward, otherwise, not only the impact energy cannot be effectively used, but also the phenomenon of useless or even counterattack will occur. Therefore, from equation (10), it is necessary to make, and to make a reach the maximum value, it is necessary to meet and

that is,

3 π/2 ≤ pT1+ θ 1 ≤ 2 π (16)

and the impact point is determined by the preload l of the power spring K2 and the initial phase difference θ 1- θ 2 jointly determined, that is, adjusting the initial phase difference can make the phase of the exciter at the maximum speed equal to the phase corresponding to a certain position (such as the best impact point) where the pile moves downward. However, in order to ensure the impact at this position, it is necessary to adjust L. when the vibrator moves downward to the maximum speed, pt1+ θ 2=3 π/2, then

l=b1sin can be derived from equations (7) and (16)( θ 1- θ 2) (17)

0≤ θ 1- θ 2 ≤ π/2 (18)

set ε It is any small positive number, and M is any large positive number. From equation (18), we can get

ε ≤tg( θ 1- θ 2) ≤ m (19)

substituting two equations (4) and (5) into equation (19), we can get

p01 ≤ P ≤ P02 (20)

after derivation, where

when m →∞, we get

equations (16) and (19) are the best impact conditions

2.2 amplitude ratio condition to make the best impact possible, in addition to satisfying equations (17), (20), it is also necessary to make b2>b1, and then consider structural design and other factors, and make b2>b1, (recorded as b) less than a positive number γ ( γ> 1) In addition, b1min ≤ B1 ≤ b1max must be met. Therefore, the computer simulation of

13 system

3.1 the flow chart of system simulation

takes a small vibration impact pile driver designed by ourselves as an example for calculation. Among them, m1=60kg, m2=25kg, eccentric moment m=2.744n · m, damping coefficient c=0.1k1 (m1+m2) Use c++ language to program simulation calculation, and the program N-S structured flow chart is shown in Figure 3

Figure 3 simulation program flow

can be obtained from table 1, table 2 and Figure 4: (1) when the dynamic spring constant K2 increases, the amplitude ratio b decreases; When the working frequency P increases, B increases; When the soil stiffness K1 increases, b decreases. This is the same as the theoretical analysis. It is not difficult to draw these conclusions from equation (24). (2) When the dynamic spring constant K2 increases, the phase difference θ 1- θ 2. Increase, that is, the impact point is delayed; When the operating frequency P increases, θ 1- θ 2. Decrease and advance the impact point; When the soil stiffness K1 increases, θ 1- θ 2. Increase and delay the impact point. from θ 1- θ The same result can be obtained by the expression of 2. For this purpose, Let f (K1, K2, P) =tg( θ 1- θ 2) , available. Thus, we can deduce. (3) When the dynamic spring constant K2 increases, the minimum working frequency P0 ensuring the best impact conditions increases; When the soil stiffness K1 increases, P0 also increases. That is, when K1 or K2 increases, a higher working speed should be selected. Incidentally, when the pile mass M1 increases, P0 decreases. (4) Generally, when the soil stiffness K1 increases or the dynamic spring constant K2 increases, the working frequency P increases in order to meet the optimal impact conditions. Amplitude ratio B and phase difference θ 1- θ 2 (i.e. the impact point) changes are jointly determined by the growth rate of the three. For example, table 2 shows that when K1 remains unchanged and K2 and P increase, B increases, θ 1- θ 2 decrease; When K2 remains unchanged and K1 and P increase, b decreases, θ 1- θ 2 increase; When p is constant, K1 increases and K2 decreases, b decreases, θ 1- θ 2 increase. (5) When the working frequency P increases, the impact velocity V0 will generally increase, and the attenuated vibration amplitude A and steady-state vibration amplitude B of the synchronous movement of the exciter and the pile will increase, but at the same time, the impact point will be advanced, so the influence of P on the synchronous movement x should be comprehensively considered. In addition, P increase is also constrained by amplitude ratio B and machine power. Table 1 Unconstrained vibration and impact parameters

Table 2 vibration and impact parameters that meet constraints

it should be pointed out that the soil spring constant changes with different soil properties. At present, there is no complete and mature theory at home and abroad on the impact of soil layer performance on the vibration and impact characteristics of pile drivers, not to mention the existing empirical formulas and soil data are for large pile drivers and machine foundations. In order to make the pile driver work effectively under different soil conditions, automatic control must be adopted to adjust frequency automatically to adapt to different soil conditions. The stepless frequency modulation technology under optimal control needs to be further studied

Figure 4 vibration curve and impact point meeting the constraint conditions

4 example

the self-designed small-scale vibration impact pile driver was tested. The relevant parameters of the pile driver are the mass of the frame and wooden pile m1=60kg, and the mass of the vibrator m2=25kg The diameter of the wooden pile is d=12cm, the length is l=2.5m, and the dynamic spring constant k2=2 × 105N·min-1。 The soil is sandy clay. Considering that the pile drives the surrounding soil to vibrate during the penetration process, M1 increases and P0 decreases. Combined with the previous calculation and analysis, take the working speed of n=1400r · min-1, test several piles, and the wood pile penetration of 1.5m is completed in about 1min. It is proved that the theoretical analysis and calculation are reasonable

5 conclusion

the motion of the vibratory impact pile driver in each cycle can be described in three stages, namely, the stage of separation of the vibrator and the pile, the stage of impact and the stage of synchronous motion of the two. In order to achieve the best match between impact and vibration, it is necessary to select appropriate parameters and appropriate impact points. The optimum impact conditions and amplitude ratio conditions established in this paper provide a basis for this. This paper presents a computer simulation algorithm, which can effectively analyze the vibration and shock characteristics, and provides convenient conditions for the selection of various parameters

references

1 pipaoqi Concrete machinery and piling machinery. Beijing: China Construction Industry Press, 1982

2 S. Prakash. Soil mechanics. Beijing: water resources and electric power press, 1984

3 Anderson J S, Bratos M. Solving Problems in vibrations, Beijing:Longman Scientific & Technical world Publishing Corp, 1990.

4 Zhang Qingguo. Construction machinery. Chongqing: Chongqing University Press, 1998

5 in recent years, a group of pests, such as pine wood nematode, has gradually entered people's vision sgy

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