# Modal analysis of soil system of vibrating wheel o

2022-07-27
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Modal analysis of vibratory roller vibratory wheel soil system

Abstract: on the basis of experimental research, the mathematical model of vibratory roller vibratory wheel soil system is established. The complex modal structure vibration theory is applied to calculate the system modal parameters and system response during soil compaction, and the variation law of the response of the front frame or vibratory wheel in the system is obtained, which constitutes the theoretical basis for identifying different compaction stages

key words: vibrating wheel; Soil; Mathematical model; Modal analysis

1 preface

in order to study and develop a complete compaction measurement method for the compaction of vibratory roller, improve the operation efficiency of vibratory roller, and explain the numerical relationship between the vibration parameters measured on the vibratory roller body and the compaction status of soil, it is necessary to establish the mathematical model of vibratory roller soil system on the basis of the experimental research on the dynamic compaction of soil and the dynamic performance of rubber shock absorber, The vibration relationship of vibrating wheel and various effects of soil compactability were studied

2 vibrating wheel soil system is supported by personnel, projects, enterprises, parks and quality standards. The mathematical model

2.1 assumptions and simplified conditions

according to the actual structure and working characteristics of the vibrating wheel, the following simplifications and assumptions are put forward before establishing the model:

(1) the unbalanced eccentric mass in the vibrating wheel ω Rotate around the wheel spindle, and ω= Constant

(2) the mass center and eccentric mass of the vibrating wheel are symmetrical to the longitudinal axis of the vibratory roller, so the vibrating wheel soil system can be simplified into a plane vibration model

(3) according to the structural characteristics of vibrating wheel and frame, it can be considered that both vibrating wheel and frame are rigid bodies

(4) when the rubber shock absorber between the vibrating wheel and the front frame and the vibrated soil are characterized as a multi degree of freedom system of spring and damping, the spring points out the direction for the future development of the relationship between the two countries, and the damping is considered to be massless

(5) the circumferential force generated by the circular motion of the eccentric block in the vibrating wheel only acts on the model with its vertical component. The test shows that , almost all the horizontal components of the vibrating wheel are dispersed by sliding with the surface of the compacted material, and are not transmitted to the soil

2.2 mathematical model of vibratory roller soil system

the mathematical model of vibratory roller soil system can be shown in Figure 1. It is composed of two equal parameter systems. The upper part describes the vibratory roller and vibratory roller, and the lower part describes the soil compaction performance

Fig. 1 mathematical model of vibrating wheel soil system

2.2.1 soil compaction performance model

according to relevant literature, the vibrated soil is divided into contact area and surrounding elastic state area. See Fig. 2. In the model, the vibrated soil is expressed as a certain amount of complex stiffness k*2 according to the half space theory. Under certain operating parameters of the vibratory roller, it can be determined by connecting the range of the considered contact area of China packaging. The soil quality in this range is the mass m3 of the vibrating soil in Figure 2. Within this range, the soil is plastic deformed, and the vibration energy of the vibratory roller is absorbed to improve the structural characteristics of the soil, which is the effective action range of the vibratory roller on the soil. The performance of its mechanical properties is related to the repeated rolling times of the vibratory roller, which has been explained by the dynamic compaction test of the soil . In the elastic region, the vibration of the vibrating wheel is transmitted to the surrounding environment through wave radiation, and this part of the vibration energy is not used to change the structure of the soil. The key requirement for the soil model is to be able to consider its plastic deformation in the model, as well as the description of its elastoplastic and even rigid properties. Based on the study of the dynamic compaction performance of soil, the soil model is divided into stage a, stage B and relatively rigid stage C, and the dynamic analysis of the vibrating wheel soil system is carried out

Figure 2 Schematic diagram of soil vibration area

2.2.2 vibrating wheel system model

it includes the front frame distribution mass M1, the vibrating wheel mass m2, and the complex stiffness k*1 of the damping support system between the vibrating wheel and the front frame. The vibrating wheel is driven at an angular speed ω The rotating exciting force Fe drives it into the vibration state

2.3 values of model parameters

values of model parameters refer to the technical data of the studied vibratory roller prototype, the dynamic test of rubber shock absorber and the dynamic analysis of damping support system, the compaction test of soil under the dynamic load of vibratory wheel and the touchdown size of vibratory wheel. See Table 1 and table 2 for values of model parameters

Table 1 vibrating wheel system parameters

Table 2 soil model complex stiffness parameter K2 (1+ η 2I)

3 modal analysis of vibrating wheel soil system

3.1 establish the system motion equation

select the static balance position of each unit in the model as the coordinate origin, and establish the coordinate system shown in Figure 3, where FV is the compressive strength, which is the force exerted by vibrating wheel M2 on vibrating soil m3. When fv>0, it is the loading stage of vibrating wheel. At this time, x3 ＝ X2, m3 and M2 shall be analyzed together; When fv=0, it is the jumping stage of the vibrating wheel. The vibrating soil mass m3 of a polymerization processing plant located in KALLO Beveren, Belgium, is separated from the vibration system. The model should be divided into two parts that are not connected up and down for analysis

Figure 3 force analysis of model

applying Newton's law, the system motion equation in matrix form is given. In the formula: {}, {x}, {f} are respectively the acceleration array, displacement array and excitation force array of the system, that is,

[m] and [k*] are respectively the mass matrix and complex stiffness matrix of the system. For the loading stage of vibrating wheel, fv>0,

for the jumping stage of vibrating wheel, fv=0,

3.2 modal analysis of the loading stage of vibrating wheel soil system ω r. Modal mass Mr, modal stiffness Kr and modal loss factor η r. See Table 3 for its value

for the vibratory wheel soil system, the modal response QR under simple harmonic excitation is:

the generalized coordinate response of the vibratory wheel soil system in the loading stage {x}:

Table 3 modal parameters of the vibratory wheel soil system in the loading stage

in equations (2) and (3) Φ? Is the system modal vector

according to this, the response amplitude of the vibrating wheel soil system under the generalized coordinates during the loading stage is shown in Table 4

Table 4 response amplitudes of generalized coordinates X1 and X2 in the loading stage of the vibratory wheel soil system m

it can be seen from table 4 that the displacement response of the front frame X1 and the displacement response of the vibratory wheel x2 in the vibratory wheel soil system changes with the change of different mechanical properties of the soil under each working condition during the low amplitude operation or high amplitude operation of the vibratory wheel

3.3 modal analysis of vibrating wheel soil system in jumping stage

the same analysis method can calculate the modal parameters of vibrating wheel soil system in jumping stage and the system response in generalized coordinates

table 5 modal parameters of the vibrating wheel soil system at the jumping stage

table 6 response amplitudes of generalized coordinates X1 and X2 of the vibrating wheel soil system at the jumping stage m

from this, it can be seen that the vibrating wheel keeps in contact with the soil from the viscosity a stage to the elastoplastic B stage of the soil compaction process by observing the changes of soil properties under the action of the generalized coordinates X1 and X2 of the vibrating wheel soil system, Under the vibratory compaction loading condition, the vibratory wheel exerts its compaction capacity, the soil produces compression deformation, the soil density increases, the soil stiffness increases, and the displacement response of the vibratory wheel and the front frame increases. When the compaction process of the vibrating wheel continues, the soil properties change to the relatively rigid C stage, the soil compression deformation under the vibrating wheel will not increase, and the vibrating wheel starts the jumping stage. At this stage, the displacement response x2 of the vibrating wheel and the displacement response X1 of the front frame are lower than those at stage B of soil compaction, which is determined by the dynamic characteristics of the system. According to the simple harmonic vibration theory of the system, the acceleration response of the vibrating wheel and the front frame in the system also has this change law, which is obtained for the first time in this study and has been confirmed by the results measured by the field test of the vibratory roller (see another article). Its direct application is to identify different compaction stages in the process of soil compaction by using the change law of the response of the vibrating wheel or front frame in the system, which is the theoretical basis for the continuous measurement of soil compaction degree and the measurement of the airborne compactor of the vibratory roller

4 conclusion

the mathematical model of the vibratory wheel soil system established in this paper is in good agreement with the actual working conditions of the vibratory wheel soil system. The model parameters obtained based on the corresponding tests are reasonable and reliable. It is a simple, practical and feasible mathematical model. The modal analysis based on the model is the dynamic basis of the compaction meter measurement. It can continuously inspect the whole rolling course, improve the measurement efficiency, identify different compaction stages, and improve the operation productivity of the vibratory roller. It has a bright future

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