Mechanical Behaviors and Numerical Simulation Analysis of a New Isolation System

Abstract

Finite element analysis is one of the key steps in evaluating the effectiveness of an isolation system. The aim of this paper is to research the mechanical properties of sliding and rolling friction systems and their application for isolating frame structures. A hybrid seismic isolation system is proposed, which aims to protect the superstructure by reducing dynamic response. The effect of different parameters on the friction coefficient of the isolation bearing was tested using a compression-shear testing machine, and the results showed that various parameters significantly affected the friction coefficient. In addition, a numerical analysis finite element model was established using SAP2000 software to compare the seismic isolation performance of the hybrid isolation system with that of traditional seismic-resistant structures. The results showed that the composite isolation system not only effectively reduced inter-story shear and acceleration, but also slightly enhanced the seismic isolation effect as the friction coefficient decreased.

1. Introduction

Earthquakes can trigger high-intensity vibrations in a short time, producing tremendous amounts of energy that may result in structural damage or even destruction. To reduce the degree of damage to superstructures under seismic excitation, researchers have developed various types of isolation devices, including rubber, friction, and composite isolation bearings.

The most typical passive isolation device is the rubber isolation system (RIS). The RIS is composed of rubber and steel plates laminated together, which is widely used in practical projects because of the elasticity of rubber and the bearing capacity of steel plates with excellent isolation performance. Over the past two decades, researchers have conducted experiments and finite element studies on the stiffness, shear deformation, temperature, and hysteresis curve properties of RIS from multiple perspectives, e.g., [1,2,3,4,5]. Taking a steel frame structure with FRP rubber bearings as the research object, WU [6] obtained the ground vibration response of the base-isolated structure under different vertical loads, different structural height and width ratios, and different site factors by shaking table testing. Meanwhile, they established a finite element model of the seismic isolated structure with OpenSees to compare the ground vibration response analysis, ensuring the correctness of the results, which showed that FRP rubber isolation bearings can effectively reduce the influence of earthquakes on the superstructure. SUN [7] verified the influence of temperature on the seismic isolation effect by analyzing the correlation between temperature and the bearing performance and stiffness of the rubber bearing, providing a theoretical reference for the engineering application and development of rubber seismic isolation bearings.

Friction isolation bearings take friction as the damping force of the isolation layer and have good isolation performance, among which the friction pendulum has a bright development prospect because of its automatic reset capability. On this basis, researchers have developed various forms of friction pendulum bearings and conducted mechanical model derivations and experimental testing to promote the development of friction isolation bearings [8,9,10]. For example, Harvey [11] proposed a coupled two-way dynamic non-linear model to numerically analyze the dynamic performance of horizontal two-way systems based on considering the rotation degree of freedom factor. Zhang [12] studied the effects of two types of vibration isolation bearings, ball and roller, on the rolling friction coefficient and analyzed the effects of the friction coefficient on the vibration isolation effect by modeling with SAP2000 software. The results showed that the seismic isolation performance is most effective when the rolling friction coefficient is within a certain range.

In recent years, composite isolation systems have become a research focus in the field of engineering earthquake resistance due to their advantages of gathering various types of seismic isolation devices and innovative combinations to improve seismic isolation performance to the maximum extent [13,14,15,16,17,18,19]. In terms of innovative combinations, Gao [20] studied the mechanical properties and seismic isolation performance of a disc spring-high damping rubber three-dimensional composite seismic isolation bearing. Numerical simulations were conducted to analyze the mechanical properties of the disc spring using ABAQUS finite element software, and test data were used to analyze the mechanical properties of the high-damping rubber seismic isolation bearing. Li [21] conducted horizontal and vertical seismic isolation performance tests on proposed disc-spring-stacked rubber three-dimensional composite seismic isolation bearings under different working conditions. In the horizontal direction, the hysteresis performance of the bearing under simple harmonic excitation was tested, and the effects of shear strain, vertical pressure, and loading frequency on its horizontal mechanical properties were investigated. In the vertical direction, the equivalent stiffness and equivalent damping ratio of the bearing were investigated, and the effects of loading amplitude, pressure, and loading frequency on its vertical hysteresis performance were investigated, as well as how changes in vertical stiffness affect the horizontal mechanical properties of the laminated rubber bearing. Hui developed a new type of variable-frequency rolling pendulum bearing consisting of a rolling bearing and an additional viscous damper to protect acceleration-sensitive equipment. The authors conducted comparative analyses using computer software and vibration table tests on different types of ground motion, including short-period (high-frequency), medium-frequency, and long-period (low-frequency) ground motion. They tested the effects of different parameters on device acceleration and relative displacement responses and the accuracy of the model.

With the advancement of science, technology, and engineering design, composite isolation bearings are constantly innovating and developing in the field of seismic resistance. In this study, a new type of composite seismic isolation system is proposed that is based on the flexibility of ball bearings and solves the limitations of traditional sliding isolation bearings. In order to analyze the dynamic friction performance of sliding and rolling, compression-shear tests were conducted. By controlling variables such as vertical pressure, horizontal velocity, number of pads, and number of rolling balls, the influence of these factors on the dynamic friction coefficient of the composite isolation bearing was studied. The obtained data can be used to analyze the structural response under earthquake excitation.

2. Design of the Isolation System

2.1. Description of the Designed Isolation System

The hybrid isolation system designed to isolate vibration comprises rolling friction and sliding friction. The physical diagram of the isolation device is shown in Figure 1, while its individual components are displayed in Figure 2. The bearing capacity is distributed by compressing the spring.

When the lower surface of the upper plate of this composite vibration isolation bearing contacts the friction surface of the upper surface of the lower plate, the spring in the upper part of the ball roller group receives extrusion, as per Hooke’s law:

$$f=-kx$$

where $x$ is the compression of the spring, mm; $k$ is the coefficient of elasticity of the spring, kN/mm; and $f$ is the pressure of a single spring, KN.

Then, the upper load borne by the rolling ball group is

$$F=nf$$

where $n$ is the number of springs in the upper part of the ball group.

The friction sliding surface of the upper load is

$$N=M-F$$

where $M$ is the total upper structure load.

The distribution of the load-bearing capacity is controlled by the bearing by changing the number of gimbals and shims. Without balls, the system relies solely on sliding friction, which is equivalent to a planar sliding bearing. With the addition of balls, rolling friction and sliding friction work together to reduce structural damage by decreasing the upward transmission path of earthquakes.

2.2. Design of the Test Bearing

This experiment uses a micro-controlled hydroelectric servo compression shear tester and a combination of two isolation systems and an intermediate steel plate. The arrangement is a double shear combination, with the isolation system located in the middle, as shown in Figure 3.

This experiment studied the variation law of the friction coefficient of the composite seismic isolation bearing under different variables. The calculation of the friction coefficient was carried out using the following formula:

$$F=\mu N$$

To facilitate the determination of the tested friction coefficient, a pair of composite isolation bearings with two friction surfaces was used. The assembly of the isolation bearing is shown in Figure 4. Therefore, the friction coefficient of the composite isolation bearing is given by the test results obtained from this setup.

$$\mu =F_1/2N_1$$

(1)

where $\mu$ is the friction coefficient of the composite seismic isolation bearing.

The upper connecting plate has a diameter of 250 mm and a thickness of 20 mm. Its lower surface is reserved by five bolt holes of diameter 20 mm and depth 7.5 mm. The middle column has a diameter of 54 mm and a total height of 92 mm, with a bolt column on the upper surface of 20 mm diameter and 7 mm depth, and two cylindrical grooves of diameter 45 mm and depth 32 mm, and diameter 32 mm and depth 43 mm on the lower surface. The lower connecting plate has a diameter of 250 mm and a thickness of 10 mm, with five cylindrical grooves of diameter 54 mm and depth 5 mm on its upper surface, and five cylindrical grooves of diameter 45 mm and depth 5 mm on its lower surface. The two cylindrical axes of the upper and lower grooves are aligned. Bearings will be equipped with different numbers of balls and shims according to the designed working conditions. To ensure the stability of the bearing, the number of balls is set to 1, 4, and 5. The materials of the parts of the bearings are different; the upper and lower connecting plates and intermediate columns are made of 45# steel; the shims, springs, and friction plates are made of 65 mn spring steel; the universal ball is made of turned heavy duty universal ball SP-25; the internal ball material is bearing steel; and the friction material is selected as PTFE.

2.3. Test Loading Procedure

A total of 75 operating conditions were established in this project, mainly focused on four parameters: vertical pressure, horizontal velocity, number of shims, and number of rolling balls. In the loading process, the vertical pressure is applied slowly at a loading rate of 0.04 MPa/s, and the application is stopped when the predetermined loading condition is reached. Then, the horizontal servo actuator drives the middle steel plate to provide horizontal force to the support friction plate with an action speed of 2 mm/s, 5 mm/s, and 10 mm/s, respectively, and ensures the horizontal uniform motion. The effect of different factors on the friction coefficient is calculated by the friction formula.

2.4. Test Results

2.4.1. Friction Performance Test under the Action of No Ball

When no ball is placed, the friction characteristics of the bearing under different pressures and speeds are investigated by a standard compression shear test, which is conducted under the action of vertical pressures of 39, 59, 102, and 204 KN and speeds of 2 mm/s, 5 mm/s, and 10 mm/s, respectively.

Figure 5 shows the relationship between the sliding speed and the sliding friction coefficient under different pressures. At a certain vertical pressure, the friction coefficient tends to decrease and then increase as the speed increases. It can be seen that the minimum sliding friction range is 0.04548–0.0516.

Figure 6 shows the relationship between the vertical pressure and the sliding friction coefficient at different velocities. The results show that at a certain speed, the friction coefficient shows a decreasing trend with an increase in vertical pressure. Obviously, the optimal friction parameters are 0.04548–0.04629, and the minimum friction coefficient is 0.04548.

2.4.2. Friction Performance Test under the Action of Balls

The ball in the system, combined with the spring and shim, plays a role. The main role played by the spring and shim is to adjust the force of the ball so that the total upper load is proportionally distributed to the ball group and PTFE.

This part of the study focuses on the effect of the bearing ratio on the dynamic friction coefficient. The effect of the number of shims and balls on the dynamic friction coefficient is shown in Figure 7 and Figure 8. The relationship between the number of shims and friction coefficient for four-roller ball and five-roller ball isolation bearings with horizontal velocities of 2 mm/s, 4 mm/s, and 10 mm/s, respectively, under different vertical pressures.

In Figure 7a, when the horizontal speed is 2 mm/s, the friction coefficients under the action of three bearing ratios show different changes with an increase in the number of shims. When the ball group occupies 25%, the friction coefficient increases first and then decreases, and the minimum is 0.5516; when the ball group occupies 50%, the friction coefficient increases continuously, and the minimum is 0.05805; when the ball group occupies 100%, the friction coefficient decreases gradually, and the minimum is 0.06757.

In Figure 7b,c, when the horizontal velocity is 5 mm/s and 10 mm/s, the friction coefficient has a tendency to increase and then decrease with the increase in the number of shims, and the minimum friction range occurs when the number of shims is 2 and the pressure-bearing ratio is between 25% and 50%, which are 0.05514–0.05614 and 0.05759–0.05804, respectively.

In Figure 8, at a certain horizontal velocity, the friction coefficients under the action of different bearing ratios showed a trend of decreasing and then increasing, and the minimum ranges, respectively, were 0.03458–0.03947, 0.03047–0.03869, and 0.02883–0.04169. Most of them were found when the number of shims was 4 and the pressure-bearing ratio was between 25 and 50%.

In Figure 7 and Figure 8, comparing the data of a four-roller ball and a five-roller ball, it can be found that the coefficient of friction decreases with the increase in the number of balls, and there is a difference in the influence of the parameters of the minimum coefficient of friction; the four-roller ball mostly appears when the number of shims is 2, the five-roller ball mostly appears when the number of shims is 4, and the pressure-bearing ratio is 25–50%.

3. Numerical Analysis of a Based Isolated System and Conventional Structure

To evaluate the effectiveness of the isolation system, we used the finite element software SAP2000 to perform numerical simulations on a four-story reinforced concrete frame structure. Through finite element analysis, we compared the performance of the isolation system with isolated supports at the bottom and traditional seismic-resistant structures in terms of base shear, inter-story displacement, and floor acceleration, and evaluated the isolation effect based on these comparisons.

3.1. Structure Model

As shown in Figure 9, the superstructure of the isolation bearing is a reinforced concrete structure. According to the engineering design requirements, the constant load of the structure, which includes the self-weight of the structure and the uniform load of the floor slab, is 3 kN/m², the live load is 2 kN/m², the total height of the building is 14.4 m, the floor height is 3.6 m, and the floor size is 12 m × 30 m. The length and width of the column section are 600 mm, the beam section length and width are 600 mm and 300 mm, respectively, and the thickness of the slab is 120 mm. The structural plan is shown in Figure 9, with longitudinal reinforcement of HRB335 and hoop reinforcement of HPB300 to meet the minimum reinforcement rate of the structure. The seismic isolation bearings are placed on the lower surface of each column and connected to the foundation. In SAP2000, beams and columns are modeled using frame elements. Non-bottom nodes are constrained using diaphragms, while the bottom nodes of non-seismic structures are all fixed support nodes. The bottom nodes of composite isolation systems use the Friction Isolator element in the Connection/Support Property with an infinite radius setting. Figure 10 shows a three-dimensional simulation model for a non-seismic structure.

3.2. Test Setup

Three seismic records were selected from the Pacific seismic station network: El Centro, Kobe, with two strong seismic records, and Shanghai artificial waves, which were used as the input excitation signals. The peak ground accelerations of 200 gal and 400 gal were selected to correspond to the seismic intensities specified in the China Code at the 8-degree preparedness level (the seismic intensity level considered in the design process). These acceleration response spectra are shown in Figure 11.

3.3. Model Results Analysis

3.3.1. Basement Shear

Based on the friction coefficient of 0.05 obtained from previous tests, Figure 12 shows the base shear curves of the composite isolation structure and the seismic-resistant structure under the same working conditions. It can be seen from the figure that the base shear of the structure varies under different earthquake waves and increases with an increase in seismic intensity.

Compared with traditional seismic-resistant structures, the composite isolation structure exhibits good isolation effects. Regardless of the input ground motion, the base isolation model can significantly reduce the structure’s shear force.

3.3.2. Floor Acceleration

Through sliding friction tests without rolling balls as well as compound friction tests with four and five rolling balls, friction coefficients of 0.04 and 0.05 were obtained. Based on

Table 1. Inter-story displacement of based isolated structures and conventional structures.

Friction Coefficient	X Acceleration/gal	Floor	El Centro Wave		Kobe Wave		Shanghai Wave
			Convention m/s2	Based Isolated m/s2	Convention m/s2	Based Isolated m/s2	Convention m/s2	Based Isolated m/s2
0.04	200	1	2.12	0.99	2.81	1.02	3.41	1.79
		2	2.62	0.82	2.89	0.93	3.82	1.51
		3	3.25	0.76	3.51	0.98	4.23	1.28
		4	3.48	0.84	4.22	0.84	4.96	1.37
	400	1	7.63	1.81	6.39	1.92	7.03	2.68
		2	8.41	1.42	7.84	1.86	8.42	2.16
		3	9.29	1.21	9.01	1.58	9.11	2.08
		4	10.54	1.34	11.46	1.49	10.96	2.43
0.05	200	1	2.43	1.12	3.11	1.37	3.88	1.97
		2	3.06	1.04	3.95	1.22	4.21	1.69
		3	3.94	0.86	4.26	1.02	4.86	1.55
		4	4.71	0.95	5.02	1.21	5.32	1.72
	400	1	9.11	2.83	9.82	3.84	7.23	3.25
		2	10.93	2.42	9.46	3.19	9.46	3.12
		3	11.16	2.15	11.59	2.93	12.77	2.97
		4	14.83	2.36	15.23	3.54	16.84	2.51

and Figure 13, acceleration response spectra for the isolation structure and seismic-resistant structure with friction coefficients of 0.04 and 0.05 under three types of earthquake waves in the X direction were obtained. The friction coefficient of the isolation layer under different earthquake waves and intensities can affect the acceleration response of each floor. However, compared to the seismic-resistant structure, the isolation structure can achieve good isolation effects under various working conditions. Overall, the Shanghai artificial wave has the greatest impact on the acceleration response of the structure, followed by the Kobe wave and the El Centro wave.

In addition, under the same working conditions, there is generally a positive correlation between the friction coefficient and the acceleration response of the structure. As the friction coefficient increases, the acceleration of the structure also increases correspondingly, but the increase in amplitude is not very significant. This indicates that increasing the friction coefficient of the isolation layer will have a certain impact on the seismic response of the overall structure, but the degree of influence is relatively small.

3.3.3. Inter-Story Displacement

Through sliding friction tests without rolling balls as well as compound friction tests with four and five rolling balls, friction coefficients of 0.04 and 0.05 were obtained. Using three types of earthquake waves to analyze the interlayer shear force in the X direction, interlayer displacement data for the isolation structure were obtained, as shown in

Table 2. Comparison of displacement of seismically isolated structures under different seismic waves.

Friction Coefficient	X Acceleration/gal	Floor	Inter-Story/mm
			El Centro	Kobe	Shanghai Wave
0.04	200	isolated	27.4	34.1	56.4
		1	15.1	18.4	33.9
		2	12.4	15.3	26.9
		3	10.4	13.2	21.5
		4	9.1	11	16.8
	400	isolated	98.1	118.1	153.7
		1	50.2	55.6	63.8
		2	32.8	42	49.6
		3	25.4	31.8	39.2
		4	16.2	18.3	21.8
0.05	200	isolated	25.3	31.4	57.2
		1	16.1	20.2	35.4
		2	11.8	15.9	28.6
		3	10.4	14.1	23.7
		4	9.3	12.8	17.2
	400	isolated	90.2	109.4	149.5
		1	45.6	57.9	68.6
		2	36.2	42.3	48.4
		3	27.5	34.5	36.2
		4	18.4	20.6	21.8

. It can be seen that the El Centro wave, Kobe wave, and Shanghai artificial wave have different degrees of influence on the interlayer displacement of the structure. Among them, the Shanghai artificial wave has the greatest influence on the interlayer displacement of the structure, followed by the Kobe wave, while the El Centro wave has a relatively small influence. In addition, at an earthquake intensity of 200 gal, as the friction coefficient increases, the interlayer displacement of the first, second, third, and fourth layers of the structure will increase, but the interlayer displacement of the isolation layer will decrease. When the earthquake intensity is 400 gal, the interlayer displacement of the first, second, and third layers of the structure will also increase with the increase in the friction coefficient, but the interlayer displacement of the isolation layer will decrease with the increase in the friction coefficient. Generally speaking, the greater the earthquake intensity, the larger the corresponding structure’s interlayer displacement. In addition, as the number of floors increases, the interlayer displacement gradually decreases.

4. Conclusions

This article introduces a new type of isolation system that takes into account the potential impact of parameters, such as the number of spheres, on the friction coefficient. Based on this, numerical simulations were conducted for both the base isolation structure and traditional seismic-resistant structures under earthquake excitation to determine their dynamic characteristics.

Firstly, in the experimental test data, we found that the number of spheres and pads has a certain influence on the friction coefficient. Without spheres, the minimum friction coefficient occurs when the horizontal velocity is 5 mm/s and the vertical pressure is 204 KN. With the involvement of spheres, there is little difference in the friction coefficient range between five and four spheres. In addition, the minimum friction coefficient appears in the bearing ratio of 25–50%, indicating that the number of spheres and pads can reduce the friction coefficient within a certain range. These results indicate that the number of spheres and pads is an important factor affecting the friction coefficient of the isolation system.

Secondly, after conducting numerical simulations for the base isolation structure and traditional seismic-resistant structures under earthquake excitation, we found that the new composite isolation system can effectively reduce the dynamic response of the model compared to traditional seismic-resistant structures. This indicates that the new isolation system has good seismic performance.

Finally, it should be pointed out that this experiment mainly studied the influence of parameters such as the number of balls on the friction coefficient of the isolation support. However, in order to better apply the new isolation support in practical engineering, we still need to further study the shear performance of the isolation support using ABAQUS finite element software and explore its applicability under different parameter conditions. These research results will help provide a theoretical basis for the practical application of the new isolation support.