Influence Analysis of the Antifriction Layer Materials and Thickness on the Contact Interaction of Spherical Bearings Elements

Abstract

Bearings are the supporting elements of bridges. They perceive vertical and horizontal loads from the bridge span. Spherical bearings are one of the construction common types. The material and configuration of the anti-friction layers determine the bearing performance. The paper performed the contact deformation analysis of spherical bearing elements at a nominal vertical load of 1000 kN. The six types of the spherical sliding layer material are considered: ultra-high molecular weight polyethylene (UHMWPE) from three different manufacturers, modified polytetrafluoroethylene (PTFE), and composite materials by PTFE with two different forms of reinforcing bronze inclusions. Young’s modulus, Poisson’s ratio, and strain curve are obtained experimentally for spherical sliding layer materials. Paper considered the influence of the sliding layer material on the contact parameters and deformation characteristics of the structure with a standard interlayer thickness by 4 mm. Research observed significant the composite interlayer deformation and the appearance of “no contact” zones on the mating surfaces. The option of increasing the sliding layer thickness up to 6–8 mm is considered. A decrease is observed in the maximum level of contact parameters by increase of the sliding layer thickness. The influence of the anti-friction layer materials becomes insignificant on the bearing deformation with an increase of the spherical sliding layer thickness.

1. Introduction

1.1. Research Objectives

The research purpose: influence analysis of the antifriction layer thickness and material on the sliding surfaces contact parameters of the bridge span bearing and the structure deformation.

The research objectives:

• Mathematical description of behavior models of the sliding layer materials.
• Comparative analysis of the bridges bearing deformation with interlayers from different materials at a standard sliding layer thickness.
• Influence analysis of the sliding layer thickness on the structure operation.

1.2. Problem Context

Bridge structures are heavy-duty assemblies of transport and logistics systems around the world. They and their elements are subject to increased requirements regarding strength, reliability, stability, durability, safety, etc. Papers [1,2] noted the load-carrying bridgeworks elements include the bearings of bridge spans [3,4,5], which are used to absorb thermal expansion and compression, creep and shrinkage, seismic disturbances [6], and others. Bridge bearings bear also vertical, horizontal, and dynamic loads from bridge spans [7,8]. These structures are designed for long-term maintenance-free operation periods [1,9]; therefore, their technical condition has a significant impact on the bridgework operation. It can lead to adverse consequences: the partial or complete destruction of the bridge spans, supports or the work as a whole. In the 1960–1980s in the field of bridge construction, there were a significant number of scientific and engineering studies related to the bearings of bridge spans [10,11]. In 1974, the book by Eggert H. et al. [12] "Lager im Bauwesen" noted that the creation of new bearing types using modern materials is associated with progress in building and bridge construction. At the same time, the problems related to it cannot be covered only by construction regulations. In the book, for the first time, an attempt was created to formulate recommendations on the selection of optimal bearing types to exclude damage to heavy-duty elements of structures and works in general.

Now it is possible to note the constant growth of the fleet worldwide, which has a certain influence on the development direction of transport and logistics systems and is associated with a significant increase in the load on the load-carrying elements of bridge structures [13,14]. Additionally, the development direction of Russia and many countries in entire world is the creation of effectively functioning transport and logistics systems that will connect remote regions and settlements. The directions of transport systems development, increase in capacity and load on bridgeworks, scientific and technical progress, including the creation of new materials and composites [15,16], suitable for work in bridgework units and having improved physical–mechanical, friction, thermo-mechanical, and rheological properties led to an increase in scientific and engineering developments in the field of bridge construction. Papers noted that over the last decade, there has been a gradual growth of technical and scientific developments aimed at the modification and optimization of bridge bearings [17,18] with a significant increase in growth rates over the last 5 years. In the bridge construction field, the modern developments are aimed at improving the performance of bridge support structures and pursue certain goals:

• to increase reliability and durability of bearings by means of changing the structural design of its elements;
• to increase the load-bearing capacity of the spherical anti-friction polymeric sliding layer at different levels and the combination of vertical and horizontal forces from the bridge span;
• to increase the bearings workability;
• to increase the wear resistance of spherical polymeric sliding layer from modern polymeric anti-friction materials and composites based on them;
• to reduce the harmful impact on the environment in the bearings manufacture;
• to increase efficiency by reducing time and labor intensity of works related to installation and preventive maintenance, etc.

A lot of engineering developments are connected with the method change of treatment of contact surfaces of bridge bearings, with the geometry and position change of anti-friction sliding layers, as well as with the design of structural elements for lubricants in the contact interaction area. Several works are aimed at increasing the anticorrosive treatment of the bearings metal parts, as well as improving the interfacing of its elements by changing the producing process spherical balance beams. There were not compared the influence of the proposed scientific and engineering solutions on the stress–strain state of the structure as a whole and the parameters of the contact zone with anti-friction sliding layers in particular. This fact hinders the efficiency of using the proposed know-how in the calculation and design of transport and logistics systems.

1.3. Problem Description

AlfaTech LLC (Perm, Russia) is a manufacturer of spherical bridge bearings (Figure 1) set a number of material and design research challenges back in 2011.

• Search and experimental studies of materials from which can be made antifriction sliding layers of a structure [18,19].
• Construction of parameterized spherical bearing models of bridges taking into account the different curvature radius of the spherical segment [18,20].
• Selection of effective settings for the contact problems numerical solution and influence evaluation of the system discretization degree on the problem solution [18,20].
• Preliminary assessment of the influence of different levels and combinations of vertical and horizontal loads [18]. Determination of the bending moments necessary for the experimental equipment calculation about the structural deformation analysis.

More than 30 polymeric and composite materials have been studied to date as sliding layers of bearing as an alternative to PTFE [19]. A number of the most promising ones have been selected and studied their frictional properties [21,22]. The mathematical description of the materials behavioral models is carried out in the first approximation within the framework of the deformation theory of plasticity [18,19].

Papers [18,20,21,22,23] presented axisymmetric and three-dimensional models’ bridges’ spherical bearing of different geometric configurations. An experimental facility has been created and put into operation for studying the deformation behavior of bridges’ spherical bearing [18].

The research direction has changed now. It is aimed at rationalizing the elements geometric configuration of the spherical bearing [21,22,23]: the sliding layers location, the antifriction layer geometry, the lubrication holes configuration, the sliding layer thickness, etc. This paper presents the influence analysis of the spherical sliding layer thickness on the structure operation.

2. Materials and Methods

2.1. Model

The research implemented two actual bridge construction problems related to the rationalization of spherical bearings elements: the influence of sliding layer materials and anti-friction layer thickness on the structure deformation behavior. The authors have performed the deformation behavior analysis of the spherical bearing elements (Figure 2) as part of the implementation of friction contact interaction of the upper plate with a spherical segment (1) and the lower plate with a spherical notch (2) of the bearing through an elastic–plastic polymeric layer (3) at a nominal vertical load of 1000 kN. The paper reviewed the spherical bearing model L-100 was produced by AlfaTech LLC (Perm, Russia).

The paper analyzes the influence of the geometrical configuration of the structural elements of the spherical bearing: the sliding polymeric layer thickness $h_p$ varies from 4 to 8 mm, the minimum height of the bottom slab has a spherical notch of $h_2=20÷16$ mm depending on the layer thickness, and the minimum bottom slab height decreases by an increment in the sliding layer thickness. The maximum top slab height and the maximum width of structure are equal to $h_1=30$ mm and $b_k=2b=155$ mm, respectively, and to the maximum top slab height.

The interlayer (3) is pressed into the recess of the lower steel plate (2). The interlayer materials are considered homogeneous. The mechanism of averaging the physical and mechanical properties of the matrix and filler is used in the composite materials modeling. The thickness relative to the free edge of the sliding layer is constant and equal to 2 mm.

The calculation scheme was implemented in the ANSYS Mechanical APDL software package (ANSYS Inc., Canonsburg, DC, USA) by the finite element method (FEM) with the use of quadrilateral axially symmetric finite elements with Lagrange approximation and two degrees of freedom in each node. Previously, the scientific team analyzed the dependence of the numerical solution of the problem on the system sampling degree. They determined the optimal elements size in terms of polymer layer thickness was determined: element size is 0.25 mm. The upper and lower slab is broken up into a finite element mesh with the size of the element two times larger than the layer element is 0.5 mm on the main volume of material. At the interface of spherical bearing elements, a contact elements pair is implemented, which allows us to employ the friction contact interaction of surface-to-surface type.

A surface-to-surface contact is implemented on the mating surfaces of the antifriction layer with steel structural elements $S_{K_1}$–$S_{K_3}$ Friction contact is implemented using a flat elements contact pair. “Close gap” is the initial settings of contact elements. An augmented Lagrangian method is the contact computation method.

2.2. Mathematical Setting, Boundary Conditions, and Methods

The general mathematical setting has been described earlier and defines the contact interaction problem of two elastic bodies through an anti-friction polymer layer, taking into account all types of friction contact [18], and during the implementation of the problem is supplemented with respect to the possibility of large deformations in the anti-friction layer volume. The problem is considered in the axisymmetric setting; the deformation theory of elastoplasticity has been chosen to describe the model of the behavior of the anti-friction layer material. The paper assumes that the contact surfaces slippage begins at the tangential stresses values much lower than the shear plasticity limit, which is associated with a relatively low friction coefficient of anti-friction materials. This assumption was confirmed earlier by direct verification of contact tangential stress values obtained from the solution for each specific case [19].

The research has implemented the task with the help of (using) the mathematical modeling method using the ANSYS Mechanical APDL application software package, which consists in the development of mathematical models and their numerical implementation algorithms based on the finite element method. The main procedures for building finite analogs are based on the Galerkin method with the selection of basic functions with compact media using the finite element method.

The general mathematical setting of the problem [18] is supplemented by kinematic boundary conditions on the surface $S_2$:

$$u_z=0, {\sigma }_{rz}=0, r\in S_2.$$

(1)

The surface $S_1$ interacts through a steel slab with a very rigid bridge span structure, which practically eliminates surface bend in space, while the integral on the surface from $P$ pressure is equal to the vertical load applied. Thus, the boundary conditions on the surface $S_1$ are as follows:

$${\displaystyle \underset{S_1}{\int }P\hspace{0.17em}d{S}_1}=-Q_z, u_z\left(r,z_{S_1}\right)=U=const, {\sigma }_{rz}=0, r\in S_1,$$

(2)

where $Q_z$ is vertical force applied to $S_1$, and $U$ is unknown value. The rest of the outer surfaces are free from loads.

2.3. Materials

The AlfaTech LLC (Perm, Russia) team and Dr. A.A. Adamov, based on the Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences (ICMM UB RAS, Perm, Russia), have studied physical–mechanical, frictional, and rheological properties of a wide range of polymer materials and composites based on them [20]. They have investigated more than 30 antifriction materials that can be used in one way or another as bearings sliding layers. The paper obtained a set of physical and mechanical characteristics of materials and several of their deformation behavior as a result of a field experiments series. The team determined the constrained compression modulus $M$ and the free compression modulus $E$ according to the experiments results. According to Adamov et al. [21], it is possible to calculate other elastic constants of the isotropic elastic body, which are expressed through the measured modules. The Poisson’s coefficient is defined by the Equation:

$$\mathsf{\nu }=E/2\mathsf{\mu }-1,$$

(3)

where $\mathsf{\mu }=E/8\left(1+3M/E-\sqrt{{\left(1+3M/E\right)}^2-16M/E}\right)$.

In the data analysis from a field experiments series, modern anti-friction polymeric materials and composites based on them were found to exhibit nonlinear properties. In the first approximation, the deformation theory of elasticity under active loading has been chosen to describe the behavior model of anti-friction materials. Six polymers and composites based on them were selected from a wide range of tested materials to analyze the effect of physical and mechanical characteristics of materials on the thin spherical sliding layer (Figure 3).

The following materials were considered as anti-friction layer materials: carbon-filled high-modulus polyethylene (UHMWPE) (Material 1); UHMWPE produced in Russia (Material 2); UHMWPE produced in Germany (Material 3); anti-friction composite material based on fluoroplastic with dendritic and spherical bronze inclusions and molybdenum disulfide (Materials 4 and 5, respectively); modified PTFE (Material 6). The antifriction layers materials have a friction coefficient of no more than 0.04 according to the AlfaTech LLC technological documentation. Friction properties data of sliding layer materials was not at the study time. The friction coefficient is set to 0.04 for all layer materials according to information provided by AlfaTech LLC.

Young’s modulus and Poisson’s ratio are obtained experimentally for spherical sliding layer materials. Compression diagrams $\sigma -\mathsf{\epsilon }$ obtained experimentally at low deformation rates or determined by building curves envelope when processing diagrams of cyclic free compression [19]. Studies were carried out on the basis of ICMM UB RAS.

3. Results

The parameters of principal interest are the contact parameters on the surface $S_{K_1}$ where the bearing spherical segment can be rotated and on the relatively free end of the surface $S_{K_3}$.

The standard anti-friction layer thickness is 4 mm. The paper considers the contact parameters distribution at the standard thickness of the anti-friction layer on $S_{K_1}$ (Figure 4).

The nature of contact parameters distribution is the same for all anti-friction polymer layers. The contact pressure level is maximum and has small differences in the full adhesion area of contact surfaces, which can be clearly seen with a sufficiently large contact area. Materials 1, 2, and 6 have minimum values of maximum contact pressure about 90 MPa; the full adhesion area of contact surfaces in these materials is maximum and reaches 50–56% of the total contact area. The maximum contact pressure is on average 1.4 times higher in layers from Materials 4–5 than in layers from other materials considered. The contact tangential stress increases from the bearing center to the zone of contact state change from "full adhesion" to "sliding", with a further level decrease in the slippage zone to the layer edge. In the most unfavorable case, there is a detachment of contact surfaces near the layer edge. The paper can note the opening of the contact near the edge in the bearings with the anti-friction layer from Materials 4–5. Contact surfaces detachment is observed on 4–5% of all contact area.

Table 1. Comparison of the maximum level of contact pressure and tangential stress.

Parameter	Material
	1	2	3	4	5	6
$\max P_K$, MPa	90.803	92.216	110.400	148.460	135.570	96.268
$\max {\tau }_K$, MPa	3.421	3.475	4.085	5.396	4.852	3.621
$\max P_K>\max {\tau }_K$	26.540	26.539	27.024	27.514	27.944	26.587

presented comparison of the contact parameters maximum level on the surface $S_{K_1}$.

The contact pressure maximum level is much higher than that of the contact tangential stress (Figure 1, Table 1). $\max P_K$ of Materials 1, 2, and 6 is approximately 26.5 times greater than $\max {\tau }_K$. For composite materials, $\max P_K>\max {\tau }_K$ by 27.5–27.9 times.

Figure 5 shows the nature of contact pressure distribution, as well as displacement along the normal relative free end of the anti-friction layer for spherical bearings with a 4 mm anti-friction layer from all materials considered.

On the contact-free surface structure, the research observed zero contact characteristics, and their peaks occur in the stress concentration zone near the lower slab shoulder with a spherical notch. Layers from Materials 4–5 have the highest contact pressure levels on $S_{K_3}$ with a sharp decrease in its value on the main contact surface which is associated with the plastic properties manifestation of materials. The layers from Materials 4–5 have undergone the greatest deformation at the same load level as well as the maximum layer edge displacement is almost four times greater than layers from other materials considered. Material 1 has maximum normal displacements, and the layers from Materials 2, 3, and 6 have values approximately at one level (about 0.5–0.6 mm).

A qualitative picture of the contact parameters distribution and normal face displacement with increasing anti-friction layer thickness has little difference from the standard layer thickness. The paper reviews the effect of polymeric anti-friction layer thickness on contact node deformation. Parameters of contact pressure, contact tangential stress, and normal displacements of the anti-friction layer end were calculated to the following Equations:

$$\Delta P_K=\left(\max P_K-{\left.\max P_K\right|}_{h_p=\hspace{0.33em}4mm}\right)/{\left.\max P_K\right|}_{h_p=\hspace{0.33em}4mm}\cdot 100\%,$$

(4)

$$\Delta {\tau }_K=\left(\max {\tau }_K-{\left.\max {\tau }_K\right|}_{h_p=\hspace{0.33em}4mm}\right)/{\left.\max {\tau }_K\right|}_{h_p=\hspace{0.33em}4mm}\cdot 100\%,$$

(5)

$$\Delta u_n=\left(\max u_n-{\left.\max u_n\right|}_{h_p=\hspace{0.33em}4mm}\right)/{\left.\max u_n\right|}_{h_p=\hspace{0.33em}4mm}\cdot 100\%,$$

(6)

where $P_K$ is maximum contact pressure on $S_{K_1}$, ${\tau }_K$ is contact tangential stress on $S_{K_1}$ and $u_n$ is normal displacements on $S_{K_3}$ at thickness $h_p$ equal to 4, 6, and 8 mm. The data obtained at a layer thickness of 4 mm were taken as a reference value.

The paper revealed in percentage terms the change of contact pressure $\Delta P_K$ and contact tangential stress $\Delta {\tau }_K$ on $S_{K_1}$ depending on the thickness of the anti-friction layer in Figure 6. $\Delta P_K$ and $\Delta {\tau }_K$ are calculated by Equations (4) and (5), respectively.

When the anti-friction layer thickness increases, the maximum level of the contact zone parameters decreases on the main surfaces of the spherical bearing elements interface. The biggest decrease of the maximum contact pressure level is observed in the bridge bearings with an anti-friction layer from composite Materials 4–5 and reaches 36–46 MPa at the anti-friction layer thickness 8 mm. The maximum contact pressure level of anti-friction composite layers is approximately 9–10 MPa higher than that of other materials. The maximum level of contact tangential stress decreases with increasing thickness of the anti-friction layer, similar to the contact pressure. The paper observes the maximum level of contact tangential stress is 1.5 MPa on average with increasing thickness of the anti-friction layer for anti-friction layers from Composite Materials 4–5 and at 8 mm thickness. The maximum level of contact tangential stress differs insignificantly within 0.35 MPa at 8 mm layer thickness for all materials considered. With the layer thickness increase, there is no contact opening near the edge of the anti-friction layer with all variants of anti-friction materials. With a 8 mm layer thickness for the most materials considered, the full adhesion area is 40–45% of contact surfaces. The full adhesion area of contact surfaces increased by 20–23% in layers from composite materials.

Figure 7 shows the maximum level change of normal displacement relative to the free end of the anti-friction layer with increasing its thickness. $\Delta u_n$ is calculated by Equation (6).

The maximum level of normal displacement increases when the thickness of the anti-friction layer increases relative to the thin anti-friction layer in most materials. With an increase in the normal displacement of the anti-friction layer end from the Materials 1, 2, 3, and 6, the maximum normal displacement level remains well below 1 mm. The maximum level of normal displacement decreases on average by 11% at 8 mm thickness in layers from Materials 4–5 while the level of normal displacement relative to the free ends remains the maximum for the layer from these materials of the entire polymers set. Since the material is deformed under the influence of pressure on the spherical support, a cut of the polymer anti-friction layer may occur at large displacement, which may affect its performance. Materials 4–5 have the most unfavorable deformation behavior, which is associated with a significant deformation of the geometric configuration relative to the free contact surface and the manifestation of a large level of plastic deformation near the layer edge.

The paper performed verification of numerical simulation results with that of the experiment on the deformation of the bearing with a layer from modified PTFE. The numerical model settlement was found to be 13.67% lower than that of the real structure.

4. Discussion

4.1. Limitation Statement

The work has a limitations number:

• constant friction coefficient. It is same for all materials;
• the spherical bearing model is simplified. A number of structural elements are not taken into account: a flat sliding layer, recesses for lubrication, etc;
• solving the problem in an axisymmetric formulation;
• no account is taken of the viscosity of the sliding layer materials.

Future research direction:

• clarification of the physical–mechanical, rheological, and frictional properties of the sliding layer materials;
• model refinement and structure modeling in a three-dimensional setting ([18] carried out approximate studies in 3D);
• the load specification and accounting for the thermal cycle;
• influence analysis of the technological holes for lubrication on the structure operation (taking into account different models of lubricant behavior).

4.2. About the Materials and Methods

Static modeling is widely used to investigate the mechanical respond of bridge elements as noted by Zhao et al. [24]. The performance assessment of modern bridge bearing cannot be carryied out only using building codes and standards [25]. This fact leads to the need to use mechanical analysis effective methods. FEM is an effective tool. It has found wide application in practice in the study of the response of bridge supports to external loads [26,27,28,29]. Liu et al. [27] note that the FEM allows one to obtain the pattern of the contact stresses distribution on the sliding surface. This makes it possible to predict the friction resistance and is an important structure performance indicator. The contact parameters analysis is the main work result.

PTFE or Teflon is one of the most common materials used as a sliding layer [25,30,31]. The limited use pure form material is noted in [32]. The material is widely used in many industries, technology, and medicine. However, over time, it turned out that its modification with various fillers or radio emission makes it possible to obtain materials with improved properties. The authors came to the same conclusions when comparing the samples and interlayers deformation from pure PTFE and composite and modified materials based on it [20]. The new materials use with improved properties is one of the bearings modernization directions [15,16]. The paper carried a comparative effect analysis of the properties from six materials’ sliding layer on the structure deformation. In 2013, the authors found that a sliding layer from modified PTFE has better deformation characteristics [20]. The results of this work confirm that modified PTFE is one of the most promising materials for sliding layers in bridge bearings.

4.3. Modification of the Structure of Bridge Bearing

According to Heggade [31] and Niemierko [25], the history of bridge building shows the continuous modification of the structural elements’ configuration of the bridges’ bearings. An increase in the load on transport systems [13,33,34] and changes in standards and requirements [25,35] led to the need to geometry bearings’ change. The elements thickness is one of the factors influencing the structure operation [26,30]. The influence of changes in the configuration elements of elastomer bearing on the construction deformation was investigated in [26]. A twofold increase in the thickness of one structural element made it possible to reduce the stress level by more than 1.8 times. Increasing the sliding layer thickness is proposed as one of the options for modifying the bearings configuration. The effect of increasing the antifriction layer thickness is considered in the work. The layer thickness magnification is possible to reduce of the contact parameters level on the sliding surface by a maximum of 31% and to increase the area adhesion of the contact surfaces. The materials properties begin to slightly affect the contact zones parameters with an increase in the sliding layer thickness. The negative effect of increasing of the sliding layer thickness was found. Displacements along the normal relative to the free surface of the sliding layer butt increase. The slice of sliding layer by structure deformation can occur because of this. This can have a negative effect on the structure performance as a whole. An increase in the sliding layer thickness in a real structure is impossible without an experimental studies series.

4.4. About Influence Vertical Load

The paper considered the deformation behavior analysis of the spherical bearing elements at a nominal vertical load of 1000 kN. The vertical load influence on the bearing operation was studied earlier [36] with a sliding layer thickness of 4 mm. The paper studied a structure with a layer from modified PTFE (Material 6).

The vertical load influence on the maximum levels of contact parameters on $S_{K_1}$ and normal displacement on $S_{K_3}$ are shown as an example in Figure 8.

A significant increase in the contact parameters on all mating surfaces and normal displacement on the antifriction layer edge is observed at the load value of more than 1000 kN. The contact surfaces detachment is observed near the antifriction layer edge on $S_{K_1}$ by about 0.37% of the contact area at the load higher than the nominal.

In the future, it is planned to research a spherical bearing part, taking into account the vertical and horizontal loads of different ratings and combinations from the bridge span in 3D setting.

5. Conclusions

During the study, the paper simulated the parameterized model of the spherical bearing of the bridge spans. The research investigated anti-friction layer materials and thickness influence on contact deformation behavior of the considered node. The paper established important quantitative and qualitative regularities within the study framework.

Analysis of the study results established the following conclusions:

• The properties of a modern antifriction materials number were obtained experimentally and described in the ANSYS Mechanical APDL application package.
• The effect of material properties on the bridges spherical bearing contact parameters has been explored. The studies were performed with a standard interlayer thickness of 4 mm and with an increase in thickness to 6–8 mm.

The highest values of contact parameters are observed for interlayers from Materials 4 and 5. Additionally, for interlayers of these materials, the largest normal displacements are observed, which leads to the appearance zones "no contact" on the mating surfaces. This effect tells us that the interlayer from Materials 4 and 5 is subjected to more deformations than interlayers from other materials for all considered thicknesses.

The maximum values of normal displacements increase with an increase in the interlayer thickness from other materials. However, the percentage zones "no contact" is reduced or absent on the mating surfaces for the entire range of anti-friction layer materials.

An increase in the interlayer thickness has a favorable effect on the bearing stress–strain state as a whole. Additional numerical studies are required for analysis influence of the interlayer thickness on the bridges bearing operation taking into account lubrication holes of the sliding layer.