# Comparative Analysis of the Work of Bridge Spherical Bearing at Different Antifriction Layer Locations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Research Objectives

#### 1.2. Problem Context

#### 1.3. Problem Description

## 2. Materials and Methods

#### 2.1. Model

#### 2.2. Materials

- −
- materials cannot be produced in the required volume;
- −
- materials have a very heterogeneous set of properties;
- −
- significantly nonlinear compressibility of materials under constrained compression has been discovered;
- −
- additional experimental studies with different histories of long-term multistage loading are required, etc.

#### 2.3. Mathematical Setting, Boundary Conditions and Methods

## 3. Results

- −
- “pressed surface” is contact surface pressed into steel plates (${S}_{{K}_{1}}$ in model A, ${S}_{{K}_{2}}$ in model B);
- −
- “turning surface” is the contact surface along which the rotation of the spherical segment is possible (${S}_{{K}_{2}}$ in model A, ${S}_{{K}_{1}}$ in model B);
- −
- “end face surface” is relatively free end face of the interlayer (${S}_{{K}_{3}}$ in model A and B);
- −
- ${S}_{adhesion}$ is area that is contact with full adhesion;
- −
- ${S}_{no\hspace{0.33em}contact}$ is area of the zone of “no contact” (divergence) of mating surfaces.

- −
- an increase in the area of full “adhesion” of mating surfaces;
- −
- lowering the maximum level of contact parameters;
- −
- absence of “no contact” zone near the end face of the model A layer.

## 4. Discussion

#### 4.1. The Compared Results to PTFE Interlayer

#### 4.2. About Materials

^{®}SLIDE [70] and MSM [71] are used as sliding layers by MAGEBA and MAURER, respectively. These materials have improved properties compared to PTFE according to the data of manufacturers. The UHMWPE improved properties compared to other polymers have been confirmed by studies [72]. Research was conducted on a limited number of characteristics. Studies also could not include the entire volume of modern polymers. In our case, pure UHMWPE showed deformation and contact characteristics having little difference from the modified PTFE according to the results of experiments and numerical studies. Alfatech LLC and our research team singled out and modified PTFE as the most promising material for antifriction layers of bearings.

## 5. Conclusions

- −
- a higher level of maximum parameters on all interfaces of steel plates of structure with an interlayer;
- −
- the “no contact” zones on the “turning surface”;
- −
- the maximum level of displacements along the normal to the “end face surface” is greater;
- −
- the plastic flow of interlayer materials from the steel plate recess, material shearing during the structure operation is possible;
- −
- the draft level of the structure is greater.

- −
- the reduction of the maximum level of contact and deformation characteristics;
- −
- the increase in the “adhesion” area of mating surfaces: the volume of the interlayer material working within the framework of the elasticity theory increases;
- −
- the absence of a “no contact” zone in interlayer from polymeric materials (mat. 1–3, 6) or a decrease in % of the “no contact” area in interlayer from composites (mat. 4–s5).

- −
- The construction with a layer placed in lower steel plate shows better performance compared to model A.
- −
- Interlayers from materials 1, 2, and 6 show a better distribution of contact parameters compared to other materials.
- −
- The constructions that have an inclination angle of the end face of 0° for model A and 25° for model B have more distributed contact parameters and lower draft values. Thus, it may be concluded that structures with these angles perform better than those with standard angles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\mathsf{\alpha}}_{p}$ | inclination angle of the antifriction layer end face; |

${h}_{p}$ | antifriction layer thickness; |

${h}_{1}$ | central section height of the upper steel plate; |

${h}_{2}$ | central section height of the lower steel plate; |

$h$ | structure height; |

$b$ | maximum length of bearing half; |

$B$ | maximum length of bearing; |

${S}_{1}$ | upper surface of the steel plate; |

${S}_{2}$ | lower surface of the steel plate; |

${Q}_{z}$ | vertical force applied to ${S}_{1}$; |

$P$ | pressure; |

${S}_{{K}_{1}}$ | upper contact surface; |

${S}_{{K}_{2}}$ | lower contact surface; |

${S}_{{K}_{3}}$ | antifriction layer end face; |

${P}_{K}$ | contact pressure; |

$\mathrm{max}{P}_{K}$ | maximum contact pressure; |

${\mathrm{max}{P}_{K}|}_{turning\hspace{0.33em}suface}$ | maximum contact pressure for the “turning surface”; |

$\mathsf{\Delta}\mathrm{max}{P}_{K}$ | relative difference of contact pressure of models A and B; |

${\mathsf{\tau}}_{K}$ | contact tangential stress; |

$\mathrm{max}|{\mathsf{\tau}}_{K}|$ | maximum modulo contact tangential stress; |

$\mathrm{max}{|{\mathsf{\tau}}_{K}|}_{turning\hspace{0.33em}suface}$ | maximum modulo contact tangential stress for the “turning surface”; |

$\mathsf{\Delta}\mathrm{max}|{\mathsf{\tau}}_{K}|$ | relative difference of maximum modulo contact tangential stress of models A and B; |

${u}_{n}$ | normal displacements on ${S}_{{K}_{3}}$; |

$\mathrm{max}{u}_{n}$ | maximum normal displacements on ${S}_{{K}_{3}}$; |

$\mathrm{max}{{u}_{n}|}_{{S}_{{K}_{3}}}$ | maximum normal displacements on ${S}_{{K}_{3}}$; |

$\mathsf{\Delta}\mathrm{max}{u}_{n}$ | relative difference of maximum normal displacements on ${S}_{{K}_{3}}$ of models A and B; |

${{u}_{z}|}_{r\in {S}_{1}}$ | structure draft; |

$\mathsf{\Delta}{{u}_{z}|}_{r\in {S}_{1}}$ | relative difference of structure draft of models A and B; |

${S}_{adhesion}$ | area that is contact with full adhesion; |

${{S}_{adhesion}|}_{turning\hspace{0.33em}suface}$ | area that is contact with full adhesion for the “turning surface”; |

${S}_{no\hspace{0.33em}contact}$ | area of the zone of “no contact” (divergence) of mating surfaces; |

${{S}_{no\hspace{0.33em}contact}|}_{turning\hspace{0.33em}suface}$ | area of the zone of “no contact” (divergence) of mating surfaces for the “turning surface”. |

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**Figure 2.**Experimental studies: (

**a**) is Brinell hardness; (

**b**) is free compression; (

**c**) is cramped compression; (

**d**) is friction studies on the MTS 316 test rig with original equipment.

**Figure 7.**Contact pressure (

**a**,

**c**) and contact tangential stress (

**b**,

**d**) on turning surface: (

**a**,

**b**) is model A; (

**c**,

**d**) is model B; solid line is ${\mathsf{\alpha}}_{p}=30$°; dash-dotted line is ${\mathsf{\alpha}}_{p}=0$°; points is ${\mathsf{\alpha}}_{p}=25$°; dotted line is ${\mathsf{\alpha}}_{p}=40$°.

**Figure 8.**Normal displacements (

**b**) on ${S}_{{K}_{3}}$: (

**a**) is model A; (

**b**) is model B; solid line is ${\mathsf{\alpha}}_{p}=30$°; dash-dotted line is ${\mathsf{\alpha}}_{p}=0$ °; points is ${\mathsf{\alpha}}_{p}=25$°; dotted line is ${\mathsf{\alpha}}_{p}=40$°.

Parameter | Material 1 (UHMWPE with Carbon Additive) | Material 2 (UHMWPE Produced in Germany) | Material 3 (UHMWPE Produced in Russia) | Material 4 (MAK Composite with Dendritic Bronze Inclusions) | Material 5 (MAK Composite with Spherical Bronze Inclusions) | Material 6 (Modified PTFE) |
---|---|---|---|---|---|---|

$E$, MPa | 1420 | 706 | 1050 | 903 | 860.52 | 863.8 |

$v$ | 0.440 | 0.470 | 0.452 | 0.447 | 0.439 | 0.461 |

**Table 2.**Comparison of the maximum level of contact pressure and tangential stress on “pressed surface”.

Parameter | Material | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Model A | ||||||

$\mathrm{max}{P}_{K}$, MPa | 95.487 | 98.264 | 121.200 | 166.030 | 160.520 | 103.500 |

$\mathrm{max}|{\mathsf{\tau}}_{K}|$, MPa | 3.629 | 3.702 | 4.451 | 6.101 | 5.871 | 3.877 |

$\mathrm{max}{P}_{K}>\mathrm{max}{\mathsf{\tau}}_{K}$ | 26.315 | 26.547 | 27.232 | 27.214 | 27.341 | 26.693 |

Model B | ||||||

$\mathrm{max}{P}_{K}$, MPa | 90.559 | 92.095 | 110.39 | 148.32 | 135.44 | 96.193 |

$\mathrm{max}|{\mathsf{\tau}}_{K}|$, MPa | 3.060 | 3.166 | 3.810 | 5.276 | 4.717 | 3.291 |

$\mathrm{max}{P}_{K}>\mathrm{max}{\mathsf{\tau}}_{K}$ | 29.599 | 29.093 | 28.971 | 28.111 | 28.716 | 29.228 |

Comparison Models A and B | ||||||

$\mathsf{\Delta}\mathrm{max}{P}_{K}$, % | 5.161 | 6.278 | 8.919 | 11.856 | 15.624 | 7.060 |

$\mathsf{\Delta}\mathrm{max}|{\mathsf{\tau}}_{K}|$, % | 15.684 | 14.481 | 14.389 | 15.785 | 19.663 | 15.121 |

**Table 3.**Comparison of the maximum level of contact pressure and tangential stress on “turning surface”.

Parameter | Material | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Model A | ||||||

$\mathrm{max}{P}_{K}$, MPa | 95.217 | 98.087 | 121.070 | 165.620 | 160.230 | 103.390 |

$\mathrm{max}|{\mathsf{\tau}}_{K}|$, MPa | 3.362 | 3.415 | 4.239 | 6.009 | 5.759 | 3.593 |

$\mathrm{max}{P}_{K}>\mathrm{max}|{\mathsf{\tau}}_{K}|$ | 28.321 | 28.724 | 28.564 | 27.561 | 27.815 | 28.773 |

Model B | ||||||

$\mathrm{max}{P}_{K}$, MPa | 90.803 | 92.216 | 110.390 | 148.460 | 135.570 | 96.268 |

$\mathrm{max}|{\mathsf{\tau}}_{K}|$, MPa | 3.421 | 3.475 | 4.085 | 5.396 | 4.852 | 3.621 |

$\mathrm{max}{P}_{K}>\mathrm{max}|{\mathsf{\tau}}_{K}|$ | 26.540 | 26.539 | 27.024 | 27.514 | 27.944 | 26.587 |

Comparison Models A and B | ||||||

$\mathsf{\Delta}\mathrm{max}{P}_{K}$, % | 4.636 | 5.986 | 8.813 | 10.361 | 15.390 | 6.888 |

$\mathsf{\Delta}\mathrm{max}|{\mathsf{\tau}}_{K}|$, % | 1.755 | 1.757 | 3.633 | 10.201 | 15.749 | 0.779 |

Parameter | Material | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Model A | ||||||

${S}_{adhesion}$, % | 37.55 | 35.27 | 13.77 | 1.18 | 1.86 | 28.87 |

${S}_{no\hspace{0.33em}contact}$, % | 1.49 | 2.97 | 2.97 | 4.73 | 4.44 | 2.23 |

Model B | ||||||

${S}_{adhesion}$, % | 31.39 | 29.31 | 14.64 | 2.78 | 5.34 | 26.28 |

${S}_{no\hspace{0.33em}contact}$, % | 0.00 | 0.00 | 0.00 | 5.17 | 4.44 | 0.00 |

Parameter | Material | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Model A | ||||||

$\mathrm{max}{u}_{n}$, mm | 0.451 | 0.802 | 0.834 | 4.423 | 4.093 | 0.700 |

Model B | ||||||

$\mathrm{max}{u}_{n}$, mm | 0.358 | 0.594 | 0.607 | 2.894 | 2.680 | 0.513 |

Comparison Models A and B | ||||||

$\mathsf{\Delta}\mathrm{max}{u}_{n}$, % | 20.621 | 25.935 | 27.218 | 34.569 | 34.522 | 26.714 |

Parameter | Material | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Model A | ||||||

${\left.{u}_{z}\right|}_{r\in {S}_{1}}$, mm | 0.120 | 0.190 | 0.147 | 0.318 | 0.312 | 0.142 |

Model B | ||||||

${\left.{u}_{z}\right|}_{r\in {S}_{1}}$, mm | 0.108 | 0.162 | 0.102 | 0.243 | 0.252 | 0.123 |

Comparison Models A and B | ||||||

$\mathsf{\Delta}{\left.{u}_{z}\right|}_{r\in {S}_{1}}$, % | 11.135 | 17.260 | 44.046 | 30.876 | 23.522 | 15.833 |

**Table 7.**Comparison of the maximum level of contact pressure and tangential stress under different ${\mathsf{\alpha}}_{p}$.

Parameter | ${\mathit{\alpha}}_{\mathit{p}},\xb0$ | Material | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

Model A | |||||||

$\mathrm{max}{P}_{K}$, MPa | 0 | 90.888 | 100.090 | 99.848 | 142.510 | 120.610 | 97.690 |

30 | 95.217 | 98.087 | 121.070 | 165.620 | 160.230 | 103.390 | |

$\mathrm{max}|{\mathsf{\tau}}_{K}|$, MPa | 0 | 3.173 | 3.493 | 3.494 | 5.080 | 4.257 | 3.393 |

30 | 3.362 | 3.415 | 4.239 | 6.009 | 5.759 | 3.593 | |

Model B | |||||||

$\mathrm{max}{P}_{K}$, MPa | 25 | 87.417 | 94.860 | 93.021 | 124.540 | 114.140 | 92.495 |

30 | 90.803 | 92.216 | 110.390 | 148.460 | 135.570 | 96.268 | |

40 | 87.878 | 94.400 | 93.434 | 126.870 | 115.650 | 92.886 | |

$\mathrm{max}|{\mathsf{\tau}}_{K}|$, MPa | 25 | 3.306 | 3.532 | 3.493 | 4.563 | 4.204 | 3.483 |

30 | 3.421 | 3.475 | 4.085 | 5.396 | 4.852 | 3.621 | |

40 | 3.322 | 3.520 | 3.514 | 4.658 | 4.286 | 3.487 |

Parameter | ${\mathit{\alpha}}_{\mathit{p}},\xb0$ | Material | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

Model A | |||||||

${S}_{adhesion}$, % | 0 | 42.81 | 28.87 | 30.10 | 4.83 | 12.94 | 33.07 |

30 | 37.55 | 35.27 | 13.77 | 1.18 | 1.86 | 28.87 | |

${S}_{no\hspace{0.33em}contact}$, % | 0 | 0.00 | 0.00 | 0.00 | 3.71 | 2.97 | 0.00 |

30 | 1.49 | 2.97 | 2.97 | 4.73 | 4.44 | 2.23 | |

Model B | |||||||

${S}_{adhesion}$, % | 25 | 38.36 | 29.80 | 27.21 | 9.39 | 14.17 | 33.10 |

30 | 31.39 | 29.31 | 14.64 | 2.78 | 5.34 | 26.28 | |

40 | 35.69 | 27.21 | 27.97 | 7.59 | 12.11 | 29.51 | |

${S}_{no\hspace{0.33em}contact}$, % | 25 | 0.00 | 0.00 | 0.00 | 4.33 | 4.33 | 0.00 |

30 | 0.00 | 0.00 | 0.00 | 5.17 | 4.44 | 0.00 | |

40 | 0.00 | 0.00 | 0.00 | 3.55 | 2.84 | 0.00 |

**Table 9.**Comparison of the maximum level displacements along the normal “end face surface” under different ${\mathsf{\alpha}}_{p}$.

Parameter | ${\mathit{\alpha}}_{\mathit{p}},\xb0$ | Material | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

Model A | |||||||

$\mathrm{max}{u}_{n}$, mm | 0 | 0.400 | 0.688 | 0.679 | 2.596 | 2.200 | 0.560 |

30 | 0.451 | 0.802 | 0.834 | 4.423 | 4.093 | 0.700 | |

Model B | |||||||

$\mathrm{max}{u}_{n}$, mm | 25 | 0.353 | 0.585 | 0.569 | 2.224 | 2.066 | 0.480 |

30 | 0.358 | 0.594 | 0.607 | 2.894 | 2.680 | 0.513 | |

40 | 0.334 | 0.553 | 0.536 | 2.550 | 2.262 | 0.454 |

Parameter | ${\mathit{\alpha}}_{\mathit{p}},\xb0$ | Material | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

Model A | |||||||

${\left.{u}_{z}\right|}_{r\in {S}_{1}}$, mm | 0 | 0.116 | 0.136 | 0.138 | 0.240 | 0.243 | 0.133 |

30 | 0.120 | 0.190 | 0.147 | 0.318 | 0.312 | 0.142 | |

Model B | |||||||

${\left.{u}_{z}\right|}_{r\in {S}_{1}}$, mm | 25 | 0.100 | 0.114 | 0.116 | 0.218 | 0.217 | 0.113 |

30 | 0.108 | 0.162 | 0.102 | 0.243 | 0.252 | 0.123 | |

40 | 0.112 | 0.130 | 0.130 | 0.224 | 0.233 | 0.127 |

Model | Parameter | |||||
---|---|---|---|---|---|---|

${\mathbf{max}{\mathit{P}}_{\mathit{K}}|}_{\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\hspace{0.33em}\mathit{s}\mathit{u}\mathit{f}\mathit{a}\mathit{c}\mathit{e}},$ MPa | $\mathbf{max}{|{\mathsf{\tau}}_{\mathit{K}}|}_{\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\hspace{0.33em}\mathit{s}\mathit{u}\mathit{f}\mathit{a}\mathit{c}\mathit{e}},$ MPa | ${{\mathit{S}}_{\mathit{a}\mathit{d}\mathit{h}\mathit{e}\mathit{s}\mathit{i}\mathit{o}\mathit{n}}|}_{\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\hspace{0.33em}\mathit{s}\mathit{u}\mathit{f}\mathit{a}\mathit{c}\mathit{e}},$ % | ${{\mathit{S}}_{\mathit{n}\mathit{o}\hspace{0.33em}\mathit{c}\mathit{o}\mathit{n}\mathit{t}\mathit{a}\mathit{c}\mathit{t}}|}_{\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\hspace{0.33em}\mathit{s}\mathit{u}\mathit{f}\mathit{a}\mathit{c}\mathit{e}},$ % | $\mathbf{max}{{\mathit{u}}_{\mathit{n}}|}_{{\mathit{S}}_{{\mathit{K}}_{3}}},$ mm | ${{\mathit{u}}_{\mathit{z}}|}_{\mathit{r}\in {\mathit{S}}_{1}},$ mm | |

A | 168.95 | 6.02 | 3.59 | 7.05 | 5.77 | 0.41 |

B | 156.58 | 5.05 | 14.59 | 5.72 | 3.90 | 0.27 |

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## Share and Cite

**MDPI and ACS Style**

Adamov, A.A.; Kamenskikh, A.A.; Pankova, A.P.; Strukova, V.I.
Comparative Analysis of the Work of Bridge Spherical Bearing at Different Antifriction Layer Locations. *Lubricants* **2022**, *10*, 207.
https://doi.org/10.3390/lubricants10090207

**AMA Style**

Adamov AA, Kamenskikh AA, Pankova AP, Strukova VI.
Comparative Analysis of the Work of Bridge Spherical Bearing at Different Antifriction Layer Locations. *Lubricants*. 2022; 10(9):207.
https://doi.org/10.3390/lubricants10090207

**Chicago/Turabian Style**

Adamov, Anatoliy A., Anna A. Kamenskikh, Anastasia P. Pankova, and Veronika I. Strukova.
2022. "Comparative Analysis of the Work of Bridge Spherical Bearing at Different Antifriction Layer Locations" *Lubricants* 10, no. 9: 207.
https://doi.org/10.3390/lubricants10090207