Engineering Calculation and Selection Logic for Sliding Bearings in Hydraulic Steel Structures

Technical Clarification and Design Framework

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1. Operating Condition Definition and Bearing Selection Strategy

1.1 Applicable Operating Conditions

Hydraulic steel structures such as gate mechanisms, hoisting systems, and underwater support assemblies typically operate under the following conditions:

• Submerged or water-exposed environment
• Limited access for periodic lubrication maintenance

• Low sliding speed

  $$v<5m/s$$

• Medium to heavy loading conditions

  $$p>10MPa$$

Under these operating conditions, conventional lubrication methods face significant limitations.

1.2 Physical Failure Mechanism of Conventional Lubrication

Grease or oil lubrication may become ineffective because:

• external water flow can remove lubricant;
• high contact pressure can squeeze lubricant out of the sliding interface;
• insufficient lubricant film formation can result in boundary lubrication failure and dry friction.

Therefore, bearing selection should focus on maintaining stable lubrication performance without continuous external lubrication.

1.3 Recommended Bearing Type

For submerged hydraulic applications, the recommended solution is:

Integrated radial self-lubricating plain bearings with:

• copper alloy matrix;
• embedded solid lubricant plugs;
• maintenance-free lubrication characteristics.

The bearing design should comply with relevant standards such as:

GB 23894 — Copper Alloy Embedded Solid Lubricant Bearings.

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2. Fundamental Bearing Verification Principles

Sliding bearing selection is mainly determined by two engineering evaluations:

1. Bearing pressure verification (p-value)
   Determines whether the bearing material can withstand the applied load.
2. PV value verification
   Determines whether friction-generated heat remains within acceptable limits.

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2.1 Bearing Pressure Calculation

The basic calculation formula is:

p=Fmaxd×L≤[p]p=fracleq[p]p=d×LFmax​​≤[p]

Where:

The calculated bearing pressure directly determines whether the selected bronze alloy has sufficient load capacity.

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2.2 PV Value Verification

The PV value is calculated as:

$$PV=p\times v\le [PV]$$

Where:

Engineering Interpretation

Hydraulic gate operating speeds are generally within:

$$1.5-2.0m/min$$

which corresponds approximately to:

$$v\approx 0.01m/s$$

Due to the extremely low sliding speed, friction-generated heat is usually limited.

Therefore:

• bearing pressure verification is the primary design criterion;
• PV verification is generally a secondary confirmation step.

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3. Allowable Material Parameters and Safety Reduction Principles

3.1 Conservative Interpretation of Engineering Standards

For commonly used hydraulic bearing alloy:

ZCuAl10Fe3 (Aluminum Bronze 10-3)

Different engineering standards provide different allowable pressure values:

Engineering Selection Principle

For critical hydraulic applications, the conservative value should be adopted.

Therefore:

$$[p]=30MPa$$

is recommended as the verification baseline.

This approach provides additional protection against:

• unexpected overload;
• impact loading;
• material degradation;
• long-term wear.

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3.2 Underwater Service Reduction Factor

Submerged components are exposed to additional environmental factors, including:

• corrosion;
• water chemistry variation;
• sediment contamination;
• fatigue degradation.

For critical underwater bearings, the allowable pressure should be reduced by applying:

[p]design=0.8×[p][p]_=0.8 times [p][p]design​=0.8×[p]

This represents a 20% reduction from the standard allowable value.

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3.3 Typical Copper Alloy Matrix Selection

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4. Friction Coefficient and Lubrication Reliability Logic

4.1 Friction Coefficient Selection for Hoisting Force Calculation

The maximum resistance of hydraulic gates usually occurs during:

transition from static condition to initial movement.

This means static friction is the controlling factor.

Using only dynamic friction values:

$$\mu =0.07-0.12$$

may underestimate starting resistance and result in:

• insufficient hoist motor capacity;
• failure during gate opening;
• incomplete gate closing.

Recommended Design Value

For steel-bronze dry sliding conditions:

$$\mu =0.25$$

should be used for hoisting force and motor power calculations.

This provides a more conservative operating condition.

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4.2 Solid Lubricant Selection Requirements

For underwater applications, lubricant selection is critical.

Conventional graphite-based solid lubricants may suffer from:

• particle detachment;
• lubrication instability;
• reduced adhesion under water exposure.

Therefore:

Underwater self-lubricating bearings should specify resin-based solid lubricant formulations.

The lubricant requirement should be clearly stated on engineering drawings and technical specifications.

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5. Bearing Fit and Tolerance Design Principles

Tolerance design should achieve two objectives:

1. Prevent loosening at the stationary interface.
2. Maintain sufficient clearance at the sliding interface for lubrication film formation and underwater dimensional changes.

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5.1 Dynamic Sliding Surface

Bearing Inner Diameter ↔ Shaft

Recommended fits:

• F7/e7
• F7/f7

Purpose:

• maintain operating clearance;
• accommodate microscopic expansion;
• support solid lubricant transfer.

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5.2 Static Fixing Surface

Bearing Outer Diameter ↔ Housing Bore

Embedded Solid Lubricant Bearings

Recommended fit:

$$H7/m6$$

Additional recommendation:

• use retaining screws or mechanical locking methods to prevent axial movement.

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Conventional Copper Alloy Bushings

Recommended fit:

$$H7/s6$$

Suitable for interference press-fit installation.

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6. Engineering Selection Workflow

A practical hydraulic bearing design process can follow the sequence below:

Step 1 — Define Operating Conditions

Confirm:

• underwater exposure;
• load level;
• speed range;
• maintenance limitations.

Select self-lubricating plain bearing technology.

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Step 2 — Calculate Bearing Pressure

Use:

p=Fmaxd×Lp=fracp=d×LFmax​​

Confirm actual operating pressure.

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Step 3 — Apply Safety Reduction

For critical underwater applications:

[p]design=0.8[p][p]_=0.8[p][p]design​=0.8[p]

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Step 4 — Select Bearing Alloy

Choose the copper alloy according to:

• load capacity;
• corrosion environment;
• service requirements.

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Step 5 — Verify PV Performance

Because hydraulic gate speeds are usually extremely low, PV verification is generally supplementary.

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Step 6 — Specify Solid Lubricant Requirements

Define:

• lubricant type;
• underwater compatibility;
• drawing requirements.

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Step 7 — Verify Hoisting Force

Use:

$$\mu =0.25$$

for conservative starting friction calculations.

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Customized Engineering Support

Bearing structure, material selection, dimensional tolerances, and load verification can be customized according to:

• actual equipment dimensions;
• operating loads;
• environmental conditions;
• service life requirements.

For project-specific engineering evaluation and bearing selection support, technical consultation can be provided by the VIIPLUS SOLUTIONS engineering team.

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Technical Disclaimer

The formulas, parameters, and selection principles presented in this document are based on publicly available engineering standards, including references such as:

• GB 1176 — Copper Alloy Casting Standard;
• GB 23894 — Copper Alloy Embedded Solid Lubricant Bearing Standard;
• SL 74 — Hydraulic Steel Gate Design Specification;

as well as established mechanical engineering calculation principles.

This document is intended for professional engineering reference during preliminary design, technical evaluation, and drawing review.

Hydraulic operating environments involve complex variables, including:

• water corrosion conditions;
• sediment erosion;
• impact loading;
• non-uniform pressure distribution;
• installation deviations.

Therefore, the information provided should not replace detailed engineering analysis, finite element simulation, or final design approval by qualified engineering organizations.

The final responsibility for equipment design verification and bearing selection remains with the project designer based on actual operating conditions.