Maximizing Bearing Life

Introduction

Bearings are critical components in various mechanical systems, supporting rotating shafts and minimizing friction. For engineers and maintenance professionals, understanding bearing life is crucial for ensuring optimal performance and longevity of machinery. This comprehensive guide delves into the intricacies of bearing life, covering everything from basic concepts to advanced calculations and real-world applications.

Table of Contents

1. Basics of Bearing Life
2. Fatigue and Failure Modes
3. Calculating Dynamic Bearing Load
4. Equivalent Dynamic Bearing Load
5. Bearing Life Calculations
6. Bearing Selection Criteria
7. Advanced Concepts and Considerations
8. Practical Examples
9. Conclusion
10. Addl Resources

1. Basics of Bearing Life

Bearing life is defined as the number of revolutions a bearing undergoes under a constant load (Equivalent Dynamic Bearing Load) before the first sign of fatigue failure occurs. Even when properly applied and maintained, bearings eventually fail due to material fatigue.

2. Fatigue and Failure Modes

Fatigue Mechanism

• Fatigue results from sub-surface shear stresses cyclically applied immediately below the load-carrying surface.
• Failure begins in the subsurface material and propagates to the surface as a small, undetectable crack.
• The condition gradually matures to flaking or spalling of the surface.

Spalling

Spalling is the primary failure mode in bearings, characterized by the flaking of material from the bearing surface. The rate of spalling depends on:

• Load
• Speed
• Lubrication condition

As spalling progresses, it spreads circumferentially around the ring surface.

3. Calculating Dynamic Bearing Load

Understanding the forces acting on a bearing is crucial for accurate life calculations. Here are some key considerations:

For Stationary Electrical Machines:

• Radial force at the center of gravity of the armature: Kr = Km + fb × G
• Magnetic pull: Km = 0.002 A (where A is the projected air gap surface)

Additional Dynamic Forces:

Factors like fb, fk, and fd account for additional dynamic forces in various machine types. These factors vary based on:

• Shaft orientation (horizontal or vertical)
• Coupling type (flexible, solid, belt drive, etc.)
• Machine type (electric machines, turbines, conveyors, etc.)

Gear Trains:

For gear trains, additional factors consider:

• Gear quality (precision, commercial, cast teeth)
• Number of engagements
• Tooth speeds

Belt Drives:

Belt drive calculations consider:

• Effective belt pull
• Belt type (toothed, V-belt, plain)
• Preload and tension

Direct Drive Through Flexible Coupling:

A simplified formula for radial force: Kr1 = 8.17 * √(W / n) + G1

Thrust Forces:

Axial loads are calculated differently for horizontal and vertical machines, considering external thrust loads and component weights.

4. Equivalent Dynamic Bearing Load

The equivalent dynamic bearing load (P) is a crucial factor in bearing life calculations. It’s calculated using the formula:

P = X Fr + Y Fa

Where:

• X = Radial load factor
• Y = Axial load factor
• Fr = Radial load
• Fa = Axial load

The values of X and Y vary depending on the bearing type (e.g., deep groove ball bearings, angular contact ball bearings, cylindrical roller bearings, etc.) and the ratio of axial to radial load (Fa/Fr).

5. Bearing Life Calculations

Several models are used to calculate bearing life:

1. Lundberg-Palmgren Equation (1947):

L10 = (C/P)^p

Where:

• L10 = Basic rating life (millions of revolutions)
• C = Basic dynamic load rating
• P = Equivalent dynamic bearing load
• p = Exponent (3 for ball bearings, 10/3 for roller bearings)

2. Adjusted Rating Life Equation (1977):

Lna = a1 * a23 * (C/P)^p

Where:

• a1 = Life adjustment factor for reliability
• a23 = Life adjustment factor for material and lubrication

3. New SKF Life Equation (1989):

Lnaa = a1 * aSKF * (C/P)^p

Where:

• aSKF = Life adjustment factor for SKF method (considering material, lubrication, contamination, and minimum load)

6. Bearing Selection Criteria

When selecting bearings, consider the following factors:

• Load capacity
• Speed ratings
• Temperature
• Environmental conditions
• Life expectancy
• Available space
• Misalignment tolerance

7. Advanced Concepts and Considerations

Basic Dynamic Load Rating

The basic dynamic load rating (C) is a fundamental parameter in bearing selection. It’s calculated differently for various bearing types (ball bearings, roller bearings) and configurations (radial, thrust).

Basic Static Load Rating

The basic static load rating (C0) is crucial for applications with slow rotations, oscillating movements, or frequent stops. It corresponds to a stress that causes a permanent deformation of 0.0001 times the rolling element diameter.

Speed Ratings

Speed limits are related to permitted operating temperatures. Factors influencing speed capability include:

• Load
• Accuracy
• Cage properties
• Clearance
• Lubrication
• Cooling

Friction

Under certain conditions, the frictional moment can be calculated using the formula: M = 0.5 * μ * F * d

Where:

• M = Frictional moment (Nmm)
• μ = Coefficient of friction
• F = Bearing load (N)
• d = Bearing bore diameter (mm)

8. Practical Examples

To illustrate the application of these concepts, let’s look at four practical examples:

Example 1: Electric Motor for a Conveyor System

Scenario:

An electric motor is being designed for a conveyor system in a manufacturing plant. The motor will operate continuously for 16 hours a day, 6 days a week.

Given:

• Motor power: 15 kW
• Motor speed: 1450 rpm
• Radial load on bearing: 3000 N
• Axial load on bearing: 500 N
• Desired life: 5 years

Solution:

1. Calculate required life in hours: L10h = 5 years × 52 weeks/year × 6 days/week × 16 hours/day = 24,960 hours
2. Select a suitable bearing: Let’s choose a deep groove ball bearing, SKF 6308
3. From the SKF catalog:
   • Basic dynamic load rating (C): 42,300 N
   • Static load rating (C0): 24,000 N
4. Calculate equivalent dynamic load: P = X × Fr + Y × Fa Assuming Fa/Fr = 500/3000 = 0.167 < e (typically 0.3 for this bearing type) P = Fr = 3000 N
5. Calculate bearing life: L10h = (C/P)^3 × 1,000,000 / (60 × n) L10h = (42,300/3000)^3 × 1,000,000 / (60 × 1450) = 56,824 hours
6. Apply life adjustment factors: Assuming a1 (reliability factor for 95% reliability) = 0.62 Assuming a23 (material/lubrication factor) = 1.5 Lna = a1 × a23 × L10h = 0.62 × 1.5 × 56,824 = 52,844 hours

Conclusion:

The selected bearing exceeds the required life (52,844 hours > 24,960 hours), making it suitable for this application.

Example 2: Wind Turbine Main Shaft Bearing

Scenario:

A wind turbine designer needs to select a suitable main shaft bearing for a new 2 MW turbine.

Given:

• Turbine power: 2 MW
• Rotor speed: 15 rpm
• Radial load: 250 kN
• Axial load: 100 kN
• Desired life: 20 years

Solution:

1. Calculate required life in hours: L10h = 20 years × 365 days/year × 24 hours/day = 175,200 hours
2. Select a suitable bearing: For this application, a spherical roller bearing is appropriate. Let’s choose SKF 23052 CC/W33
3. From the SKF catalog:
   • Basic dynamic load rating (C): 2,120 kN
   • Static load rating (C0): 3,350 kN
4. Calculate equivalent dynamic load: P = 0.67 × Fr + Y2 × Fa (assuming Fa/Fr > e) Y2 = 2.6 (from SKF catalog for this bearing) P = 0.67 × 250 + 2.6 × 100 = 427.5 kN
5. Calculate bearing life: L10h = (C/P)^(10/3) × 1,000,000 / (60 × n) L10h = (2,120/427.5)^(10/3) × 1,000,000 / (60 × 15) = 206,708 hours
6. Apply life adjustment factors: Assuming a1 (reliability factor for 99% reliability) = 0.21 Assuming aSKF = 1.5 (considering clean conditions and good lubrication) Lnaa = a1 × aSKF × L10h = 0.21 × 1.5 × 206,708 = 65,113 hours

Conclusion:

The selected bearing does not meet the required life (65,113 hours < 175,200 hours). The designer should consider a larger bearing or a different bearing arrangement to meet the life requirements.

Example 3: High-Speed Spindle for CNC Machine

Scenario:

A CNC machine manufacturer is designing a high-speed spindle and needs to select appropriate bearings.

Given:

• Spindle speed: 20,000 rpm
• Radial load: 2000 N
• Axial load: 1000 N
• Desired life: 10,000 hours

Solution:

1. Select a suitable bearing: For high-speed applications, angular contact ball bearings are often used. Let’s choose a pair of SKF 7010 CE/HCP4A bearings in a back-to-back arrangement.
2. From the SKF catalog:
   • Basic dynamic load rating (C): 24,500 N (for the pair)
   • Static load rating (C0): 18,600 N (for the pair)
3. Calculate equivalent dynamic load: For a pair in back-to-back arrangement: P = 0.57 × Fr + 0.93 × Fa P = 0.57 × 2000 + 0.93 × 1000 = 2,070 N
4. Calculate bearing life: L10h = (C/P)^3 × 1,000,000 / (60 × n) L10h = (24,500/2,070)^3 × 1,000,000 / (60 × 20,000) = 13,764 hours
5. Apply life adjustment factors: Assuming a1 (reliability factor for 95% reliability) = 0.62 Assuming aSKF = 2 (considering very clean conditions and optimal lubrication) Lnaa = a1 × aSKF × L10h = 0.62 × 2 × 13,764 = 17,067 hours

Conclusion:

The selected bearing arrangement exceeds the required life (17,067 hours > 10,000 hours), making it suitable for this high-speed application.

Example 4: Pump Bearing for Chemical Processing Plant

Scenario:

A chemical processing plant needs to replace the bearings in a centrifugal pump used for corrosive fluid transfer.

Given:

• Pump speed: 3000 rpm
• Radial load: 5000 N
• Axial load: 2000 N
• Desired life: 3 years of continuous operation
• Harsh environmental conditions (corrosive atmosphere)

Solution:

1. Calculate required life in hours: L10h = 3 years × 365 days/year × 24 hours/day = 26,280 hours
2. Select a suitable bearing: For this application, we’ll choose a stainless steel deep groove ball bearing, SKF W 6208-2RS1
3. From the SKF catalog:
   • Basic dynamic load rating (C): 17,800 N
   • Static load rating (C0): 11,200 N
4. Calculate equivalent dynamic load: P = X × Fr + Y × Fa Assuming Fa/Fr = 2000/5000 = 0.4 > e (typically 0.3 for this bearing type) X = 0.56 and Y = 1.8 (from SKF catalog) P = 0.56 × 5000 + 1.8 × 2000 = 6,400 N
5. Calculate bearing life: L10h = (C/P)^3 × 1,000,000 / (60 × n) L10h = (17,800/6,400)^3 × 1,000,000 / (60 × 3000) = 4,792 hours
6. Apply life adjustment factors: Assuming a1 (reliability factor for 90% reliability) = 1 Assuming aSKF = 0.8 (considering harsh conditions and potential contamination) Lnaa = a1 × aSKF × L10h = 1 × 0.8 × 4,792 = 3,834 hours

Conclusion:

The selected bearing does not meet the required life (3,834 hours < 26,280 hours). The maintenance team should consider:

1. Using a larger or higher capacity bearing
2. Implementing more frequent bearing replacements
3. Improving sealing and lubrication systems to extend bearing life in the harsh environment
4. Exploring alternative bearing materials or coatings that may offer better corrosion resistance

9. Conclusion

Understanding bearing life is crucial for engineers and maintenance professionals to ensure optimal performance and longevity of mechanical systems. By considering factors such as load calculations, life equations, and selection criteria, you can make informed decisions when designing or maintaining bearing systems.

The practical examples provided demonstrate how these principles are applied in various industrial scenarios, from electric motors and wind turbines to high-speed machine tools and chemical processing equipment. They highlight the importance of considering not only the basic life calculations but also factors such as reliability, operating conditions, and environmental factors.

Remember that while these calculations provide valuable insights, real-world conditions can be complex. Advanced computer programs and consultation with bearing manufacturers can provide more accurate predictions for specific applications.

By applying these principles and staying updated with the latest advancements in bearing technology, you can significantly improve the reliability and efficiency of your mechanical systems. Regular monitoring, proper maintenance, and timely replacement of bearings based on calculated life expectations will help minimize downtime and optimize the performance of your machinery.

10. Resources and Additional Information

To further your understanding of bearing life and related topics, we’ve compiled a list of valuable resources and additional information. These materials can help you deepen your knowledge and stay up-to-date with the latest developments in bearing technology.

Useful Resources:

• ISO Standards
• SKF Bearing Calculator
• NTN Bearing Life Calculator

Technical Standards and Catalogs

1. ISO 281:2007 – Rolling bearings — Dynamic load ratings and rating life This international standard provides methods for calculating the dynamic load ratings and rating life of rolling bearings.
2. ANSI/ABMA 9:2015 – Load Ratings and Fatigue Life for Ball Bearings This standard covers the methods of calculating basic dynamic load ratings and basic static load ratings for ball bearings.
3. SKF General Catalogue A comprehensive resource for bearing selection, including technical data, life calculations, and application examples.
4. Timken Engineering Manual Offers detailed information on bearing design, selection, and maintenance across various industries.

Educational Resources

1. “Rolling Bearing Analysis” by Tedric A. Harris and Michael N. Kotzalas A comprehensive textbook covering bearing theory, design, and applications.
2. “Handbook of Lubrication and Tribology, Volume II: Theory and Design” edited by Robert W. Bruce Provides in-depth coverage of bearing lubrication and tribology principles.
3. SKF Bearing University Online courses and webinars covering various aspects of bearing technology and maintenance.
4. NSK Technical Insight Series A collection of technical articles and guides on bearing-related topics.

Professional Organizations and Conferences

1. American Bearing Manufacturers Association (ABMA) Offers industry standards, technical resources, and networking opportunities.
2. Society of Tribologists and Lubrication Engineers (STLE) Provides education, certifications, and a platform for sharing the latest research in tribology and lubrication.
3. Bearing World Conference An international conference focusing on the latest developments in bearing technology.
4. Hannover Messe One of the world’s largest trade fairs for industrial technology, often featuring the latest in bearing innovations.

Online Tools and Calculators

1. SKF Bearing Select An online tool for bearing selection and calculation based on application parameters.
2. Schaeffler BEARINX A comprehensive bearing analysis software for complex systems.
3. NTN Bearing CAD Provides 3D models and technical data for various bearing types.
4. Timken Bearing Selector An online tool to help select the right bearing based on application requirements.

By exploring these resources, you can expand your knowledge of bearing life calculations, selection criteria, maintenance practices, and the latest technological advancements in the field. Remember that bearing technology is continuously evolving, so staying updated with the latest research and industry practices is crucial for optimizing bearing performance and longevity in your applications.