CALCULATING THE LIFESPAN OF LINEAR MOTION COMPONENTS

How long will this linear guide last? This is a question that design engineers ask, a lot. It is a good question, in fact, it may be the single most important question: If I put this bearing in my machine, how often will I have to replace it? Taking a quick look at how to calculate the theoretical life expectancy and a review of additional factors that may reduce it could help.

WHAT IS LIFE? The theoretical or nominal life expectancy of a linear bearing is always the best starting point because it represents the maximum possible lifespan of the bearing. It is generally calculated in terms of distance. The 1947 theory published in Sweden by Lundberg and Palmgren calculates nominal life expectancy as a function of the load placed on the bearing:

• L = Nominal Life (100km for linear guides or 1 million revolutions for ballscrew assemblies)
• C = dynamic load capacity in Newtons (N)
• F = bearing loading and/or sum of external force components acting on the bearing (N)
• p = exponent of the nominal life equation, depending on the type of rolling element
• p = 3 for linear ball bearings and ballscrew assemblies
• p = 10/3 for linear roller bearings

This calculation method is based on the Hertz theory of impact, which enables conclusions to be made about the maximum surface pressure of two curved bodies. The dynamic load capacities are calculated from this, dependent on the surface factors. For both guides and screws, the Nominal Life calculation is based on the method from DIN ISO 281 for rolling bearings.

Of course, even this calculation does not get you much closer to understanding how long a given bearing will last in a real-world application. For that reason, DIN ISO 281 also defines the calculation of what is called "Modified Nominal Life Expectancy." Modified nominal life expectancy calculations apply a life expectancy coefficient to the formula above to calculate the probability that a sufficiently large sample of identical bearings operating under identical conditions will achieve or exceed the theoretical life expectancy before material fatigue occurs. Typically, a 90% survival rate (the industry standard) in this formula is given a coefficient of 1, so if you want a higher survival rate, the life expectancy will be reduced. (See Table 1) So now our formula becomes:

• L_na = modified life expectancy (100km for linear guides or 1 million revolutions for ballscrew assemblies)
• a₁ = life expectancy coefficient
• C = dynamic load capacity (N)
• F = bearing loading and/or sum of external force components acting on the bearing (N)
• p = exponent of the nominal life equation, depending on the type of rolling element (-)
• p = 3 for linear ball bearings and ballscrew assemblies
• p = 10/3 for linear roller bearings

In other words, to ensure a 99% bearing survival rate, the Modified Nominal Life Expectancy becomes only one-fifth that of the result you would expect with a 90% life expectancy Of course, these calculations are just the starting point for determining how long a given linear guide or ballscrew will last in real world application. Generally, the factors that affect the expected lifespan of linear motion components fall into three categories: environmenatl, operating and installation conditions.

ENVIRONMENTAL CONDITIONS

With many applications in the medical industry, the typical production environment easily meets the "normal" standard. Laboratories, especially, are often well-controlled environments, if not highly-controlled ones. Colonypickers, measuring devices, fluid dispensing systems and similar applications easily fit into what would be considered a "normal" environment.

Indeed, in medical applications requiring a cleanroom environment, it might even be possible to achieve close to the calculated theoretical life expectancy, since adverse effects from the environment itself are virtually nonexistent.

In medical device assembly and some pharmaceutical packaging applications, the environment may present some challenges, however. A saline spray environment, for example, could accelerate corrosion of metal bearing components if corrosionresistant versions of the linear motion components are not specified.

OPERATING CONDITIONS

In any application involving linear guides or ballscrews with roller or ball bearings, it is critical to ensure proper lubrication at all times. In cleanrooms, depending on the cleanroom class, the lube may need to be classified as "permanent" and be approved by the FDA. Here it is also worth noting that the same seals that protect the bearing from contamination will also protect the clean working environment. If nothing from outside the bearing can get in, then lubricants inside the bearing also will not be able to get out. This is equally important in harsher environments, such as high-speed metalworking, where metalworking fluids used for cooling can penetrate inadequately sealed linear motion components and interfere with, or even wash out, the lubricant. In addition to reinforcing the seals in these machines, it might be prudent to consider hard chrome plating of the components, the use of corrosion-resistant steel versions, adjustments to the lubrication or additional measures.

INSTALLATION CONDITIONS

Catalogs from most suppliers of linear motion components offer clear tolerance and application guidelines.

Failure to adhere to these guidelines in the application's design phase can shorten life expectancy, even if the environmental and operating conditions are conducive to long component life. Incorrect mounting of the components, uneven mounting surfaces and misalignments, can also cause internal stresses.

Of course, each application is different, and some products have been designed specifically to handle uneven surfaces or minor shaft or running surface misalignments. It is easy to underestimate the damage that can be caused by even minor misalignment issues, especially when high-precision and significant loads are involved.

A FEW FINAL COMMENTS

Throughout this article, we have mostly discussed why it is difficult to achieve the calculated theoretical nominal life expectancy of linear motion components in real world applications. While it is desirable to come as close to the theoretical life as possible, the engineering team needs to ensure competitive performance and durability within the framework of a customer's performance - and price - expectations. Yes, it is possible to optimize the life of the components that you ultimately choose.

The calculations and considerations presented here are intended to help you do just that. But choosing the right components for a real application with given price, performance and lifespan expectations - well, that is the fun part. That is where an experienced designer, with supplier help, can achieve a competitive advantage for his or her company.

The end result will be a satisfied customer and a satisfied employer.

Formulae and definitions in this article are extracted from chapter 2.4 of Bosch Rexroth Corp.'s "Linear Motion Technology Handbook." The complete text book, including more detailed formulae on calculating linear motion lifespan, can be downloaded at boschrexroth-us.com/lmthandbook.