Motion System Design

# Better shafts for better linear motion performance

Recent developments in materials and finishing techniques for linear-motion shafts offer new opportunities for improving performance. Here is a look at what you need to know to make the best selection for your applications

When selecting components for your linear motion system, the linear ball bearing is not the only element you must consider. The design of the shaft plays a crucial role. Unlike a rotary antifriction bearing, a linear ball bearing uses the shaft it runs on as its inner race. Thus, the travel lives of linear ball bearings and shafts are interdependent — the bearing’s performance is directly influenced by the characteristics of the shaft; ball track configurations (such as the number of tracks) of linear bearings influence shaft travel life. How much of an influence? In some applications, the right combination of shaft hardness and bearing design can give you a 40-fold increase in shaft travel life or a 3.42-times increase in load capacity.

For example, travel life can increase eight times by changing from a shaft with a hardness of HRc 50-55 to a shaft with HRc 60-65. In addition, increasing the number of balls riding on the inner and outer races increases the amount of surface area carrying the load. A linear bearing with 10 ball tracks increases shaft life to five times that of a bearing with six tracks. Combine this increase with a change from the softer to harder shaft, and you can reach that 40-fold increase in shaft travel-life.

To get the most travel life from the shaft, it must be hard on the surface, cylindrical, and smooth. If not, the shaft will wear rapidly, offer reduced ball contact area, and can reduce the number of balls carrying the load. Any of these problems reduces the bearing’s performance in terms of load capacity and travel life.

### Hardness

A shaft of HRc 40 hardness will have only 20% of the rated life of a system with a shaft at HRc 60. To get the most rated life, heat treating shafts to a surface hardness of HRc 60-65 is essential. Figure 1 shows how steeply bearing load capacity falls off, especially between HRc 60 and 50. Harder shaft surfaces resist permanent deformation under the high point-loading of the bearing balls, maintaining bearing life and shaft life at expected levels.

The depth of hardness must be engineered for the bearing size and load expectations. For example, linear systems with large bearing balls supporting large loads will subject the shaft to deep bearing ball penetration and stress concentrations. Therefore, both larger bearings and their shaft inner races require deep resistance to deformation. Typically, hardness depths are one tenth of an inch. Uniform depth of hardness is important for proper performance.

In the past, stainless steel could not offer hardness comparable to steel. Thus, engineers reduced rated load for applications needing stainless steel shafts by 50%. The typical hardness of 440C stainless was HRc 50 versus the HRc 60 needed for a full bearing-life rating. Today, however, with new stainless grades and proprietary heat treating operations, you can obtain stainless steel shafting of HRc 60/63 that permits full system ratings.

### Cylindricity

Cylindricity refers to a combination of roundness, straightness, and taper. It is a measure of the degree of conformance of the outside surface diameter, along the length of the race, to a true cylinder.

Roundness, in general, is the difference between a shaft’s largest and smallest radii. These variations can cause rapid alternate loading as the bearing rides along the shaft: Balls on the end of the track are overloaded as the bearing goes over a valley, and all balls are shock loaded when the bearing rides over a hill.

Shafts that are out of round (circumferential variation) by even 0.0001 in. create preloading on some of the ball tracks causing uneven wear and shortening bearing life by as much as 50%. Figure 2 compares such a shaft with one held to a roundness of 0.000040 in.

Straightness is essential to positioning accuracy in linear bearing systems. In many applications, a straightness of 0.001 in./ft cumulative (0.001 TIR) will suffice, but a straightness of 0.0005 in./ft cumulative (0.0005 TIR) is available for applications requiring extreme accuracy.

Taper is a change in diameter any place along the shaft. It subjects the bearing to shock and preloading variations, sacrificing accuracy and load capacity, Figure 3. A taper specification of 0.00001 in. per 15 ft is preferred.

### Shaft material

A shaft used with a linear bearing should be made of steel that meets the ASTM-A-295, “Standard Specification for High-Carbon Ball and Roller Bearing Steel,” requirements. Such a steel will have few nonmetallic inclusions, frequently termed “clean” steel. The exact amount of allowable inclusions under the term “clean” depends on a number of variables and calculations beyond the scope of this article. Refer to the ASTM standard for a thorough discussion. Laboratory tests, though, show that if steel meets these tight cleanliness specifications, shaft performance improves by 50% over commercial grade steel.

Clean steel decreases the chance that bearing balls will roll over detrimental inclusions on or near the shaft surface. These inclusions are the sites of spall initiations that lead to shaft failure. Plus, clean steel has a more consistent grain structure that results in better heat treating and grinding accuracy.

### Surface finish

In a perfect bearing, the ball and shaft surface would be in 100% contact. In real life, contact area can be 50% or less as a result of traditional grinding methods. A major improvement to shaft life involves variations on finishing techniques. By increasing the amount of shaft surface the ball bearings can ride on, you spread the load over a larger area.

Superfinishing goes beyond surface grinding and levels more of the peaks of the ground shaft surface to produce a series of plateaus, Figure 4. On a superfinished shaft, 92% of the possible shaft surface area is available to the linear bearing. Superfinishing typically gives you a contact surface area of 92% minimum at a mean depth of 8 min. (a typical “wear-in” value). Such a shaft provides three to four times the performance of shafts with conventional finishes even though both have an average roughness reading of 2 Ra.

The Ra reading is a measure of the vertical displacement of a sharp tip dragged over a surface. The dragging gives an average reading of peak-to-valley height of the surface without regard to the quality of surface for bearing applications. Flattened peaks can show the same Ra value even though they provide much more surface area. The bearing ratio curve, produced on test equipment, measures the percentage of bearing area over the entire surface, offering a more accuarate reading. You want to strive for a bearing ratio reading of 90% or better.

### Special platings and materials

Shaft performance is also affected by special platings put on the shaft. Some applications require platings to protect the shaft in corrosive environments or to conform to certain appearance requirements. In general, however, a coated shaft must be derated by 50% because loaded balls cause stress that extends below the shaft coating, potentially loosening it.

Plating options include chrome, thindense chrome, nickel (electrolytic, polytetrafluoroethylene- impregnated and bright) and black oxide. Chrome is selected when the appearance of the shaft is important. Thin-dense chrome offers corrosion resistance without changing shaft dimensions. Nickel coating handles special corrosive conditions and black oxide is chosen to give a shaft a special appearance. Coating thickness is precisely controlled. For example, thindense chrome plating used for corrosion resistance is held to 50 millionths of an inch (or 2 μm) over the entire surface of a shaft.

In corrosive environments, non-hardenable 300 Series stainless steel shafts can be used with light loads or cycling requirements, or with polymer bearings.

### Short stroke operation

When the stroke is extremely short, higher stress cycles accumulate on the shaft (inner race) rather than on the bearing plate (outer race). Shaft life is shorter than bearing life. If the stroke is less than 1.5 times the bearing length, you must decrease load capacity to 42% of the normal system load. For example, if a 2-in. long bearing operates with a 1-in. stroke, its load capacity should be multiplied by 60%.

For optimum results in selecting bearings and shafts for your linear motion application, it is best to consult suppliers of both to take advantage of the latest developments.

Al Ng manages product development of RoundRail bearings for Thomson Industries Inc. He holds a B.S. in mechanical engineering from Columbia University and four U.S. and 16 international patents.