Machine Design
The Fundamentals of Ball Screws

The Fundamentals of Ball Screws

Proper ball-screw selection involves a number of design and application considerations.

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Of all the screws used for industrial motion control, ball screws rise to the head of the class, offering several advantages over other options such as roller screws and acme screws. Featuring efficiencies of at least 90%, ball screws are one of the most economical ways of converting rotary motion into precision linear motion. They’re able to move heavy loads at fast speeds with outstanding accuracy. Moreover, ball screws can be cost-effective alternatives to pneumatic and hydraulic actuators.

Ball screws are noted for efficiently moving high loads with outstanding accuracy. Here, they’re used in solar arrays that track the sun.

A ball screw consists of a threaded shaft and a nut, and either one can act as the traversing component. Ball screws work in a similar fashion to ball bearings, where hardened steel balls move along an inclined-hardened inner and outer race.

To select the correct ball screw and nut for a specific application, engineers should consider design factors like loads, life expectancy, speed, length, and mountings. Application considerations include lubrication and environment. Here’s a closer look.

Loads and Life

Several loading considerations impact ball-nut screws. For instance, static loads are generally straightforward and reach the maximum limit when screw and nut are loaded to their capacity without damage.

Dynamic loads are thrust loads that, when applied to the ball nut and rotating screw assembly, result in a specific minimum life. Dynamic-load ratings for metric screws indicate a load in Newtons that can be carried for 1 million revolutions. Inch/imperial screws, which factor in the lead of the screw, have dynamic-load ratings for 1 million inches of linear travel.

Due to their steel-on-steel design, bearing manufacturers have developed techniques to calculate the life expectancy of ball screws. However, contamination, lubrication, and improper mounting and installation techniques can also shorten a ball screw’s lifetime. For manufacturers looking to extend the life of their screws, it’s often beneficial to order a larger-size screw to handle a larger load.

Life expectancy, L, can be calculated from the following equations:

where L = life in revolutions; Ca = basic dynamic-load rating; Fm = equivalent axial load (N); and fw = fatigue factor.

Calculate the equivalent axial load, Fm, using:

where Fi = each increment of axial load (N); qi = percent of stroke at load Fi; and ni = rotational speed at load Fi (rpm). The final variable nm = equivalent rotational speed (rpm) and is calculated using:

As an alternative to hand calculations, charts can help determine life expectancy.

For metric ball screws:  http://www.nookindustries.com/LinearLibraryItem/Ballscrew_Life_Exp

For inch versions: http://www.nookindustries.com/LinearLibraryItem/Life_Expectancy__SRT_Rolled_Inch_Screws

Ball screws handle both compression and tensile loads. Compression loads tend to compress or squeeze the screw axially, which can make screws bow out. Tensile loads, on the other hand, often stretch the screw axially. While compression loads can be more problematic, tensile loads may cause a screw to elongate and crack.

Three widely used types of ball nuts are (left to right) cylindrical body with key, flanged, and v-thread. The flanged configuration is common to all ball nuts, and actuator companies and OEMs often use the cylindrical body with key style. V-threads are custom-made to be threaded into or attached to a flange.

It’s also important to note that screws are only designed for thrust loads or straight-line axial thrust motion. Any type of overturning or side load can reduce screw life by up to 90%.

Ball-Screw Basics

For any engineer working with ball screws, it helps to understand some key terminology.

Ball circle diameter is the diameter of the circle created by the center of the ball bearings when they contact both the screw and nut.

Root diameter is the minimum diameter of the screw measured at the bottommost point of the threads. Both ball-circle and root diameters are important when calculating application characteristics and sizing parameters for factors such as column loading and critical speed.

Pitch is the axial distance between two consecutive threads on a screw.

Lead is the linear distance traveled by the nut or screw during one full rotation.

Starts are the number of independent threads on the screw shaft. Screws typically have one, two, or four starts, which resemble a helix that wraps around the shaft. The pitch multiplied by the number of starts equals the lead of the screw.

Lash is the result of axial movement between a nut and screw without rotation. While lash can disrupt the accuracy of the screw, it typically occurs without any serious issues. Normal screws come with a relative amount of lash, and screws which are only loaded in one direction won’t be affected by lash. Lash can be controlled through preloading.

Mounting Considerations

Determining the screw’s load direction as well as the type of mounting (end fixity) helps when selecting screws, as engineers must account for both critical speed and buckling (discussed later). The end fixity of bearings defines how a screw is supported at both ends. The degree of end fixity relates to the amount of restraint at the ends of a screw. End fixity breaks down into three basic types: free (no support); simple (supported at a single point); and fixed (rigidly restrained). End bearings give the screw stability and rigidity. Fixity also affects critical speed, column loading, and overall performance.

Multiple or spaced pairs of bearings are more rigid than simple supports. However, they aren’t truly fixed because of their inherent compliance. A screw can be supported with different end-fixity combinations, such as:

• One end supported with a double bearing, the other end free. This setup is not recommended, except for applications with short travels and slow speeds.

• One end with a double bearing, the other with a single bearing.

• Both ends with double bearings.

• Both ends supported with quad bearings. Note that in such cases, the screw is highly rigid and extra care should be taken to ensure compliance.

When using fixed bearing mounts on both ends, experts recommend reviewing the setup with the ball-screw manufacturer’s application engineers to determine the mount-to-mount length tolerance of the final assembly.

Critical Speed

The speed that excites the natural frequency of the screw is referred to as the critical speed. The screw will resonate regardless of screw orientation or whether the nut rotates about the screw.

Critical speed varies with diameter, unsupported length, end fixity, and speed (rpm). Shaft straightness and assembly alignment can also play a role, so manufacturers recommend that maximum speed be limited to 80% of theoretical critical speed.

Critical speed, the speed at which a screw resonates, varies with unsupported length, diameter, end fixity, and rotational speed.

Calculate critical speed, ncr, in rpm from:

where L = distance between supports (mm); E = modulus of longitudinal elasticity (2.05 × 106 N/mm2; I = minimum second area moment of inertia of screw shaft cross section (mm4), where I = (πdr4)/64; dr = screw shaft root diameter (mm); g = acceleration of gravity (9.81 × 103 mm/sec2); γ = specific weight (7.71 × 10-5 N/mm3); and A = minimum cross-sectional area of the screw shaft (mm2), A = π dr2/4.

In addition, λ = a factor determined by the ball-screw support method, where:

• One end fixed and the other free, λ = 0.59π.

• Both ends simply supported, λ = π.

• One end fixed and the other simply supported, λ = 1.25π.

• Both ends fixed, λ = 1.49π.

Charts to help calculate critical speed can be found at:

Metric: www.nookindustries.com/LinearLibraryItem/Ballscrew_Life_Exp

Inch: www.nookindustries.com/LinearLibraryItem/Critical_Speed__Ball_Inch_Screws

Notes on Preloading

Preloading is the result of an internal force introduced between a ball nut and screw assembly that eliminates free axial and radial lash. There are three methods for preloading:

The double-nut method uses two ball nuts loaded in opposing directions by a spacer, so that they don’t wiggle when stationary.

Lead shifting manufactures a shift or offset in the lead of the ball nut. For example, a lead might be shifted from 5.00 mm to 5.05 mm to shift the ball bearings in a different direction inside the ball nut. This is the preferred method when considering compactness, but it reduces load capacity.

Ball selection is a low-cost method that involves using preselected, oversized ball bearings to create four points of contact between the nut and screw. This permits heavier loads, but friction from the contact can reduce bearing life.

Column Loading

When a screw loaded in compression exceeds its limit of elastic stability, the screw will fail through bending or buckling. To calculate the column strength to verify a screw can carry the required load without buckling, solve for:

Fc = (C × π2 × E × I)/L2

where Fc = permissible axial load to buckling (N); and C = a factor determined by the ball-screw support methods, where:

• One end fixed and the other free, C = 0.25.

• Both ends simply supported, C = 1.

• One end fixed and the other simply supported, C = 2.

• Both ends fixed, C = 4.

If the selected screw does not meet compression-load criteria, consider the following options:

• Change end fixity; for example, from simple to fixed.

• Design to use the screw in tension.

• Increase screw diameter.

Charts to help calculate column loading can be found at:

Metric: www.nookindustries.com/LinearLibraryItem/Col_Stren_w_EZM

Inch: www.nookindustries.com/LinearLibraryItem/Column_Strength__SRT__XPR_and_SGT_Inch_Screws

Application Considerations

Accuracy: Because manufacturers use different processes to make ball screws, engineers have several options for weighing accuracy versus cost.

Rolled screws are manufactured in a process that uses rotating dies to deform round metal bars and generate a helical thread pattern. This is a cost-effective manufacturing method, but typically produces screws with lower accuracy, compared to ground screws. Some manufacturers do, however, produce highly accurate screws through tightly controlled rolling processes.

Ground screws are made from a process by which a grinding wheel cuts screw threads into case-hardened material. As a result, lead accuracies are typically much tighter than in rolled screws. Ground screws are generally preferred over rolled versions in aerospace applications, because the seam formed close to the major diameter of the screw shaft is thought to have potential for crack propagation.

Backdriving: When loading ball screws, it’s important to remember backdriving. Backdriving occurs when a motor-driven ball screw free-falls once the motor shuts off. To avoid this, install brakes on motors or use safety pins to lessen the risk and catch the load. Acme screws, which have lower effiicency, are less likely to experience backdriving.

Environment: Because ball screws often work in environments exposed to dirt and debris, manufacturers should take precautions to keep out contaminants and prevent premature failure. Screws often are coated with a thin dense chrome, black oxide, or nickel-plated finish as a first line of defense.

Another option is to equip ball screws with bellows boots that cover the screw and exclude contamination. As the nut traverses, the boot expands and contracts like an accordion. Bellows boots come in various materials that suit everything from light-duty to the most extreme applications.

Wipers offer another form of protection. Nut wipers made of felt or plastic brush the nut free of dirt and other debris and keep contaminants from entering the ball nut.

Download this article in .PDF format
This file type includes high resolution graphics and schematics when applicable.

Lubrication: The types of ball-screw applications vary widely, so there’s no definitive recommendation for the type and amount of lubrication needed. However, factors such as frequency of use, temperature, and viscosity are essential considerations for lubrication options. While a light oil or grease suits most applications, avoid using lubricants containing molydisulfide or graphite. A good rule of thumb is to always apply enough lubrication to maintain a thin lubricant film between the nut and screw.

Jonathan Kasberg is Program Manager for Nook Industries, Cleveland, Ohio.

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