Authored by
Igor Glikin
Senior Mechanical Engineer,
Tolomatic
Hamel, Minn.

Edited by Stephen J. Mraz
stephen.mraz@penton.com

Resources:
Tolomatic, www.tolomatic.com

Before engineers can specify the type and size of leadscrew needed for a linear-motion application, they must understand the demands of that the job. These include thrust, speed, accuracy, repeatability, and resolution.

Thrust
The more thrust an application requires, the larger the diameter screw will be needed. That’s because the screw is similar to a column subject to compression and tension. During compression, the screw should not bow or deflect. And during tension, the screw must support the load without failing.

Engineers can calculate a column’s theoretical strength (in lb) based on:

Pcr = (14.03 × 106 × FC × d4)⁄L2

where Pcr = maximum load; Fc = end fixity factor (this is 0.25 for one end fixed, one end free; 1.0 for both ends supported; 2.0 for one end fixed, one end simple; and 4.0 for both ends rigid); d = root diameter of screw; and L = the distance between nut and load-carrying bearing.

For linear actuators, consider two thrust values: peak and continuous. Peak thrust normally lasts just a short period of time, such as during acceleration or deceleration for a high-speed move or when pressing or pushing a product. Peak thrust can be anywhere from one to five times continuous thrust, depending on application.

Continuous thrust is a root-mean-square or RMS value. In some cases, such as in volumetric piston pumps, continuous thrust can last the entire length of a relatively long stroke. (Continuous thrust is also an important variable in determining a ball or roller screw’s estimated L10 life.) Under either peak or continuous-thrust values, engineers must verify the screw shaft that can support all applied forces.

For Acme screws, the material used to make the nut significantly affects thrust. For example, on a 1-in.-diameter Acme screw with a 0.125-in. lead, a resin nut may have an operating load rating of 625 lb, as compared to 1,250 lb for a bronze nut.

In ball screws, nut design and lead can affect the quantity and diameter of ball bearings circulating inside the nut. As the number of balls in the nut increases, for example, so to do the number of thrust-supporting contact points. Therefore, the thrust rating increases. For comparison, consider two 1.0-in. ball screws, the first has a 0.20-in. lead and the second a 0.50-in. lead. The first screw has a dynamic load rating of 973 lb and is a single-start screw with two 40-ball circuits.

The second screw has a dynamic load rating of 786 lb and is a double-start screw with two 30-ball circuits. In these two screws, the number of balls in the nut helps determine the thrust rating. The number of rollers in a roller nut plays a similar role on its thrust rating.

The screw’s lead also affects the linear actuators thrust capacity. To calculate linear thrust of a screw assembly, use the following equation: Torque = Thrust required × Screw lead/(2 × Efficiency).

For example, if the goal is to produce 100 lb of continuous thrust using a 1-in. Acme screw with a lead of 0.2 in. and an efficiency of 40%, then this equation would indicate you need an input torque of 8 lb-in. If the lead changes to 0.5 in, input torque becomes 20 lb-in.

The above equation assumes a screw assembly with no losses. But engineers should account for additional forces such as bearing preloads, gravity, friction, and breakaway torque. The simplest and easiest way to account for all forces is to use a sizing tool such as sizing and selection software.

Speed
How fast will the linear motion be? The answer to this question provides the second most-important parameter to evaluate when selecting a screw. All screw mechanisms have a critical velocity — the rotational velocity limit of the screw after which vibrations develop due to the shaft’s natural harmonic frequency. This is also commonly called “screw whip” and depends on the diameter and length of the screw between supports. It is important to note that a screw’s critical velocity is not a function of orientation (horizontal, vertical, etc).

Designers can calculate theoretical critical velocities when both ends of a screw are fixed into bearings. However experts recommend that maximum velocity should be less than 80% of this calculated value.)

N = (4.76 × 106 × d × Fc)/L2 where N = critical speed, d = root diameter of screw, Fc is end fixity factor (0.36 for one end rigidly fixed, one end free; 1.00 for both ends supported; 1.47 for one end rigidly fixed, one end supported; and 2.23 for both ends rigidly fixed), and L = the length between bearing supports.

In ball nuts, bearings run along rolled or ground tracks between the screw and nut and through recirculation mechanisms. As screw speed increases, ball velocities increase to the point they become projectiles zooming through the ball circuit. This complicated action, which needs to be controlled, can also limit speed.

With all leadscrews, there is direct ratio between input rpm and output linear velocity, which depends on the lead. For high-speed applications, specifying a larger lead lowers the screw’s input rpm. Here is how to calculate the required rpm of a screw assembly: rpm = (60 × Linear velocity (in ips)) /lead.

Accuracy and repeatability
It is important to understand the difference between accuracy and repeatability, as these two terms are often used interchangeably. If misapplied or misunderstood, engineers can run into significant and unnecessary costs.

Accuracy measures how well an assembly can move a load to a desired location within a tolerance level. Accuracy depends on the accuracy of the leadscrew. The most accurate screws will almost always be the most expensive.

Repeatability measures how well a screw assembly can consistently move a load to the same location. Many applications don’t need a high level of accuracy but will likely require a high level of repeatability. It is possible for ball and other types of leadscrews to have repeatability but not accuracy.

Ball and roller nuts, because they do not wear like Acme nuts, maintain higher levels of repeatability. Backlash, the next area of discussion, is also important for bidirectional repeatability.

Backlash
Backlash is the amount of linear movement between screw and nut without turning the screw or nut. This can be critical for applications requiring stiffness or accuracy and repeatability from both travel directions. For example, say a load travels in a positive direction to an absolute position of 10.0 in. Then the direction reverses and the load moves to an absolute position of 5.0 in. using a motion controller. However, the load is really at 5.010 in. if you have a 0.010 in. of backlash.

External forces acting on the actuator can also help determine if backlash will be a factor for an application. For vertical motion, gravity normally keeps a downward or negative force on actuators, thus eliminating the effects of backlash. In some applications, an external force may act against the actuator, such as products on a conveyor belt or a pneumatic cylinder, which also gets rid of backlash.

Most solid nuts wear over time and backlash then increases. Some solid nuts have backlash mechanisms. However, it is important to note that such nuts still wear which affects accuracy.

Ball nuts can use standard methods to lower backlash to between 0.005 and 0.015 in. or special methods that lower backlash even more. Typically, there are two methods to lower backlash in ball nuts. The first uses oversized balls loaded into the nut. This lowers backlash to a specified level. It is also the most common and cost effective. The second method uses two nuts biased against one another. This is more expensive and may increase overall nut length, which may affect the actuator’s dead length.

Resolution
Resolution is normally a function of the motion controller, motor, and feedback devices in linear actuators. But preload, break-away torque, and torsional twist of long screws also play important roles if moving loads less than 0.001 in. (Components suppliers should know your expected accuracy and repeatability requirements as well as your smallest incremental move.)

Screw leads also affect resolution. Finer screw leads provide higher resolutions. This is important to note because an application may need a lower-resolution feedback device or lower-cost motor and drive if a higher resolution screw is installed. Keep in mind that the screw’s lead also affects the maximum linear speed and the linear force generated.

As an example, consider a leadscrew that has a 0.5-in. lead as compared to a 0.2-in. lead. Looking at the linear travel per degree of motor rotation, there is a considerable difference that may let engineers use a less expensive motor and drive. (The 0.5-in. lead travels 0.0014 per degree of rotation while the 0.2-in. lead moves 0.0006 in. per degree of rotation.