



Fatigue Calculations Predict Actuator Life
Wellcharacterized bearing fatigue mechanisms make it easy to understand trade offs between load and lifetime for ballscrew actuators.
Linear actuators such as ballscrew actuators (see figure 1) represent an economical, effective method for converting the rotational motion of a rotary servo motor or stepper motor into linear motion. Just as a motor must be sized correctly for the application, so must an actuator be sized correctly to ensure that it will both support the load and operate for the desired lifetime of the application. Screwtype actuators encompass socalled leadscrew actuators, which consist of a threaded screw and a nut (see figure 2); ballscrew actuators, in which ball bearings placed in the raceways between the nut and the screw act to reduce friction and wear; and planetary roller screws, which feature an array of secondary screws placed around a central shaft in a planetary configuration. Lead screw actuators tend to be most economical but suffer where elements lifetime, while planetary roller screws provide highreliability operation with even higher loads. Ballscrew actuators provide a good compromise solution. A combination of factors can impact the lifetime of screwtype actuators. The material of the actuators can be compromised by frictioninduced wear, corrosion, contamination, intrinsic flaws, and material fatigue. In the case of leadscrew actuators, the sliding friction increases wear as well as generating heat that might cause speed material fatigue. The combination of factors makes predicting the lifetime of leadscrew actuators challenge. In contrast, the lifetime and sizing of ballscrew actuators and rollerscrew actuators are well characterized. The effects of fatigue, for example, can be described by a simple set of equations that simplify the task of sizing a component. By leveraging these equations, users can easily make tradeoffs between load and lifetime, for example choosing an additional support bearing for the load, if necessary.
Determining Lifetime The performance of real systems does not meet theoretical predictions. For purposes of sizing an actuator, it's more useful to think of L_{10}, which is defined as the lifetime that 90% of a group of representative actuators would survive to 10^{6} revolutions. We can determine L_{10} by: (1) where F_{app} is the application load and 10^{6} is the number of revolutions specified for the L_{10} lifetime by the ISO standard. It is important to note that the application load F_{app} bears an inversecube relationship to the L_{10} lifetime—modifying the application load can have a profound effect, pro and con, on the lifetime. With equation 1, we can determine how long an actuator will last in a given application. Conversely, we can solve for C_{d}, using the application load and desired lifetime to arrive at a dynamic axial load rating to guide the search for the right hardware.
Accounting for realworld conditions With the introduction of f_{s}, we can define a service lifetime L_{10h} as: (2) The dynamic axial load rating is an ideal quantity. In reality, applications often involve moving varying loads over different distances. We can represent that using a quantity called equivalent load (F_{e}). We define F_{e} as the mean load that produces the same amount of fatigue as a collection of varying loads applied over different time frames: (3) where x is total travel, x_{1…N } represent the incremental distances that make up the total travel, and F_{1…N } represent the incremental forces that the ball screw must move over the course of those incremental distances. It is important to remember that systems do not exert force identically in both directions of travel. When performing these calculations, calculate F_{e} in both directions and apply whichever of the two values is largest. Now we can restate the L_{10h} lifetime as: (4)
(6) In which case, equation 5 becomes: (7)
At very high speeds, actuators typically do not achieve the lifetimes predicted by equation 2, especially as loads increase. It's very important to use an appropriate safety factor. Equation 2 does not hold at very low speeds (less than 10 rpm), either. In these cases, system designers must base their selection on the static axial load rating (C_{s}), which is defined as the static load that permanently deforms the ball/ball track at point of highest load over a distance of 0.0001d, where d is ball diameter. Calculating time to fatigue as shown provides a useful estimate of actuator life. Fatigue is not the only failure mode for allscrew actuators, however. To build a robust system, it is important to evaluate all aspects of the application and adjust lifetime estimates to take into account all effects that may degrade lifetime.
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