Engineering Information / Life

Life of Linear System / Rated Life / Basic Dynamic Load and Basic Dyanamic Torque
/ Rated Life Estimation / Hardness Coefficient(H) / Temperature Coefficient(s)
/ Contact Coefficient(fb) / Applied Load Coefficient(v)
/ Method for Determining Applied Load / Average Applied Load




* Life of Linear System

If a linear system reciprocates when it is under a load, a continuous stress acts on it, ultimately causing Flaking of its rolling elements and/or rolling surfaces due to material fatigue, making it inoperable. The distance a linear system travels before this flaking condition first occurs is called the Life of the system. A linear system can also become inoperable due to sintering, cracking, pitting, or rusting. These factors are differentiated from those affecting the life because they are related to installation accuracy, operating environment, or the selected lubrication method of the installer.




* Rated Life

Even when two linear systems are manufactured at the same time, have the same part number, and are used under identical conditions, their lifetimes can differ due to differences in their fatigue failure characteristics. This prevents determining the life of any particular linear system. Therefore, the Rated life is determined statistically and is defined as the distance 90% of linear systems travel before experiencing flaking.




* Rated Basic Dynamic Load and Rated Basic Dyanamic Torque

The life of a linear system is expressed in terms of the distance traveled. Therefore, the life of a linear system is calculated using the allowable load that corresponds to a certain distance traveled. This allowable load is a measure of the system's performance relative to the applied load and is called the Rated basic dynamic load. It is defined as a constant-direction load with a magnitude corresponding to a life of 50x10³m. In some cases or linear systems, the basic dynamic load rating may vary depending on the direction of the applied force. In the NB Linear System catalog, the value of the basic dynamic load rating is assumed when a force is applied from directly above and is indicated in the dimension tables. For ball splines, the linear motion may involve torque loading, so the basic dynamic torque rating is defined in a similar fashion.




* Rated Life Estimation

The rated lifetime estimation depends on the type of rolling element used. Both Equations (3) and (4) are used for ball and roller elements respectively. In cases when torque loading is applied, Equation (5) is to be used.

Numerous variables, such as guide rail accuracy, mounting conditions, operating conditions, vibration and shock while under linear motion affect an actual application. Therefore, calculating the actual applied load accurately is extremely difficult. In general, the calculation is simplified by using coefficients representing these effects. These coefficients include hardness (fH), temperature (fT), contact (fC), and applied load (fW). By using these coefficients, Equations (3)-(5) can be expressed by Equations (6)-(8).

If the distance traveled per unit time is known, the life can be expressed in terms of time, which may be easier to understand. The relationship between the stroke distance, the stroke frequency per minuit, and the life time is expressed by Equation (9)




* Hardness Coefficient(H)

In a linear system, the guide rail serves the same purpose as an inner race of a ball bearing. Therefore, the hardness of the guide rail plays an important role in determining the rated load. If the surface hardness is less than HRC58, the rated load is reduced. NB uses an advanced heat treatment method to maintain an appropriate level of hardness. However, if guide rails with inadequate hardness must be used, the rated load must be re-calibrated based on the hardness coefficients given in the right Figure.




* Temperature Coefficient(s)

NB linear systems are heat treated to reduce the amount of wear. Therefore, if the operating temperature exceeds 100 degrees C, hardness is reduced and the life of the system is shortened. The variation in hardness with temperature is shown in the right Figure.




* Contact Coefficient(fb)

When two or more linear systems are used in contact with each other, the variation in each system and the accuracy of the mounting surfaces must be taken into consideration. In general, the coefficient values given in the right Table should be used to compute the life.




* Applied Load Coefficient(v)

When computing the applied load, the weight of the mass, inertial force, moment resulting from the motion, and the variation with time should be accurately estimated. However, it is very difficult to accurately estimate the applied load due to the existence of numerous variables, including the start/stop conditions of the reciprocating motion and of the shock/vibration. Estimation is simplified by using the values given in the right Table.




* Method for Determining Applied Load

Typical cases that linear systems are set and the equations for determining the applied load for each case example are summarized in the lower Tables.
W : applied load (N) P1 - P4 : load applied to linear system (N) X,Y : linear system span (mm) x, y,

: distance to load applied or to working center ofgravity (mm) g : gravitational acceleration (9.8 x 103 mm/s2) V : velocity (mm/s) t1 : duration of acceleration (sec) t3 : duration of deceleration (sec)