## Load rating and rating life of the linear ball bearing

Basic Dynamic Load Rating ( C )

This term is arrived at based on an evaluation of a number of identical linear systems individually run in the same conditions, if 90% of them can run with the load (with a constant value in a constant direction) for a distance of 50km without damage caused by rolling fatigue. This is the basis of the rating.

Basic Static Load Rating (Co)

This term defines a static load such that, at the contacting position where the maximum stress is exercised, the sum of the permanent deformation of the rolling elements and that of the rolling plane is 0.0001 time of the diameter of the rolling elements.

Allowable Static Moment (M)

This term defines the allowable limit value of static moment load, with reference to the amount of permanent deformation similar that used for evaluation of basic rated load(Co)

Static Safety Factor (fs)

This factor is used based on the application condition as shown in table 1.

Table 1. Static Safety Factors

 Loading Conditions Low limit of fs When the shaft has less deflection and shock 1 to 2 When elastic deformation should be considered with respect to pinch load 2 to 4 When the equipment is subject to vibration and impacts 3 to 5

Rating Life

Rating life of the linear system

As long as the linear system reciprocates while being loaded, continuous stress acts on the linear system to cause flaking on the rolling bodies planes because of material fatigue. The travelling distance of linear system until the first flaking occurs is called the life of the systems of the same dimensions, structure, material, heat treatment and processing method, when used in the same conditions, this variation is brought about from the essential variations in the material fatigue itself. The rating life defined below is used as an index for the life expectancy of the linear system.

Rating Life (L)

Rating life is the total travelling distance that 90% of a group of systems of the same size can reach without causing any flaking when they operate under the same conditions.

The rating life can be obtained from the following equation with the basic dynamic load rating and the load on the linear system:

Consideration and influence of vibration impact loads and distribution of load should be taken into account when designing a linear motion system. It is difficult to calculate the actual load. The rating life is also affected by the operating temperature. In these conditions, the expression(1) is arranged as follows:

The rating life in hours can be calculated by obtaining the travelling distance per unit time. The rating life in hours can be obtained from the following expression when the stroke length and the number of strokes are constant:

Working Coefficient

Hardness Coefficient (fH)

The shaft must be sufficiently hardened( not less HRC58) when a linear bearing is used. However, if linear shaft with inadequate hardness must to be used, permissible load is lowered and the life of the bearing will be shortened.

Temperature Coefficient (fT)

If the temperature of linear system exceeds 100oC, hardness of the linear system and the shaft lowers to decrease the permissible load compared to that of the linear system used at room temperature rise shortens the rating life.

Contact Coefficient (fC)

Generally two or more linear bearings are used on one shaft. Thus, the load on each linear system differs depending on each processing accuracy. Because the linear bearings per shaft changes the permissible load of the system.

When calculating the load on the linear system, it is necessary to accurately obtain object weight, inertial force based on motion speed, moment load, and each transition as time passes. However, it is difficult to calculate those value accurately because reciprocating motion involves the repetition of start and stop as well as vibration and impact. A more practical approach is to obtain the load coefficient by taking the actual operating conditions into account.