Load carrying capacity and rating life

Dimensioning of driven linear units

The performance capacity of a driven linear unit is essentially determined by the bearings, guidance systems and drive elements used.

The required size of these elements is dependent on the following requirements:

• rating life
• load carrying capacity
• operational reliability.

As a result of the complex interaction of the bearings, guidance systems and drive elements, it is advisable in practice to use manual calculation for preselection only. Precise calculation should be carried out using software from the BEARINX range.

Monorail guidance systems in driven linear units

The size of a monorail guidance system is determined by the demands made on its load carrying capacity, rating life and operational reliability.

Load carrying capacity

The load carrying capacity is described in terms of the basic dynamic load rating C, the basic static load rating C₀ and the static moment ratings M_0x, M_0y and M_0z, ➤ Figure.

The basic dynamic load rating is the load in N at which the guidance system achieves a distance of 100 km at a survival probability of 90% (C₁₀₀).

Calculation of basic load ratings according to DIN

The calculation of the basic dynamic and static load ratings for each carriage in the dimension tables is based on DIN 636-1 and 2.

Differences between DIN and suppliers from the Far East

Suppliers from the Far East frequently calculate basic load ratings using a basic rating life based on a distance of only 50 km compared with 100 km to DIN.

Linear recirculating ball bearing and guideway assemblies

C50	N	Basic dynamic load rating C for a distance of 50 km
C100	N	Basic dynamic load rating C for a distance of 100 km – definition according to DIN 636.

Basic rating life

The basic rating life L or L_h is achieved or exceeded by 90% of a sufficiently large group of apparently identical bearings before the first evidence of material fatigue occurs.

Equivalent load and speed

The equations for calculating the basic rating life are based on the assumption that the load P and travel velocity 

are constant. Non‑constant operating conditions can be taken into consideration by means of equivalent operating values. These have the same effect as the loads occurring in practice.

Equivalent dynamic load

Where the load varies in steps, the equivalent dynamic load is calculated as follows:

Equivalent dynamic travel velocity

Where the travel velocity varies in steps, the equivalent dynamic travel velocity is calculated as follows:

Combined load

If the direction of the load acting on an element does not coincide with one of the main load directions, an approximate value for the equivalent load is calculated as follows:If an element is simultaneously subjected to a force F and a moment M, an approximate value for the equivalent dynamic load is calculated as follows:

Symbols, units and definitions

C	N	Basic static load rating in the direction of the force acting on the element
C0	N	Basic static load rating in the direction of the force acting on the element
F	N	Force acting on the element
Fy	N	Vertical component
Fz	N	Horizontal component
H	m	Single stroke length for reciprocating motion
L, Lh	km,  h	Basic rating life in 100 km or in operating hours
M	Nm	Moment acting on the element
M0	Nm	Static moment rating
nosc	min–1	Number of return strokes per minute
P	N	Equivalent dynamic load
p		Life exponent: monorail guidance systems based on balls = 3
qz	%	Duration as a proportion of the total operating time
vz	m/min	Variable travel velocity
	m/min	Equivalent dynamic travel velocity.

Operating life

The operating life is the life actually achieved by a rolling bearing or a monorail guidance system. It may differ significantly from the calculated life.

The following influences can lead to premature failure through wear or fatigue:

• deviations in the operating data
• excess load due to misalignment as a result of temperature differences and manufacturing tolerances in the adjacent construction (elasticity of the adjacent construction)
• contamination of the guidance systems
• inadequate lubrication
• operating temperature too high or too low
• reciprocating motion with very small stroke length (false brinelling)
• vibration during stoppage (false brinelling)
• overloading of the guidance system, for example by shock loads (even for short periods)
• overloading of the linear unit (even for short periods)
• impermissible shaft deflection in linear tables LTE and LTS
• preliminary damage (plastic deformation) occurring during assembly of the adjacent construction.

Static load carrying capacity

The static load carrying capacity of the monorail guidance system incorporated in driven linear units is limited by:

• the permissible load on the monorail guidance system
• the load carrying capacity of the guideway
• the mounting position
• the permissible load on the screw connections
• the permissible load on the adjacent construction.

Basic static load ratings and moment ratings

The basic static load ratings and static moment ratings are those loads under which the raceways and rolling elements undergo a permanent overall deformation corresponding to 1/10 000 of the rolling element diameter.

Static load safety factor

The static load safety factor S₀ is the security against impermissible permanent deformation at the rolling contact:

S0		Static load safety factor
C0	N	Basic static load rating in the load direction
P0	N	Equivalent static bearing load in the load direction
M0	Nm	Static moment rating in the load direction (M0x, M0y, M0z)
M	Nm	Equivalent static moment in the load direction.

The equivalent static bearing load is determined in approximate terms from the maximum loads occurring:

Track roller guidance systems

The general methods for calculating the rating life are:

• the basic rating life according to DIN ISO 281
• the adjusted rating life according to DIN ISO 281
• the expanded calculation of the adjusted reference rating life according to DIN ISO 281-4.

These methods are described in Catalogue HR1, Rolling Bearings, in the chapter Load carrying capacity and life.

Rating life of track rollers

The carriages of series MLF, MLFI and MKLF are fitted with four profiled track rollers or in some sizes with three profiled track rollers.

The track rollers are subject to the corresponding principle. The corresponding parameters are taken into consideration in the basic load ratings C, C₀ and the permissible moment ratings M_0x, M_0y and M_0z, ➤ Figure.

CI	N	Basic dynamic load rating in the y (compressive) direction
C0I	N	Basic static load rating in the y (compressive) direction
CII	N	Basic dynamic load rating in the y (tensile) direction
C0II	N	Basic static load rating in the y (tensile) direction
CIII	N	Basic dynamic load rating in the z (lateral) direction
C0III	N	Basic static load rating in the z (lateral) direction
M0x	Nm	Static moment rating about the X axis
M0y	Nm	Static moment rating about the Y axis
M0z	Nm	Static moment rating about the Z axis.

In the case of track rollers with a profiled outer ring, calculation is carried out exclusively by means of the basic rating life according to DIN ISO 281.

Rating life for carriages with four track rollers

Lh	h	Basic rating life in operating hours
CI, CII, CIII	N	Effective dynamic load rating
H	m	Single stroke length for reciprocating motion
nosc	min–1	Number of return strokes per minute
P	N	Equivalent dynamic load in the corresponding load direction (for applications with combined loads, please contact us).

Static load safety factor

The indicator of static loading is the static load safety factor S₀. It indicates the security with regard to permissible permanent deformation of the bearing.

Static load safety factor
for carriages with four track rollers

S0	N	Static load safety factor
C0	N	Basic static load rating in the load direction according to the dimension table
P0	N	Equivalent static bearing load in the load direction
M0	Nm	Permissible static moment in the x, y and z direction according to the dimension table
M	Nm	Equivalent static moment rating in the load direction (Mx, My, Mz).

Minimum load safety factors for actuators with track roller guidance systems, see tables.

Linear tables with linear ball bearings

The size of a linear table is determined by the requirements made on its load carrying capacity, rating life and operational reliability.

The load carrying capacity is described in terms of:

• the basic dynamic load rating C
• the basic static load rating C₀.

The calculation of the basic dynamic and static load ratings in the dimension tables is based on DIN 636-1.

The carriages in linear tables with linear ball bearings are each fitted with four linear ball bearings, ➤ Figure. The calculation equations for these correspond to the equations for individual bearings. The corresponding parameters are taken into consideration in the basic load ratings of the linear tables C_I, C_II and C_III, or C_0I, C_0II and C_0III, and the moment ratings M_0x, M_0y and M_0z.

Static load carrying capacity

The static load carrying capacity of the shaft guidance systems fitted in the linear tables LTE and LTS is restricted by:

• the permissible load on the linear ball bearings
• the permissible load on the adjacent construction
• the permissible deflection of the guidance shafts in linear tables LTE
• the load carrying capacity of the shaft and support rail units (aluminium support rail with screw mounted guidance shaft) in linear tables LTS
• the mounting position.

Basic static load ratings and moment ratings

The basic static load ratings and static moment ratings are those loads under which the raceways and rolling elements undergo a permanent overall deformation corresponding to 1/10 000 of the rolling element diameter.

Static load safety factor

The static load safety factor S₀ is the security against permanent deformation at the rolling contact:

S0		Static load safety factor
C0	N	Basic static load rating in the load direction C0I, C0II, C0III) according to dimension tables
P0	N	Equivalent static bearing load in the load direction
M0	Nm	Basic static moment rating in the load direction (M0x, M0y, M0z) according to dimension tables
M	Nm	Equivalent static moment in the load direction.

The equivalent static bearing load is determined in approximate terms from the maximum loads occurring:

Bearing arrangement in return units for toothed belts

The bearing arrangements in the return shaft units of actuators are dimensioned such that their operating life exceeds the operating life of the guidance systems fitted in the actuator.

For this reason, checking of the load carrying capacity and rating life of the return shaft units is only necessary in exceptional cases, such as increased preload of the toothed belt and high loads on the toothed belt.

In such cases, please contact the Schaeffler engineering service.

Support bearings for ball screw drives

Actuators and linear tables with ball screw drive are fitted on the locating bearing side with double row axial angular contact ball bearings of series ZKLF..-2RS(-PE) or axial angular contact ball bearings of series ZKLN..-2RS(-PE). Linear tables with trapezoidal screw drive are fitted with single or double row angular contact ball bearings of series 30, 33 and 72.

Basic rating life of the locating bearing arrangement

The decisive factors in determining the suitability of the linear unit for the specific application are the basic rating life, the static load safety factor and the axial limiting load of the locating bearing arrangement.

The basic rating life is calculated as follows:

L	106 Umdrehungen	Basic rating life in millions of revolutions
Ca	N	Dynamic axial bearing load
P	N	Equivalent dynamic bearing load
Lh	h	Basic rating life in operating hours
n	min–1	Operating speed.

Needle roller bearings or ball bearings are used in the non-locating bearing arrangement of the screw drive. These are adequately dimensioned such that, with correct usage, their operating life exceeds the operating life of the ball screw drive.

Resultant equivalent bearing load P for ZKLN and ZKLF

The axial angular contact ball bearings of series ZKLN and ZKLF fitted in actuators and linear tables have a defined axial preload. The resultant bearing load F_a res must be determined from the axial operating load F_aB taking account of the axial preload, ➤ Figure and ➤ Figure.

Axial and radial operating loads

If the linear unit is mounted as a vertical axis, this gives an equiv­alent dynamic bearing load P = F_a res. If it is mounted horizontally, the screw drive bearing arrangement is subjected to an additional load due to the inherent mass of the spindle. For the purposes of approximate calculation, this can be disregarded.

Load varying in steps

If the load values vary in steps, the equivalent load P and speed n are calculated as follows:

q

%

Time period.

Static load safety factor

The static load safety factor S₀ indicates the security against impermissible permanent deformations in the bearing.

In the case of driven linear units with ball screw drive, it is calculated as follows, see ➤ equation:

S0	–	Static load safety factor
C0a	N	Basic static axial load rating
P0	N	Maximum static axial load of bearing.

Permissible static axial load for ZKLF

For bearings of series ZKLF fitted in driven linear units with ball screw drive, the static axial load in the direction of the screw connections is shown in ➤ Figure.

Basic static load rating C_0a

Application-oriented static load safety factor

The static load safety factor of monorail and track roller guidance systems in actuators must not be utilised to its full extent. At all times, a minimum load safety factor S₀ must be observed, see tables.

In the case of actuators and linear tables with monorail guidance system, guidance systems with high load carrying capacity and rigidity are combined with adjacent parts made from aluminium. Since these adjacent parts are made from aluminium section or aluminium plates, the static load carrying capacity of the monorail guidance systems cannot be used to its full extent since this is only partially permitted by the screw connections.

Furthermore, geometrical inaccuracies of the aluminium parts, alignment defects in multi-axis arrangements and deformations due to load in mounting with unsupported lengths must be taken into consideration. Since it is difficult to specify these influences, minimum load safety factors determined by the application and specific to the product must be taken into consideration in the design, see tables.

Even in the case of actuators with track roller guidance systems, the load carrying capacity of the track roller guidance systems cannot be used to its full extent. In addition, the full static load carrying capacity of the track rollers cannot be supported, since the bolts in the track roller undergo deformation due to load.

Minimum load safety factor S₀

Type of actuator	Precondition	Minimum load safety factor S0
Linear actuators and linear tables	Predominantly oscillating load with stationary guidance system	20
	All load parameters are known, a linear unit supports the useful load at both ends, deflection ＜ 0,1% of the support distance	8
Linear actuators with track roller guidance system and linear tables LTE and LTS	Not all load parameters are known, heavy contamination influence, a linear unit supports the useful load over its complete surface, milled, flat screw mounting surfaces	12
	All load parameters are known, no particular contamination, a linear unit supports the useful load over its complete surface, milled, flat screw mounting surfaces	6
Actuators with monorail guidance systems	Not all load parameters are known, heavy contamination influence, a linear unit supports the useful load over its complete surface, milled, flat screw mounting surfaces	12
	All load parameters are known, smooth, vibration-free running, no particular contamination, a linear unit supports the useful load over its complete surface, milled, flat screw mounting surfaces	4
Linear tables LTP and LTPG	Not all load parameters are known, heavy contamination influence, a linear unit supports the useful load over its complete surface, milled, flat screw mounting surfaces	12
	All load parameters are known, smooth, vibration-free running, a linear unit supports the useful load over its complete surface, no particular contamination, milled, flat screw mounting surfaces	4

Minimum load safety factor S₀ for overhead suspended arrangement

Type of actuator	Precondition**	Minimum load safety factor S0
Linear actuators and linear tables	Not all load parameters are known, overhead suspended arrangement, fewer than 2 linear units support a coherent mass	20
	Not all load parameters are known, overhead suspended arrangement, at least 2 linear units support a coherent mass or all load parameters are known, overhead suspended arrangement, fewer than 2 linear units support a coherent mass	8	to	12
	All load parameters are known, overhead suspended arrangement, at least 2 linear units support a coherent mass	6	to	8

^**In the case of an overhead suspended arrangement, a drop guard is recommended.