Calculating Loads and Life Expectancy in Roller Rail Systems with Bosch Rexroth

Linear rail system experts Bosch Rexroth share with us the proper definitions, calculations, and formulas to determine the life expectancy of their roller rail systems.

In Bosch Rexroth Roller Rail Systems the tracks are arranged at a pressure angle of 45°. This results in the same high load capacity of the entire system in all four main directions of loading. The Roller Runner Blocks may be subjected to both forces and load moments.

Forces in the four main directions of loading
Tension Fz (positive z-direction)
Pressure –Fz (negative z-direction)
Side load Fy (positive y-direction)
Side load –Fy (negative y-direction)

Moments
Moment Mx (around the x-axis)
Moment My (around the y-axis)
Moment Mz (around the z-axis)

Definition of load capacities

Dynamic load capacity C

The radial load (whose extent and direction does not change) that a linear anti-friction bearing can theoretically absorb for a nominal life covering 105 m (according to ISO 14 728-1).

Static load rating C0

Static load in the load direction that corresponds to a calculated load in the center of the contact point with the greatest load between the rolling element and the track zone (rail) of 4000 MPa.

Note: With this stress at the contact point, permanent overall deformation of the rolling element and the track zone occurs that corresponds to about 0.0001 times the rolling element diameter (according to DIN ISO 14 728-1).

Definition of load moment capacities

Dynamic torsional moment load capacity Mt
Comparative dynamic moment around the longitudinal axis x, which causes a load equivalent to the dynamic load capacity C.

Static torsional moment load capacity Mt0
The comparable static moment around the longitudinal axis x, which causes a load corresponding to the static load capacity C0.

Dynamic longitudinal moment load capacity ML
The dynamic comparable dynamic moment around the transverse axis y or the vertical axis z that induces a load corresponding to the dynamic load capacity C.

Static longitudinal moment load capacity ML0
The static comparable dynamic moment around the transverse axis y or the vertical axis z that induces a load corresponding to the static load capacity C0.

Definition and calculation of the nominal life
The calculated service life which an individual linear rolling bearing or a group of apparently identical rolling element bearings operating under the same conditions can attain with a 90% probability using contemporary, commonly used materials and manufacturer quality under conventional operating conditions (according to DIN ISO 14 728-1).

Nominal life in meters

(1)

Fm is the dynamic equivalent load on bearing.

Service life in operating hours with constant stroke and constant stroke repetition rate

(2)

If the stroke length s and the stroke repetition rate n are constant over the total service life, you can use formula (2) to determine the service life in operating hours h.

Nominal service life at variable travel speed

(3)

As an alternative, it is possible to use formula (3) to calculate the service life in operating hours using the average travel speed vm.

This average travel speed vm is calculated with speeds that can be changed on a stepwise basis using discrete time steps qtn of the individual load stages (4).

(4)

Modified life expectancy

If a 90 percent requisite reliability is not enough, you must reduce the service life values by a factor of a1 in accordance with the table below.

Load on bearing for calculating the service life

Combined equivalent bearing load
Using formula (5), you can combine all the partial loads that occur in a load case into one single comparison load. i.e. the combined equivalent load on bearing.

(5)

Notes
Including moments as stated in formula (5) only applies to an individual Roller Guide Rails with just one Roller Runner Block. The formula is simpler for other combinations.

The forces and moments plotted in the coordinate system can also have an effect in the opposite direction. Reduce an external load that affects the Roller Runner Block at any angle to Fy and Fz and insert the amounts into formula (5). The structure of the Roller Runner Block permits this simplified calculation.

Considering the internal preload force Fpr
To increase the rigidity and precision of the guide system, it is advisable to use pre-tensioned Roller Runner Blocks (cf. “System preload selection criterion”).

When using Roller Runner Blocks of preload classes C2 and C3, it may be necessary to consider the internal preload force; this is because both rows of rollers a and b are pre-tensioned against one another by a specific oversize at an internal preload force Fpr and deform by the amount δpr (see the diagram).

a = Loaded (lower) row of rollers
b = Non-loaded (upper) row of rollers
δ = Deformation of the rollers at F
δpr = Deformation of the rollers at Fpr
F = Load on the Roller Runner Block
Fpr = Internal preload force

Effective equivalent load on bearing
From an external load amounting to 2.8 times the internal preload force Fpr onward, a row of rollers becomes preload-free.

(6)

Case 1 Fcomb > 2.8 · Fpr
In this case, the internal preload force Fpr does not affect the service life.

(7)

Case 2 Fcomb ≤ 2.8 · Fpr
The preload force Fpr is included in the calculation of the effective equivalent load on bearing.

Note
Under highly dynamic load conditions, the combined equivalent bearing load should be Fcomb < 2.8 · Fpr to prevent damage to anti-friction bearings due to slippage.

Dynamic equivalent load on bearing
The determination of the dynamic equivalent load on bearing Fm for the calculation of the service life is implemented according to track ratios qsn according to formula (8).

(8)

Equivalent static load on bearing
With a combined vertical and horizontal external static load in conjunction with a static torsional or longitudinal moment, calculate the static equivalent load on bearing F0 comb according to formula (9).

(9)

Notes
The static equivalent load on bearing F0 comb must not exceed the static load capacity C0. Formula (9) only applies when using a single Roller Guide Rail.
Reduce an external load that affects the Roller Runner Block at any angle to F0y and F0z and insert the amounts into formula (9).

Definitions and calculation for dynamic and static load ratios
Using the ratio of load rating to load of the Roller Runner Block, you can make a preselection of the guideway. The dynamic loading ratio C/Fmax and the static loading ratio C0 /F0 max should be selected according to the application. The necessary load ratings are calculated from this. The load rating overview yields the corresponding dimensions and format.

Recommended values for load ratios
The table below contains guideline values for the load ratios.
The values are offered merely as a rough guide reflecting typical customer requirements (e.g. service life, accuracy, rigidity) by sector and application.

Case 1: Static load F0 max > Fmax:

Case 2: Static load F0 max < Fmax:

Static load safety factor S0

You must verify mathematically any structural design involving rolling contact with regard to the static load safety factor. The static load safety factor for a linear guide results from the following equation:

(10)

In this connection, F0 max represents the maximum load amplitude that can occur, which can affect the linear guide. It does not matter whether this load is exerted only for a short period. It may represent the peak amplitude of an overall dynamic loading. For dimensioning, the data shown in the table applies.

Every application is unique and requires special attention to load capacities. Working out these calculations can help you select the right linear guide for your application providing longer life to your linear guide and machines.

Check out MISUMI’s selection of Bosch Rexroth linear guides here.

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One Comment


  1. Dilip

    June 5, 2021 at 3:43 am

    Hi Carlicia seen your article about force analysis. It is helpful.
    I request you to give such type of knowledge.
    I m also BE mech
    Thanks

    Reply

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