Number of Bearings required given Reliability Calculator

✖Reliability of bearing system is the minimum percentage probability of 90% of a group of identical bearings system achieving their L10 design life expectancy.ⓘ Reliability of Bearing System [R_s]			+10% -10%
✖Reliability of bearing is the minimum percentage probability of 90% of a group of identical bearings system achieving their L10 design life expectancy.ⓘ Reliability of Bearing [R]			+10% -10%

✖Number of Bearings Value is defined as the number of bearings in a bearing system.ⓘ Number of Bearings required given Reliability [N_b]

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Formula

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Number of Bearings required given Reliability

Formula

`"N"_{"b"} = (log10("R"_{"s"}))/(log10("R"))`

Example

`"3.369878"=(log10("0.65"))/(log10("0.88"))`

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Number of Bearings required given Reliability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Bearings = (log10(Reliability of Bearing System))/(log10(Reliability of Bearing))
N_b = (log10(R_s))/(log10(R))
This formula uses 1 Functions, 3 Variables

Functions Used

log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)

Variables Used

Number of Bearings - Number of Bearings Value is defined as the number of bearings in a bearing system.
Reliability of Bearing System - Reliability of bearing system is the minimum percentage probability of 90% of a group of identical bearings system achieving their L10 design life expectancy.
Reliability of Bearing - Reliability of bearing is the minimum percentage probability of 90% of a group of identical bearings system achieving their L10 design life expectancy.

STEP 1: Convert Input(s) to Base Unit

Reliability of Bearing System: 0.65 --> No Conversion Required
Reliability of Bearing: 0.88 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_b = (log10(R_s))/(log10(R)) --> (log10(0.65))/(log10(0.88))

Evaluating ... ...

N_b = 3.36987838937772

STEP 3: Convert Result to Output's Unit

3.36987838937772 --> No Conversion Required

FINAL ANSWER

3.36987838937772 ≈ 3.369878 <-- Number of Bearings

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Rolling Contact Bearing » Rolling Contact Bearing Configuration » Number of Bearings required given Reliability

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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National Institute Of Technology (NIT), Hamirpur

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< 21 Rolling Contact Bearing Configuration Calculators

Radial Factor of Roller Contact Bearing given Race Rotation Factor

Go Radial Factor = (Equivalent dynamic load on bearing-(Thrust Factor for Bearing*Axial or thrust load acting on bearing))/(Race-rotation factor*Radial load acting on bearing)

Radial Load on Bearing given Race Rotation Factor

Go Radial load acting on bearing = (Equivalent dynamic load on bearing-(Thrust Factor for Bearing*Axial or thrust load acting on bearing))/(Radial Factor*Race-rotation factor)

Race Rotation Factor of Roller Contact Bearing

Go Race-rotation factor = (Equivalent dynamic load on bearing-(Thrust Factor for Bearing*Axial or thrust load acting on bearing))/(Radial Factor*Radial load acting on bearing)

Axial Thrust Load on Bearing given Race Rotation Factor

Go Axial or thrust load acting on bearing = (Equivalent dynamic load on bearing-(Radial Factor*Race-rotation factor*Radial load acting on bearing))/Thrust Factor for Bearing

Thrust factor of Bearing given Race Rotation Factor

Go Thrust Factor for Bearing = (Equivalent dynamic load on bearing-(Radial Factor*Race-rotation factor*Radial load acting on bearing))/Axial or thrust load acting on bearing

Radial Factor of Roller Contact Bearing

Go Radial Factor = (Equivalent dynamic load on bearing-(Thrust Factor for Bearing*Axial or thrust load acting on bearing))/(Radial load acting on bearing)

Radial Load on Bearing

Go Radial load acting on bearing = (Equivalent dynamic load on bearing-(Thrust Factor for Bearing*Axial or thrust load acting on bearing))/(Radial Factor)

Axial Thrust Load on Bearing given Thrust Factor

Go Axial or thrust load acting on bearing = (Equivalent dynamic load on bearing-(Radial Factor*Radial load acting on bearing))/Thrust Factor for Bearing

Thrust factor of Bearing

Go Thrust Factor for Bearing = (Equivalent dynamic load on bearing-(Radial Factor*Radial load acting on bearing))/Axial or thrust load acting on bearing

Number of Bearings required given Reliability

Go Number of Bearings = (log10(Reliability of Bearing System))/(log10(Reliability of Bearing))

Load on Bearing given Moment on bearing

Go Load Acting on Bearing = Friction moment on bearing/(Coefficient of friction for bearing*(Bore Diameter of bearing/2))

Coefficient of Friction of Roller Contact Bearing

Go Coefficient of friction for bearing = 2*Friction moment on bearing/(Bore Diameter of bearing*Load Acting on Bearing)

Friction Moment on Roller Contact Bearing

Go Friction moment on bearing = Coefficient of friction for bearing*Load Acting on Bearing*(Bore Diameter of bearing/2)

Bore Diameter of Bearing

Go Bore Diameter of bearing = 2*Friction moment on bearing/(Coefficient of friction for bearing*Load Acting on Bearing)

Reliability of Bearing

Go Reliability of Bearing = e^(-(Corresponding Life of Bearing/Constant a of Bearing)^Constant b of Bearing)

Train Wheel Diameter considering Bearing Life

Go Train Wheel Diameter = (1000/(pi*Rated Bearing Life))*Nominal Life in Millions of Kilometers

Nominal Life of Roller Contact Bearing

Go Nominal Life in Millions of Kilometers = Rated Bearing Life/(1000/(pi*Train Wheel Diameter))

Speed of Rotation of Bearing

Go Speed of bearing in rpm = Rated Bearing Life*(10^6)/(60*Rated Bearing Life in Hours)

Reliability of Bearing given Number of Bearings

Go Reliability of Bearing = Reliability of Bearing System^(1/Number of Bearings)

Reliability of Complete Bearing System

Go Reliability of Bearing System = Reliability of Bearing^Number of Bearings

Median Life of Roller Contact Bearing

Go Median Life of Bearing = 5*Rated Bearing Life

Number of Bearings required given Reliability Formula

Number of Bearings = (log10(Reliability of Bearing System))/(log10(Reliability of Bearing))
N_b = (log10(R_s))/(log10(R))

What is a rolling contact bearing?

The term rolling contact bearings refers to the wide variety of bearings that use spherical balls or some other type of roller between the stationary and the moving elements. The most common type of bearing supports a rotating shaft, resisting purely radial loads or a combination of radial and axial (thrust) loads.

How to Calculate Number of Bearings required given Reliability?

Number of Bearings required given Reliability calculator uses Number of Bearings = (log10(Reliability of Bearing System))/(log10(Reliability of Bearing)) to calculate the Number of Bearings, Number of Bearings required given Reliability is the number of bearings required in the bearing system to account for the net bearing load required. Number of Bearings is denoted by N_b symbol.

How to calculate Number of Bearings required given Reliability using this online calculator? To use this online calculator for Number of Bearings required given Reliability, enter Reliability of Bearing System (R_s) & Reliability of Bearing (R) and hit the calculate button. Here is how the Number of Bearings required given Reliability calculation can be explained with given input values -> 3.369878 = (log10(0.65))/(log10(0.88)).

FAQ

What is Number of Bearings required given Reliability?

Number of Bearings required given Reliability is the number of bearings required in the bearing system to account for the net bearing load required and is represented as N_b = (log10(R_s))/(log10(R)) or Number of Bearings = (log10(Reliability of Bearing System))/(log10(Reliability of Bearing)). Reliability of bearing system is the minimum percentage probability of 90% of a group of identical bearings system achieving their L10 design life expectancy & Reliability of bearing is the minimum percentage probability of 90% of a group of identical bearings system achieving their L10 design life expectancy.

How to calculate Number of Bearings required given Reliability?

Number of Bearings required given Reliability is the number of bearings required in the bearing system to account for the net bearing load required is calculated using Number of Bearings = (log10(Reliability of Bearing System))/(log10(Reliability of Bearing)). To calculate Number of Bearings required given Reliability, you need Reliability of Bearing System (R_s) & Reliability of Bearing (R). With our tool, you need to enter the respective value for Reliability of Bearing System & Reliability of Bearing and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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