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Mechanical EngineeringPower Transmission

Shaft & Bearing Workspace

Determine equivalent stress, bending deflection, structural safety factors, and L10 bearing life based on operational torque, point loads, and rotational speed.

Von Mises Yield CriterionL10 Fatigue LifeEuler-Bernoulli Beam Theory

Engineering Schematic

Shaft & Load Geometry

ShaftBearing
STRUCTURAL DIAGRAMF = 4500 NR₁R₂TL = 600 mmLb = 500 mm

Shaft Geometry

Dim
mm

Shaft OD

mm

Total length

mm

Distance betw. supports

Operational Loads

Forces
N·m

Transmitted torque

N

Central point load

rpm

Rotational speed

Material & Bearings

MPa

Material limit

N

Bearing capacity

Calculated Results

Stress & Deflection

Eq. Stress (Von Mises)

95.9MPa

Max combined stress

Safety Factor

4.17

Against yield (Sy)

Max Deflection

0.466mm

Central displacement

Bending Stress

89.5MPa

Normal stress component

Shear Stress

19.9MPa

Torsional component

Bearing Load

2250N

Per bearing (R1=R2)

Fatigue Analysis

L10 Bearing Life

31.964hrs

90% reliability metric

Load Ratio (C/P)

14.22

Dynamic rating margin

Engineering Check

No Basic Warnings

The current shaft dimensions, material, and bearing selection fall within generally acceptable structural and fatigue ranges. Verify dynamic resonance and detailed localized stress concentrations separately.

Engineering Relations

Governing Formula

σv = √(σb² + 3τ²)
σvMPa

Eq. Stress

σbMPa

Bending

τMPa

Shear

Governing Formula

δ = (F·L³) / (48·E·I)
δmm

Deflection

FN

Load

EMPa

Modulus

Governing Formula

L10 = (10⁶ / 60n) · (C/P)³
L10hrs

Life

nrpm

RPM

CN

Dyn. Rating

Governing Formula

FS = Sy / σv
FS-

Safety Factor

SyMPa

Yield Strength

σvMPa

Eq. Stress

Fundamentals of Shaft and Bearing Design

Designing a power transmission shaft requires ensuring that the mechanical component can safely transmit torque while supporting transverse loads (such as those from gears, pulleys, or sprockets) without experiencing permanent deformation, excessive vibration, or fatigue failure.

Equivalent Stress and Failure Theories

Shafts are typically subjected to multiaxial loading states: torsion from power transmission and bending from transverse loads. To evaluate the safety of the shaft, engineers use the Von Mises Equivalent Stress, which combines normal and shear stresses into a single value that can be directly compared against the material's yield strength to find the Safety Factor (FS).

Deflection and Bearing Life

Even if a shaft is structurally safe against yielding, excessive Deflection can cause gear misalignment and rapid bearing wear. Simultaneously, the bearings supporting the shaft must be evaluated for fatigue. L10 Bearing Life predicts the operational hours before 10% of a sample group of bearings show signs of fatigue spalling, heavily dependent on the operational RPM and the ratio of the dynamic load rating to the applied equivalent load.

Frequently Asked Questions

What is Equivalent Stress in shaft design?

Equivalent stress (often Von Mises stress) combines the normal stresses from bending and the shear stresses from torsion into a single value. This allows engineers to compare complex multiaxial loading states directly against the material's one-dimensional yield strength to ensure the component will not plastically deform.

How is Bearing Life (L10) calculated?

L10 bearing life is the number of hours that 90% of a group of identical bearings will exceed before fatigue failure. It is calculated using the bearing's dynamic load rating (C), the equivalent applied load (P), and the operational speed (RPM). For ball bearings, the relationship is cubic; doubling the load reduces the life by a factor of eight.