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Rotor Deflection at Supports Calculator

Calculate permissible rotor deflection or sag at bearing supports

Calculation Parameters

Based on Roark’s formulas and machinery design standards

Metric System

Imperial System

Shaft Diameter

Span Length Between Bearings

Rotor Weight

Shaft Material

Loading Configuration

Rotation Speed

RPM

Bearing Clearance Class

Calculation Results

Maximum Static Deflection:
—

Permissible Deflection Limit:
—

First Critical Speed:
—

Safety Margin:
—

Shaft Stiffness:
—

Deflection Assessment:

Excellent: < 25% of bearing clearance

Good: 25-40% of bearing clearance

Acceptable: 40-60% of bearing clearance

Poor: > 60% – redesign recommended

How the Calculator Works

Deflection Calculation

For a simply supported shaft with center load:

δ = F × L³ / (48 × E × I)

where:

δ — maximum deflection (mm)
F — applied force (N)
L — span length (mm)
E — modulus of elasticity (N/mm²)
I — moment of inertia = π×d⁴/64 (mm⁴)

Critical Speed Relationship

The first critical speed is related to static deflection:

Nc = 946 / √δ

where Nc is in RPM and δ is in mm.

Deflection Limits

Typical permissible deflection limits:

General machinery: L/10,000 to L/5,000
Precision equipment: L/20,000 or less
Heavy machinery: L/3,000 to L/5,000
At bearings: 40-60% of bearing clearance

Loading Configurations

Uniform load: δ = 5FL³/(384EI)
Center load: δ = FL³/(48EI)
Two-point load: δ = 23FL³/(648EI)
Cantilever: δ = FL³/(3EI)

Bearing Clearance Classes

Class	Description	Typical Clearance
C0	Tight fit	0-25 μm
CN	Normal	25-45 μm
C3	Loose	45-75 μm
C4	Extra loose	75-120 μm

Design Considerations

Operating speed should be < 70% of first critical speed
Consider dynamic loading and imbalance forces
Account for thermal growth and misalignment
Include safety factor of 2-3 for critical applications
Check bearing load distribution

📘 Complete Guide: Rotor Deflection Calculator

🎯 What This Calculator Does

Calculates shaft deflection under load and critical speed. Essential for shaft design and vibration analysis.
Rayleigh formula: ncrit = 946 / √δ [RPM], where δ is deflection in mm.

💼 Key Applications

Shaft Design: Pump with cantilever impeller. Check deflection and critical speed. If ncrit close to operating speed - increase diameter.
Vibration Analysis: High vibration at 2950 RPM. Calculation shows ncrit = 2980 RPM. Cause: Resonance! Change stiffness.
Spindle Precision: Machine tool spindle. Requirement: δ < 0.01 mm for accuracy. Calculate minimum diameter needed.

Operating Regimes:

Subcritical: n < 0.7×ncrit - safest operation
Supercritical: n > 1.3×ncrit - requires fast pass through resonance
Resonance Zone: 0.7×ncrit < n < 1.3×ncrit - operation prohibited

📖 Example: Centrifugal Pump

Shaft Ø50 mm, length 400 mm between bearings
Cantilever impeller 80 kg at 120 mm from bearing
Material: Steel (E = 210 GPa)
Result: Deflection 0.18 mm, ncrit = 2230 RPM
Operating: 1480 RPM. Safety ratio: 1480/2230 = 0.66 < 0.7 ✓

Rotor Deflection at Supports Calculator | Vibromera.eu

Published by admin on October 20, 2025 October 20, 2025