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SPUR GEAR

How Engineers Calculate It
Design Formula Calculation Manufacturing
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Definition

What Is a Spur Gear?

A cylindrical gear with straight, parallel teeth used to transmit rotational motion and power between parallel shafts.
Straight teeth Parallel shafts Power transmission
The simplest and most common gear type.
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Benefits

Why Spur Gears?

⚙️ Simple design
📈 High efficiency
🔧 Easy manufacturing
➡️ No axial thrust
🏭 Widely used
💰 Cost-effective
The workhorse of mechanical power transmission.
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Mechanism

How Does It Work?

1 Driver gear rotates
2 Teeth engage
3 Force transfers through tooth contact
4 Driven gear rotates at determined ratio
i = z₂ / z₁
Gear ratio = Driven teeth ÷ Driver teeth
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Essential Formulas

5 Formulas Every Engineer Uses

m = d / z
Module
d = m × z
Pitch diameter
dₐ = m × (z+2)
Outside diameter
d_f = m × (z−2.5)
Root diameter
i = z₂ / z₁
Gear ratio
Reference: AGMA 2001, ISO 6336, DIN 3990
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Force Analysis

Torque → Tooth Force

Ft = 2T / d
Tangential force from torque & pitch diameter
⚡ Torque → Gear → Tooth Force
Critical for tooth strength calculations.
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Worked Example

Real Calculation

z₁ 20 teeth
z₂ 60 teeth
module 3 mm
d₁
60 mm
d₂
180 mm
3:1 REDUCTION
Center distance: 120 mm
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Production

How It's Made

⬇ Raw material
⬇ Gear cutting (hobbing / shaping / milling)
⬇ Heat treatment
⬇ Finishing (grinding)
⬇ Inspection
Hobbing Shaping Milling Broaching Grinding
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Applications

Where Are They Used?

🚗 Automotive
🏭 Industrial machinery
🤖 Robotics
🏠 Consumer appliances
🏥 Medical equipment
✈️ Aerospace
🌿 Renewable energy
⚙️ Gearboxes
Everywhere motion and power are transmitted.
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Failure Analysis

Why Do Gears Fail?

⚡ Bending fatigue
🔴 Pitting
🟠 Spalling
⚪ Wear
💥 Tooth breakage
↔️ Misalignment
🧴 Lubrication failure
Prevention starts with proper design and maintenance.
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Maintenance

Engineer's Checklist

✓ Check lubrication
✓ Inspect tooth surfaces
✓ Check backlash
✓ Verify alignment
✓ Monitor noise / vibration
✓ Check wear
✓ Replace severely damaged gears
Regular inspection extends gear life.
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Calculate Your Spur Gear

Enter module, teeth, face width and torque to calculate key gear parameters.
Open Spur Gear Calculator Read the Full Spur Gear Guide →
Share this with a machinist or mechanical engineer.
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