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MODULE 4 OF 8

Understanding Gearing, Selecting Gears

5 units · approx. 35 minutes total · Step 1 of 8

Getting Started

This module covers gear technology, from geometry to selection criteria: How are the module, reference circle, and center distance related? What is an involute, and why is the pressure angle almost always 20°? And when is helical gearing preferable to spur gearing?

The final step is the practical selection process: material, gear quality, and the decision between a catalog part and a custom-made part. Calculation exercises, a selection exercise, flashcards, and a case study bring the theory to life; a self-test at the end shows whether you’ve mastered the material.

Learning Objectives – After completing this module, you will be able to:

  • Calculate the pitch diameter, head/foot circle, and center distance based on the module and number of teeth;
  • Explain involute gearing, pressure angle, operating pitch circle, and profile shift in a technically accurate manner;
  • Distinguish between straight and helical gearing based on running smoothness, load capacity, and axial force;
  • Select gear materials and gear quality grades appropriate for the application;
  • Select an appropriate gear based on a given set of requirements.

Learning units

Five short learning units (6–8 minutes) with learning objectives, examples, and knowledge checks—standalone learning content for this module, maintained independently of the website’s guides. Progress is saved locally in this browser.

0 of 5 units

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Computer Exercise 1: Gear Geometry

A pinion with m = 2 mm and z₁ = 20 meshes with a gear with z₂ = 40.

Calculate the pitch diameter d₁ of the pinion and the center distance a.

For verification: Gear geometry calculator (opens in a new tab)

Calculation Problem 2: Rack Feed

A rack with a module of m = 3 mm is driven by a pinion with z = 20 teeth.

Calculate the feed per gear revolution (in mm).

For verification: Rack-and-pinion calculator (opens in a new tab)

Selection Exercise: Identify the type of gear teeth

Use the website’s gear type wizard to solve the problem—it asks for shaft configuration, load, speed, noise level, and budget, and provides a well-reasoned recommendation.

Assignment

Determine the gear type for a conveyor belt drive: The shafts are parallel, the belt runs at high speed in a factory with workstations nearby (noise is a factor), and the goal is to transmit as much torque as possible. Use the wizard to check whether straight or helical gearing is recommended—and whether this aligns with what you learned in Learning Units 2 and 3 about smooth operation, load capacity, and axial force.

Go to the Gear Type Wizard (opens in a new tab)

Flashcards: Gear Terminology

Eight technical terms from the glossary—click on the card (or press Enter or the spacebar) to see the definition.

Flashcards

Tap to see the definition.

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Modules (m)
Ratio of pitch diameter d to number of teeth z: m = d/z (mm). Determines the tooth size and is standardized according to DIN 780. Two gears mesh only if they have the same module. Source: Glossary “Modules (m)”
Reference circle
Pitch circle of a single gear with d = m·z. It separates the tooth tip from the tooth root and is a fixed geometric property—independent of the gear pairing. Source: Glossary “Reference circle”
Operating pitch circle
A circle on which two meshing gears roll without slippage during operation. For standard gearing, it coincides with the reference circle; in the case of profile shift, it differs from it. Source: Glossary “Operating pitch circle”
Pressure angle (α)
Angle between the line of contact and the tangent to the operating pitch circle at the rolling point. Standard value of 20° according to DIN 867—a compromise between tooth strength, overlap, and bearing forces. Source: Glossary “Pressure angle (α)”
Involute gearing
A standard tooth profile whose flank follows the involute of the base circle. It maintains a constant gear ratio even with slight variations in center distance and can be manufactured cost-effectively. Source: Glossary “Involute gearing”
Profile shift
Offset of the tool reference profile by x·m during gear cutting. This prevents undercut with a small number of teeth and specifically adjusts the center distance. Source: Glossary “Profile shift”
Undercut
Unintended material removal at the tooth root when the number of teeth is too small (below z ≈ 17 at a 20° pressure angle). This weakens the tooth—solution: profile shift or more teeth. Source: Glossary “Undercut”
Backlash (j)
Distance between the load-bearing and non-load-bearing tooth flanks in mesh. Necessary for lubrication and thermal expansion; too large causes backlash, too small leads to jamming. Source: Glossary “Backlash (j)”

Case Study: A Quiet Drive for a Laboratory Device—Straight or Angled?

A customer in the laboratory technology sector is developing an analytical instrument with a small helical gearbox located directly next to the operator’s station. The instrument operates continuously at moderate to medium speeds. Noise levels are a key selling point, as the device is located in the same room as the lab staff. The designer has always used straight-toothed spur gears because they are easier to manufacture and more cost-effective, but is unsure whether this is still the right choice for this device. A switch to helical gearing would generate additional axial bearing forces, requiring the shaft bearings to be redesigned.

Key Questions

  1. Which of the two designs is generally quieter, and why?
  2. What disadvantage does the designer accept when using helical gearing, and how can this disadvantage be remedied without changing the type of gearing?
  3. Is there a situation in which spur gearing would remain the better choice despite noise requirements?
View Worked Solution

1. Helical gearing operates significantly more quietly: The inclined tooth profile ensures a smooth, progressive tooth engagement rather than the abrupt contact found in spur gearing—thereby preventing shocks and the resulting noise.

2. The disadvantage is the resulting axial force that the shaft bearings must absorb. Without changing the type of gearing, this can only be solved using helical-bevel gearing: Two mirror-image tooth halves cancel out the axial forces—though this requires more complex manufacturing.

3. Yes: If manufacturing costs and design simplicity are the top priorities and noise is only a secondary consideration, or if the bearing design cannot accommodate any axial force and helical gearing is not economically feasible, spur gearing would remain the more pragmatic choice despite its higher noise levels.

Technical basis exclusively: Helical gearing vs. spur gearing (opens in a new tab)

Self-test

10 questions about this module—immediate feedback with explanations and source links. The module is considered complete if you score 7 out of 10 points or higher.

Self-test

10 questions for this module. You see right after each answer whether it was correct.

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Before each answer, you state how confident you feel. This helps distinguish knowledge gaps from uncertainty. It has no effect on the score.

Question 1 of 10

Question 1 of 10

What is the formula for the module m of a gear?

Explanation

The module is the quotient of the pitch diameter d and the number of teeth z: m = d / z. It is the key parameter of any gear system.

Source: Calculate Gear Module →
Question 2 of 10

A gear has a pitch circle diameter d = 90 mm and a number of teeth z = 30. What is the module m in mm?

mm
Explanation

m = d / z = 90 / 30 = 3 mm.

Source: Calculate Gear Module →
Question 3 of 10

Which of the following values belongs to the DIN 780 Series 1 (preferred modules)?

Explanation

Series 1 according to DIN 780 includes, among others, 1·1.25·1.5·2·2.5·3·4·5·6 mm. 1.375 and 2.75 belong to the alternative Series 2; 3.6 is not standardized.

Source: Calculate Gear Module →
Question 4 of 10

What does the fundamental law of gearing state for involute gears?

Explanation

The common normal to the tooth flanks of two meshing involute gears is always tangent to both base circles—this fixes the rolling point, and the gear ratio remains constant even if the center distance varies slightly.

Source: Gear Technology: Basic Concepts →
Question 5 of 10

What effect does a larger pressure angle (e.g., 25° instead of 20°) have on involute gearing?

Explanation

A larger pressure angle increases the load-carrying capacity and lowers the undercut limit, but also generates higher bearing forces—which is why 20° remains the standard compromise in general mechanical engineering.

Source: Gear Technology: Basic Concepts →
Question 6 of 10

Which statements about helical gearing are correct? (Multiple choice)

Explanation

Helical gearing runs more quietly and can handle up to about 30% more load (higher total overlap)—but in return, it generates an axial force that the bearings must absorb. The last two statements are incorrect.

Source: Helical Gearing vs. Spur Gearing →
Question 7 of 10

Which material is manufactured using powder metallurgy to closely match the final contours and is particularly suitable for high-volume production?

Explanation

Sintered metal is manufactured using powder metallurgy to a shape close to the final contour—the teeth are formed directly during the pressing process without time-consuming machining, making it cost-effective for high-volume production. Its load-bearing capacity lies between that of plastic and hardened steel.

Source: A Comparison of Gear Materials →
Question 8 of 10

According to the learning unit, which gear quality class per DIN 3961/3962 (internationally ISO 1328-1; the classes there are only approximately comparable) is typically suitable for automotive applications and automotive transmissions?

Explanation

Levels 7–8 are for automotive applications and automotive transmissions. Levels 5–6 are for high precision (robotics, measurement technology), 9–10 for material handling, and 11–12 for heavy-duty manufacturing.

Source: Gear Technology: Basic Concepts →
Question 9 of 10

A rack with a pinion module m = 2 mm and number of teeth z = 25 moves a distance of s = π · m · z mm per revolution of the pinion. What is the value of s in mm?

mm
Explanation

s = π · m · z = π · 2 · 25 ≈ 157.08 mm.

Source: Rack-and-Pinion Calculator →
Question 10 of 10

How can a precisely specified center distance be achieved for a pair of spur gears without changing the module or the number of teeth?

Explanation

A targeted profile shift on one or both gears adjusts the center distance without changing the module or number of teeth—it also prevents undercut in gears with a small number of teeth.

Source: Selecting the Right Gear →

Advanced Topics (optional)

The website’s five gearing guides, in case you’d like to delve deeper into the subject. Reading them is not required for the learning units and self-test in this module.

Curriculum v0.1 (Beta) · As of 17.09.2026 · content carefully prepared and reviewed – final sign-off to follow

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