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Uma engrenagem cilíndrica transmite potência entre dois eixos paralelos e é o tipo de engrenagem mais básico. Este guia explica como escolher o módulo, o número de dentes, o furo e a largura, as fórmulas das dimensões principais (diâmetros primitivo, externo e de raiz), por que engrenagens que engrenam precisam ter o mesmo módulo e dicas de impressão 3D, incluindo por que menos de 17 dentes não é possível (interferência).

Two spur gears with 20 and 40 teeth (module 2) shown side by side from above

Guia de engrenagem cilíndrica: módulo, dentes, furo e largura

Publicado 2026-06-03 7 min de leitura

A spur gear is the most basic type of gear, transmitting rotation and power between two parallel shafts. With teeth cut straight and parallel to the axis, it is simple to design and manufacture, and is used in applications ranging from robots and DIY projects to 3D-printed mechanisms. With meta-matic's spur gear generator you only specify four values — module / number of teeth / bore diameter / face width — to produce a 3D model. This guide covers the basic structure of spur gears, how to choose the module, teeth, bore, and face width, how to calculate key dimensions such as the pitch circle diameter, and tips for 3D printing.

What is a spur gear?

A spur gear uses a smooth curve called the involute for its tooth profile. The involute profile keeps the speed ratio constant as two meshing gears rotate and tolerates small errors in center distance, which is why it has become the mainstream for mechanical gears. Two meshing spur gears rotate in opposite directions.

Fig. 1: Meshing spur gears rotate in opposite directions (20T × 40T, module 2)

meta-matic's spur gear generator holds fixed parameters internally — 20° pressure angle, addendum 1.0m, dedendum 1.25m, and 0 backlash — and produces shapes conforming to the JIS B 1701-1 / ISO 53 standard basic rack tooth profile.

Engrenagem cilíndrica GeradorSPUR GEARhttps://meta-matic.com/pt/3d/spur-gear/

Positioning as a reference model

This tool generates gear geometry based on standard tooth proportions and should be regarded as a reference model. Because values such as the pressure angle and backlash are fixed, for precision applications or when combining with off-the-shelf gears, always verify the meshing with the mating gear on the actual machine or in CAD.

How to choose the module

The module (symbol m) is the standard value that determines tooth size; it relates to the pitch circle diameter by d = m × z (module × number of teeth). A larger module means larger, stronger teeth, while a smaller module means finer, more compact teeth. The most important rule is that meshing gears must have the same module. As a rough guide: 0.5–1 for small devices, 1–2 for robots and DIY, and 3 or more for high-torque uses. How to decide the module and how to mesh with off-the-shelf gears are explained in detail in the related article.

モジュールの異なるラックギアを2つ並べた比較画像（module 1.0 / 3.0）

Módulo de engrenagem explicado — Como escolher para impressão 3D e DIYhttps://meta-matic.com/pt/learn/gear-module/

How to choose the number of teeth

The number of teeth can be set in the range 17–120. It is the most fundamental parameter governing the gear's outer diameter and reduction ratio. For the same module, fewer teeth make the gear smaller and more compact, while more teeth make it larger and make it easier to achieve a large reduction ratio with the mating gear.

Spur gears with 20, 40, and 80 teeth (module 2) side by side showing the difference in outer diameter — Fig. 2: Even at the same module (m=2), more teeth means a larger outer diameter

Fewer teeth (17–20): small and compact; often used as a pinion (small gear) on the driving side
More teeth (40+): larger diameter and easier to get a large reduction ratio; suited to the larger driven gear
Gear ratio: for one gear pair it is determined by "driven teeth ÷ driving teeth"

Why fewer than 17 teeth cannot be made (undercut)

With a standard, non-profile-shifted involute gear at a 20° pressure angle, when the tooth count drops below about 17, the cutting tool removes too much of the tooth root, causing undercut that makes the root thin and weak. Based on this limit, the generator sets the minimum to 17 teeth. If you truly need fewer teeth, a different method such as a profile-shifted gear is required.

How to choose the bore diameter

The bore diameter is set from 0 to 100 mm; specifying 0 produces a spur gear with no bore. Basically match it to the shaft diameter. As a starting point, increasing the bore diameter by approximately 0.1–0.2 mm can compensate for typical FDM printing tolerances and make the shaft easier to insert after printing.

Bore 3–5 mm: common for small motors and hobby shafts
Bore 6–8 mm: medium mechanisms and metal shafts
Bore = 0 (solid center): choose when you want to machine it later in CAD

Using a keyway or D-cut shaft

The generator supports only circular bores. To fit special shapes such as a keyway or D-cut shaft, generate with a bore of 0 and post-process in CAD software such as Fusion 360 or FreeCAD.

How to choose the face width

The face width can be set in the range 1.0–50 mm. A wider face increases the tooth contact area and the transmittable torque, but it also adds weight and lengthens 3D-printing time. As a guide, a face width of about 6–10 times the module (e.g. 12–20 mm for m=2) balances strength and practicality well.

20-tooth spur gears with face widths of 5, 10, and 20 mm side by side showing the difference in thickness — Fig. 3: A wider face increases strength but adds weight and printing time

Narrow face: light and fast to print, but low transmittable torque
Wide face: higher strength and torque, but heavier and slower to print

Calculating key dimensions

The key dimensions of a spur gear can be calculated from just two values: the module m and the number of teeth z. meta-matic's generator screen also shows the pitch circle diameter and other values automatically as you enter inputs.

Name	Symbol	Formula	Example (m=2, z=20)
Pitch circle diameter	d	`m × z`	40.00 mm
Tip circle diameter	Da	`m × (z + 2)`	44.00 mm
Root circle diameter	Df	`m × (z − 2.5)`	35.00 mm
Circular pitch	p	`π × m`	6.28 mm

Table 1: Key dimensions of a spur gear (20° pressure angle, standard profile)

Line drawing of a module-2, 20-tooth spur gear used to explain the circle names — Fig. 4: Positional relationship of the tip, pitch, and root circles

Tip circle (Da): the circle through the tooth tips; corresponds to the outer diameter
Pitch circle (d): the reference circle for meshing; the central dimension in gear design
Root circle (Df): the circle through the tooth roots (bottoms)

The center distance between two meshing spur gears is given by a = m × (z1 + z2) ÷ 2. For example, meshing a 20-tooth and a 40-tooth gear at m=2 gives a center distance of 2 × (20 + 40) ÷ 2 = 60 mm.

How to generate a STEP file

meta-matic's spur gear generator lets you download a STEP file instantly just by entering parameters in your browser.

Decide the module
Choose the same module as the gear it will mesh with. If used on its own, decide the module from the required strength and size.
Decide the number of teeth
Decide from the required reduction ratio and outer diameter. You can check the gear ratio of the driving and driven sides with the gear ratio calculator.
Decide the bore and face width
Enter the bore to match the shaft diameter and the face width to match the required torque. For 3D printing, make the bore slightly larger.
Generate and download in the generator
Enter the values above and press "Generate STEP file" to download the STEP file automatically.
Open and check in CAD
Open it in Fusion 360 / SolidWorks / FreeCAD and verify the center distance and meshing with the mating gear in an assembly.

Engrenagem cilíndrica GeradorSPUR GEARhttps://meta-matic.com/pt/3d/spur-gear/

Notes on 3D printing

Spur gears have a relatively simple tooth profile and are well suited to 3D printing, but tooth-face accuracy governs how smoothly they mesh. Keep the following points in mind to print practical gears.

Material: PLA or PETG for general use; Nylon and similar for high-load uses
Print orientation: printing with the gear axis aligned with the Z-axis makes the tooth profile perpendicular to the layers, improving accuracy
Shrinkage: specify the bore +0.1 to 0.2 mm larger and finish with a reamer if needed
Layer height: 0.16 mm or less makes the tooth faces smoother and reduces meshing noise

If meshing is noisy or binds

The main causes of noise or binding are insufficient backlash, shaft misalignment, and print accuracy. Re-check the center distance with the mating gear; if the tooth faces are rough, a finer layer height can help.

Frequently asked questions

QDo gears with different modules mesh?

No. Tooth size is determined by the module, so the two meshing gears must have the same module. See the related article "What is gear module?" for details.

QDo gears mesh even with different numbers of teeth?

As long as the module is the same, gears mesh even with different tooth counts. The difference in teeth becomes the reduction ratio directly. For example, a 20-tooth and 40-tooth combination gives a reduction ratio of 2.

QCan I make a spur gear with fewer than 17 teeth?

Not with this generator. With the standard profile at a 20° pressure angle, below 17 teeth undercut occurs and weakens the tooth root, so the minimum is set to 17 teeth.

QAre 3D-printed spur gears practical?

For low-speed, low-load uses they are perfectly practical. Spur gears printed in PLA or PETG are widely used in hobby robots and prototypes. However, for high-speed, high-load, or continuous operation the tooth faces wear faster than metal gears.

QCan I edit the generated STEP file in Fusion 360 or FreeCAD?

Yes. The output is standard STEP format, so you can open it in major CAD software such as Fusion 360, SolidWorks, or FreeCAD to machine the bore, add a boss or keyway, and so on.

Related resources

Here are gears often combined with spur gears and calculation tools useful for design. Use them as needed.

Rack gear generator — for building rack-and-pinion mechanisms
Gear ratio calculator — automatically calculates the reduction ratio from the driving and driven tooth counts