Comprehensive Guide to Spur Gears: Definitions, Types, Profiles, Calculations & Applications

A spur gear is the most common type of mechanical gear, with a simple design. What is the profile of a spur gear, and how does it work? Here, let’s learn about spur gear definition, functions, applications, manufacturing, types, tooth profile, module, terminology, calculation formulas, dimensions chart & spur gear vs helical gear.

What Is a Spur Gear?

The spur gear is a classic gear type that consists of a cylinder or disk with straight, radially protruding teeth, which are parallel to the central rotating axis. The teeth of a spur gear can be located on the outside or inside of the cylinder. An external gear can mesh with another external gear or an internal gear. An internal gear can only mesh with one external gear. Spur gears are widely recognized for their uncomplicated shape and ease of manufacture. They can vary slightly in hub shape or thickness, but these differences do not affect the gear’s basic face or tooth design.

The most notable feature of a spur gear is its straight teeth, which mesh smoothly with the teeth of another spur gear. This design ensures efficient and reliable power transmission between parallel shafts. Since spur gears only work with parallel shafts, they do not generate any axial thrust during operation. The teeth profiles are usually involute curves, which help maintain a constant speed ratio as the gears rotate. Spur gears are commonly made from materials like steel, brass, bronze, or plastic, and can be hardened for enhanced strength and durability.

What Does a Spur Gear Do?
Functionally, spur gears transmit mechanical motion and power between two parallel shafts. By engaging the straight teeth of one gear with another (with the same pitch and pressure angle), spur gears transfer rotational movement efficiently, controlling speed, torque, and power within the system. Depending on their size and arrangement, spur gears can either increase or decrease the speed of rotation and adjust torque accordingly.

Applications and Uses of Spur Gears
Spur gears are widely used across various industries, including automotive, industrial machinery, and consumer products, because of their simplicity, cost-effectiveness, and reliability. For example, in vehicle transmissions, spur gears help transfer power from the engine to the wheels, enabling movement. Their uniform tooth load distribution leads to smooth operation and a long service life. Additionally, spur gears can be customized with different tooth profiles and sizes to fit specific application needs.

Spur Gear Manufacturing Process & Materials

• Hobbing: This is the most common method for cutting the teeth of external spur gears. A rotating cylindrical cutter called a hob gradually cuts the gear teeth as the gear blank and hob rotate in synchronization. Hobbing creates accurate tooth profiles efficiently.
• Shaping: Gear shaping uses a reciprocating cutter shaped like a gear to cut teeth into the blank. It is especially useful for internal gears or gears with special profiles.
• Planing: Planing involves a rack-shaped cutter that moves linearly against the rotating gear blank to cut the teeth. It is less common but used for specific gear sizes and shapes.
• Broaching: This technique is mainly used for cutting internal gear teeth. A broach tool with progressively larger teeth is pulled or pushed through the gear blank, producing precise internal profiles with smooth finishes.
• Milling: Milling removes excess material from the gear blank to prepare it or to cut gear teeth in low-volume or custom production. CNC milling machines use rotary cutters to shape the gear.
• Drilling: Drilling is used to create central holes or mounting holes in the gear blank.
• Deburring: After cutting, burrs on the gear teeth are removed through mechanical or manual deburring to ensure smooth operation and reduce wear.

Regarding materials, carbon steel is the most commonly used for gear manufacturing because it offers an excellent balance of machinability, wear resistance, strength, and cost-effectiveness. Carbon steel is available in grades such as mild, medium, and high carbon steel, each suitable for different strength and hardness requirements. Depending on the application, other materials like alloy steels, brass, bronze, or plastics may also be used to make spur gears.

Different Types of Spur Gears

The main categories of spur gears are external and internal. There are also other types of spur gears for specific purposes, like anti-backlash, pin hub, rack and pinion, pin hub, split hub, etc.

1. External Spur Gear
The external spur gear is the most common and simplest type, with straight teeth cut on the outside surface of a cylindrical gear. These gears mesh with other external spur gears to transmit rotary motion between parallel shafts, with the gears rotating in opposite directions. Their simple design makes them highly efficient and easy to manufacture, which is why they are found in countless gearboxes, motors, timers, and speed reducers across many industries.

2. Internal Spur Gear
Internal spur gears have their teeth cut on the inner surface of a cylindrical ring. These gears mesh with smaller external gears, causing both gears to rotate in the same direction. This configuration is often used in compact planetary gear systems and specialized drives where space is limited. Internal spur gears provide smooth torque transmission and are common in compact gear reducers and timing devices.

3. Anti-Backlash Spur Gear
Anti-backlash spur gears are designed to minimize the play, or backlash, between the teeth of gears that mesh together. Backlash is generally needed to allow for tooth deflection, thermal expansion, tolerance for tooth profile errors, and proper lubrication. However, in applications requiring high precision, minimal to zero backlash is important. Gear manufacturers have developed anti-backlash gears to meet these demands, adjusting the amount of backlash according to the load requirements. In the case of spur gears, adjustable backlash is achieved by overlapping and slightly shifting two identical gears to control the tooth thickness. These gears are commonly used and are a cost-effective way to reduce inaccuracies in low-torque gear trains.

Anti-backlash spur gears typically consist of two spur gears mounted side by side on an axle, linked by springs. The springs pull the gears against each other, creating a “pinching” effect on the mating gear. This pinching motion compensates for backlash, significantly reducing it upon installation. The precision of anti-backlash gear design makes them suitable for industries such as aerospace, robotics, and high-precision machinery. For example, high-precision telescopes utilize anti-backlash gears to ensure accuracy by eliminating gear play that could distort positioning.

4. Spur Gear Rack and Pinion
Rack and pinion systems combine a cylindrical spur gear (pinion) with a linear toothed rack to convert rotary motion into linear motion or vice versa. This setup is very useful in steering systems, CNC machines, and mechanical actuators, offering precise linear positioning and improved power transmission efficiency. Rack and pinion drives are used in automotive steering, robotics, elevators, and industrial automation.

Spur Gear Tooth Profile & Terminology Calculation Formula

Multiple parameters determine the profile or shape of spur gears, including pitch (module/diametral pitch), pressure angle, the number of teeth, and more. When viewed from the side, the tooth faces are straight and aligned parallel to the axis. When it comes to the types of spur gear teeth profiles, they come in involute and cycloidal.

• The involute profile spur gear is the most common and is widely used in modern industry. The pressure angle remains the same when the gear is working. It is favored because its shape ensures smooth and consistent transfer of motion between gears, even if the center distance between the gears changes slightly. The involute curve is generated by unwinding a taut string from a circle, and this shape helps maintain a constant pressure angle during gear rotation. An involute gear is also easier to manufacture than a cycloidal gear. 

• The cycloidal profile spur gear is an older design, often found in older or specialized equipment. Its pressure angle is always changing during the operation. The cycloidal tooth shape is based on the path traced by a point on the circumference of a rolling circle, which differs from the involute curve. While cycloidal gears can be effective, they are more sensitive to slight changes in the center distance between gears, and their manufacturing is generally more complex.

Spur Gear Tooth Profile Diagram

Gear Terminology Meaning Calculation Formula Explanation Number of Teeth (N) Total teeth count on the gear N = P × D N: Number of teeth
P: Diametral pitch
D: Pitch diameter Pitch Diameter (D) Diameter of the pitch circle where the teeth mesh D = N / DP D: Pitch diameter
N: Number of teeth
DP: Diametral pitch Diametral Pitch (DP) Number of teeth per unit pitch diameter DP = N / D DP: Diametral pitch
N: Number of teeth
D: Pitch diameter Pressure Angle (α) Angle between tooth face and tangent to pitch circle Usually 20° (common value) α: Pressure angle Module (m) The metric gear size parameter defines tooth size m = D / N m: Module
D: Pitch diameter (mm)
N: Number of teeth Reference Diameter (d) Diameter used in gear design calculations Related to module, center distance, pressure angle d: Reference diameter Face Width / Tooth Height (h) Width of gear tooth along axis of rotation h = ha + hf h: Face width / tooth height
ha: Addendum
hf: Dedendum Addendum (ha) Height of tooth above the pitch circle ha = m ha: Addendum
m: Module Dedendum (hf) Depth of tooth below the pitch circle hf = 1.25 × m hf: Dedendum
m: Module Center Distance (C) Distance between the centers of two meshing gears C = (N₁ + N₂) / (2 × DP) C: Center distance
N₁: Teeth on driving gear
N₂: Teeth on driven gear
DP: Diametral pitch Number of Teeth on Driving Gear (N₁) Teeth count on the driving gear (input gear) Used in gear ratio and center distance calculations N₁: Number of teeth on driving gear Number of Teeth on Mating Gear (N₂) Teeth count on the mating (driven) gear N₂ = (N₁ × R) / S₂ N₂: Teeth on mating gear
N₁: Teeth on driving gear
R: Gear ratio
S₂: Desired output speed Gear Ratio (mG) Ratio of driven gear teeth to driving gear teeth mG = N₂ / N₁ mG: Gear ratio
N₂: Teeth on driven gear
N₁: Teeth on driving gear Input Speed (S₁) Rotational speed of driving gear (RPM) S₁ = (S₂ / mG) × (N₂ / N₁) S₁: Input speed
S₂: Output speed
mG: Gear ratio
N₁, N₂: Teeth on driving and driven gears Desired Output Speed (S₂) Rotational speed required from the driven gear (RPM) S₂ = (S₁ × mG) / 60 S₂: Output speed
S₁: Input speed
mG: Gear ratio
60: Time conversion factor (seconds to minutes) Outside Diameter (DO) Total gear diameter, including full tooth height DO = (N + 2) / DP DO: Outside diameter
N: Number of teeth
DP: Diametral pitch Tooth Strength (S) The capacity of a tooth to withstand applied forces without failure S = (Y × K × Wt) / FOS S: Tooth strength
Y: Lewis form factor (tooth shape-based)
K: Geometry factor
Wt: Tangential force on tooth
FOS: Factor of safety

Spur Gear Dimension & Module

The module essentially measures the size of each gear tooth relative to the pitch diameter. The module directly indicates the size and thickness of gear teeth. A larger module means bigger teeth and a larger overall gear, while a smaller module means smaller teeth and a more compact gear. Two gears must have the same module to mesh correctly. If gears have different modules, their teeth will not fit together properly, causing mechanical failure. Standard modules can ensure gears properly engage without interference and allow manufacturers worldwide to produce compatible gears.

The spur gear module (denoted as m) is calculated by dividing the pitch circle diameter (d) of the gear by the number of teeth (z). The pitch circle is an imaginary circle that runs through the gear teeth where the gears effectively mesh. For example, a spur gear with a pitch diameter of 100 mm and 20 teeth will have a module of 5 (100 / 20 = 5 mm). This means each tooth corresponds to a 5 mm segment of the pitch circle diameter.

Spur Gear Size Chart

The actual gear dimensions need to be calculated by the designer based on standard tooth profile parameters, the selected module, and the number of teeth. Below are two spur gear dimension tables for reference in actual production.

1.0 Mod Spur Gear Dimensions Chart

The letters “A” and “B” in Cat.No. indicates the gear type, type A gear with 1 mod has a 25mm width, and the width of type B gear with 1 mod is 15mm.

Cat. No. No. Teeth Pitch Dia. dp Min Bore d Max. Bore Hub ⌀ C Outside Dia. D Weight kg S1012B 12 12 6 6 9 14 0.012 S1013B 13 13 6 7 10 15 0.016 S1014B 14 14 6 7 11 16 0.020 S1015B 15 15 6 8 12 17 0.025 S1016B 16 16 6 8 13 18 0.030 S1017B 17 17 7 9 14 19 0.033 S1018B 18 18 8 10 15 20 0.038 S1019B 19 19 8 10 15 21 0.045 S1020B 20 20 8 11 16 22 0.055 S1021B 21 21 8 11 16 23 0.058 S1022B 22 22 8 12 18 24 0.060 S1023B 23 23 8 12 18 25 0.065 S1024B 24 24 8 13 20 26 0.070 S1025B 25 25 8 13 20 27 0.075 S1026B 26 26 8 13 20 28 0.085 S1027B 27 27 8 13 20 29 0.090 S1028B 28 28 8 13 20 30 0.095 S1029B 29 29 8 13 20 31 0.100 S1030B 30 30 8 13 20 32 0.105 S1031B 31 31 10 16 25 33 0.110 S1032B 32 32 10 16 25 34 0.120 S1033B 33 33 10 16 25 35 0.130 S1034B 34 34 10 16 25 36 0.135 S1035B 35 35 10 16 25 37 0.140 S1036B 36 36 10 16 25 38 0.150 S1037B 37 37 10 16 25 39 0.155 S1038B 38 38 10 16 25 40 0.160 S1039B 39 39 10 16 25 41 0.170 S1040B 40 40 10 16 25 42 0.180 S1041B 41 41 10 20 30 43 0.190 S1042B 42 42 10 20 30 44 0.200 S1043B 43 43 10 20 30 45 0.210 S1044B 44 44 10 20 30 46 0.220 S1045B 45 45 10 20 30 47 0.230 S1046B 46 46 10 20 30 48 0.240 S1047B 47 47 10 20 30 49 0.250

1.5 Mod Spur Gear Dimensions Chart

The type A gear with 1.5 mod has a 30mm width, and the width of the type B gear with 1.5 mod is 17mm.

Cat. No. No. Teeth Pitch Dia. dp Min Bore d Max. Bore Hub ⌀ C Outside Dia. D Weight kg S1512B 12 18.0 8 9 14 21.0 0.03 S1513B 13 19.5 8 9 14 22.5 0.04 S1514B 14 21.0 8 12 18 24.0 0.06 S1515B 15 22.5 8 12 18 25.5 0.07 S1516B 16 24.0 8 13 20 27.0 0.08 S1517B 17 25.5 8 13 20 28.5 0.09 S1518B 18 27.0 8 13 20 30.0 0.10 S1519B 19 28.5 8 20 25 31.5 0.11 S1520B 20 30.0 8 16 25 33.0 0.13 S1521B 21 31.5 10 16 25 34.5 0.14 S1522B 22 33.0 10 16 25 36.0 0.15 S1523B 23 34.5 10 16 25 37.5 0.17 S1524B 24 36.0 10 16 25 39.0 0.18 S1525B 25 37.5 10 16 25 40.5 0.19 S1526B 26 39.0 12 20 30 42.0 0.20 S1527B 27 40.5 12 20 30 43.5 0.21 S1528B 28 42.0 12 20 30 45.0 0.22 S1529B 29 43.5 12 20 30 46.5 0.23 S1530B 30 45.0 12 20 30 48.0 0.25 S1531B 31 46.5 12 24 35 49.5 0.27 S1532B 32 48.0 12 24 35 51.0 0.28 S1533B 33 49.5 12 24 35 52.5 0.30 S1534B 34 51.0 12 24 35 54.0 0.32 S1535B 35 52.5 12 24 35 55.5 0.34 S1536B 36 54.0 12 24 35 57.0 0.36 S1537B 37 55.5 12 27 40 58.5 0.38 S1538B 38 57.0 12 27 40 60.0 0.40 S1539B 39 58.5 12 27 40 61.5 0.42 S1540B 40 60.0 12 27 40 63.0 0.45 S1541B 41 61.5 14 34 50 64.5 0.52 S1542B 42 63.0 14 34 50 66.0 0.55 S1543B 43 64.5 14 34 50 67.5 0.57 S1544B 44 66.0 14 34 50 69.0 0.60 S1545B 45 67.5 14 34 50 70.5 0.62 S1546B 46 69.0 14 34 50 72.0 0.65 S1547B 47 70.5 14 34 50 73.5 0.68 S1548B 48 72.0 14 34 50 75.0 0.70 S1549B 49 73.5 14 34 50 76.5 0.72 S1550B 50 75.0 14 34 50 78.0 0.75 S1551B 51 76.5 15 40 60 79.5 0.86 S1552B 52 78.0 15 40 60 81.0 0.87 S1553B 53 79.5 15 40 60 82.5 0.89 S1554B 54 81.0 15 40 60 84.0 0.91 S1555B 55 82.5 15 40 60 85.5 0.93 S1556B 56 84.0 15 40 60 87.0 0.95 S1557B 57 85.5 15 40 60 88.5 0.97 S1558B 58 87.0 15 40 60 90.0 1.00 S1559B 59 88.5 15 40 60 91.5 1.05 S1560B 60 90.0 15 40 60 93.0 1.10 S1561B 61 91.5 20 46 70 94.5 1.20 S1562B 62 93.0 20 46 70 96.0 1.23 S1563B 63 94.5 20 46 70 97.5 1.25 S1564B 64 96.0 20 46 70 99.0 1.27 S1565B 65 97.5 20 46 70 100.5 1.30 S1566B 66 99.0 20 46 70 102.0 1.35 S1567B 67 100.5 20 46 70 103.5 1.38 S1568B 68 102.0 20 46 70 105.0 1.42 S1569B 69 103.5 20 46 70 106.5 1.45 S1570B 70 105.0 20 46 70 108.0 1.48 S1572A 72 108.0 20 65 – 111.0 1.18 S1575A 75 112.5 20 68 – 115.5 1.28 S1576A 76 114.0 20 68 – 117.0 1.32 S1580A 80 120.0 20 72 – 123.0 1.45 S1585A 85 127.5 20 80 – 130.5 1.60 S1590A 90 135.0 20 85 – 138.0 1.85 S1595A 95 142.5 20 90 – 145.5 2.04 S15100A 100 150.0 20 95 – 153.0 2.30 S15110A 110 165.0 20 105 – 168.0 2.81 S15114A 114 171.0 20 107 – 174.0 3.30 S15120A 120 180.0 20 115 – 183.0 3.39 S15127A 127 190.5 20 120 – 193.5 3.78

Spur Gear vs Helical Gear: What Are the Differences?

Both spur gears and helical gears are commonly found in industrial applications. What are the actual differences between them?

1. Tooth Design
   Spur gears have straight teeth that are parallel to the axis of rotation, so the teeth will engage all at once along a single line when two gears mesh. In contrast, helical gears feature teeth that are cut at an angle, forming a helix shape around the gear. This angled tooth design enables the teeth to engage gradually from one end to the other.
2. Contact Pattern
   The way teeth make contact differs significantly between the two gear types. Spur gears have a line contact where one pair of teeth meshes at a time, causing sudden impact forces and higher stress on the teeth. Helical gears, however, maintain multiple teeth in contact simultaneously due to their angled teeth.
3. Axial Thrust
   Because spur gear teeth are straight and mesh along a single plane, they do not generate any axial thrust (force along the axis of the shaft). Helical gears produce an axial force as the teeth slide against each other during rotation. This axial thrust requires additional support on the shaft, such as thrust bearings, to prevent unwanted shaft movement and ensure smooth operation.
4. Noise and Vibration
   Spur gears tend to generate more noise and vibration. Helical gears operate much more quietly and smoothly. This makes helical gears preferable in applications where noise reduction is important, such as automotive transmissions.
5. Load Bearing
   Helical gears generally have a higher load-bearing capacity than spur gears. The angled teeth of helical gears create more surface contact area between mating gears, which distributes the load over multiple teeth. This leads to less wear and longer gear life. Spur gears bear the load on fewer teeth, which can lead to higher wear under heavy loads.
6. Speed Performance
   Helical gears can handle higher torque and maintain quieter operation at faster rotational speeds. Spur gears, although capable of high efficiency at moderate speeds, experience increased noise, vibration, and wear when operated at high speeds.
7. Manufacturing Complexity and Cost
   Spur gears are simpler in design and easier to manufacture. This means lower production costs and easier maintenance. Helical gears require more complex manufacturing processes involving precise angled cuts and three-dimensional motion, increasing their cost.
8. Applications and Shaft Orientation
   Spur gears are primarily used for transmitting motion between parallel shafts in simpler, lower-speed applications like clocks, washing machines, and conveyors. Helical gears can be used for parallel shafts as well, but also allow transmission between crossed or non-parallel shafts. This versatility makes helical gears suitable for automotive transmissions, aerospace, power plants, and marine propulsion systems.
9. Contact Ratio
   The contact ratio is a measure of how many teeth are in contact during gear meshing. Spur gears typically have a contact ratio between 1.2 and 1.6, meaning usually only one tooth is fully engaged at a time. Helical gears have a higher contact ratio, often exceeding 2. This higher contact ratio contributes to smoother power transmission and less vibration.
10. Efficiency
    Spur gears provide very high efficiency, especially in simpler, medium-speed applications where minimizing friction and axial forces is key, often reaching efficiencies of 98-99%. Helical gears are slightly less efficient due to sliding and axial thrust, typically ranging from 95% to 98%, but have other advantages that may justify their small efficiency penalty.