SPUR GEAR DESIGN: Manufacturing, Quality & Measurement.


The spur gear is one of the most basic types of gears and spur gear design is not that complicated.

Its teeth are straight and parallel to the axis of the shaft that supports the gear.  

The teeth have the described involute shape.  

Therefore, in general, the action of a tooth on a mating tooth is similar to the action of two convex curved parts in contact. 

As the drive gear rotates, it exerts force on the mating gear whose teeth touch the pitch circle of two gears.  

This force acts at a distance equal to the pitch radius of the gear, creating torque on the shaft that supports the gear.  

When the two gears rotate, a force proportional to the torque is transmitted. Indeed, this is the main purpose of spur gear drive systems.  


Gear manufacturing begins with the process of blanking gears.  

Small gears are often made from wrought plate or bars, and hubs, webs, spokes, and rims are machined to final or near-final dimensions before gear teeth are manufactured.  

At this stage, the width of the tooth and the outer diameter of the tooth are also generated.  

Other gear blanks can be forged, sand cast, or die cast to achieve the basic shape before machining. Some gears, which require only moderate precision, can be die-cast with teeth in near net shape.  

Large gears are often made from individual parts.  

The processed parts of the rim and teeth can be rolled into a ring from the flat bar and welded.  

The web or spokes and hub are then welded inside the ring.  

Very large gears can be manufactured in segments by finally assembling the segments by welding or mechanical fasteners.  

Using a milling machine shaped like a tooth space, cut each space completely before indexing the gear blank to the next adjacent space position.  

This method is mainly used for large gears and requires great care to obtain accurate results.  

Shaping is the process by which the cutter moves back and forth, usually on a vertical spindle.  

The shaping cutter rotates while reciprocating and is inserted into the gear blank.  

In this way, involute tooth profiles are gradually generated.  

This method is often used for internal gears.  

Hobbing is a process similar to a milling machine, except that the workpiece (gear blank) and cutter (hob) rotate in concert.  

Hob for small pitch gears having large teeth
Hob for small pitch gears having large teeth

Again, when the hob is thrown into the blank, tooth profile is continuously generated.  

Gear teeth are more accurately finished by grinding, shaving, and honing after form milling, forming, or honing.  

Form milling cutter
Form milling cutter

Since they are secondary process products, they are expensive and should only be used if the operation requires high precision in tooth shape and spacing.  


Gear quality is the accuracy of a particular characteristic of an individual gear, or the combined error of a gear that rotates in mesh with an accurate master gear.  

The factors that are usually measured to determine quality are:  

Index Deviation: The difference between the actual position of a point on the tooth surface of the gear on the pitch circle and the corresponding point on the reference tooth measured on the pitch circle.  

This variation causes the teeth of the meshing gears to behave incorrectly.  

Tooth alignment: Deviation of the actual line of the tooth surface of the gear in a pitch circle from the theoretical line.  

Measurements are made end-to-end across the face.  

For spur gear design, the theoretical line is a straight line. In helical gears, it is part of the helical. 

Spur gear shaper cutter
Spur gear shaper cutter

Tooth alignment measurement is sometimes called spiral measurement.  

This is important because excessive misalignment puts an uneven load on the gear teeth.  

Tooth profile: Measurement of the actual profile of the tooth surface of the gear from the starting point of the active profile to the tip of the tooth.  

The theoretical profile is a true involute curve.  

The deviation of the actual profile from the theoretical profile causes the deviation of the instantaneous velocity ratio between the two gears in the mesh, which affects the smoothness of movement.  

Root radius: The radius of the fillet at the base of the tooth.  

Deviations from the theoretical values ​​can affect the meshing of the meshing gears, create the possibility of interference and affect the stress concentration factor associated with the bending stress of the teeth.  

Runout:  A measure of gear eccentricity and runout.  

If the runout is too large, the contact points of the meshing gear teeth will move radially during each rotation.  

Total Composite Variation: A measure of the variation related to the center distance of one revolution between the exact master and test gears.  

The shaft of one gear is fixed, and the shaft of the mating gear can move freely with the teeth in close contact.  


The actual tooth shape tolerance, or compound deviation, from the theoretical shape is designated as a quality number by AGMA (American Gear Manufacturers Association).  

Detailed charts showing many functional tolerances are included in the AGMA Standard 2000-A88 Gear Classification and Inspection Handbook, Unassembled Spur and helical gear tolerances and measurement methods. 

Quality numbers range from 5 to 15 for higher accuracy.  

Actual tolerances are a function of figure of merit, gear tooth diameter pitch, and gear tooth count.  

The International Organization for Standardization (ISO) defines the accuracy of cylindrical gear ISO systems in its standard 1328-1-1995.  

These standards are very different from the AGMA standard 2000-A88.  

The main difference is that the quality numbering system is reversed. In AGMA standard 2008, the higher the number, the higher the accuracy, but in the ISO standard, the smaller the number, the higher the accuracy.  

The tangential measurement of cylindrical gears employs a system similar to the ISO method but not identical, with lower orders and lower tolerances.  


Two different approaches are used to determine gear quality, functional measurements, and analytical measurements.  

Functional measurements typically use a system to measure the overall combined error.  

The change in pitch is recorded for each revolution.  

The sum of the compound fluctuations is the maximum range between the highest and lowest points on the chart.  

In addition, the maximum spread on the chart of two adjacent teeth is determined as a measure of the variation in the composite resin between the teeth.  

The runout can also be determined from the deflection of the centerline of the entire graph.  

Based on this data, the AGMA figure of merit can be determined primarily on the basis of total composite variation and is often considered sufficient for general purpose gears in industrial machinery.  

Analytical CD measurements measure individual errors in index, alignment (helix), involute profile, and other features.  

The device is a specially designed coordinate measurement system CMM & create variations of electronic and print records using precision probes that scan the various major surfaces of the test gear.  

A comparison of theoretical tooth shapes and tolerances is made automatically to report the quality values ​​of the results defined as the standard.  

In addition to providing quality figures, detailed data from analytical measurement systems helps manufacturers adjust cutter and equipment settings to improve overall process accuracy.  

You can also use the general features of the analytical measurement system to dimension features other than gear teeth while the gear is mounted.  

For example, when machining gears on a shaft, you can check the diameter and geometric features of the main shaft to see dimensions, squareness, parallelism, and concentricity.  

Gear segments, compound gears with two or more gears on the same shaft, keyways, cam surfaces, and other special features can be inspected along with the gear teeth. 


Gears can be made from a variety of materials to achieve application-specific characteristics.  

From a mechanical point of view, strength and pitting corrosion resistance are the most important properties.  

However, in general, designers need to consider the manufacturability of the gear and the entire manufacturing process, from the preparation of the gear blank to the formation of the gear teeth and finally the assembly of the gear into the machine.  

Other considerations are weight, appearance, corrosion resistance, noise, and of course cost.  

Steel gear material: 

Through-hardened steel.  

Gears for machine tool drives, and many types of medium to large speed reducers and gearboxes, are usually made of medium carbon steel.  

Wide range of carbon and alloy steels are used which is stated as follows:  

AISI1020            AISI1040       AISI 1050       AISI 3140         

AISI 4140           AISI 4340      AISI 4620       AISI5120   

AISI 6150           AISI 8620       AISI 8650   AISI 9310 

The range of hardness covered by the AGMA data is from 180 to 400 HB (Brinell Hardness), corresponding to a tensile strength of approximately 87 to 200 ksi.   

Due to inconsistent gear performance during use, it is not recommended to use penetration hardening above 400 HB.  

Case Hardening is typically used to achieve surface hardness greater than 400 HB.  

The hardness against the allowable bending stress should be measured at the root of the tooth.  

This is because the maximum bending stress is generated here.  

The allowable contact stress value is related to the surface hardness of the tooth surface of the gear where the meshing teeth are subject to high contact stress.  

Case-Hardened Steels: 

Flame hardening, induction hardening, carburizing and nitriding are processes that produce high hardness on the surface of gear teeth.  

These processes provide surface hardness values ​​of 50-64 HRC (Rockwell Hardness).  

  1. Carburizing: 

Carburizing produces surface hardness in the range 55-64HRC.  

The result is the highest strength commonly used for gears.  

The effective case depth is defined as the depth from the surface to the point where the hardness reaches 50HRC.  

  1. Nitriding: 

Nitriding produces a very hard but very thin case.  

Designated for smooth load and known applications.  

Nitriding should be avoided if overload or impact is possible because the case is not strong enough or is not sufficiently supported to withstand such stress.  

Iron and bronze gear material: 

Cast iron: 

There are two types of iron used in gears gray cast iron and ductile (sometimes called nodular) iron.  

The commonly used ASTM grades and the corresponding allowable bending and contact stresses.  

Cast iron is brittle, so be careful when impact loads can occur.  

Also, the higher strength morphology of other irons has a low ductility.  

Austempered Ductile Iron (ADI) is used in several major automotive applications. However, the standardized allowable load capacity has not yet been established. 


Simplicity. The design of spur gearbox is simple and compact that can be easily assembled and installed in limited or tight spaces.   

Constant speed drive. These gears increase or decrease the shaft speed with high precision at a constant speed.  





They are low speed gear.  

Power cannot be transmitted between non-parallel axes.  

Spur gears are too noisy when driven at high speeds.  

There is a lot of stress on the teeth of the wheel.  

It cannot be used for long-distance power transfer. 


Spur gears are used in mechanical applications to increase or decrease the speed of a device or multiply torque by transmitting motion and power from one shaft to another through a series of mated gears. 

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