Mechanical Systems

# Gear Geometry 261

Gear Geometry provides an overview of the important design features of common gears. Involute gears have teeth that are shaped by an involute curve. In order to work properly, involute gears must meet precise geometrical specifications. Gear geometry includes tooth profile, pressure angle, pitch circle, clearance, and backlash. A gear's geometry significantly affects the way in which it meshes with another gear in order to transmit power and motion.

The geometry of a gear affects its ability to function correctly and consistently transmit power throughout a mechanical system. Understanding a gear's geometrical features is essential to ensuring gears mesh together properly. After taking this class, a user will be able to describe the basic involute design of gears, its purpose, and define necessary terms for gear specifications.

• Difficulty Intermediate

• Format Online

• Number of Lessons 16

• Language English

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Course Outline
• Gear Trains
• Gear Teeth
• Involute Curve
• Gear Teeth Contact
• Pressure Angle
• Gear Geometry Basics Review
• Pitch Circle and Pitch Point
• Other Gear Nomenclature
• Circular Pitch
• Diametral Pitch and Module
• Nomenclature Review
• Clearance and Backlash
• Gear Ratio
• Gear Design Variations
• Gear Standards
• Final Review
Objectives
• Describe gear trains.
• Identify parts of a gear tooth.
• Describe an involute curve.
• Describe tooth contact for involute gears.
• Describe pressure angle.
• Describe pitch circle and pitch point.
• Identify the other nomenclature used to describe gear geometry.
• Describe circular pitch.
• Distinguish between diametral pitch and module.
• Describe clearance and backlash.
• Describe gear ratio and its effect on speed and torque.
• Describe how gear designs may vary from the basic spur gear.
• Describe gear standardization.
Glossary
Vocabulary Term
Definition

accuracy

The exactness of a measurement produced compared to the desired result. Gear accuracy standards are established by the American Gear Manufacturer's Association (AGMA).

acute angle

An angle that measures more than 0 degrees and less than 90 degrees. The pressure angle between two involute gears is an acute angle.

The distance between the top land of a gear tooth and the pitch circle. The addendum is above the pitch circle.

An imaginary circle that passes through the addendums of gear teeth. The addendum circle coincides with the tops of gear teeth and is larger than the pitch circle.

American Gear Manufacturerâ€™s Association

AGMA. An organization of gear manufacturers that creates standards for gears manufactured in the United States. The American Gear Manufacturer's Association's standards allow for gears made by different manufacturers to be used together.

angle

A shape formed by two lines sharing a common endpoint. Angles can also be formed by two lines that intersect.

angle of obliquity

An angle made by the sides of a gear tooth as the sides incline toward the top of the gear. The degree of a gear's angle of obliquity, or pressure angle, can affect a gear's strength and resistance to wear.

axis

An imaginary straight line passing through the center of an object. A round component, such as a gear, typically rotates around its axis.

backlash

The distance that a drive gear tooth is able to move without moving its driven gear. Backlash, or lost motion, is necessary for gear trains to operate properly.

base circle

In an involute curve, the circle from which the curve is unwound in a spiral shape. For involute gears, the size of the base circle determines involute tooth profiles.

bearings

Friction-reducing devices that allow one moving part to glide past another moving part. Bearings operate using a sliding or rolling mechanism.

bevel gear

A type of gear with conical teeth that are cut at an angle. Bevel gears are often used in angular gear trains.

bottom land

The bottom part of a gear tooth. The bottom land, or root, ends below the pitch circle.

center distance

The amount of space between the gear shaft axes of two meshing gears. Center distance must be carefully controlled in order for gears to mesh and function properly.

circular pitch

The distance along the pitch circle from a point on one gear tooth to the corresponding point on the next gear tooth. Circular pitch is most often used to specify dimensions for making and designing gears.

circular thickness

The width of a gear tooth. Circular thickness is measured on the pitch circle.

clearance

The distance between the top land of a gear tooth and the bottom land of the meshing gear's tooth. Clearance is necessary so that the gears can rotate with less friction and wear.

coarse-pitch gears

A gear with a diametral pitch of 18 or less. Coarse-pitch gears have teeth that are larger and have greater spaces between them than the teeth of fine-pitch gears.

conjugate gears

A pair of gears with pitch circles that connect at a single pitch point. Conjugate gears produce uniform motion because the drive gear's teeth generate the same rate of motion in the driven gear's teeth as they move.

contact point

The precise location where two objects physically touch each other. The contact point for involute gears starts close to the drive gear's top land and ends near the driven gear's top land.

dedendum

The distance between the bottom land of the gear tooth and the pitch circle. The dedendum is below the pitch circle.

dedendum circle

An imaginary circle that passes through the dedendums of gear teeth. The dedendum circle coincides with the bottom part of gear teeth and is smaller than the pitch circle.

diametral pitch

The number of teeth given per inch of a gear's pitch diameter. Diametral pitch is the most common method of classifying gears used within the United States.

diametral pitch

The number of teeth per inch of a gear's pitch diameter. Diametral pitch is the most common method of classifying gears used within the United States.

drive gear

A gear that receives energy from a power source, such as an electric motor. Drive gears transmit power to meshing driven gears in order to perform work.

driven gear

A gear that receives motion from the drive gear. Driven gears often transmit power to another meshing gear or an output shaft in order to perform work.

energy

The ability to do work. Energy may be electrical, mechanical, thermal, or chemical.

face

The surface of a gear tooth located between the pitch circle and the addendum circle. The face is closest to the top land.

fine-pitch gears

A gear with a diametral pitch of 20 or greater. Fine-pitch gears have teeth that are smaller and closer together than the teeth of coarse-pitch gears.

flank

The surface of a gear tooth located between the pitch circle and the dedendum circle. The flank is closest to the bottom land.

force

An influence, like a push or a pull, that produces a change in an object's motion or state of rest. Forces have specific directions and magnitudes.

friction

The resistance to motion between the contact surfaces of two objects. Friction generates heat and increases the wear between components.

gear ratio

The relationship between the number of teeth on two meshing gears, or the number of times a drive gear turns in relation to a driven gear. Gear ratios reflect the change in mechanical advantage resulting from the gears.

gear shafts

A cylindrical rod used to support rotating components or transmit rotation in a mechanical system. Gear shafts and gears compose a basic gear train.

gear trains

A system of gears used to transmit rotary motion from one part of a mechanical system to another. Gear trains are a common method of power transmission.

gears

A round or cylindrical mechanical component with teeth that is used to transmit power. Gears are designed to mesh with one another in order to alter the speed, torque, or direction of mechanical energy.

geometry

A branch of mathematics that involves the measurements, properties, and relationships of all shapes and sizes of objects. Geometry combines simple shapes such as circles, triangles, and squares to create more complex shapes, such as gears.

herringbone gear

A type of helical gear that has angled teeth in the shape of the letter "V." Herringbone gears resist side loading but are expensive to manufacture.

involute

A curved line that gradually becomes more distant from a center point. An involute, or involute curve, can be traced by a point on a taut string as it unwinds from a cylinder.

involute curve

A curved line that gradually becomes more distant from a center point. An involute curve, or involute, can be traced by a point on a taut string as it unwinds from a cylinder.

involute gears

A gear that is designed with an involute tooth profile. Involute gears are the most common gears used because they transmit motion uniformly.

line of action

A constant line upon which all contact between involute gears occurs. The line of action is also called the pressure line.

The overall force applied to a material or structure. Loads may be applied to an object from different directions.

lost motion

The distance that a drive gear tooth is able to move without moving its driven gear. Lost motion, or backlash, is necessary for gear trains to operate properly.

lubrication

The act of applying lubricant to machines, which reduces friction and wear between mechanical components. Lubrication is a common task in preventive maintenance.

mechanical energy

Energy transmitted through the physical interaction and motion of instruments or tools. Mechanical energy is used to perform work.

mechanical system

A collection of machines functioning together to perform useful work. Mechanical systems often use gear trains.

mesh

The act of interlocking with another object. Gears are designed to mesh with one another in order to transmit mechanical energy.

metric gears

Any gear used outside the United States with specifications that are measured in metric units. Metric gears cannot be used with US gears.

module

The distance along a gear's pitch circle, measured in millimeters, for each gear tooth. Module is for classifying metric gears.

motion

A change in an object's original position as a result of a force applied to the object. Motion is typically described in terms of displacement, direction, velocity, acceleration, and time.

nomenclature

A system of naming objects in a given category. Gear nomenclature refers to the terminology used to describe and specify gears.

parallel

Two lines or axes that are equidistant from each other at all points along their length. Parallel shafts never intersect with one another.

pi

A special constant value that relates the diameter of a circle to its circumference. Pi is roughly 3.14 and is used to find the circumference and area of a circle.

pitch

A property used to classify gears. Pitch most often refers to a gear's diametral pitch, but it may also refer to a gear's circular pitch.

pitch circle

An imaginary circle on a gear that divides the gear teeth into top lands and bottom lands. Pitch circles of two meshing gears contact each other at the pitch point.

pitch diameter

d. The length of any line that separates a gear's pitch circle into two equal halves. A gear's pitch diameter can be determined by measuring from the top of one gear tooth to the bottom of the opposite gear tooth.

pitch point

The point at which the pitch circles of two gears contact each other. Involute gears with connecting pitch points produce uniform motion.

power transmission

The movement of energy from a source to an output device that performs work. Power transmission can be performed in many mechanical systems, including gear trains, belt drives, and chain drives.

precision

The ability of an object to repeatedly function in the same manner over time. Gear precision standards are established by the American Gear Manufacturer's Association (AGMA).

pressure angle

An angle made by the sides of a gear tooth as the sides incline toward the top of the gear. The degree of a gear's pressure angle, or angle of obliquity, can affect a gear's strength and resistance to wear.

pressure line

A constant line upon which all contact between involute gears occurs. The pressure line is also called the line of action.

rack

A flat bar with teeth used in a rack and pinion system to produce linear motion. Racks slide in a linear direction as circular pinions turn against them.

rack and pinion

A gear train that converts rotary motion into linear motion. A rack and pinion consists of a circular gear, or pinion, that meshes with a flat-toothed bar, or rack.

reversal error

Motion lost when reversing a gear train's direction, as a result of both the drive and driven gears not rotating at the same time. Reversal error increases as backlash increases.

root

The bottom part of a gear tooth. The root, or bottom land, ends below the pitch circle.

specifications

A description of the essential physical and technical properties of a device or machine. Gears must meet precise geometrical specifications in order to function properly.

speed

The rate at which an object travels a given distance in a given period of time. Speed is used to measure both linear and rotational movement.

speed increasers

A gear train that increases the speed of mechanical energy while decreasing the torque. Speed increasers have larger drive gears and smaller driven gears.

speed reducers

A gear train that reduces the speed of mechanical energy while increasing the torque. Speed reducers have smaller drive gears and larger driven gears.

spur gear

A type of gear that has straight, flat-topped teeth set parallel to the shaft. Spur gears are the most basic and common type of gears used in industry.

standards

A unit of measurement to which other units are compared. Standards for gears are established by the American Gear Manufacturer's Association (AGMA).

strength

A material's ability to resist forces that attempt to break or deform it. Strength is an important mechanical property.

taut

To be pulled tightly or stretched out so no slack remains. A taut thread unwinding from its spool creates the shape of an involute curve.

tooth profile

The basic shape of a gear tooth cross section. The most common gear tooth profile is the involute profile.

top land

The top part of a gear tooth. The top land extends above the pitch circle.

torque

A force that produces rotation. Torque is measured with pound-feet (lb-ft) in the English system and newton-meters (Nm) in the metric system.

wear

The erosion of material as a result of friction. Wear typically is caused by two or more objects rubbing or sliding against each other.

wear resistance

The ability of a material to resist the gradual degradation caused by abrasion and friction. Wear resistance in a gear refers to a gear tooth's ability to withstand stresses that cause it to wear during rotation.

whole depth

The total height of a gear tooth or the total depth of the tooth space. The whole depth is equal to the addendum, dedendum, and clearance.

work

The result of a force applied to an object and the distance through which the force is applied. Work is equal to force multiplied by distance.

working depth

A measurement of how deeply a gear tooth extends into the tooth space of the mating gear. The working depth is the sum of the two meshing gear teeth's addendums.