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Gear Applications

Gears are used to transmit power positively from one shaft to another by means of successively engaging teeth.

Gears are used in place of belt drives and other forms of drives when exact speeds and power transmission must be accurately maintained.

Gears may be used to change the direction of rotation of a power transmission unit, or they may be used to increase or decrease the speed of the driven shaft, thus decreasing or increasing the torque of the driven unit.

Gears are rolling cylinders or cones having teeth on their contact surfaces to ensure positive motion. There are many types of gears, and they may be grouped according to the position of the shafts that they connect. Gears can be used between two or more shafts where the centerlines are parallel or at any angle relative to each other, and they may or may not be in the same plane.

Gear Terminology

Involute- Involute is the curved line produced by a point of a stretched string when it is unwrapped from a given cylinder, as shown in Figure 1.

Figure 1: Involute

It is this curve that forms the most common gear tooth. This form provides the smoothest possible tooth action with the minimum amount of noise and vibration. This form of tooth is also easy to produce with a milling machine or a gear shaper, and any gear having a particular sized tooth can be made to mesh accurately with any other gear having the same size tooth without regard to the number of teeth in the two gears.

The addendum is the height of the gear tooth above the pitch circle. It can also be defined as "the radial distance between the pitch circle and the outside diameter," as indicated in Figure 2.

Figure 2: Gear Nomenclature

Clearance- The clearance in a gear is "the radial distance between the top of one tooth and the bottom of the mating tooth space."

Dedendum- The dedendum is the radial distance from the pitch circle to the bottom of the tooth. The dedendum is equal to the addendum plus the clearance.

Whole Depth- The whole depth is the full depth of the tooth or the distance equal to the addendum plus the dedendum.

Working Depth- The working depth of a gear tooth in full mesh is the distance the gear tooth extends into the tooth space of a mating gear.

Pitch- The pitch of a gear is normally defined as "the distance from the center point of one tooth to the corresponding center point on the next tooth."

Circular Pitch- Circular pitch is the distance from a point on one tooth to a corresponding point on the next tooth measured on the pitch circle.

Pitch Circle- The pitch circle is defined as "the circle which has the radius of half the pitch diameter with its center at the axis of the gear."

Outside Diameter- The outside diameter is the overall diameter of the gear, which includes the pitch circle plus two addendums.

Root Circle- The root circle is formed by the bottoms of the gear tooth spaces.

Pitch Diameter- The pitch diameter is the diameter of the pitch circle, which is equal to the outside diameter minus two addendums.

Diametrical Pitch- To have two gears mesh properly, they must each have the same diametrical pitch. Diametrical pitch is the ratio of the number of teeth for each inch of pitch diameter of the gear. For example, a gear having 28 teeth and a 4-inch pitch diameter would have a diametrical pitch of 7.

Pressure Angle- The pressure angle is the angle formed by a line through the point of contact of two mating teeth and tangent to the base circles and in a line at right angles to the center line of the gears. Standard gears have a pressure angle of either 14.5 or 20 degrees. All mating gears must be of the same pressure angle to mesh properly. Figure 3 illustrates the concept of pressure angle.

Figure 3: Pressure Angle

The only major difference between the 20-degree tooth and the 14.5-degree tooth is the pressure angle. The 20-degree tooth is wider at the base and consequently is stronger than the 14.5-degree tooth form.

In the 14.5-degree tooth, undercutting begins when the number of teeth is less than 32 and may become excessive if the number is less than 22 teeth. The 20-degree pressure angle helps to reduce the undercutting, which usually begins when the number of teeth is less than 18 and may become excessive if the number of teeth is less than 14. Refer to Figure 3 for an illustration of both the 14.5- and 20-degree tooth forms.

Face of the Tooth- The face of the tooth is the contacting surface of the gear tooth from the pitch circle to the addendum circle.

Flank of the Tooth- The flank of the tooth is the contacting surface of the gear tooth from the pitch circle to the dedendum circle.

Face of the Gear-The face of the gear is the thickness of the gear measured parallel to the axis of rotation.

Fillet- The fillet is the rounded corner between the flank and the dedendum circle.

Backlash - In general, backlash in gears is the play between mating teeth. For purposes of measurement and calculation, backlash is defined as "the amount by which a tooth space exceeds the thickness of an engaging tooth."

Shaft Position

The position of the driver and driven shafts upon which gears are mounted determines the type of gears used. The shafts used with gears can be in one of three positions:

        1. Shafts parallel to gears
        2. Shafts intersecting at right angles
        3. Shafts crossing over

Shaft Parallel Gears

Spur gears are used to transmit power between two parallel shafts. Spur gears are considered the simplest and most economical type of gear to manufacture. The teeth on these gears are cut straight and are parallel to the shafts to which they are attached.

Spur gears usually have teeth of the involute design and may be constructed of cast iron, cast steel, bronze, fiber, or synthetic materials such as plastic and nylon. Spur gears are generally used for moderate loads and speeds. Because only one pair of teeth is in full mesh at any one time, the load that spur gears transmit is limited. Spur gears can also be noisy because the contact occurs over the full face width of the mating teeth instantaneously.

When two spur gears turn together, their pitch circles turn in rolling contact, like the rolling cylinders that they represent. Equal portions of their pitch circles are turned past a reference point in any given time interval. Figure 4 shows the teeth in contact on two spur gears A and B.

Figure 4: Spur Gears

When a tooth and a space on A pass the centerlines, a space and a tooth on B must pass also. One gear drives another through the contact at the face and flank of each tooth. Contact between the addendum surface of one tooth and the dedendum surface of the other is undesirable.

The space measured on the line of centers between the addendum circle of one gear and the dedendum circle of the other is called the clearance.

Spur gears may be classified as external, internal, and rack and pinion.

External Spur Gear

An example of an external spur gear set is shown in Figure 5. The shafts that support each gear must remain parallel to each other; therefore, the shaft bearings and supports must be accurately mounted for alignment and strength.

Figure 5: External Spur Gear

Internal Spur Gear

Figure 6 shows an example of an internal spur gear set. Internal gears are an essential component in planetary gear sets. Internal spur gears are used where shafts are parallel and the centers must be closer together than could be achieved with an external spur gear system. This system is a stronger drive as there is a greater area of contact than with the standard external spur gear drive. The internal gear system also provides speed reductions with a minimum of space requirements where much torque is required and both the input and output shafts rotate in the same direction.

Figure 6: Internal Spur Gear

Rack and Pinion

A typical rack and pinion spur gear arrangement is shown in Figure 7. It is used to convert rotary motion to linear motion if the pinion is the driver and the rack is driven. If the rack is the driver and the pinion is driven, the linear motion is converted to rotary motion. This is a specialized form of spur gearing where the pinion teeth mesh with gear teeth on a flat rack.

Figure 7: Rack and Pin Spur Gear

Spur Gear Tooth Profiles

The most common spur gear tooth profiles are the 14.5- and the 20-degree involute tooth profiles. The difference between the 14.5-degree and the 20-degree full-depth tooth form is the pressure angle, as shown in Figure 8. The addendum, dedendum, and total tooth depths are the same for both tooth profiles. The 20-degree tooth form is wider at the base and is stronger than the 14.5-degree tooth form. A larger pressure angle also reduces the undercutting when gears are hobbed (the angle between the top and the face of gear teeth are relieved). The 20-degree tooth form has a greater factor of safety in strength, runs smoother, wears longer, and is no more expensive to manufacture than the 14.5-degree tooth form.

Figure 8: Spur Gear Tooth Profiles

Spur Gear Installation

The standard center distance between two spur gears is one-half the sum of their pitch diameters. Spur gears that are manufactured to operate at standard center distances will have sufficient clearance and backlash to allow for lubrication, slight misalignment problems, and minor gear tooth irregularities.

When a set of spur gears are properly installed, no end thrust loads should be produced. The shafts that support the spur gears can be efficiently carried by a bearing designed for radial loads and with low thrust capacities.

If end thrust develops in a spur gear system, the thrust could be caused by misalignment due to coupling, by belt or chain misalignment, or by thrust forces transmitted from either the driver or the driven units.

For a pair of spur gears to mesh accurately they must have the same pitch, pressure angle, and diametrical pitch.

Parallel Shafts with Helical Gears

Helical gears are most commonly found on machinery where the shafts are in parallel positions. Helical gears resemble spur gears, but the teeth are cut at an angle rather than parallel to the shaft axis like on spur gears. Figure 9 shows a pair of helical gears.

Figure 9: Pair of Helical Gears

The angle that the helical gear tooth is on is referred to as the helix angle. The angle of helix depends upon the condition of the shaft design and relative position of the shafts.

For parallel shafts, the helix angle should not exceed 20 degrees to avoid excessive end thrust. To ensure that the gears run smoothly, the helix angle should be such that one end of the gear tooth remains in contact until the opposite end of the following gear tooth has found a contact. Figure 10 illustrates the concept of helix angle.

Figure 10: Helix Angle

Helical Gear Strength

This design feature makes the helical gear stronger than straight tooth spur gears and also decreases tooth deflection.

The helical gear tooth design permits an increased surface area. With one end of the tooth advanced over the other, tooth engagement takes place progressively. The line of contact is a diagonal line extending from some point on the face of the advanced end to a point on the flank of the trailing end. As a result, the engagement of the teeth on a helical gear is smoother than on a straight tooth spur gear; the gears run quieter and operate effectively at higher pitch line velocities. The smooth engagement results in very slight wear.

In straight tooth spur gears there is a time in each period of contact when the load is concentrated at the upper edge of the tooth, thus acting with a leverage equal to the height of the tooth. With helical teeth, the points of contact are, at all times, distributed over the entire working surface of the tooth. Therefore, the mean lever arm of the bending action of the load is about half the height of the tooth.

Hand of the Helical Gear

For a pair of helical gears located on shafts that are parallel to mesh properly, they must have the same helix angle, pitch, and pressure angle but the gears must be of opposite hands. Helical gears of the opposite hand will operate on shafts that are parallel (see Figure 11).

Figure 11: Hand of Helical Gears

Cross-Shaft Helical Gears

Helical gears of the same hand operate on shafts crossing over each other as indicated in Figure 12. The sum of the two helix angles of these two mating gears determines at what angle the shafts cross over each other. If each gear were manufactured with a 45-degree helix angle, the shafts would cross over each other at 90 degrees. The hand of the gear, either left or right, is the direction the teeth lean or twist with the gear in a horizontal position and the bore in a vertical position.

Figure 12: Helical Gears

The main disadvantages of helical gears as compared to spur gears are cost factors and thrust problems. As previously stated, helical gears provide smoother teeth engagement, the gears run quieter, and possess more strength.

Manufacturing a helical gear is more expensive than manufacturing a spur gear due to the helix angle and because of the greater accuracy required in helicals to ensure smooth and quiet operation. Axial thrust is produced by helical gears; therefore, some form of bearing must be used to support the shafts and to accept the thrust load that develops from the helix angle.

Thrust Direction on Helical Gears

The direction of thrust depends on three things: 1) direction of the helix, 2) relative position of driver and driven gears, and 3) direction of rotation.

The thrust may be changed to the opposite direction by changing any one of these three conditions, as shown in Figure 13.

Figure 13: Thrust Direction on Helical Gears

Any alteration of conditions, including interchanging the driver or driven gear, reversing the direction of rotation, or changing the direction of the helix will produce a thrust in the opposite direction.

In practical use, either radial bearings, which can accept minor amounts of end thrust are used on helical gears, or thrust bearings are used in conjunction with radial load bearings to accept the thrust loads developed by the helical gears.

Double Helical Gears

Double helical gears consist of opposed helix angle gear teeth manufactured on a hub. A very evident space separates the two opposed sets of teeth as shown in Figure 14.

Double helical gears and herringbone gears are commonly used in parallel shaft transmissions as either speed reducers or increasers.

Figure 14: Double Helical Gears

Double helical gears and mating pinions produce no axial thrust because one helix angle gear form counteracts the other. The two sets of teeth are separated at the center by a narrow gap or recess for better tooth alignment and to prevent lubricating oil from being trapped at the apex of the gear.

Double helical gears are used when a smooth, continuous action is essential, as in high-speed, high-torque drives where the pitch line velocity may range from 1,000 feet per minute to 3,000 feet per minute and up to 12,000 feet per minute or higher.

These high speeds are encountered in marine reduction units, steam and gas turbine drives, electric motor drives, high-speed blowers and compressors, and various speed-increasing and speed-reducing units found on conveyor drives, mining equipment, and pumping applications.

Herringbone Gears

Herringbone gears, Figure 15 , are similar to double helical gears. The herringbone has no space separating the two opposed sets of teeth. It is more expensive and difficult to manufacture a herringbone gear to high accuracies, but both the herringbone and double helical gears stand up well for long periods under heavy load conditions.

Figure 15: Herringbone Gears

When failure occurs in double helical and herringbone gear systems, it is rarely due to tooth breakage. Failure is usually associated with excessive wear or sub-surface gear tooth failures, such as pitting and spalling.

Research and tests have established that, for both spur gears and herringbone gears, there is a significant critical surface pressure value for gear teeth having given physical properties and coefficient of friction.

According to the research, pressure above the critical value results in rapid wear and short gear life, whereas when pressures are below the critical value, wear is negligible. The yield point of the gear material indicates the critical loading point, and for practical design a reasonable factor of safety must be considered.

90-Degree Shafts

Bevel gears are used for the transmission of power between shafts with intersecting centerlines. These gears are cut on an angular surface such as would be represented by a truncated cone. Most bevel gears may be classified as being either of the straight tooth type or of the curved tooth type. The latter type includes "Zerol" and spiral bevels.

Figure 16 identifies the various angles and dimensions referred to in describing bevel gears. Additionally, along with the face angles indicated in the diagram, it should be noted that the face cones are manufactured parallel to the root cones of the mating gears to provide accurate and uniform clearance along the length of the teeth.

Figure 16: Bevel Gear Angles and Dimensions

Bevel Gears

The various types of bevel gears discussed here include straight, "Zerol", spiral, and miter.

Straight Bevel Gears

The gear teeth of this type of bevel gear are straight but their sides are tapered so that they would intersect the axis at a common point, called the cone apex, if extended inward.

A straight bevel gear is the simplest type of gear for intersecting shafts. It is commonly used on shafts that intersect at right angles as shown in Figure 17.

Figure 17: Straight Bevel Gear

Angular Bevel Gears

Straight bevel gears can also be used on shafts meeting at angles other than 90 degrees. This type of gearing, referred to as angular bevel, is shown in Figure 18.

Figure 18: Angular Bevel Gear

"Zerol" bevel gears are superior to straight bevel gears. They are smoother and quieter than the straight bevel due to their tooth curvature and the slight overlap of teeth.

The form of tooth used for straight bevel gears is the involute. A straight bevel gear tooth exhibits the same disadvantages as straight spur gears. Noise and roughness occur more frequently in this type of gearing than in the spiral bevel. No thrust is produced by a straight bevel gear and they are used for slow speeds to avoid excessive vibration where high impact forces are minimal.

"Zerol" Bevel Gears

The teeth of "Zerol" bevel gears are curved but lie in the same direction as the teeth of straight bevel gears. "Zerol" bevel gears are similar to spiral bevel gears except the "Zerol" gears have zero spiral angle and are manufactured on the same machines as spiral bevel gears.

As in straight bevel gearing, "Zerol" bevel gears have no inward axial thrust. Their zero degree spiral angle produces no thrust load. These two types of bevel gearing are interchangeable in equipment; thus, no changes are required for thrust bearings. Figure 19 shows a "Zerol" bevel gear.

Figure 19: "Zerol" Bevel Gear

Spiral Bevel Gears

One of the major advantages of spiral bevel gears is the complete control of the localized tooth contact. These gears, as shown in Figure 20, have curved teeth set at an angle to radial lines. Therefore, they have curved oblique teeth on which contact begins gradually and continues smoothly from end-to-end. This type of gear mesh allows more than one tooth to be in full contact, permitting greater loads than straight bevel gears. They are smoother and quieter in operation, even in high-speed applications.

Figure 20: Spiral Bevel Gears

By making a slight variation in the radii of curvature of the mating tooth surfaces, the amount of surface over which the tooth contact occurs can be changed to meet the specific requirements of each application. This feature of localized tooth contact ensures smooth, quiet running spiral bevel gears. This also permits minor amounts of mounting deflections without subjecting the load dangerously near either end of the gear tooth.

Spiral bevel gears have a distinct advantage in applications requiring hardened gears of high accuracy because their tooth surfaces can be precisely ground.

The bottom of the tooth spaces and the tooth profiles may be ground simultaneously, resulting in a smooth and accurate meshing of the tooth profile, tooth fillet, and bottom of the tooth space. This feature increases the gear strength because it eliminates cutter marks and various tooth surface irregularities that result in stress concentrations, excess tooth wear, and eventual tooth failure.

Miter Gears

Miter gears are bevel gears having the same pitch, pressure angle, and number of teeth. Miter gears may use the straight bevel gear tooth form, "Zerol" bevel tooth form, or spiral bevel tooth form. Miter gears are usually used on shafts intersecting at right angles where a one-to-one speed ratio is required. Figure 21 shows a miter gear arrangement.

Figure 21: Miter Gears

Bevel Gear Mounting

Straight bevel, "Zerol" bevel, and spiral bevel gears are designed and manufactured in pairs; therefore, the mating gears are not interchangeable. The large gear (driving gear) is referred to as the pinion gear. Figure 22 illustrates the crown and pinion.

Figure 22: Crown and Pinion

Rigid mountings must be provided for bevel gears to keep the positions of the gears under operating loads within recommended limits. To position and align gears accurately, extreme care should be practiced to ensure precise machine mountings, properly fitted keys, and couplings that run true and square.

For bevel gears from 6 to 15 inches in diameter, the allowable deflections on gears and their mountings are:

  • Neither the pinion nor the crown should lift or depress more than .003 inch at the center of the face width.
  • The pinion should not yield axially more than .003 inch in either direction.
  • The crown should not yield axially more than .003 inch in either direction on one-to-one ratio gears (miter gears) or near miter gear ratio, or more than .010 inch away from the pinion on higher ratios.

When deflections exceed these allowable limits, additional problems are introduced in obtaining satisfactory gear operation. It is then necessary to narrow and shorten the tooth contacts to suit the more flexible mounting. This decreases the bearing area, raises the tooth pressure, and reduces the number of teeth in contact.

These deflections also result in increased noise and vibration, plus the danger of surface failure as well as tooth breakage.

From the contact pattern transfer, the relative position of the crown and pinion can be determined, and the pattern will indicate the actual concentration of tooth mesh. The backlash can be calculated by using feeler gauges or dial indicators.

Spiral bevel gears should be mounted on anti-friction bearings in an oil-tight case. Maintaining bevel gear alignment is usually easier with ball or roller bearings than with plain bearings.

Provisions are made on bevel gears for axially shimming the position of both the crown and pinion gear at the time of assembly or overhaul. The mounting distance of the crown is usually the "pitch apex to back" (see Figure 23) and may be stamped or etched on the bevel gear. During assembly, shims are used to obtain the distance exactly. The correct mounting procedures for bevel gears will have the meshing teeth flush on the outer ends.

Figure 23: Incorrect Bevel Mounting

If the teeth are not flush on the back, the gears are set with either:

Too little clearance, and the teeth will bind and be subject to excess wear;

~ or ~

Too much clearance, and the teeth are not in full mesh and excess backlash may exist.

Bevel gears, when properly mounted, should have the proper tooth contact pattern and backlash. These conditions should be checked during assembly. The tooth contact pattern is checked by applying pressure bluing to the bevel gear teeth and turning the meshed gears over using a light load condition.

Hand of Spiral Bevel Gears

The hand of the spiral on spiral bevel gears is indicated by the direction in which the teeth curve away from the axis. Left-hand spiral bevel teeth curve away from the axis in a counterclockwise direction when an observer looks at the face of the gear as in Figure 24.

Figure 24: Hand of Spiral Bevel Gears

Right-hand spiral bevel teeth curve away from the axis in a clockwise direction when an observer looks at the face of the gear (see Figure 25).

Figure 25: Right-Hand Spiral Bevel Teeth

The hand or spiral of one gear is always the opposite of that of its mating gear, and it is quite common to specify the spiral of the pinion gear when identifying the combination.

The direction of rotation of a bevel gear is determined as clockwise, or counterclockwise by viewing the gear from the back.

Hand of Spiral and Thrust Loads

A right-hand spiral bevel pinion gear rotating clockwise will tend to move toward the cone center, while a left-hand spiral bevel pinion tends to move away from the cone center because of the oblique direction of the curved teeth. If end play exists in the pinion shaft, the movement of a right-hand spiral bevel pinion driving in the clockwise direction will take up the backlash under heavy load and the teeth of the crown and pinion may wedge together.

A left-hand spiral bevel pinion under similar conditions will back away from the crown; therefore, this introduces additional backlash between the teeth.

It is recommended that when the ratio, pressure angle, and spiral angle are specified, the hand of the spiral should be selected to provide an axial thrust that tends to move the pinion out of mesh. In many applications, the mounting conditions will typically dictate the hand of spiral to be used.

For example, on a reversing drive unit, there is no choice of hand of spiral unless the crown and pinion performs a heavier power transmission in one direction for longer periods of time.

Cross Shafts

Two types of gear designs are used in conditions where the shafts cross over each other at 90 degrees and never intersect. The gears that are found on shaft crossover designs are hypoid gears and worm gear sets.

Hypoid Gears

Hypoid gears are a modification of the spiral bevel gear and the worm gear, with the axis offset. The distinguishing feature of hypoid gears is that the shafts of the pinion and ring gear may continue past each other, never having their axis intersecting. Figure 26 shows an example of a hypoid gear.

Figure 26: Hypoid Gear

Spiral bevel pinion gears have equal pressure angles and symmetrical profile curvatures on both sides of the teeth. A hypoid pinion gear properly coupled to a mating ring gear having equal pressure angles on both sides of the teeth must have non-symmetrical profile curvatures for proper tooth action. To obtain equal arcs of motion for both sides of the teeth, it is necessary to use unequal pressure angles on hypoid pinions. Therefore, hypoid pinions are normally designed so that the pinion has a larger spiral angle than the ring gear.

The major advantages of the hypoid gear design are that the pinion diameter is increased, and it is stronger than a corresponding bevel gear pinion. The increased diameter size of the pinion permits the use of comparatively high gear ratios without having the pinion become too small and unable to accept adequate bore or shaft sizes for the required horsepower.

The teeth of the pinion are manufactured longer and stronger for a given ratio; therefore, these gears are recommended for industrial applications:

  • When maximum smoothness of operation is required
  • For high reduction ratios where compactness of design, smoothness of operation, and maximum pinion strength are important
  • For non-intersecting shaft requirements such as automotive applications where the offset permits lowering of the drive shaft

The sliding action along the lengthwise direction of the hypoid gear teeth is a function of the difference in the spiral angles on the gear and pinion. The hypoid gear tooth action consists exclusively of this sliding action, consequently, this makes the hypoid gear system smoother running than even the spiral bevel gear system. Because of the significant sliding action, hypoid gears are one of the most difficult to lubricate, and it is essential that extreme pressure (EP) lubricants be used.

Worm Gears

Worms and worm gears are best suited for applications where a great ratio reduction is required between the driving and driven shafts.

Worm gears are used to transmit power between two shafts that are at right angles to each other and are non-intersecting. As shown in Figure 27, the worm is the cylinder upon which is cut a single or multiple start Acme-type thread. The pressure angle of this thread ranges from 14.5 to 30 degrees. As the lead angle of the worm increases, the greater the pressure angle is on the side of the thread.

Figure 27: Worm Gears

The worm is the drive gear (input) and the driven gear (output) is referred to as the worm gear or worm wheel. The teeth on a worm gear are curved to conform with the teeth on the worm. The worm gear teeth are machined on a peripheral groove which has a radius equal to half the root diameter of the worm.

Figure 28 identifies the various angles and dimensions referred to in describing worm gearing.

Figure 28: Worm Gear Nomenclature


The pitch of the worm is the distance measured axially from a point on one thread of the worm to the corresponding point on the adjacent thread. The pitch of the worm is equal to the lead divided by the number of threads or starts on the worm.


The lead is the distance that one thread advances in one complete revolution of the worm. The lead is equal to the pitch of the worm multiplied by the number of worm threads or starts.


Starts or number of threads on the worm can be one or multiple. A single thread worm can be referred to as having one start. By visually inspecting the end of the worm thread area, an observer can determine the number of starts. Starts may be either right- or left-hand.

Worm Gear Ratio

To determine the gear ratio of a worm gear set, divide the number of teeth on the worm gear by the number of starts on the worm. A single start worm in one revolution advances the worm gear only one tooth and space, but a large reduction in speed is obtained. A worm gear with 33 teeth and a worm with a single start has a ratio of 33:1. A worm gear with 33 teeth and a worm with a multiple thread of 3 (3 starts) has a gear ratio of 11:1.

Pitch Diameter of the Worm

The pitch diameter of the worm is the diameter of a circle which is tangent to the pitch circle of the mating gear in its mid-plane. The worm must be strong enough to transmit its maximum load without excessive deflection. The pitch diameter of the worm should be as small as is consistent with the necessary strength to minimize the rubbing speed.

Worm Contact

There are two types of worm gearing sets, which have different contacting patterns when the worm and worm gear are in their proper position. These two types of contact are referred to as non-throated and throated, of which there are two styles: single-throated and double-throated.

Non-Throated Worm Gear Set

In a non-throated worm gear set, the tooth contact between the worm and the worm gear takes place at a point or several points, depending on the number of teeth in contact. Contact at a point concentrates the load pressure on small areas of the teeth, and this leads to early tooth wear and failure.

Single-Throated Worm Gear Set

The straight tooth form of the worm and worm gear can be modified to obtain greater contact area. By altering the shape of the worm gear teeth to produce a concave shape that conforms to the circumference of the worm more contact area is developed. The single-throated worm gear is shown in Figure 29.

Figure 29: Single-Throated Worm Gear

Double-Throated Worm Gear Set

In double-throated worm gear sets, the profile of the worm accurately matches the circumference of the worm gear. The teeth of a double-throated worm gear are flat and have a larger area of contact. The larger tooth bearing area and multiple tooth contact obtained with this type of worm gearing increases the load carrying or horsepower capacity so that, as compared with a non-throated or single-throated worm gear set, a double-throated worm drive may be considerably smaller in size. Figure 30 shows a double-throated worm gear set.

Figure 30: Double-Throated Worm Gear

Hands of Worm Gearing

Worms and worm gears operating in a drive unit can either be right- or left-handed, and like helical gears, the hand of the worm and worm gear are checked with the gear standing on one end. This is shown in Figure 31.

  • The left-hand threads of the worm and the left-hand teeth of the worm gear lean to the left.
  • The right-hand threads of the worm and the right-hand teeth of the worm gear lean to the right.

Assembly of the worm and worm gear is done by using gears of the same hand. This will establish a shaft crossover position.

Figure 31: Hands of Worm-Gearing

Worm Gearing and Thrust Loads

The action of the worm and worm gear produces a heavy thrust load parallel to the worm and the worm gear shaftÔÇÖs axis. The position of the bearings that are intended to take up the thrust load is variable as indicated in Figure 32. This depends upon the position of the worm and worm gear and the direction of rotation of the worm.

Taper roller bearings or angular contact bearings are frequently used on worm units. Both bearings can accommodate the axial thrust load produced by the worm gear action and provide the necessary radial load support, which helps to reduce shaft deflections. On smaller worm units designed for light loading, the bearings can be standard single row-deep groove ball bearings or maximum capacity ball bearings.

Figure 32: Worm Gearing and Thrust Loads

Worm Gearing Mesh Patterns

The mesh pattern of a worm and worm gear set is critical. A clear mesh pattern indicates the position of the worm gear in relation to the worm. By adding or removing shims from one side to the other side of the worm gear bearing covers, the mesh pattern can be adjusted to the recommended position.

The mesh can be checked by first wiping the worm and worm gear free of oil and giving the worm a light coating of Prussian bluing. Have all of the bearing covers and housing covers bolts tightened in the correct sequence and torqued to the recommended amounts.

The worm is rotated by hand in the normal direction of rotation while the worm gear is partially snubbed. A bluing mark should transfer to the worm gear. The marking on the worm gear teeth should be close to centered on the gear teeth and inclining slightly to the leaving side. This is indicated in Figure 33.

Figure 33: Worm Gearing Mesh

Worm gear sets used on reversing drive applications should have the contact area from the center of the worm gear tooth to the leaving side on both faces as indicated in Figure 34.

Figure 34: Worm Gear Mesh

Figure 35 indicates the direction necessary to move the worm gear to obtain the correct mesh pattern on the worm.

Figure 35: Moving the Worm Gear

Upon initial assembly of worm gear units, a number of shims are installed behind the bearing cover plates of the worm gear shaft. By removing shims from one side and adding them to the opposite side of the cover, the mesh pattern is shifted to a new location. Changing the position of the shims changes the position of the worm gear in relation to the worm. This does not change the clearance in the bearings if all of the shims in the original shim pack provided by the manufacturer of the unit are used.

Worm-Gearing and Self-Locking

Most worm gear sets are employed for speed reduction and have the ability to self-lock when a backward motion is attempted. It is difficult to rotate the output shaft in reverse rotation because of the high-lead angle worm that can be of single- or double-throated design. When worm gearing is self-locking or irreversible, the worm gear cannot drive the worm. Worm gear drives can act as backstops on inclined belt and chain conveyors. The self-locking action of the gears will prevent a heavily loaded conveyor from reversing back down the inclined slope when the drives have been stopped.

Planetary Gears

Note that the sun gear, planet pinions, and ring gear are constantly in mesh. Planetary gearing or epicyclic gearing provides an efficient means of obtaining a compact design of power transmission with driving and driven shafts parallel to each other. Planetary gear units can use spur or helical gear tooth forms.

Planetary gears are suitable for installations requiring a/an:

  • Increase or decrease in speed of the driven component
  • Change in direction of rotation of the output
  • Torque increase or decrease

As shown in Figure 36, planetary gears are similar to the solar system. The planet pinion gears or carriers each turn on their own axis while rotating around the centrally positioned sun gear. The planet pinion or carrier gears mesh with the inside gear teeth of the ring gear.

Figure 36: Planetary Gears

The planet pinions are mounted on shafts in the carrier assembly and can rotate on their axis to walk around the sun gear or the ring gear.

When power is applied to drive the sun gear, on either the planet pinion carrier or the ring gear, the entire planetary system will rotate as a unit.

A restraining force (reactionary device) applied to one of the other two planetary members will hold the system stationary. With no reactionary device in place, a neutral situation results in the drive unit.

When power is applied to one member of the planetary system and a brake mechanism is applied to restrain a second member from rotating, the remaining part will become a power output source as illustrated by the following examples.

When the sun gear is driven, as shown in Figure 37, and a brake is applied to the ring gear, the planet pinions walk around the ring gear, forcing the planet pinion carrier to rotate in the same direction as the sun gear, but at a slower speed.

Figure 37: Planetary Gear Movement

When the planet pinion carrier is driven, as shown in Figure 38, and a brake is applied to the ring gear, the planet pinions revolve around the ring gear, forcing the sun gear to rotate in the same direction at a higher speed.

Figure 38: Planetary Gear Movement

In both examples, as shown in Figure 37 and Figure 38, one member of the planetary system is driven, one is held stationary by a reactionary device, and the third member becomes the power output.

In actual application, there are six possible combinations that will create gear reduction, change of direction, or speed increase from a simple planetary system as shown below in Table 1.

SunCarrierRingLarger reduction Low speed
SunRingCarrierLow reverse
CarrierSunRingFast overdrive
RingSunCarrierReverse overdrive
RingCarrierSunSpeed reductionTable 1: Gear Reduction, Direction Change or Speed Increase Combinations

Methods Used to Determine Planetary Arrangements

The R-PC-S system is a quick method of determining which gear the output is taken from, whether there is a speed increase or decrease, and whether there is a direction or rotation change from the input member to the output member in planetary gear systems.

Review the various drawings in Figure 39 that identify six planetary gear combinations. First, you must determine which gear is the driving gear, which gear is the held gear, and which gear is the driven gear.

Planetary Gear Combinations

Once the driving gear are determined, it must then be determined whether the gear is turning clockwise or counterclockwise. Draw a horizontal line in the direction the gear is turning (right for clockwise and left for counterclockwise).

One can determine where the output is from, whether there is a speed increase or decrease, and if there has been a change in direction of rotation from the driving gear rotational direction by drawing a line from the end of the horizontal line through the held gear.

For example, Figure 39A shows the sun gear as the driving gear (input gear), and it is turning in a clockwise direction. A horizontal line is then drawn to the right, showing the direction that the gear is turning. A semi-vertical line has been drawn connecting the end of the input line up through the ring gear which is the held gear. The output line is then drawn horizontally from the planet carrier (driven) to the right, connecting with the semi-vertical line.

The result is that the output is taken from the planet carrier, which is rotating clockwise (right); since the output line is shorter than the input line, there has been a speed reduction, and a torque increase occurs.

Backlash in Gears

Backlash in gears is the play between mating teeth. For purposes of calculation and measurement, backlash is defined as the amount by which a tooth space exceeds the thickness of an engaging tooth. It does not include the effect of center-distance changes of the mountings and variations in bearings.

When not otherwise specified, numerical values of backlash, usually in thousandths of an inch, are understood to be given on the pitch circles.

The general purpose of backlash is to prevent gears from jamming together and making contact on both sides of their teeth simultaneously.

Lack of backlash may cause noise, overloading, vibration, overheating of the gears and bearings, and possibly seizing and failure.

Excessive backlash is questionable, especially if the drive is frequently reversing or if there is an over-running load, as found in cam drives. Specification of an unnecessarily small amount of backlash allowance will increase the cost of gears because errors in runout, pitch, profile, and mounting must be kept at much smaller amounts. Backlash does not affect the involute action, nor is it overly detrimental to proper gear action.

Determining the Proper Amount of Backlash

In specifying proper backlash and tolerances for a mating gear, the major factor is the maximum permissible amount of runout in both meshing gears. Also, factors such as allowable errors in tooth profile, pitch, tooth thickness, and helix angle must be considered. The amount of backlash between a pair of gears will vary as successive teeth make contact because of the effect of overall tooth errors in gear mounting and bearing installation. Other important considerations for determining proper backlash are:

Speed of the Gears

Slow-turning gears, in general, require the least backlash, while fast-turning gears may require more backlash because of heat and lubrication difficulties.


Fast-turning, fine-pitch gears are usually lubricated with relatively light oil, but if there is insufficient clearance for an oil film, and if oil trapped at the root of the gear tooth cannot escape, heat and excessive tooth loading will result.

Heat Factors

Heat is an important factor because gears may operate at higher temperatures than other components and, therefore, expand more than gearbox housings. The heat may result from friction between the gear teeth, oil churning, hot bearings, oil seals, or external causes.

Helix Angle

The higher the helix angle, or spiral angle, the more transverse backlash is required for a given normal backlash. The transverse backlash is equal to the normal backlash divided by the cosine of the helix angle.

Housing Errors

Errors in boring the gear housings, both in center distance and in alignment, are of major importance in determining allowable backlash.

Mounting Gears

When the gears are mounted on their shafts, their position and placement is important to how they will operate. The type and adjustment of the support bearings will also effect the position and overall backlash of the gear set.

Other Influences

Other factors that can influence backlash specifications are heat-treatment processes subsequent to cutting the teeth, lapping operations, the possibility of re-cutting teeth for some mechanical reason, and reduction of tooth thickness through normal wear.

Zero Backlash

Minimum backlash is important in applications where timing, indexing, and certain instrumentation equipment have to be functioning precisely. If the operating speed is low and the necessary precautions are taken in manufacturing the gear set, the backlash may be held to extremely low limits. However, the specification of zero backlash, often required for gear systems, usually involves special and expensive manufacturing techniques and can be difficult to obtain.

Recommended Backlash

Table 2 through Table 4 contain the American Gear Manufacturers Association recommendations for backlash ranges for various types of gears.

For purposes of calculation and measurement, backlash is defined as the amount by which a tooth space exceeds the thickness of an engaging tooth. When not otherwise specified, numerical values of backlash are understood to be measured at the tightest point of mesh on the pitch circle in a direction normal to the tooth surface when the gears are mounted in their specified position.

Table 2

Table 3

* Measured at tightest point of mesh.

Table 4

Measurement of Backlash

Backlash is commonly measured by holding one gear of a pair stationary and rocking the other back and forth. There are various methods to detect the movement. One common method is with the dial indicator having its pointer contacting the gear tooth near the pitch diameter and in a direction parallel to a tangent to the pitch circle of the moving gear. This is shown in Figure 40.

Figure 40: Backlash Measurement

In spur gears, parallel helical gears, and bevel gears, it does not make any difference whether the pinion or the gear is held stationary for the backlash test. With crossed helicals (helicals of the same hand) and hypoid gears, backlash readings may vary according to which member is stationary; therefore, it recommended to hold the pinion stationary and take the backlash measurement off the gear.

Another method to measure backlash is by using thickness or feeler gauges in some gear applications. The gauge is inserted into the tooth space between the engaged gear teeth.

Backlash can also be measured by lead wire being inserted between the teeth as they pass through full mesh. After removing the flattened lead wire, a micrometer can be used to determine the thickness of the wire which relates to the amount of backlash.

Measurement of backlash may vary in the same pair of gears, depending on the accuracy of manufacture and assembly. Change of backlash at different phases of the tooth action will be caused by incorrect tooth profiles. Eccentricity could cause a great difference between maximum and minimum backlash at different positions around the gears.

It should always be remembered that simply making allowances on tooth thickness does not guarantee the minimum amount of backlash that will exist in actual gears when assembled.

Control of Backlash

To control or adjust backlash on gear sets, some provision can be made for shifting one gear relative to the other. This allows control over backlash at initial assembly and throughout operating life. These provisions are common in bevel and hypoid gearing.

Controlling backlash in spur and parallel helical gearing is not common, as most manufacturers do not permit changes between shaft centers in their assemblies. Provisions for controlling backlash are practical in worm gearing only for single thread worms with low lead angles; otherwise, faulty contact occurs.

Another method of controlling backlash in bevel gears and less commonly in spur and helical gears is to match the high and low spots of the runout gears of one-to-one ratio and mark the engaging teeth at the point where the runout of one gear cancels the runout of the mating gear.

Gear Materials

The dominant factor in choosing gear material is the ability to resist wear.

When choosing gears for a given application the metallurgy and manufacturing processes, particularly as they affect surface finish must be considered. Gears are made from a wide variety of materials ranging from steel to synthetics.

Steel Gears

Steel for gears may be either plain carbon or alloy, the choice being determined by the strength required and cost. In some types of gears, particularly worm gears, the dominant factor in material selection is the ability to resist wear. In other types, the main factor may be maximum strength, speed, operating temperature, or cost.

Steel is a commercial alloy of iron containing carbon in amounts ranging from 0.25 percent to 1.7 percent. Although not all gear steels are hardened, they are usually heat-treated to some specification to attain the best combination of machinability and durability. Gear steel can be modified by adding small quantities of alloying elements such as manganese, nickel, and chromium. If maximum strength is required, the machined gear can be hardened through heat treatment methods such as carburizing, nitriding, flame or induction hardening, or a combination of these methods.

Cast Iron Gears

Cast iron is primarily an alloy of iron and carbon, with the carbon content ranging from 1.7 to 4 percent. Cast iron differs from steel in that most of the carbon is present as free graphite with only a minor portion combined with the iron. The free graphite in the metallurgical structure reduces the strength, ductility, and elasticity]] of the material, but does allow a cast iron gear to operate with minimal lubrication. Cast iron gears are not recommended for high speeds or heavy-duty applications, as they cannot carry as much load as steel gears of comparable size.

Non-Ferrous Gears

Bronze is one of the most widely used non-ferrous gear materials. Bronze is an alloy of approximately 90 percent copper and 10 percent tin.

Other metals such as aluminum, zinc, manganese, lead, silicon, phosphorous, iron, and nickel may be used in addition to or instead of tin. Each of these elements modifies the strength and bearing characteristics of the alloy in a particular way; therefore, each component has applications for which it is best suited.

Bronze tolerates high sliding friction loads. Its primary use in gearing is in worm wheels where the tooth action is almost total sliding. Worm gear tooth flanks are subject to the same contact stresses as the worm. However, the number of stress cycles each worm gear tooth is subjected to compared to each worm thread is reduced by a factor equal to the ratio. This is the reason the worm gear material can be a manufactured in a softer material such as bronze.

Non-Metallic Gears

Non-metallic gears are lower in cost, lighter in weight, and easier to machine when compared to metal gears. Non-metallic gears are primarily plastic and are molded of nylon, acetal, acrylonitrile/butadiene/styrene copolymer (ABS), or polycarbonate. Non-metallic gearing is used primarily where quietness of operation at high speed is the first consideration.

Other non-metallic gear materials are sold by different firms under various trade names, such as Micarta, Celeron, Formica, Fabroil, Phenolite, etc. The majority of these gear materials consist of layers of canvas or cloth impregnated with bakelite and forced together under hydraulic pressure. When combined with an application of heat, a dense rigid mass is formed.

The primary application of non-metallic gears are small, high-speed units such as portable power tools, appliances, instruments, and automotive parts. With a high starting torque, widely fluctuating load, or high shock loads, these gears may deflect and be unsatisfactory. Glass fiber fillers or material such as silicone enhances the strength, lubrication, and durability qualities.

Gear Lubrication

The lubrication in any gear assembly has two purposes:

        1. To reduce friction and wear at the tooth surfaces
        2. To carry away heat that is generated at the contact surfaces of the teeth

Extremely high instantaneous contact temperatures occur at the lines of contact, and a continuous flow of oil is necessary to dissipate this heat quickly to the oil reservoir.

The proper lubricant to use on specific gears depends on decisions made by the following people:

  • The gear manufacturer depends on previous experience with certain types of lubricant; the manufacturer prefers those lubricants which have performed well in similar service in the past.
  • The manufacturer of equipment in which the gears are used is usually consulted on lubrication problems.

The user of the gears can apply whatever lubricant they desire (after the warranty period), but it is very important to have the right lubricant in the equipment.

The lubricant supplier, on the basis of research and field experience, has definite recommendations as to the best lubricant to use.


Some gear set applications will operate at higher internal temperatures because of gear design, bearing type, loads, and gear materials. External temperatures such as high or extremely low ambient air temperatures can also greatly affect the lubrication of gears. The affect of high operating temperatures tends to thin out the lubricant; therefore, the oil film may be insufficient between the meshing gears. A heavier bodied oil is normally recommended for high operating temperature conditions; this oil will have the proper viscosity at the running temperature.


Gears operating at high speeds need a lubricant of reduced viscosity to provide adequate lubrication, cooling, and operation with minimum tooth friction. Under lower speed conditions, heavier lubricants are required according to the prospective operating temperatures. Friction is of less consideration when lower speeds are involved. The ability of the lubricant to flow with the teeth and maintain a complete film is more important.


The load, or pressure to which gear teeth may be subjected, is a major consideration when choosing the viscosity of the lubricant. Heavily loaded gears require higher-viscosity, more adhesive-type lubricants. High-viscosity lubricants tend to provide a thick oil film that acts as a cushioning effect to offset the effect of tooth impact.

Friction Type

Due to the nature of worm gearing and hypoid gearing where heavy sliding and rubbing action occurs, the lubrication recommended contains extreme pressure (EP) additives. The purpose of the EP additive is to modify the rubbing surfaces as to prevent welding of the high spots or galling (destructive pitting) due to inadequate oil film strength on the gear tooth surfaces.


The entrance of water or other contaminants into the gear lubricant makes it necessary to use lubricants that can be separated easily from the contaminating materials. The application of heat, air, and moisture causes the oxidation process to occur rapidly on metal gears. A sufficient coating of oil on the metal helps to prevent oxides from forming and the oil works to carry the contaminants away.

Methods of Lubrication

How the gears are lubricated in the assembly determines the type of lubricant to be used. Ideally, gears should have oil-tight housings that will keep out contaminants and retain the oil. This is not always possible, and the lubricant must function under conditions that are far from ideal.

Circulating Systems

A pump delivers lubricant by spray or flood to a location near or directly at the point of tooth mesh. The pump operates with a separate drive or is sometimes directly connected (internally or externally) with the gears being lubricated. This method is suitable for gears being operated at normal speeds. A comparatively low-viscosity product is recommended for ease of pumping and an oil-tight housing is required. Oil heaters or coolers may be used with a circulating system depending on the service and location of the gear assembly.

Bath/Splash Systems

The fluid lubricant is stored in a sump or bath in the bottom of an enclosed gear set. One of the gears dips into the oil and lubricant is transferred to the contacting gears. The excess is thrown against the housing and is guided by means of troughs into the bearings or back to the sump.

It is recommended that the level for helical and spur gears, and for most worm gear reducers, on units operating at speeds above 500 feet per minute be such that either the largest gear or the underslung worm is a to 2 immersed in oil. At lower speeds, the entire mesh is usually covered with oil. At speeds above 2,500 feet per minute, a lighter grade of oil is used to help reduce heat generation due to oil churning. An oil-tight gear housing is required for the bath/splash system.

Idler Immersion System

This system is similar to the bath/splash system. The lubricant is picked up from the sump by an idler and delivered to the gear teeth. This system works well on slow-turning gear assemblies.

Intermittent Lubrication Systems

In this method, heavy viscous lubricants are applied by paddle, brush, drip, or hand pouring. The intermittent method is suitable for heavily loaded gears running at low speeds and can be used when the gears are not enclosed in an oil-tight housing.