List of gear nomenclature
The addendum is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line; also, the radial distance between the pitch diameter and the outside diameter.
The addendum circle coincides with the tops of the teeth of a gear and is concentric with the standard (reference) pitch circle and radially distant from it by the amount of the addendum. For external gears, the addendum circle lies on the outside cylinder while on internal gears the addendum circle lies on the internal cylinder.
Apex to back
The back angle of a bevel gear is the angle between an element of the back cone and a plane of rotation, and usually is equal to the pitch angle.
The back cone of a bevel or hypoid gear is an imaginary cone tangent to the outer ends of the teeth, with its elements perpendicular to those of the pitch cone. The surface of the gear blank at the outer ends of the teeth is customarily formed to such a back cone.
Back cone distance
In mechanical engineering, backlash is the striking back of connected wheels in a piece of mechanism when pressure is applied. Another source defines it as the maximum distance through which one part of something can be moved without moving a connected part. It is also called lash or play. In the context of gears, backlash is clearance between mating components, or the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established. In a pair of gears, backlash is the amount of clearance between mated gear teeth.
Backlash is unavoidable for nearly all reversing mechanical couplings, although its effects can be negated. Depending on the application it may or may not be desirable. Reasons for requiring backlash include allowing for lubrication and thermal expansion, and to prevent jamming. Backlash may also result from manufacturing errors and deflection under load.
Center distance (operating) is the shortest distance between non-intersecting axes. It is measured along the mutual perpendicular to the axes, called the line of centers. It applies to spur gears, parallel axis or crossed axis helical gears, and worm gearing.
The central plane of a worm gear is perpendicular to the gear axis and contains the common perpendicular of the gear and worm axes. In the usual case with axes at right angles, it contains the worm axis.
Composite action test
The composite action test (double flank) is a method of inspection in which the work gear is rolled in tight double flank contact with a master gear or a specified gear, in order to determine (radial) composite variations (deviations). The composite action test must be made on a variable center distance composite action test device.
Outer cone distance in bevel gears is the distance from the apex of the pitch cone to the outer ends of the teeth. When not otherwise specified, the short term cone distance is understood to be outer cone distance.
Mean cone distance in bevel gears is the distance from the apex of the pitch cone to the middle of the face width.
Inner cone distance in bevel gears is the distance from the apex of the pitch cone to the inner ends of the teeth.
Conjugate gears transmit uniform rotary motion from one shaft to another by means of gear teeth. The normals to the profiles of these teeth, at all points of contact, must pass through a fixed point in the common centerline of the two shafts. Usually conjugate gear tooth is made to suit the profile of other gear which is not made based on standard practice.
Crossed helical gear
A crossed helical gear is a gear that operate on non-intersecting, non-parallel axes.
The term crossed helical gears has superseded the term spiral gears. There is theoretically point contact between the teeth at any instant. They have teeth of the same or different helix angles, of the same or opposite hand. A combination of spur and helical or other types can operate on crossed axes.
The crossing point is the point of intersection of bevel gear axes; also the apparent point of intersection of the axes in hypoid gears, crossed helical gears, worm gears, and offset face gears, when projected to a plane parallel to both axes.
Equivalent pitch radius
Equivalent pitch radius is the radius of the pitch circle in a cross section of gear teeth in any plane other than a plane of rotation. It is properly the radius of curvature of the pitch surface in the given cross section. Examples of such sections are the transverse section of bevel gear teeth and the normal section of helical teeth.
Face (tip) angle
A face gear set typically consists of a disk-shaped gear, grooved on at least one face, in combination with a spur, helical, or conical pinion. A face gear has a planar pitch surface and a planar root surface, both of which are perpendicular to the axis of rotation. It can also be referred to as a face wheel, crown gear, crown wheel, contrate gear or contrate wheel.
Total face width is the actual dimension of a gear blank including the portion that exceeds the effective face width, or as in double helical gears where the total face width includes any distance or gap separating right hand and left hand helices.
For a cylindrical gear, effective face width is the portion that contacts the mating teeth. One member of a pair of gears may engage only a portion of its mate.
For a bevel gear, different definitions for effective face width are applicable.
Form diameter is the diameter of a circle at which the trochoid (fillet curve) produced by the tooling intersects, or joins, the involute or specified profile. Although these terms are not preferred, it is also known as the true involute form diameter (TIF), start of involute diameter (SOI), or when undercut exists, as the undercut diameter. This diameter cannot be less than the base circle diameter.
The front angle, in a bevel gear, denotes the angle between an element of the front cone and a plane of rotation, and usually equals the pitch angle.
The front cone of a hypoid or bevel gear is an imaginary cone tangent to the inner ends of the teeth, with its elements perpendicular to those of the pitch cone. The surface of the gear blank at the inner ends of the teeth is customarily formed to such a front cone, but sometimes may be a plane on a pinion or a cylinder in a nearly flat gear.
The gear range is difference between the highest and lowest gear ratios and may be expressed as a percentage (e.g., 500%) or as a ratio (e.g., 5:1).
The heel of a tooth on a bevel gear or pinion is the portion of the tooth surface near its outer end.
Helix angle is the angle between the helical tooth face and an equivalent spur tooth face. For the same lead, the helix angle is greater for larger gear diameters. It is understood to be measured at the standard pitch diameter unless otherwise specified.
Hobbing is a machining process for making gears, splines, and sprockets using a cylindrical tool with helical cutting teeth known as a hob.
The displacement of any tooth flank from its theoretical position, relative to a datum tooth flank.
Distinction is made as to the direction and algebraic sign of this reading. A condition wherein the actual tooth flank position was nearer to the datum tooth flank, in the specified measuring path direction (clockwise or counterclockwise), than the theoretical position would be considered a minus (-) deviation. A condition wherein the actual tooth flank position was farther from the datum tooth flank, in the specified measuring path direction, than the theoretical position would be considered a plus (+) deviation.
Involute polar angle
Involute roll angle
Lead is the axial advance of a helix gear tooth during one complete turn (360°), that is, the Lead is the axial travel (length along the axle) for one single complete helical revolution about the pitch diameter of the gear.
Lead angle is 90° to the helix angle between the helical tooth face and an equivalent spur tooth face. For the same lead, the lead angle is larger for smaller gear diameters. It is understood to be measured at the standard pitch diameter unless otherwise specified.
A spur gear tooth has a lead angle of 90°, and a helix angle of 0°.
See: Helix angle
Line of centers
The line of centers connects the centers of the pitch circles of two engaging gears; it is also the common perpendicular of the axes in crossed helical gears and wormgears. When one of the gears is a rack, the line of centers is perpendicular to its pitch line.
A normal plane is normal to a tooth surface at a pitch point, and perpendicular to the pitch plane. In a helical rack, a normal plane is normal to all the teeth it intersects. In a helical gear, however, a plane can be normal to only one tooth at a point lying in the plane surface. At such a point, the normal plane contains the line normal to the tooth surface.
Important positions of a normal plane in tooth measurement and tool design of helical teeth and worm threads are:
- the plane normal to the pitch helix at side of tooth;
- the plane normal to the pitch helix at center of tooth;
- the plane normal to the pitch helix at center of space between two teeth
Offset is the perpendicular distance between the axes of hypoid gears or offset face gears.
In the adjacent diagram, (a) and (b) are referred to as having an offset below center, while those in (c) and (d) have an offset above center. In determining the direction of offset, it is customary to look at the gear with the pinion at the right. For below center offset the pinion has a left hand spiral, and for above center offset the pinion has a right hand spiral.
The outside diameter of a gear is the diameter of the addendum (tip) circle. In a bevel gear it is the diameter of the crown circle. In a throated wormgear it is the maximum diameter of the blank. The term applies to external gears, this is can also be known from major diameter.
A pitch circle (operating) is the curve of intersection of a pitch surface of revolution and a plane of rotation. It is the imaginary circle that rolls without slipping with a pitch circle of a mating gear. These are the outlines off the imaginary smooth roller or friction discs in every pair of mating gears. Many important measurements are taken on and from this circle.
The base helix of a helical, involute gear or involute worm lies on its base cylinder.
Base helix angle
Base helix angle is the helix angle on the base cylinder of involute helical teeth or threads.
Base lead angle
Base lead angle is the lead angle on the base cylinder. It is the complement of the base helix angle.
The outside (tip or addendum) helix is the intersection of the tooth surface and the outside cylinder of a helical gear or cylindrical worm.
Outside helix angle
Outside helix angle is the helix angle on the outside cylinder.
Outside lead angle
Outside lead angle is the lead angle on the outside cylinder. It is the complement of the outside helix angle.
A normal helix is a helix on the pitch cylinder, normal to the pitch helix.
The pitch plane of a pair of gears is the plane perpendicular to the axial plane and tangent to the pitch surfaces. A pitch plane in an individual gear may be any plane tangent to its pitch surface.
The pitch plane of a rack or in a crown gear is the imaginary planar surface that rolls without slipping with a pitch cylinder or pitch cone of another gear. The pitch plane of a rack or crown gear is also the pitch surface.
Principal directions are directions in the pitch plane, and correspond to the principal cross sections of a tooth.
The axial direction is a direction parallel to an axis.
The transverse direction is a direction within a transverse plane.
Profile radius of curvature
Rack and pinion
Radial composite deviation
Tooth-to-tooth radial composite deviation (double flank) is the greatest change in center distance while the gear being tested is rotated through any angle of 360 degree/z during double flank composite action test.
Tooth-to-tooth radial composite tolerance (double flank) is the permissible amount of tooth-to-tooth radial composite deviation.
Total radial composite deviation (double flank) is the total change in center distance while the gear being tested is rotated one complete revolution during a double flank composite action test.
A shaft angle is the angle between the axes of two non-parallel gear shafts. In a pair of crossed helical gears, the shaft angle lies between the oppositely rotating portions of two shafts. This applies also in the case of worm gearing. In bevel gears, the shaft angle is the sum of the two pitch angles. In hypoid gears, the shaft angle is given when starting a design, and it does not have a fixed relation to the pitch angles and spiral angles.
See: Crossed helical gear.
Spiral bevel gear
Standard pitch circle
Standard pitch diameter
The standard reference pitch diameter is the diameter of the standard pitch circle. In spur and helical gears, unless otherwise specified, the standard pitch diameter is related to the number of teeth and the standard transverse pitch. The diameter can be roughly estimated by taking the average of the diameter measuring the tips of the gear teeth and the base of the gear teeth.
The pitch diameter is useful in determining the spacing between gear centers because proper spacing of gears implies tangent pitch circles. The pitch diameters of two gears may be used to calculate the gear ratio in the same way the number of teeth is used.
Where is the total number of teeth, is the circular pitch, is the diametrical pitch, and is the helix angle for helical gears.
Standard reference pitch diameter
The standard reference pitch diameter is the diameter of the standard pitch circle. In spur and helical gears, unless otherwise specified, the standard pitch diameter is related to the number of teeth and the standard transverse pitch. It is obtained as:
The test radius (Rr) is a number used as an arithmetic convention established to simplify the determination of the proper test distance between a master and a work gear for a composite action test. It is used as a measure of the effective size of a gear. The test radius of the master, plus the test radius of the work gear is the set up center distance on a composite action test device. Test radius is not the same as the operating pitch radii of two tightly meshing gears unless both are perfect and to basic or standard tooth thickness.
Throat form radius
It is convenient to choose one face of the gear as the reference face and to mark it with the letter “I”. The other non-reference face might be termed face “II”.
For an observer looking at the reference face, so that the tooth is seen with its tip uppermost, the right flank is on the right and the left flank is on the left. Right and left flanks are denoted by the letters “R” and “L” respectively.