Gears

*SPUR GEARS-NOMENCLATURE-1.pdf*download*SPUR GEARS-NOMENCLATURE-2.pdf*download*SPUR GEARS-INVOLUTE.pdf*download*SPUR GEARS-DIAMETRAL PITCH PRESSURE ANGLE TOOTH DIMENSIONS.pdf*download*SPUR GEARS-BACKLASH UNDERCUT FORMULAS.pdf*download*SPUR GEARS-LEWIS FORMULA.pdf*download*HELICAL GEARS-NOMENCLATURE HELIX ANGLE.pdf*download*HELICAL GEARS-FORMULAS.pdf*download*HELICAL GEARS-THRUST LOADS.pdf*download*MITER BEVEL GEARS-NOMENCLATURE.pdf*download*MITER BEVEL GEARS-MOUNTING DISTANCE.pdf*download*MITER BEVEL GEARS-TOOTH STRENGTH THRUST.pdf*download*WORMS WORM GEARS-HAND EFFICIENCY THRUST LOADS.pdf*download*WORMS WORM GEARS-FORMULAS SELF LOCKING.pdf*download*COUPLING UNIVERSAL JOINTS.pdf*download*Gears-MOUNTINGS ALTERATIONS LUBRICATION.pdf*download*Gears-MATERIALS STYLES KEYWAYS SETSCREWS.pdf*download*Gears-HOW TO FIGURE HORSEPOWER TORQUE.pdf*download*Gears-APPLICATION CLASSIFICATIONS-1.pdf*download*Gears-APPLICATION CLASSIFICATIONS-2.pdf*download*Metric Equivalents and Conversions*05-27*Tensile Strength*05-27*Draft Angles*05-27*Steel Designations*05-27*Determining Metric Tolerances*05-27*American Standard MoldBase Features*05-27

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SPUR GEARS GEAR NOMENCLATURE

ADDENDUM (a) is the height by which a tooth projects
beyond the pitch circle or pitch line.

BASE DIAMETER (D/b )is the diameter of the base cylinder
from which the involute portion of a tooth profile is generated.

BACKLASH (B) is the amount by which the width of a tooth
space exceeds the thickness of the engaging tooth on the
pitch circles. As actually indicated by measuring devices,
backlash may be determined variously in the transverse, nor-
mal, or axial-planes, and either in the direction of the pitch cir-
cles or on the line of action. Such measurements should be
corrected to corresponding values on transverse pitch circles
for general comparisons.

BORE LENGTH is the total length through a gear, sprocket, or
coupling bore.

CIRCULAR PITCH (p) is the distance along the pitch circle or
pitch line between corresponding profiles of adjacent teeth.

CIRCULAR THICKNESS (t) is the length of arc between the
two sides of a gear tooth on the pitch circle, unless otherwise
specified.

CLEARANCE-OPERATING (c) is the amount by which the
dedendum in a given gear exceeds the addendum of its mat-
ing gear.

CONTACT RATIO (m/c) in general, the number of angular
pitches through which a tooth surface rotates from the begin-
ning to the end of contact.

DEDENDUM (b) is the depth of a tooth space below the pitch
line. It is normally greater than the addendum of the mating
gear to provide clearance.

DIAMETRAL PITCH (P) is the ratio of the number of teeth to
the pitch diameter.

FACE WIDTH (F) is the length of the teeth in an axial plane.
FILLET RADIUS (r/f) is the radius of the fillet curve at the base
of the gear tooth.

FULL DEPTH TEETH are those in which the working depth
equals 2.000 divided by the normal diametral pitch.

GEAR is a machine part with gear teeth. When two gears
run together, the one with the larger number of teeth is called
the gear.

HUB DIAMETER is outside diameter of a gear, sprocket or
coupling hub.

HUB PROJECTION is the distance the hub extends beyond
the gear face.

INVOLUTETEETH of spur gears, helical gears and worms
are those in which the active portion of the profile in the trans-
verse plane is the involute of a circle.

LONG- AND SHORT-ADDENDUM TEETH are those of
engaging gears (on a standard designed center distance) one
of which has a long addendum and the other has a short
addendum.

KEYWAY is the machined groove running the length of the
NORMAL DIAMETRAL PITCH (P/n) is the value of the bore. A similar groove is machined in the shaft and a key fits
into this opening.
diametral pitch as calculated in the normal plane of a helical
gear or worm.

NORMAL PLANE is the plane normal to the tooth surface at a
pitch point and perpendicular to the pitch plane. For a helical
gear this plane can be normal to one tooth at a point laying
in the plane surface. At such point, the normal plane contains
the line normal to the tooth surface and this is normal to the
pitch circle.

NORMAL PRESSURE ANGLE in a normal plane of helical tooth.
OUTSIDE DIAMETER (D/0)
is the diameter of the addendum
(outside) circle.

PITCH CIRCLE is the circle derived from a number of teeth
and a specified diametral or circular pitch. Circle on which
spacing or tooth profiles is established and from which the
tooth proportions are constructed.

PITCH CYLINDER is the cylinder of diameter equal to the
pitch circle.

PINION is a machine part with gear teeth. When two gears
run together, the one with the smaller number of teeth is called
the pinion.

PITCH DIAMETER (D) is the diameter of the pitch circle. In
parallel shaft gears, the pitch diameters can be determined
directly from the center distance and the number of teeth.

PRESSURE ANGLE (?) is the angle at a pitch point between
the line of pressure which is normal to the tooth surface, and the
plane tangent to the pitch surface. In involute teeth, pressure
angle is often described also as the angle between the line of
action and the line tangent to the pitch circle. Standard pressure
angles are established in connection with standard gear-tooth
proportions.

ROOT DIAMETER (D)
is the diameter at the base of the tooth Space.
PRESSURE ANGLE?TM)OPERATING () is determined by the
center distance at which the gears operate. It is the pressure
angle at the operating pitch diameter.
TIP RELIEF is an arbitrary modification of a tooth profile
whereby a small amount of material is removed near the tip of
the gear tooth.(D)

UNDERCUT is a condition in generated gear teeth when any
part of the fillet curve lies inside a line drawn tangent to the
working profile at its point of juncture with the fillet.(D)
WHOLEDEPTH (h/t) is the total depth of a tooth space, equal
to addendum plus dedendum, equal to the working depth plus
variance.

WORKING DEPTH (h/k ) is the depth of engagement of two
gears; that is, the sum of their addendums.

SPUR GEARS INVOLUTE FORM

Gear teeth could be manufactured with a wide variety of
shapes and profiles. The involute profile is the most commonly
used system for gearing today, and all Boston spur and helical
gears are of involute form.

An involute is a curve that is traced by a point on a taut cord
unwinding from a circle, which is called a BASECIRCLE. The
involute is a form of spiral, the curvature of which becomes
straighter as it is drawn from a base circle and eventually
would become a straight line if drawn far enough.

An involute drawn from a larger base circle will be less curved
(straighter) than one drawn from a smaller base circle.
Similarly, the involute tooth profile of smaller gears is considerably curved, on larger gears is less curved (straighter), and is straight on a rack, which is essentially an infinitely large gear.

Involute gear tooth forms and standard tooth proportions are
specified in terms of a basic rack which has straight-sided
teeth, for involute systems.

DIAMETRAL PITCH SYSTEM

All stock gears are made in accordance with the diametral
pitch system. The diametral pitch of a gear is the number of
teeth in the gear for each inch of pitch diameter. Therefore, the
diametral pitch determines the size of the gear tooth.

PRESSURE ANGLE

Pressure angle is the angle at a pitch point between the line of
pressure which is normal to the tooth surface, and the plane tan-
gent to the pitch surface.The pressure angle, as defined in this
catalog, refers to the angle when the gears are mounted on their
standard center distances.
Boston Gear manufactures both 14-1/2?and 20?PA, involut
full depth system gears. While 20?PA is generally recognize
as having higher load carrying capacity, 14-1/2?PA gears hav
extensive use. The lower pressure angle results in less
change in backlash due to center distance variation and con-
centricity errors. It also provides a higher contact ratio and
consequent smoother, quieter operation provided that under-
cut of teeth is not present.

TOOTH DIMENSIONS

For convenience, Tooth Proportions of various standard
diametral pitches of Spur Gears are given below.

BACKLASH

Stock spur gears are cut to operate at standard center dis-
tances. The standard center distance being defined by:
Standard Center Distance = (Pinion PD + Gear PD)/2

When mounted at this center distance, stock spur gears will
have the following average backlash:

An increase or decrease in center distance will cause an
increase or decrease in backlash.

Since, in practice, some deviation from the theoretical stan-
dard center distance is inevitable and will alter the backlash,
such deviation should be as small as possible. For most appli-
cations, it would be acceptable to limit the deviation to an
increase over the nominal center distance of one half the aver-
age backlash. Varying the center distance may afford a practi-
cal means of varying the backlash to a limited extent.
The approximate relationship between center distance and
backlash change of 14-1/2?and 20?pressure angle gears
shown below:

For 14-1/2?(R)CChange in Center Distance = 1.933 x Change in Backla
For 20?(R)CChange in Center Distance = 1.374 x Change in Backla
From this, it is apparent that a given change in center dis-
tance, 14-1/2?gears will have a smaller change in backlas
than 20?gears. This fact should be considered in cases wher
backlash is critical.

UNDERCUT

When the number of teeth in a gear is small, the tip of the mating
gear tooth may interfere with the lower portion of the tooth pro-
file. To prevent this, the generating process removes material at
this point. This results in loss of a portion of the involute adjacent
to the tooth base, reducing tooth contact and tooth strength.

On 14-1/2?PA gears undercutting occurs where a number of
teeth is less than 32 and for 20?PA less than 18. Since thia
condition becomes more severe as tooth numbers decrease, it
is recommended that the minimum number of teeth be 16 for
14-1/2?PA and 13 for 20?PA

In a similar manner INTERNAL Spur Gear teeth may interfere
when the pinion gear is too near the size of its mating internal
gear. The following may be used as a guide to assure proper
operation of the gear set. For 14-1/2?PA, the difference in
tooth numbers between the gear and pinion should not be less
than 15. For 20?PA the difference in tooth numbers should no
be less than 12.

LEWIS FORMULA

Gear failure can occur due to tooth breakage (tooth stress) or
surface failure (surface durability) as a result of fatigue and
wear. Strength is determined in terms of tooth-beam stresses
for static and dynamic conditions, following well established for-
mula and procedures. Satisfactory results may be obtained by
the use of Barth°Os Revision to the Lewis Formula, which consid
ers beam strength but not wear. The formula is satisfactory for
commercial gears at Pitch Circle velocities of up to 1500 FPM. It
is this formula that is the basis for all Boston Spur Gear ratings.
METALLIC SPUR GEARS

W=SFY/ P(600/(600+V))

W=Tooth Load, Lbs. (along the Pitch Line)

S =Safe Material Stress (static) Lbs. per Sq. In. (Table II)

F=Face Width, In.

Y =Tooth Form Factor (Table I)

P=Diametral Pitch

D=Pitch Diameter

V=Pitch Line Velocity, Ft. per Min. = .262 x D x RPM
For NON-METALLIC GEARS, the modified Lewis Formula
shown below may be used with (S) values of 6000 PSI for
Phenolic Laminated material.

W=SFY/p(150/(200 + V) + .25)

HELICAL GEARS GEAR NOMENCLATURE

The information contained in the Spur Gear section is also
pertinent to Helical Gears with the addition of the following:

HELIX ANGLE () is the angle between any helix and an element of its cylinder. In helical gears, it is at the pitch diameter
unless otherwise specified.

LEAD (L) is the axial advance of a helix for one complete turn,
as in the threads of cylindrical worms and teeth of helical
gears.

NORMAL DIAMETRAL PITCH (P/n ) is the Diametral Pitch as
calculated in the normal plane.

HAND (R)C Helical Gears of the same hand operate at righ
angles, see Fig. 1

Helical Gears of opposite hands run on parallel
shafts. Fig. 2

All Boston Helicals are cut to the Diametral Pitch system,
resulting in a Normal Pitch which is lower in number than the
Diametral Pitch.

INVOLUTE?TM)The Helical tooth form is involute in the plane o
rotation and can be developed in a manner similar to that of
the Spur Gear. However, unlike the Spur Gear, which may be
viewed as two-dimensional, the Helical Gear must be viewed
as three-dimensional to show change in axial features.

Helical gears offer additional benefits relative to Spur Gears,
those being:

Improved tooth strength due to the elongated helical wrap-
around.

Increased contact ratio due to the axial tooth overlap.

Helical Gears thus tend to have greater load carrying capac-
ity than Spur Gears of similar size.

Due to the above, smoother operating characteristics are
apparent.

When Helical gears are operated on other than Parallel shafts,
the tooth load is concentrated at a point, with the result that
very small loads produce very high pressures. The sliding
velocity is usually quite high and, combined with the concentrated pressure, may cause galling or excessive wear, especially if the teeth are not well lubricated. For these reasons,
the tooth load which may be applied to such drives is very lim-
ited and of uncertain value, and is perhaps best determined by
trial under actual operating conditions. If one of the gears is
made of bronze, the contact area and thereby the load carrying capacity, may be increased, by allowing the gears to ?run
in°± in their operating position, under loads which graduall
increase to the maximum expected.

THRUST LOADS

As a result of the design of the Helical Gear tooth, an axial or
thrust load is developed. Bearings must be adequate to
absorb this load. The thrust load direction is indicated below.
The magnitude of the thrust load is based on calculated
Horsepower.

Axial Thrust Load =126,050 x HP/ (RPM x Pitch Diameter)

Boston Helicals are all 45?Helix Angle, producing a tangentia
force equal in magnitude to the axial thrust load. A separating
force is also imposed on the gear set based on calculated
Horsepower.

Separating Load = Axial Thrust Load x .386
Above formulae based on Boston 45?Helix Angle and 14-1/2
Normal Pressure Angle.

MITER ANDBEVEL GEARS

Gear geometry for both straight and spiral tooth Miter and
Bevel gears is of a complex nature and this text will not
attempt to cover the topic in depth.

The basic tooth form is a modification to the involute form and
is the common form used in production today. All Boston stan-
dard stock Miter and Bevel gears are manufactured with a 20?
Pressure Angle. Bevel gears are made in accordance with
A.G.M.A. specifications for long and short Addendum system
for gears and pinions (pinion is cut long Addendum) which
serves to reduce the amount of pinion tooth undercut and to
nearly equalize the strength and durability of the gear set.

NOMENCLATURE

NOMENCLATURE Nomenclature may best be understood by means of graphic
representation depicted below:

Similar in nature to Helical gearing, Spiral Miters and Bevels
must be run with a mating pinion or gear of opposite hand.

The teeth of a Left Hand
gear lean to the left when
the gear is placed on a hori-
zontal surface.

The teeth of a Right Hand
gear lean to the right when
the gear is placed flat on a
horizontal surface.

All Boston Spiral Miter and Bevel gears are made with 35?spi
ral angles with all pinions cut left hand.

Straight tooth bevel (and miter) gears are cut with generated
tooth form having a localized lengthwise tooth bearing known
as the ?Coniflex tooth form. The superiority of these gears
over straight bevels with full length tooth bearing, lies in the
control of tooth contact. The localization of contact permits
minor adjustment of the gears in assembly and allows for
some displacement due to deflection under operating loads,
without concentration of the load on the end of the tooth. This
results in increased life and quieter operation.

Boston Gear Bevel and Miter Gears will provide smooth, quiet
operation and long life when properly mounted and lubricated.
There are several important considerations in mounting these
gears.

1.All standard stock bevel and miter gears must be mounted
at right angles (90?) for proper tooth bearing

2.Mounting Distance (MD) is the distance from the end of the
hub of one gear to the center line of its mating gear. When
mounted at the MD specified, the gears will have a proper
backlash and the ends of the gear teeth will be flush with
each other (see drawings).

3.All bevel and miter gears develop radial and axial thrust
loads when transmitting power. See page 145. These
loads must be accommodated by the use of bearings.

Incorrect

If Mounting Distance of one or both gears is made less than
dimension specified, the teeth may bind. Excessive wear or
breakage can result. Drawing below shows gears mounted
incorrectly with the Mounting Distance too short for one gear.

Incorrect

If Mounting Distance of either gear is made longer than dimension specified, as shown in drawing below, the gears will not
be in full mesh on a common pitch line and may have excessive backlash. Excessive backlash or play, if great enough,
can cause a sudden impulse or shock load in starting or
reversing which might cause serious tooth damage.
WORMS ANDWORM GEARS

Boston standard stock Worms and Worm Gears are used for
the transmission of motion and/or power between non-inter-
secting shafts at right angles (90?). Worm Gear drives ar
considered the smoothest and quietest form of gearing when
properly applied and maintained. They should be considered
for the following requirements:

HIGH RATIO SPEED REDUCTION

LIMITED SPACE

RIGHT ANGLE (NON-INTERSECTING) SHAFTS
GOOD RESISTANCE TO BACK DRIVING

General nomenclature having been applied to Spur and
Helical gear types, may also be applied to Worm Gearing with
the addition of Worm Lead and Lead Angle, Number of
Threads (starts) and Worm Gear Throat diameter.

THRUST LOADS

As is true with Helical and Bevel gearing, Worm gearing, when
operating, produces Thrust loading. The Chart below indicates
the direction of thrust of Worms and Worm Gears when they
are rotated as shown. To absorb this thrust loading, bearings
should be located as indicated.

EFFICIENCY

The efficiency of a worm gear drive depends on the lead angle
of the worm. The angle decreases with increasing ratio and
worm pitch diameter. For maximum efficiency the ratio should
be kept low.

Due to the sliding action which occurs at the mesh of the
Worm and Gear, the efficiency is dependent on the Lead
Angle and the Coefficient of the contacting surface. A com-
mon formula for estimating efficiency of a given Worm Gear
reduction is:

For a Bronze Worm Gear and hardened Steel Worm, a
Coefficient of Friction in the range of .03/.05 may be assumed
for estimated value only.

SELF-LOCKING ABILITY

There is often some confusion as to the self-locking ability of a
worm and gear set. Boston worm gear sets, under no condition should be considered to hold a load when at rest. The
statement is made to cover the broad spectrum of variables
effecting self-locking characteristics of a particular gear set in
a specific application. Theoretically, a worm gear will not back
drive if the friction angle is greater than the worm lead angle.

However, the actual surface finish and lubrication may reduce
this significantly. More important, vibration may cause motion
at the point of mesh with further reduction in the friction angle.
Generally speaking, if the worm lead angle is less than 5?
there is reasonable expectation of self-locking. Again, no guarantee should be made and customer should be advised. If
safety is involved, a positive brake should be used.

WORM GEAR BACK-DRIVING

This is the converse of self-locking and refers to the ability of
the worm gear to drive the worm. The same variables exist,
making it difficult to predict. However, our experience indicates
that for a hardened worm and bronze gear properly manufac-
tured, mounted and lubricated, back-driving capability may be
expected, if the lead angle is greater than 11?. Again, no guar
antee is made and the customer should be so advised.

RATING

The high rate of sliding friction that takes place at the mesh of
the Worm and Gear results in a more complex method of rating these Gears as opposed to the other Gear types. Material
factors, friction factors and velocity factors must all be consid-
ered and applied to reflect a realistic durability rating.

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