Gear Cutting And Gear Calculations
After the completing of this article the students should be able to
- Define gear technology
- Calculate hear blank size
- Calculate gear module
- Calculate number of teeth
- Calculate full depth and clearance
- Know about the plain indexing method and its calculation
- Know about the differential calculation methods and its calculation
- To developed skill and apply it in gear cutting
This article will supply the beginner with sufficient information to enable him to understand gear, gear terms, types of gears and the rules used in making spur gears. It will give him the application of the rules necessary to turn a gear blank in a table and to tromp the teeth on a milling machine.
DEFINITION OF GEAR
The term gear may be used in engineering practice for almost many kind of mechanism. But it refers specially to toothed wheel, in other words a gear is a wheel on which teeth hake been formed.
GEAR TYPES AND THEIR USES
The gears most commonly used in industry are
- Spur gears
- Bevel and miter gears
- Internal gear
- Helical gear
- Herringbone gear
- Worm gears
- Rack and pinion
This type of gear is a cylinder, wheel, or disk on the surface of which are cut parallel teeth. The larger gear is called the Gear and the smaller, the Pinion. Usually when two gears are in mesh and one is larger than the other, the names gear and pinion are applied. Spur gears are used to transmit power from one shift to another in cases where those shifts hake their axes parallel.
BEVEL AND MITER GEARS
Bevel gears are used when it is necessary to transmit power from one shaft to another where the communication shaft are located at an angle, with their axial lines intersecting. Bevel gears are not restricted to shafts at right angles. There are right angle bevel gears and angular bevel gears. In cases where the ration of a pair of bevel gears is 1:1, both gears being the same size and having the same number of teeth, they are known as MITER GEARS. These gears permit the driving of one shaft at right angles to the other. In a bevel gear the teeth are cut on a conical cone. A pair of gears is used to transmit power from one shaft to another, and share the two shafts have their extended axial lines intersecting at some angle other than 90deg. the gears are called angular bevel gears.
This type of gear has parallel teeth similar to the spur gear but cut on the inside of a cylinder of a ring. The mating gear may be a spur gear. However there are internal helical gears and internal bevel gears. The use such a combination of gears gives a much more compact mechanism, because the centers on which the two gears revolve are so much closer together than they can be efficiently made with two external spur gears operating as a pair.
This type of gear the teeth are cut spiraled around the body. Spiraling the teeth gives a smoother operation, such gears can be used to connect parallel shafts, and they operate far more smoothly than ordinary spur gears, because action of the teeth is progressive as they roll upon one another. Helical gears may be used not only to connect parallel shafts but also to connect shafts at angles with one and other, provided that their axial lines do not intersect.
HERRING BONES GEARS
The herring bones gears resembles two helical gears with half right-hand and half left band teeth, placed side by side, so that the teeth come together to from a chevron pattern. Herringbone gears are always used with parallel shafts.
A worm is an integral part of the worm gear mechanism is made of a blank, which has teeth cut into it in the form of a helix, or screw. It resembles a screw and its teeth are referred to as threads. The function of worm gearing is that of speed reduction. Worms may be made with single, double, triple, etc, threads. A double thread worm will revolve the worm gear twice as fast as a single thread a triple thread worm will revolve it three times as fast.
RACKS AND PINIONS
The functions of rack and pinions are to transform circular motion to rectilinear motion. Many types of racks are used in industry. Some have their teeth cut as spur, while other have helical teeth. The larger are called helical racks. Many such racks are used for adjusting the position of parts of machine tools.
METHODS OF CUTTING GEARS
Gear teethes are cut in the following ways:
On a milling machine using from a cutter, on a gear shaper using special cutters having the shape of tooth in them, and on a gear hobbler using cutters called Hobs.
Since most polytechnics institutes and colleges of technology of this country do not have gear shapers or gears hobblers as standard equipment. The method of cutting spur gears and simple helical gears on a milling machine will be explained in detail.
The student should know the meaning of the commonly used gear terms; he should be able to make the necessary calculations for spur gears. It is not necessary to learn all the rules, but it is well worthwhile to know where to find them when needed and how to use them.
The radial or perpendicular distance between the pitch circle and the top of the tooth.
The diameter of the circle from which the involutes are generated.
The diameter of the hole in the gear
The surface between the flanks of adjacent teeth
The shortest distance between the axes and the minting gears.
The distance on the circumference of the pitch circle between corresponding points of adjacent teeth.
The thickness of the tooth on pitch circle
The radial distance between the top of a tooth and the bottom of the mating tooth space.
The radial or perpendicular distance between the pitch circle and the bottom of the tooth space.
The ratio of the number of teeth to the number of inches in the pitch diameter. It indicates the number of teeth in the gear for each inch of pitch diameter
Face width (face of gear) :
The width of the pitch surface
Face of tooth :
The surface between the pitch-line element and the bottom. It includes the fillet, which is the curved surface that adjoins the bottomland of the space.
Module (in English measure):
The module (meaning measure) is the same proportional part of the pitch diameter as the circular pitch is of the pitch circumference that is if the pitch diameter of a gear is divided into as many equal parts as there are circular pitches (teeth) in the gear, for example 3-in pitch diameter, 30 teeth, the module is 1/10 in, and in a gear 2-in pitch diameter, 24 teeth, the module is 1/12 in. Note in each case, the module is fractional part of an inch and equals one divided by the pitch1/DP. In other words, module is the reciprocal of the diametric pitch. The term module is seldom used in this country; the expression 1/DP is used instead.
Module (in SI. System) :
In S.I system module is the ratio of the pitch circle diameter to the number of teeth. It is denoted by (m) the module is the index of tooth size.
Module, m=(PD)/N=(pitch circle diameter)/(No of teeth)
The recommended series of modules are:
1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40 and 50.
The module of second choice are:
1.25, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9, 11, 14, 18, 22, 28,36, and 45.
Outside diameter :
The diameter of the circle that contains the top of the teeth.
The circle through the pitch point having its center at the axis of the great
Pitch circumference :
Circumference of the pitch circle
Pitch diameter :
The diameter of the pitch circle, equals number of teeth divided by the diametric pitch PD=N/(DP)
The circle containing the bottom of the tooth spaces
The diameter of the pitch circle equal pitch diameter minus two addendum.
It is width of space between the two adjacent teeth measured along the pitch circle
It is width of the tooth measured along the pitch circle
It is the difference between the tooth space and the tooth thickness as measured o the pitch circle.
The radial distance between the outside circle and the root circle; equals addendum plus addendum.
The greatest depth to which a tooth of one gear extends into the tooth space of a mating gear; equals addendum of pinion plus addendum of gears or (usually) twice the addendum of either.
FORMULAS FOR DIMENSIONS OF SPUR GEARS:
The following formulas are for 14 1/2 deg. Composite system; 14 1/2 deg. involutes (generated) system, and 20-geg, full depth stub in volute system
DP= diametric pitch
PD= pitch diameter of the gear
Pd= pitch diameter of the pinion
CP= circular path
N= number of teeth on gear
n= number of teeth in opinion
OD= out side diameter or diameter of the gear blank
CD= center distance between gear and pinion
WD= whole depth
T= tooth thickness