Involute gear

The involute toothing is one of several types of gears. It is the most gearing type in mechanical engineering. The involute is derived from a series of geometrical requirements on the tooth flank geometry, gearing law. The force exerted on each other should always been normal to the gear profile, tangential to the base circle diameters of both gears and through the pitch point C. The geometry, which satisfies these requirements is the involute of a circle. The aim of the geometric requirements is to minimize the mutual sliding and associated wear and heat generation and a uniform transmission of torque and a constant translation.

• 2.1 Constant torque transmission
• 2.2 center distance
• 2.3 Simple manufacturability and compatibility

Basic concepts

Designations

Da = diameter

D = pitch circle diameter

Df = root diameter

HaP = head height

HfP foot height =

S = tooth thickness ( at the pitch circle )

E = tooth gap ( at the pitch circle )

P = s e = pitch ( the pitch )

Z = number of teeth

X = profile shift factor ( unitless )

X * m = profile displacement (in mm)

In the sketch the gear light gray shown has a positive profile shift.

Reference profile

The reference profile corresponding to the theoretical rack profile on which the gear rolls play-free. In practice, it is the shape of the tool, with which the gear is formed in the hobbing.

The reference profile in use today gears is standardized in DIN 867.

Module

The module (symbol m, unit mm ) is the main reference for involute gears. All dimensions of the reference profile are given as factors of the module, as indicated by an asterisk ( *) is indicated in the variable name. For example, if the Fußhöhenfaktor ( hfP *) of the tooth 1.2 we obtain with a modulus of 2 mm, a base height of 2.4 mm. The module is in a sense the size category of gear, gears only with the same module can be paired with each other. If you change a gear in only the module and keeps the other factors, the result is therefore a geometrically similar gear. It can be seen that the gear diameter is proportional to the module via the link:

Passing

The point of contact of two tooth flanks moves during the entire procedure on a straight line, the length of path of AE ( see Figure 3). The angle at which the engagement section is disposed is called pressure angle. This corresponds to the pitch angle of the reference profile (only without profile shift). Are usual in this case 20 °, where there are gears with up to 5 ° pressure angle ( high gears ), especially in precision engineering. In vehicle transmissions for noise reasons (longer contact length and therefore larger contact ratio ) reference profiles are often used with a profile angle of 17.5 °. Although larger pressure angle result in a higher gear root and flank load capacity in general, are at large values ​​( > 30 ° ) but of limited use, as this significantly shortens the length of path, which is a disadvantage in general in terms of the smoothness.

During travels along the point of contact on the contact length varies with each other, the sliding speed of the teeth. From the standpoint of the driving gear from there at the beginning of the procedure before -shifting slipping which decreases up to the center of the engagement path toward. The center of the contact length, the pitch point C as above ( also the contact point of the two pitch circles of dw ), the sliding speed becomes zero. On this point there is pure Antiskid rolling. In the second half of the base section, the sliding velocity increases in the pulling direction of motion again. The signs of the velocities are accordingly for the driven gear swapped.

Profile shift

Under a profile shift is understood that the distance of the manufacturing tool for increased gear or decreased. The profile shift factor usually carries the symbols x and returns the related to the normal module radial displacement of the tool (see Figure 2), with external teeth, a positive value means a shift from the gear center away and a negative value means a shift toward the center.

Benefits

Constant torque transmission

With proper design, manufacture and assembly of involute there is always at least one pair of teeth in mesh. This allows the involute uniform transmission of torque by a constant translation. To increase the transmitted torque and to improve the smoothness is attempted as many pairs of teeth at the same time to participate in the torque transmission.

When a tooth with a standard 20 -degree reference profile but no transverse contact ratio of about 2.0 or higher can be characterized are given a spur alternately either a tooth pair or two pairs of teeth in engagement; the stiffness of the teeth varies considerably, which can lead to torsional vibrations and noise.

In helical gears, however, the total coverage is greater. There are thus at the same time more pairs of teeth in engagement, whereby the variation of tooth stiffness is smaller.

Center distance

The involute toothing is in contrast to other species is relatively insensitive to changes in the center distance of the two gears to one another. Thereby, the position tolerances of the bearing points, the concentricity of the shafts and their mounting non-critical in terms of the influence on the sliding speed and the overlap of the gearing. Only the pressure angle and thus the coverage change.

Simple manufacturability and compatibility

The involute is suitable for making the hobbing process.

Since the reference profile has straight edges, the hob used in construction of the teeth have straight edges and are thus easy to produce. The reference profile of conventional gears is standardized in DIN 867.