 |
 |
 |
| |
|
|
10.1 SPUR GEARS
À pSpur gears are in very wide use throughout engineering.
These gears are flat, and either circular or straight (a rack).
The figure below shows a typical gear with common terms marked,
When gears are properly mated their pitch circles will be tangent. And the faces of the teeth will touch along the addendum and dedendum surfaces, down to the clearance circles.
Some terms of use when discussing gears,
backlash - the difference is the gap between gear teeth where they mesh. This leads to `play' in the gears.
diametral pitch is defined by,
The following relationships are also applicable,
The ratio between angular velocities of two gears can be determined with the law of gearing,
As seen above the law of gearing assumes that the pitch point is found at a constant radius. If this were to move the driven gear would accelerate /decelerate as the teeth mesh and separate.
To keep the gears meshing constantly an involute profile is typically used for the shape of the teeth.
To construct an involute profile, we need to construct a line that is tangential to both gears. The teeth on both gear will be constructed to contact only on this line.
The involute profiles for a single tooth will trace out a line as shown below (later we will develop an equation for the point on the unwrapping string).
The pressure angle is shown below,
Standards geometries for spur gears include, (based on American Gear Manufacturers Association and ANSI standards)
Typical diametral pitches and modules include, (based on American Gear Manufacturers Association and ANSI standards)
10.1.1 Involute Profiles
(|The figure below shows the triangulated layout for the basic involute function,
Next the involute curve is applied to the generation of gear teeth.
To generate points on these curves we must select values of XXXX and calculate (x, y) positions. These will be correct for one face of the tooth. If these are used to generate a splined curve, or graphed, they will form the tooth profile. The upper and lower bounds are determined by the addendum and dedendum.
10.1.2 Design of Gears
(|The basic steps to design a gear are outlines below,
If we are dealing with a rack, it is effectively a circular gear with an infinite radius.
When we have internal gears (one gear inside another) we need to adjust the methods to reflect that both gears are on the same side of the pitch line.
10.1.3 Design Issues
(|During motion the gear teeth undergo a combination of sliding and rolling. The direction of sliding reverses at the pitch point, where the motion is pure rolling.
10.1.3.1 - Undercutting and Contact Ratios
´ ð´ 0Undercutting occurs on some gears. This is a gouging of teeth that occurs when teeth contact below the base circle of the gear during motion.
During manufacturing some processes (generation) can remove the excess material that lead to undercutting. But this can reduce the base width of the teeth and weakening of the gear.
Undercutting problems can be reduced by increasing the radius of the gear, and increasing the number of teeth.
The gear teeth are in contact along the pressure line between the points where it intersects the addendum lines.
The contact ratio is as defined below. A value of 1 means that at any time only one tooth is engaged. A value greater than 1 means that only one tooth is engaged. A value of 2 would mean that at any time 2 teeth are engage. A value less than 1 means that at times the teeth are not in contact (bad).
Undercutting will not occur during production of the profiles if the following addendum values observed,
10.1.3.2 - Changing the Center Distance
´ ð´ 0If the center distance between gears is changed, then the pitch circles on both gears will move away from the center.
The result of the enlarging of pitch circles will be a reduction in the contact ratio. This will lead to a smaller contact ratio.
This condition also allows some play in the gears (backlash). This play means that a reversing of direction can lead to a small reversing rotation before the other tooth is impacted. This leads to errors and the impact forces can shorten the life of gears significantly.
10.1.4 Practice Problems
(|
| |
|
|