Involute Gear Profile
Gears are mechanisms used to transmit power. There are many different types of gears that can be specialized to a specific application. Gears transmit power through the messing of gear teeth at single point along a line of action.
The tooth profile is one side of a tooth in a cross section between the outside circle and the root circle of the gear. It normally refers to the curve of the intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane. The most common type of gear tooth profile is the involute gear tooth profile, standard and corrected.
An involute gear profile means that the profiles of the gear teeth are involutes of a circle, while the involute of a circle is the locus of a point on a piece of string as the string is unwrapped from a circle. The equations for the involute of a circle are the following:
The standard involute gear profile only depends on the number of teeth, pressure angle and pitch which means that the majority of gear calculations can be output from those three pieces of gear data. The form or shape of an involute curve depends upon the diameter of the base circle from which it is derived. Using a standard involute gear tooth profile will mean that virtually any gear that has the same pitch, pressure angle and helix angle will be able to operate with one another, because in this type of gear design, contact between a pair of gear teeth occurs at a single instantaneous point where two involutes of the same spiral hand meet. A major factor of the involute gear profile matters is the number. For large number of teeth the gear tooth profile will look more like a rack while the smaller number of teeth will have a large root fillet radius, but a profile shift can correct this root fillet radius.
The involute gear profile affects the intermeshing between two gears. Intermeshing is a term used to mean when two gear teeth come in contact with one another in order to transmit power. Contact between intermeshing involute teeth on a driving and driven gear is along a straight line that is tangent to the two base circles of these gears. The contact can affect the effectiveness at which the gears transmit power, the noise that occurs while the gear set is operating and the precision of the entire system.
The other common gear profile is the cycloidal gear profile, but involute gears have certain advantages over cycloidals gears such as ease of design and manufacture. The involute profile also has the advantage of the constant pressure angle throughout the engagement of two gears. Cycloidal gears have the advantage in strength due to their wider flanks, and the lack of interference that may occur in involute gear teeth where the root of one tooth undercuts the tip of another tooth during meshing. Undercut is when the top of a gear will cut a radius into the root of another gear. Gears with undercut have lower strength in the dedendum and creates lower gear contact due to shortened involute curve on the tooth.
Profile Shift
Profile Shift or ‘addendum modification’ or ‘correction’ is simply the displacement of the basic rack datum line from the reference diameter of the gear. A positive profile shift increases the tooth thickness while a negative profile shift reduces the tooth thickness. For a standard gear tooth profile the base circle radius does not change, regardless of whether the gear has profile shift, all other gear data being standard. Gears with profile shift can still be manufactured in the same methods and cutters that standard gears are such as hobbing and shaping. Some limits can be reached when designing a profile shifted gear, the upper resulting in an extremely narrow tip and the lower resulting in a severely undercut gear respectively. But while it is rare in some application the limits of profile shifting are used.
While most engineers would prefer the use of standard gear profiles, shifted gears can be needed in various specialized applications. Profile shift helps to prevent undercut that can occur when the number of gear teeth to be cut becomes small, the generating tool sweeps out its paths, and removes some of the profile. It can also help to adjust the center distance between gears when a failure in center distances occurs. The center distance influences the contact ratio between two gears. Contact ratio can affect gear noise, sliding between the gears in mesh, and reduce backlash. Profile shifting does have its advantages in balancing several aspects of the gear such as:
- The bending fatigue in both the pinion and the gear.
- Specific sliding of the pitch point which leads to maximized pitting resistance.
- Peak contact flash temperatures at the pitch point which will minimize the probability of scuffing.
The gear’s performance in terms of pitting resistance and scuffing resistance is based on the location of the theoretical standard generating rack, but for practical manufacturing and operating considerations the manufacturing tool usually must be at a different location than the theoretical standard generating rack.
While rack gears do not change the shape of the gear tooth profile with corrections, gears that have a smaller amount of teeth are much more sensitive to profile shift due to the relationship between the number of teeth in a gear and the standard gear tooth profile as stated above.
Formulas for Profile Shift:
Where,
|
m |
Module |
|
x |
Coefficient of Shift |
|
z |
Number of Teeth |
|
⍺ |
Pressure Angle |
Marples Gears is a precision gear manufacturing machine shop. Marples Gears specializes in high precision fine pitch gear manufacture up to Q13 quality standard on our gear products that we custom manufacture in house. At Marples Gears, we also use software in order to analyze the gear tooth profile of your part. While we are not certified to design gears through AS9100-D, but we can consult on the best method of manufacturing of your gears. Marples Gears also has the ability to reverse engineer as gear through the method discussed above and through the analysis of the original gear. For a custom engineer reviewed quote email info@marplesgearsinc.com or visit our custom quote page under the contact us tab above.
