Gear Terminology - Spur and Helical Gears
Spur Gear: a traditional gear with straight teeth parallel to the axis of rotation.
Helical Gear: a gear with the teeth wrapped helically around the axis of rotation. The helix maintains a constant radius from the axis of rotation, unlike Spiral Bevel Gears and Hypoid Gears. As Helical Gears rotate with each other, they engage each tooth gradually, making them generally quieter and more efficient than Spur Gears. However, they introduce an axial force in each shaft that cannot be ignored.
Involute: An involute curve is defined as the path the end of a string takes as it is unwrapped from a circle. This curve is particularly useful as a gear tooth shape because it always pushes with the same direction and transmission ratio no matter where it is making contact with another involute curve of the same module and pressure angle. The involute curve is not the only curve with these properties, but it is the most tolerant to manufacturing errors, changes in center distance, etc. The “rack gear” of an involute has straight-walled triangular teeth with an included angle of twice the pressure angle. All CogChamp gear teeth are made with involute tooth profiles.
In order for two involute gears to mesh correctly, they must have the same:
- Module or Diametral Pitch, and
- Pressure Angle
Module: Module is the ratio of the pitch diameter of a spur gear divided by the number of teeth, and the units are typically millimeters. The larger the module, the larger the gear teeth, and the more power the gear can transmit given the same material and gear width. For reference, LEGO® Technic gears are made with a module of 1mm, while watch gears are in the range of 0.2mm module, and high-power transmission gears are in the range of 10mm module. For calculating the module on a helical gear, see Normal Module.
Module and Diametral Pitch give the same information, one is just the mathematical inverse of the other. Module is typically used when talking about metric gear systems, while Diametral Pitch is typical for inch gear systems. When designing a gear, it is highly recommended to select a standard module or diametral pitch.
Diametral Pitch (DP): (Not to be confused with Pitch Diameter) Diametral Pitch is the number of teeth per inch of Pitch Diameter on a spur gear, and the units are typically teeth per inch. The larger the Diametral Pitch, the smaller the gear teeth, and the less power the gear can transmit given the same material and gear width. For calculating the DP on a helical gear, see Normal Module.
Pitch Diameter: Imagine if you replace every gear in your system with a perfectly-sized non-slipping cylinder that holds the exact same transmission ratios. The Pitch Diameter (also called Reference Diameter) is the diameter of that cylinder. It is somewhere between the outermost diameter that touches the tooth tips (Addendum Circle) and the innermost diameter that touches the tooth roots (Dedendum Circle).
The Pitch Diameter is a completely imaginary quantity, but it is one of the most useful numbers for simulating the behavior of a gear and describing its overall size.
Rack Gear: A rack gear is a straight line of gear teeth, useful for turning rotary motion into linear motion. A rack gear can be thought of as a section of gear with infinite teeth - the pitch diameter is so large that a section of the circumference is effectively a straight line.
Addendum: The radial distance from the pitch diameter to the outermost tips of the teeth. For a standard gear, the addendum is typically 1*module or 1/DP.
Dedendum: The radial distance from the pitch diameter to the innermost roots of the teeth. For a standard gear, the dedendum is typically 1.25*module or 1.25/DP.
Outer Diameter / Addendum Circle: The outermost diameter of a gear that circumscribes the tips of all the teeth. The diameter is the Pitch Diameter plus two addendums.
Root Diameter / Dedendum Circle: The innermost diameter of a gear that inscribes the roots of all the teeth. The diameter is the Pitch Diameter minus two dedendums.
Normal Module: For Spur and Helical gears, CogChamp considers the Module and Normal Module to be the same. All of our helical gears are manufactured with a normal profile. This means they will mesh with a spur gear of the same module and pressure angle if held non-parallel. This also means a helical gear's pitch diameter will be larger than teeth * module. Instead, a helical gear's pitch diameter will be teeth * module / cos(helix angle).
For a deeper explanation:
If you take a spur gear and perfectly twist it into a helical gear, the teeth get thinner and closer together. Even though the number of teeth and the pitch diameter did not change, the teeth can no longer mesh with a spur gear of the same module and pressure angle. This would essentially form a gear with a “transverse module”, which CogChamp does not do.
In order to minimize the number of tools in our automated systems, Cogchamp chose to use normal module for all helical gears. This means one tool can be used to cut a helical gear of any helix angle.
Profile Shift: Profile Shift is an adjustment of how deep and wide the teeth are cut into a gear without changing the module/DP or the number of teeth. A negative profile shift pushes the cutter deeper into the gear, causing thinner teeth, wider gaps, and a decrease in the Outer Diameter, Root Diameter, and Base Circle Diameter (for an external gear). A positive profile shift does the opposite: wider teeth, thinner gaps, and larger gear diameters (for an external gear).
Typically, the driving gear is given a positive profile shift (such as 0.1), and the driven gear is given a negative profile shift (such as -0.15). The sum of the driving and driven profile shifts should be net negative - this gives a little wiggle room for manufacturing tolerances, center distance tolerances, and lubricants. However, a net negative profile shift between two gears is expected to increase the backlash between those gears. This isn't necessarily a bad thing - gears with zero backlash will bind up and have a very hard time moving.
Profile Shift is a value between -1 and 1 that represents how much of the Normal Module the cutting tool is shifted by. The radial difference between a gear with 0 profile shift and y profile shift (also known as Profile Shift Displacement) is y * Normal Module.
When CogChamp calculates the profile shift's effect on the gear diameters, we consider that the Pitch Diameter is unaffected by profile shift. Instead, the addendum and dedendum are modified by the profile shift displacement. We recognize that other schools of thought exist that do modify the pitch diameter. However, it is important to remember that the pitch diameter is purely an imaginary circle. As long as the real diameters and number of teeth are the same, the gear's design and behavior will be respected no matter where the pitch diameter is.
The effects of profile shift:
| Positive Profile Shift | Negative Profile Shift | |
|---|---|---|
| Tooth width | Wider | Thinner |
| Tooth strength | Stronger | Weaker |
| Likelihood of undercutting | Less Likely | More Likely |
| Backlash (at nominal center distance between 2 gears) | Less | More |
| Likelihood of binding (between 2 gears) | More Likely | Less Likely |
| Outer Diameter | Larger | Smaller |
| Root Diameter | Larger | Smaller |
| Base Circle Diameter | Larger | Smaller |
Backlash: The gap distance along a pitch diameter that one gear can move without contacting a mating gear. Backlash is determined by several factors including profile shift, manufacturing tolerances, and the actual center distance between the two gears. A little bit of backlash is required for involute gears to prevent binding and premature wear.
Undercutting: Many gear manufacturing processes can introduce a narrowing of each tooth at the base, especially if the tooth count is low. An ideal gear tooth is strongest near the root and narrows toward the tip. Gears with less than 12 teeth typically have an undercut at the base which significantly decreases the strength.
Pressure Angle: The angle between the normal vector coming off a tooth surface and the plane tangent to the pitch surface. This is typically 20° (sometimes 14.5°) and is a characteristic of the gear cutting tool geometry. A gear with a lower pressure angle will have more rectangular-looking teeth while a higher pressure angle will result in more triangular-looking teeth.
Helix Angle: If you “unroll” a helical gear, the helix angle is defined as the angle between the tooth direction vector and the rotation axis. A spur gear has a helix angle of 0. A helix angle can have a “Left Hand” or a “Right Hand” rotation direction defined below:
Center Distance: The distance between the centers of 2 meshing gears' pitch diameters. Nominally, the center distance should be the sum of the pitch radii of the two gears. Changing the center distance from nominal can be an effective way to control backlash and binding.
Base Circle: When designing an involute curve, the base circle is the circle around which the imaginary string is unwrapped. This circle doesn't exist as a measurable diameter anywhere on a gear. It is only used to define the tooth geometry.