pitch and pressure angles

[irishwoodsman]

could someone explain this to me, i think i know what pressure angle is, its when the gear is coming of the meshing with another gear that the angle of the tooth is just enough to not put pressure on the other tooth to keep it from breaking[i think] but what is pitch:thinking:

 

[12bolts]

Bevel gears are commonly used to change the direction of drive between two shafts, ie vertical drive transferred to horizontal drive. Similar to a worm and crown gear. Your car differential is fitted with a bevel pinion gear and a bevel crown gear. "Simplified, this takes the longditudinal drive from your gearbox and transfers it to the cross axial drive to your wheels".
Pitch angle is used in reference to bevel gear design and is used to describe the angle required to mesh between two gears. Because the teeth are cut in a conical shape, pitch angle refers to the angle between that of the cone and the shaft it is mounted on.
Hope this is clear enough.
If I can find a drawing I will post it up.
...Ok could'nt find what I wanted so you get a crappy hand drawn sketch....



If you were to start with a blank to cut a bevel gear on, the pitch angle is the included angle between the centre line of the gear axis and the conical shape of one side of the blank.

Cheers Phil

 

[British Steel]

On normal spur gears (lathe change gears, those in your car's gearbox), the pressure angle is easiest to think of like this:

imagine a line between the centres of the two gears (shaft axis), and two teeth meeting so that their contact point is on that line and at their pitch circles. the contact force between the teeth (at 90 degrees to the tooth surface) will be tilted through the pressure angle, usually 14.5 degrees or 20 degrees, and the tooth faces will be tilted through the same angle from the line between the centres.

This leads to "OK, what's the pitch circle?"!

the pitch circle is the diameter of a *roller* meshed with another *roller* to give the required ratio of rotation between the two shafts - given enough friction this will work as well as a gear, but as we don't live in a world with infinite friction we have to add teeth that lock the two rollers together and prevent slip - this is done by giving each tooth an "addendum" that sticks up above the roller surface, and a "dedendum" dug out of the surface for the other "roller"'s tooth addendum to fit into.

In most gears the addendum adds an extra diameter of 2 tooth diametral pitches**, the dedendum subtracts 2 (and a smidge of clearance) - which leads on to...

"What's a diametral pitch?" in the roller example, to work out the ratio we only need to look at the diameter of the two rollers, and we can add them together and take half as the distance between centres - easy peasy
When we add teeth, we need them to mesh correctly, and such is the way of geometry that if we have the same ratio of teeth as we have of pitch diameters, they will (if the right shape) mesh nicely and give the ratio we want - this leads to the gear's diametral pitch, the number of teeth per inch of diameter (or in metric, the gear's module, diameter in mm per tooth). Gears with the same module or diametral pitch number will mesh with each other...

"but you said 'if the right shape' didn't you?" - yep, and there are two classes of gears commonly found - cycloid (mostly in clocks and watches or very old machinery) and involute (almost everything else!) - these have curves which complement each other, the involute curve can be generated by the simple method of unwinding a string from around our roller and marking where fixed points on the string go as we do it - not that gears are made that way

The simplest way of creating an accurate involute is with a gear shaper, which uses a rack as a cutter against a gear blank - the rack is moved along and the gear is rotated in synchrony as the rack is moved back + forth, shaving away the spaces between the teeth - the rolling and linear motions combine to give the "unwinding" motion that creates the involute curve, and the angle of the rack faces sets the pressure angle (e.g 14.5 or 20 degrees), the rack being effectively an infinite tooth gear.

** so a 46-tooth 16 diametral pitch will be 48/16 inches = 3 inches over the tops of the teeth, 44/16 or 2.75 inches (less a little bit for clearance) from dip-to-dip - similar for metric module gears, +2 module and -(2 module and a bit for clearance)

Hope this helps rather than confuses!

Dave H.

 

[irishwoodsman]

ah ok i seem to understand it some, i will do some reading on this cause i'm sure its going to come in handy on some of these older machines and for that matter the newer one too:biggrin:

 

[Video_man]

Pitch was explained to me as being like thread pitch, or how many bumps are there per inch (of diameter, in this case). Gears have to have the same pitch to mesh just like a 1/4-20 screw needs a 1/4-20 nut....I think I got this right....:huh: err, maybe it's bumps per inch of circumference...come to think of it.... but analagous to thread pitch, all the same.....

 

[irishwoodsman]

Pitch was explained to me as being like thread pitch, or how many bumps are there per inch (of diameter, in this case). Gears have to have the same pitch to mesh just like a 1/4-20 screw needs a 1/4-20 nut....I think I got this right....:huh:

ty Vman:biggrin:

 

[irishwoodsman]

Think of it in terms of a rack - how far apart are the teeth? That is the pitch.

We (yanks) usually think of gears in terms of Diametral Pitch. It's a way of representing the number of teeth scattered about the Pitch Circle - a diameter about halfway between the tooth tip and the tooth root. The Pressure Angle is an arbitrary number used to define the Base Circle from which the involute curve begins. The number 14.5 has been used for years - something to do with it being easier on engineering slide rules. In cases of where there are but a few teeth on the gear, that Base Circle can be below the root and causes the tooth to be undercut. Increasing that angle to 20 brings that Base Circle back out and makes for stronger teeth.

DP and PA define the gear set where all teeth mesh together. A simple formula: Number of Teeth + 2 divided by the OD more-or-less-equals the DP (written another way: (N+2)/OD=DP). A word of caution - we don't always use the exact OD, so the DP might be off. Use the closest, best guess. DP is always a whole number.

Nice formulas/charts and loads of other info are found in Machinery's Handbook.

ty blue chips, trying to figure which machinery book to get they are so many of them ok ebay:thinking:

 

[irishwoodsman]

understand, if you got a certain diameter there is only so many teeth you can put on it that would be called the pitch and for it to mesh with another gear the opposing gear would need the same pitch[teeth]:thinking: