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How can you find the pitch circle diameter overall diameter and diametrical pitch of two gears working together?
I will start with the Formula for DP(diametral pitch) and PCD (pitch circle diam in Inches) Formula :- PCD = N/ DP (N is number of teeth) I will also assume that the gears are straight tooth gears (Spur Gears) First assume that the pitch circle is at a point half way between the crest and the root of the teeth (this is not true,but it is where we start to find what we want) Count the number of teeth in each gear. Suppose the result is 28 & 70 teeth. Now measure the exact distance between the very centre of the 2 gears, which is called the Centre Distance. Suppose the result is 3.5 inch. The individual PCD's will be in the ratio 28:70 which is the same as 2:5 The radii will of course also be in the ratio 2:5. Now 2 plus 5 equals 7, so this means that the 2 radii will be; 2/7 of 3.5 for the small gear, and 5/7 of 3.5 for the large gear. Result of these calculations is : Small Radii is exactly 1inch. Large radii is 2.5 inch. These 2 radii must total the distance between the centers of the 2gears, otherwise you have made an error. Now, the 2 PCD's will each be double the radii you calculated, so they will be , 2 inch and 5 inch. Now you can use these PCD's to calculate the Diametral Pitch of the gears. Use the formula I have given you up top. PCD = N/DP which is the same as DP = N / PCD so 28/ 2= 14. So DP is 14. Check using the large gear details, 70/5= 14 which is the same result so we know we are correct. Finally, the Addendum (distance between the Pich Circle and the Outer Diameter) Addendum = 1/DP = 1/14 = 0.071 Inch. The outer diameter of the gear will be it's Pitch Circle Diam PLUS 2 addendums = 2+ 0.142 = 2.142 Overall Diam for small gear and 5+ 0.142= 5.142 Inch Outer Diam for the larger gear. ALSO, there other types of Gear Pitch which are used. There is Circular Pitch and there is Module Pitch. Be sure that your gear does in fact have teeth which are Diametral Pitch, otherwise all these calculations will give the incorrect result. any factory which cuts gears will be able to check if your gears are DP or not. It is a job for specialists.
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