This may be simple to some, but this is my first experience with designing gears, so bear with me... I'm trying to "cut" a spur gear to match the profile of the pinion gear I designed. This gear won't carry any load, it's basically for esthetics, but I want good contact between the two gears. I have an 8 tooth pinion & 60 tooth spur gear. Here is my pinion gear: I am working with one tooth profile and trying to simulate it moving out of the mating gear. Seems simple enough... This is the shape of one tooth, and the line/arc segments are something I drew that approximates what I should end up with (I used the assembly and adjusted the points until it was close). I could just use those line segments, but I really want to figure this out mathematically. This is what I figured should be right, but obliviously it's not... -I drew a circle around the main gear with a radius of the distance between my gear shafts. -Keeping the center of the pinion gear tooth coincident with that circle I rotated it 5 degrees (I plan on making this increment smaller once I get the calculation figured out). -Then I rotated the tooth around the center of the spur gear at the increment that it would rotate if the pinion rotated that 5 degrees. That was .6666666667 degrees. My math: 60 tooth spur - 8 tooth pinion 1 rotation = 7.5 rotations 360 degrees = (360 * 7.5) 2700 degrees 2700 / 5 (sketch increment) = 540 360 / 540 = .666666667 I'm sure I’m over simplifying this because here is my result: The red line is the line/arc that represents where I should be. I know it's really cluttered, but I figure once I get this figured out I can just use this file as a template. So obliviously .66666667 is too much of an increment. Just playing with the numbers I found .59 is really close to what I need. But I don't know how to get there mathematically. Does anyone know if I'm just completely over simplifying this, or am I doing something wrong in the math???? Please help!! Thanks, Bill Not sure if it will work but I also attached a .gif depicting what I'm trying to accomplish.
I'm surprised there aren't any replies yet. As I mentioned this is my first attempt at designing gears, I'm learing alot. I've found out about Involutes and how they apply to the gear profile, but I still don't know/understand how to draw this in my SW sketches. Anyone???
Looks like you got an interesting reply on the Physics Forum. http://www.physicsforums.com/showthread.php?t=663691 Would love to get that software just to play with.
I know i posted this in a few places, and have got a few replies. I just figured this would have been my best bet for replies. Thanks, tho. Bill
What you are trying to do is generate a conjugate profile from your pinion profile, graphically. When you generate a conjugate profile curve, it will be different from the parent curve. How did you arrive at the correct curve shown in the 2nd figure? The generated profile in the last figure appears to be fine.
Not trying to be rude, but it seems like i've had to restate everything I put in my original post everywhere i've posted this. As stated in the original post, The "correct" curve in fig in the 2nd figure was just a rough sketch from the assembly. It's not right, but it's close. The profile from the last figure is just a Gif from another website that visually represents what I was trying to figure out. Either way I've figured it out. So for anyone else trying to draw odd gears here it is. And it's rather simple... The Movement of the Pinion Tooth Around the Main Gear is this: 360 / Nm = Tm (Nm=Number of Teeth on Main Gear, Tm=Angle Between Teeth on Main Gear) Tm / X = M (X=Increment Factor, M=Increment Around Main Gear) And for the Pinion: 360 / Np = Tp (Np=Number of Teeth on Pinion Gear, Tp=Angle Between Teeth on Pinion Gear) Tp + Tm = Y Y / X = P (X=Increment Factor, M=Increment Around Pinion Gear) So from my original post: Main Gear is 60t, Pinion is 8t 360 / 60 = 6 / 12 = .5 (I drew 20 teeth and linked them, and with the increment factor set at 12, the 20th tooth was just outside the main gear max OD, so I had plenty of steps inside to cut a good profile) 360 / 8 = 45 + 6 = 51 / 12 = 4.25 As I drew it, each tooth is rotated around the center of the main gear .5 deg. Then the C/L of each tooth is rotated 4.25 deg. from the last. That's it plain n simple. I've already made a few gears using this and it works every time.
