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Root Fillet Equation (Spur Gear ) Trochoid Equation Needed
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Source：Internet Author：Unknow Pubdate：2008-04-15
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mechanical999 (Mechanical)
8 Apr 08 18:37
I am building a spur gear calculator. I did so much research about the Trochoid Equation Which i didnt fnd and i did not know how to implement. May anyone step forward and tell me what that equation is ?
- http://files.engineering.com/getfile.aspx?folder=9ee63354-0f31-4cfb-a5ad-28
mechanical999 (Mechanical)
8 Apr 08 20:45
I found this equation while doing some ttp://img101.imageshack.us/img101/1349/trochcc1.jpg" border="0">
mechanical999 (Mechanical)
9 Apr 08 21:12
May anyone tell me what a , theta and b represent ?
Pitch Circle ? Outer Circle ?
Theta ? Pressure angle ? 字串5
gearcutter (Industrial)
9 Apr 08 22:04
You need to get hold of these books;
Gear Geometry & Applied Theory by Faydor L. Litvin
Analytical Mechanics Of Gears by Earl Buckingham
On The Geometry Of External Involute Spur Gears by T. W. Khiralla.
I got my second-hand copies by searching the online book suppliers & Ebay.
Study these and all your questions will be answered. Ron Volmershausen
Brunkerville Engineering
Newcastle Australia
http://www.aussieweb.com.au/email.aspx?id=1194181
mechanical999 (Mechanical)
9 Apr 08 23:26
Thanx man. I did a pg=PR1&dq=Gear+Geometry+and+Applied+Theory+By+Faydor+L.+Litvin,+Alfonso+Fuentes&sig=ZFiC0UX1g57bteQqBrzvfTa-BOI#PRA1-PA267,M1" target="_blank">http://books.pg=PR1&dq=Gear+Geometry+and+Applied+Theory+By+Faydor+L.+Litvin,+Alfonso+Fuentes&sig=ZFiC0UX1g57bteQqBrzvfTa-BOI#PRA1-PA267,M1 字串6
But still cant find the Root Filler or undercut Equation.
if you have the books can you extract that one equation
for me please ?
Thanx in advance.
gearcutter (Industrial)
10 Apr 08 0:01
Start at page 97 in Litvin’s book. Also chapter 3 in Buckingham’s book. Ron Volmershausen
Brunkerville Engineering
Newcastle Australia
http://www.aussieweb.com.au/email.aspx?id=1194181
mechanical999 (Mechanical)
10 Apr 08 0:29
Thanx for pointing me to the correct direction. "Will Post Back After Im done Reading"
Also chapter 3 in Buckingham’s book. If you have a pdf version of the book or could tell me useful information regarding the fillet radius would be helpful.
mechanical999 (Mechanical)
10 Apr 08 1:08
字串9
Thanx again. After reading from page 97- . I got a general idea or the physical meaning. I still could not implement what i read with what im facing. The book is using a rack - cutter in my case im using the tool from the CNC Machine. I still dont know whats the equation of the root fillet & what are its variables ( What do they depend im my case).I tried looking hard in that book but ended up with nothing.I also used the "Search In Book" Feature but still without a clue.If you have any idea what that equation is , ill be so so so thankful.
israelkk (Aerospace)
10 Apr 08 10:55
mechanical999
The trochoid in the root of the tooth is the trace of the generating hob/rack/fellow tooth tip of the outside diameter of the hob/rack/fellow that cuts the gear blank while generating the gear. The fact that you use a CNC machining does not matter you need to create the trochoid as though as the hob/rack/fellow would create. When the manufactured gear is meshed with the second gear or pinion the mated gear teeth tips will follow the same trochoid path as the hob/rack/fellow would have done if you were cutting your gear with them. 字串5
I do not think there is a simple formula for the trochoid but you can simulate the generation process of the tooth root trochoid using the mated gear rotation with respect to the generated gear when it is meshed with the gear you want to cut. In fact you can create your gear completely by the same generation process. Just use the mated gear as your "hob/rack/fellow".
There is a Lisp code for Autocad created by one of the users of this forum that do the same process just do a search on past postings.
mfgenggear (Aerospace)
10 Apr 08 13:32
Mechanical999
In addition to the the previous very good advice heres some more.
What you normally look for is the min & max radii that can be produced between the Minor dia & Total Involute of the Gear & or pinion. Generally most designers (my customers)will specify a minimum fillet radii at the root on their engineering drawings, how ever the shapping or hob cutter must be designed as not to cut the root radii undersize or the radii does not extend into the required profile or above TIF(The start of the Total Involute form). 字串3
There is a formula for calculating the fillet radii possible
.
I will give a try to find it in my notes.
mechanical999 (Mechanical)
10 Apr 08 15:04
Israelkk ,
Thanx for your post. I think i found the lisp code on this thread:
http://www.eng-tips.com/viewthread.cfm?qid=157290
May you verify if thats the one ?
BTW how do i execute the lisp code ive never seen anything
like that before.
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mfgenggear ,
Thanx for your addition and for the info. Looking forward for the equation.
dimjim (Mechanical)
11 Apr 08 6:30
You can also check out Darle W. Dudley's book
Gear Handbook Section 8-2 on Trochoidal Fillet
for a fairly clear explanation and example of 字串9
how to calculate the coordinates of a trochoidal
fillet developed by a rack. A trochoidal fillet
developed by a shaper cutter is more complex but
is explained in the references above too as well
as in Dudley's book. Have fun!
mechanics2008 (Mechanical)
12 Apr 08 4:38
Hi guys its me mechanical999 i had some registration problem. So i recreated a new account.
Thanx Jim for your post. Thanx for all your help guys i appreciate that. But im really sorry for insisting. I have done some much reading and 0% implementing. It's not even straight forward in books. All your posts mean so much to me. I understand there are many cases for fillet generation. Minces is basically related to "Spur Gear" ; the simplest types of gears. I hope anyone gives me an equation for the fillet generation, so i can implement and get the desired shape straight forward.
字串3
dimjim (Mechanical)
12 Apr 08 9:55
While Israelkk sites the lisp program that I wrote it does not draw the trochoid but draws the involute portion from the based diameter to the outside diameter of the part, rotates it, mirrors it, and then makes an array of the tooth form exclusive of the the trochoidal fillet radius.
I was working on that early on and realized how difficult it was. I then wrote a lisp program to insert a hob profile rotate it, insert the hob again to its next position, etc until it outlined the tooth form and trochoidal radius based on the hob tip radius. I did have a basic file that I wrote based on that listed the coordinates of the trochoidal based on Buckingham's example but who uses gwbasic anymore. I also wrote some autolisp files to simulate a shaper cutter that would form the tooth space and fillet radius based on a particular number of tooth cutter. I had to modify the lisp program for each unique number of tooth cutter and create the shaper profile for that number of teeth. One advantage of a hobbed tooth rather than a shaped tooth is that the trochoidal fillet radius will never interfere with its mating pinion as it essentially simulates a shaper cutter of infinite number of teeth but it may provide an undercut if cutting small number of teeth in the gear or pinion.
字串4
mechanics2008 (Mechanical)
12 Apr 08 11:19
Thanx , How do i execute the lisp code ? Or have you built an exe file ?
gearcutter (Industrial)
12 Apr 08 21:15
This should help you figure out how to plot the trochoid generated by a rack cutter.
Don't allow yourself to get confused with other forms of generation such as other users have suggested. These forms are not relevant to what you are trying to do.
As dimjim correctly points out, the rack generated profile will correctly mesh with all the other profiles.
For what you are trying to achieve; I would highly recommend you study the books I have already listed. If you still have questions after reviewing the sheets below; go out and buy or loan the books.
I wasn't able to get the images to load into the thread, the site seems to be playing up, so here are direct links. 字串3
http://i200.photobucket.com/albums/aa127/ronvol/ToothGeometry1.jpg
http://i200.photobucket.com/albums/aa127/ronvol/ToothGeometry2.jpg
http://i200.photobucket.com/albums/aa127/ronvol/ToothGeometry3.jpg Ron Volmershausen
Brunkerville Engineering
Newcastle Australia
http://www.aussieweb.com.au/email.aspx?id=1194181
dimjim (Mechanical)
13 Apr 08 12:13
The autolisp files are executable and were written intitially for acad users. If you are an acad user,
instructions are in your help section as well as old
books. Once loaded, you simply type in its name
and use the enter key and the program takes over until
it completes its instruction or you use control c to stop it.
（Click：）
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