Involute gear

[Zestje]

Hi,

I'm trying to make a parametric involute gear. I have taken a good hard look at all the examples I could find, but have some questions I can't find the answers to.

Let's start with these:

When I create the involute curve which defines the shape of the tooth, at which diameter does it start? I've seen the base and root diameter being used as well as sometimes even the pitch diameter.

E.g. in examples which use the base diameter the tooth geometry between the base and root diameter is drawn as a straight line which doesn't seem logical to me.

And does the start of the involute shift when changing nothing on the gear except the clearance?

If I find some time I'll post some pics or an example part...

 

[jbuckl]

As far as I was aware, the involute needs to start at the base circle diameter in order for it to allow conjurgate motion ie rolling against the next / mating tooth flank.
If using tooth thinning method, just offset the involute curve to achieve tooth thinning.
Is your intention to model a spur-gear?
Julian

 

[Zestje]

Thank you for your answer! It confirms what I've found in my old book from my studying time. And yes, I'm modeling a spur gear, for starters.

I've also found that the tooth geometry between
the base and root diameter is drawn as a straight line, because the involute curve simply isn't defined there. So far I think it's best to use a straight line, tangent to the start of the involute.

Furthermote I've found the formulae from here:
http://www.profilesmagazine.com/p33/marsalek.html
to be mathmatically correct. Several others base their involute equations on an involute corresponding to 90 degree angle. Those above are general formulae and correct for any angle.

I'm now implementing profile shift and the factor to increase tooth height (don't know what it's called). I'm not sure I'll be implementing undercut, since it's probably not necessary for my CAD needs and probably to complicated.

Then on to the next types of gears, helical and bevel. I love this kind of practice

 

[audctrl]

Did you look at these?


[url]http://www.mcadcentral.com/proe/files/gallery.asp?action=sea rch[/url]


I just searched for "gear"

 

[boydt]

I have a UDF of a spur gear tooth that is fully adjustable for size and number of teeth. PM me and I will send it to you.

 

[Zestje]

@audctrl: Yes I did look at those, most are not parametric or use incorrect equations. Two of them are actually quite good and I used the principles/equations as a basis to make my own gear.

@boydt: Please send it, I'll PM you my E-mail address. Thank you!

 

[audctrl]

@audctrl: Yes I did look at those, most are not parametric or use incorrect equations. Two of them are actually quite good and I used the principles/equations as a basis to make my own gear.

@boydt: Please send it, I'll PM you my E-mail address. Thank you!

I thought those models would be good for a starting point. The method I use is by creating two datum curves by equation and the equation comes from the industry standard book on involute splines. It works out pretty well, though I haven't had time to make it a Pro/Program part.

 

[Zestje]

One more question: want to adjust my equations to be able to take into account profile shift, but so far I haven't been able to find the error in my equations. Does anyone know the correct equation?

The equation for the -default- involute is this:

r=(pitch_diameter/2)*cos(contact_angle)
theta=90*t
x=r*cos(theta)+r*theta*(3.1415926536/180)*sin(theta)
y=r*sin(theta)-r*theta*(3.1415926536/180)*cos(theta)

 

[GearHead22]

You can find some useful info at this location --> http://true-involute-gear.comxa.com/


There are some free CAD models samples created to the true geometry. True involute gear profileand true trochold profile.


Download it and compare your creation to true model someone else has created.


Good Luck.
Edited by: GearHead22

 

[audctrl]

Here is a method that works pretty well.


/* For cylindrical coordinate system, enter parametric equation
/* in terms of t (which will vary from 0 to 1) for r, theta and z
/* For example: for a circle in x-y plane, centered at origin
/* and radius = 4, the parametric equations will be:
/*&nbs p; r = 4
/* theta = t * 360
/*&nbs p; z = 0
/*---------------------------------------------------------- ---------
todeg=180./pi
prad=58.83305/2.
/*58.83305 = Pitch diameter of the external spline.
bp=sqrt(1/cos(14.5)/cos(14.5)-1.)
/*14.5 = Pressure angle of the external spline.
offset=-todeg*1.13306/58.83305-bp*todeg+atan(bp)
/*1.13306 = Mean of the Max Actl. and Min Actl. of the spline.
/*58.83305 = Pitch diameter of the external spline.
brad=prad*cos(14.5)
/*14.5 = Pressure angle of the external spline.
cp=prad+6*prad/83
/*83 = Number of teeth of the external spline
cp2=cp*cp/brad/brad-1.
cp3=sqrt(cp2)
t1=t*cp3
r=brad*sqrt(1+t1*t1)
theta=-(t1*todeg-atan(t1)+offset)
z=0

 

[Zestje]

Thank you for the links & tips. I have been too busy lately to check it out, but I hope to find some time soon...

 

[Foggy]

Try my demo application to produce a involute form.
www.f099y.webs.com

 

[yffffonz]

I have a UDF of a spur gear tooth that is fully adjustable for size and number of teeth. PM me and I will send it to you.

Not sure if this topic is too old or if you are still around, but I have been dabbling on making a Gear Generator type UDF and having a hard time at it. I PM'd you to see if you still have access to the UDF you mentioned.
Thanks

 

[goodbrother]

Same here...Im having hard time figuring it out,if anyone have UDF file can you please send it to me,i would appreciate it much..