trochoid & involute 1

[berto]

what is the difference?
why the root fillet of a gear teeth is generated by trochoid
and not by an involute?
someone help me ..
thank you very much

 

[EnglishMuffin]

The simple answer is that they are generated by different things. The involute is generated from the envelope of a series of overlapping straight lines, and is the only kinematically important part of the resulting profile. But these straight lines have to end somewhere in practice, and points on the end of these lines move along a trochoid. The "only" important significance of the trochoidal fillet is one of strength. If there is no interference, the trochoid always blends smoothly with the involute - this is one of the aims of good gear design. (Its complicated by considerations of grinding allowance etc).

 

[EnglishMuffin]

Actually, Ester, I should add that you don't necessarily have to have trochoids in the root fillet of gears - they only occur naturally when the profile is "generated" - as my first reply describes.. If you form or mold the teeth, for example, you can theoretically have any root fillet curve you desire.

 

[diamondjim]

Ester,
From the Base diameter out to the
od is the unrolled involute form.
Below the Base diameter to the root
of the gear is a fillet formed by
the method of cutting. If it is generated
by a hob cutter or pinion style shaper
it forms a trochoidal fillet radius.
If the trochoidal fillet radius is formed
by a hob style cutter any gear with the
same pressure angle and form can operate
with that cut gear without having involute
interference although it may have been
undercut by the hob style cutter if there
are very small number of teeth in the pinion.
This is the large advantage of hobbed gear
teeth.

 

[EnglishMuffin]

Diamondjim:
Just to clarify that the interference I was referring to was generating interference - which probably most people call undercut. My trouble is that I use the Maag gear handbook all the time, and it's translated from the German.

 

[berto]

first of all thank you.

1_diamondjim: what is "hob style cutter"?

2_so, trochoid exist only when i got interference or undercut becouse of the small number of teeth. Right?
becouse if i have no undercut, trochoid and involute blend toghether.
to clarify, they have the same origin, straight lines that
rollin on a circle.

 

[EnglishMuffin]

Ester :

If gears are generated,(which includes "Hobbing&quot, you will always get a trochoid in the root, and an involute on the flank. If you try and generate a standard gear with too few teeth (seventeen or less) you will get "undercut" or "cutter interference", and the trochoid will not blend properly with the involute.
I'm going to leave this to Diamondjim to clarify! He can probably recommend some good books too.

 

[diamondjim]

Ester,
Yes you are right in that when the gear teeth
are not undercut you have a tangent trochoidal
fillet radius.
As English Muffin said hobbing
is the correct term for a rack type
or hob cutter. He is also right in
that the lowest number of teeth
without undercut is dependent on the
pressure angle and is 17 for a full depth
tooth form and 14 for a stub tooth form for
a 20 degree pressure angle system.
The lowest number of teeth without undercut
is listed in almost all gear books as well
as Machineries Handbook which is a nice
gear section to start out with. Many basic
gear formulas are there and it is a good
reference book.
Module gearing is full depth form and can be
stubbed by truncating the addendum so can be
formed by using the same tooling.
There are so many things good about the metric
system.

 

[berto]

ok, thank you very much for the reply.
i write just now becouse of a little holiday ..
best regards

 

[roseda]

Does anyone know how to construct the correct involute for a given gear tooth form?

Is there an equation based on given gear data such as base circle, pressure angle, addendum modification etc.?

 

[roseda]

What type of trochoid is the fillet formed by a hob cutter?

Is it a cycloid, curtate cycloid, prolate cycloid or something else entirely.

 

[diamondjim]

The basic coordinates from the centerline
of the gear or pinion is

X = r x sin theta
Y = r x cos theta

where theta is the vectorial angle from
the vertical centerline.
keep substituting theta values from 0 to
about 45 degrees to get different coordinates.
You want to use small angular interval differences
from 0 to 2 degrees and progressively larger
intervals thereafter.

 

[gearman1234]

Hi Diamondjim,

I am trying to construct a trochoid along with an involute. Involute is fine but to consruct a trochoid what r is to be used. Is it the Base dia of the gear?

 

[diamondjim]

I have a hob lisp program that will simulate
the hobbing of the trochoid. The trochoid is
unique for each number of teeth hobbed.
Any hobbed tooth will operate with another
hobbed tooth if both are external gears.
The trochoid can be generated with a shaper
style cutter as well but then you need the
full shaper cutter details.
If you give me the number of teeth in the
pinion and gear I can send you the hobbed
gear teeth acad drawings for each.
330 678 0226
In Dudley's book there is a program that will
allow you to created the coordinates of the
trochoid.
You should become familiar with the term SAP Diameter
(Start of Active Profile Diameter). Also learn
about undercutting in small number of teeth that
are generated by a hob or shaper cutter.