Cutting parallel tooth gears

I'm building a 1/8 scale working model of a 1940/50's era mechanical shovel and presently working on the vertical bevel gear

drive to power the whole machine along forward or backwards.

The horizontal bevel is has 22 teeth of 14 DP and a PCD of 1.5714 inch

The verical Bevel is 24 teeth with 14 DP and a PCD of 1.7142

The teeth will be parallel cut and I have been using information gleaned from'Gears & Gear Cutting' by Ivan Law.

Each gears has been set out and drawn as per the text and blanks have been machined ready for cutting teeth. Whoopee!

I have a dividing plate with both 22 and 24 holes so the basic cut should not be a problem. I am a little confused with the

calculations on page 106 however for establishing the amount of offset required.

The illustration used is pretty straight forward using a mite gear having 90 degree cone which I assume is waht is

refered to in the following calculation:-

Offset for second cut = 1/2 chordal thickness = 1/2 X PD X SIN 90/20 = 1/2 X 1 X 078 + 0.039

At other points prior to this calculation he refers to SIN 45 = 0.707

My problem is that the 22 tooth gear has a cone angle of 85 Degrees

and the 24 tooth gear a cone angle of 95 Degrees

SINE, TANGENT and COSINE are calculations based on a right angle triangle

so in one sense I cannot use it for my 24 tooth gear.

HOWEVER! When I punch in SIN 85 and SIN 95 on my calculator they both give the same answer of 0.9962

On page 111 left hand column it says : The calculation is always the same and concists of simply multiplying

half the pitch diameter by the sine of the angle, 90/ Number of teeth.

AM I MISSING SOMETING?

Any clarification of the above would be much appreciated.

Hi Geoff,

Two essential points:

1 there is an error in Ivan's book. On P108 column 2 the calvculations for o/dia small end and o'dia big end should BOTH use COS not SIN.

2 Ivan's cone angle is HALF the included angle so, assuming your bevels are at 90 degrees the angles are 42.5 and 55.5.

I have made asymmetrical bevels using Ivan's method and they worked! If you have any furher questions - just ask

Neil

Whoops Page 106

Hi Geoff,

I do have an excel spreadsheet that calculates all the various parameters. It was on line but the webspace got shut. I'll dig it out and post it here somewhere.

Steve

No files folder on the site?

Not tried this before, but here is a link to the file in my Dropbox:

https://www.dropbox.com/s/e1vyhn042t1qth8/Gears_Final_180410.xls

Steve

I have used Steve spread sheet and it is easy to use and the gears I made worked very well.

Oliver

I have used Steve spread sheet and it is easy to use and the gears I made worked very well.

Oliver

Many thanks to all you guys who have responded to my query. I move forward another notch.

Regards

Geoff Lewis

I have been looking again at the formula for establishing the movement off the cutter in conjunction with the rotary movemet of the bevel being cut.:-

Formula :- Offset = Half Chordal Thickness X 1/2 PCD X SIN Included angle (which in my gears will be 85 & 95 Degs).

Can anybody tell me the logic to this formula and how it is derived? I am trying to understand it's physical relationship to the gear being cut and the drawings in Ivan Law's book.

Hi Geoff,

Offset = half chordal thickness = 1/2 PCD X SIN included angle

The 'blank roll' is 1/4 of a tooth pitch.

The 'chordal thickness' is the distance across a tooth on the PCD i.e. the width of the cutter on the PCD or 1/2 the pitch if the gear was a straight rack).

To follow the blank roll around 1/4 of a tooth it has to move by half this distance (chordal width/2) and adjusted for the angle of the blank roll. This angle is where his example of 90/20 comes from 360/4=90 and 20 is the DP of his gear.

So imagine a right angled triangle with an included angle theta at the centre of the gear. The hypotenuse is the PCD of the gear and the opposite side is the distance the cutter has to move to keep itself lined up with the small end of the teeth. (Note that PCD must be measured as the true diameter at the small end of the bevel.)

As SIn = opposite over hypotenuse the distance the cutter is offset (opposite) = sine * hypotenuse

It would have been VASTLY easier to follow if Ivan had used the exactly equivalent formula of:

CUTTER OFFSET = SINE (BLANK ROLL) * PCD OF SMALL END OF BEVEL

Hope that helps. It has confused the hell out of me. Careful study of the picture on p. 110 helps, or see below.

Finally, if you have the courage and the eyesight, you can just execute tha blank roll and very carefully realign the cutter with the small end of the gear - this way you would HAVE to cut the theoretically unnecessary central cut first.

Neil

Hi Neil,

Many thanks for responding to my latest query. The one thing about it that resonates with me is your remark about it confusing the hell out of you. I identify with that completely. I keep looking at it but still do not see a clear picture. What's throwing me is what 360/4 = 90 has to do with anything. I would have thought that dividing 360/N would have been more likely angle but there you go. I will keep looking at it untill something clicks - or falls off.

If you don't hear from me for a while I'm out in the widerness looking for the golden tooth.) I had a rivet but threw it away)

Regards

Geoff

Prompted by this thread I've been looking at the design of parallel bevel gears this evening, as I need to produce some bevel gears for the governors on my traction engines. The gears are a bit small for my normal CNC method of producing bevel gears, so I'm planning to use the parallel-depth method.

According to my book on gear design the rotation and offset to be used are as follows:

1. Rotate the blank one quarter of the indexing movement required for one tooth space

2. Offset the table by one quarter of the circular pitch at the small end of the teeth

Reverse the rotation and offset for the second cut. Intuitively this seems correct and is simple to calculate; no trigonometry required. It does however assume that the indexing required for one tooth space can be exactly divided by four on whatever dividing head is used.

Regards,

Andrew

There was an excellent [and brief] article by R.S. Minchin, in Model Engineer 15-Nov-1964

"Cutting Bevel Gears by the Parallel Depth Method"

MichaelG.

Hi Geoff,

360/4 is because you turn by 1/4 of a gear.

Neil

Hi Andrew

Moving by 1/4 the circular pitch is slightly too far, as CP is measured along an arc of the PCD.

Ivan's formula compensates for this (by calculating half the length of a chord joining the ends of an arc of length of half the circular pith!), although it is only really significant for smaller gears, bearing in mind the whole thing is an approximation.

Neil

Edited By Stub Mandrel on 09/11/2013 12:23:02

https://www.dropbox.com/s/2apmxluzcxph8th/BEVEL%20GEARS.PDF

A description of cutting parallel depth bevel gears which I think is far clearer that Ivan Laws book.

I should have added that  this is from the classic work by Franklin Jones.

Steve

Edited By Steve Withnell on 09/11/2013 13:13:56

Edited By John Stevenson on 13/09/2015 17:37:56

thank you Steve,

both files are most useful

In case anyone is interested, I have converted Steve's excel spreadsheet to MathCad (Prime, but can easily be produced in a version 15 option). Why - I just prefer MathCad as I can see all the formula.

Thanks to everybody who has contributed to my queries. I now believe I know where I am going with this. If I don't screw things up in the process I will post some pictures of the result.

Many thanks

Geoff Lewis