Calculation of Tight Mesh Center Distance - on a Crossed Axis Helical 1

[Spurs]

I am having problems with a calculation and am looking for guidance from this forum.

I am looking for an accurate method to calculate the tight mesh center distance of a crossed axis helical gear mesh with heavily modified tooth thicknesses. The calculation method that I have found in most published literature is accurate only for the case where the sum of the normal circ. tooth thicknesses is equal to the normal circ. pitch. When I create designs whith shifted profiles I am finding that the calculation methods that I am aware of become less accurate.

This calculation method must be published somewhere as this is also the basis for all helical gear hobbing principles where a hob must be plunged to a center distance with the workpiece with zero backlash in order to create a perfect tooth thickness on the workpiece.

Below is a calculation example:

Driving Member Worm - 1 start
Driven Gear - 14 Tooth Helical Gear

Normal Module of both parts 3.5
Helix Angle on Gear - 23 Deg
Lead Angle on Worm 23 Deg
Shaft Angle 90 deg.

Normal Pressure Angle - both parts 20 deg

Normal Circ Tooth Thickness of worm 7.770 mm
Normal Circ Tooth Thickness of gear 5.500 mm

For reference info - although it isnt needed
OD of worm 20.950 mm
OD of gear 60.000 mm
Root dia of worm 7.150 mm
Root dia of gear 44.100 mm


By conventional calculation methods, the tight mesh center distance is calculated as 33.8168 mm - I get this result when I calculate by hand, and when I use a leading commercial software package.

If you model the parts in CAD and look at tight mesh center distance - the distance is 34.200

My actual experience on a double flank tester seems to match the CAD

I am looking for any published info that would seem to provide the accurate solution. As I said earlier, I suspect that the hobbing industry has published info related to this since the same calculation must be used.

Any help would be appreciated - if someone has a more general solution that works at any shaft angle (even non 90 deg) it would be very much appreciated.

 

[gearcutter]

It looks like you may not have allowed for the difference between the generating pressure angle and the operating pressure angle.

See Litvin's "Gear Geometry & Applied Theory" 1994 edition, pages 323 - 329 where he discusses operating centers in detail.

Follow this link and google books will show you the relevant pages from Litvin's revised edition,

http://books.google.com.au/books?id...&hl=en&sa=X&oi=book_result&resnum=2&ct=result

Also see this thread,

http://www.eng-tips.com/viewthread.cfm?qid=146377&page=2

Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

http://www.aussieweb.com.au/email.aspx?id=1194181

 

[Spurs]

Gearcutter

Thank you for your response. I will look it up and respond to this forum on what I found.

I do however take into account the operating pressure angle in my current calculation procedure. Did you happen to run the sample calculation that I provided? If so, I am curious as to the result you obtained.

 

[gearcutter]

What are the corrections you are using?


Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

http://www.aussieweb.com.au/email.aspx?id=1194181

 

[Spurs]

Gearcutter

I obtained a copy of the 1994 edition. Pages 323-329 is related to spur gears. However, on pages 454-457 there is a similar write up on Crossed Axis Helical Gears.

I have followed the steps 1-4 as outlined on page 457 and programmed them using Excel. One of the calculations requires a goal seek function which I performed.

I tested the calculation for the test case where the sum of the normal circ. tooth thicknesses for the two gears in mesh was equal to the normal circular pitch. The calculation checks out for this instance in my Excel spread sheet.

I reran the calculaion for the test case where the sum of the normal circular tooth thicnesses is not equal to the normal circular pitch. The calculation did not accurately predict the same center distance that my CAD system predicted. As I stated before, I have excellent agreement between my CAD system and the real world.

I will try to contact Faydor Litvin about this calculation in his book.

In the meantime, does anyone else have a recomendation on how to calculate accurately either the backlash in a set of crossed axis helical gears, or the tight mesh center distance, or the center distance during hobbing of a helical gear which works for a case where we have non-standard tooth thicknesses?

It seems odd that the industry has not raised this issue before. The amount of error in conventional calculation techniques may be small for fine pitch gears where the tooth thicknesses are close to standard, but as the module increases, and the helix angle, and the tooth thicknesses deviate farther from standard, the classical calculation techniques become inaccurate.

 

[israelkk]

Spurs

Why are you referring to it as cross axis helical? This is according to your description a worm and a worm gear.

A far as I know cross axis helical gears are two helical gears where the axes are not aligned.

 

[Spurs]

Isreaelkk

The gearing industry - at least in the USA - refers to a worm gear set as one where there is a worm - either globoidal (ie hour glass shaped) or cylindrically shaped - which mates with a worm wheel which has a thoated region across its face width.

A crossed axis helical gear mesh is one where two helical gears are meshed at any shaft angle other than parallel. A cyclindrical worm meshing with a helical gear falls into this catagory. - FYI - A cyclindrical worm meshing with a spur gear also falls into this catagory.