worm shaft thrust force calculation 2

[windell747]

Aloha,

I have a 270in-lb moment acting on a worm gear and I'm trying to calculate the thrust force extered on the shaft of the worm. The worm gear is about 3.3 inches in diameter.

For a static thrust load calculation the thrust force exerted on the worm shaft is about 270in-lbs/1.67in = 160lbs.

I was told that I should perform a dynamic thrust load calculation since the thrust force will increase while the worm is rotating. The worm will be spinning at about 24RPM max. The equation I was given to use is this one.

T=P/tan of lead angle
where T=thrust force,P=input torque/pitch radius of worm

Well, I know my output torque must be at least 270in-lbs. My worm gear ratio is 40:1. So I first divide 270in-lbs by 40. I get 6.75 in-lbs. I then multiply this by 1/worm gear efficiency. The efficiency I calculated for this worm gear set is 15%. By multiplying 6.75 in-lbs by 1/.15

I get 45 in-lbs as my input torque on the worm.

Then to solve for P, I divide 45in-lbs by 0.5in, the pitch radius of the worm. This gives me 90in-lbs.

Then to solve for the thrust force I divide 90 in-lbs by tan(4.08deg).

This gives me a thrust load of about 1260lbs. This dynamic thrust load does not seem to be right since by static calculation is only 160lbs.

Can anyone point out what I am doing wrong with this calculation? Is there another way I can calculate the thrust load exerted on the worm shaft? I'll be using this thrust load calculation to choose the proper thrust bearings for my worm gear box.

Mahalo

 

[BobM3]

Not sure what is meant by dynamic torque. But your equation is probably supposed to be:

T=P x tan of lead angle
where T=thrust force,P=Input torque/pitch radius of worm

This gives the component of the torque producing force acting along the shaft direction (axial thrust).

 

[windell747]

What I meant by dynamic thrust force is the thrust force developed as the worm is rotating.

Although, your reply makes perfect sense, When I calculate P x tan of lead angle I get 6.41 lbs. I know that this isn't correct since my static calculation is 160lbs. Would it be 160lbs plus 6.41 lbs?

 

[desertfox]

Hi windell747

Looking at the "Mechanical Engineers Data Book" by J.Carvill
I quote the following formula's:-

Tangential force on worm (wFt) = axial force on gear (gFa)

these forces are = 2*Tw/(Dw)

where Tw = worm torque

Dw = worm pitch circle diameter

further:-

Tangential force on gear (gFt) = axial force on worm

(gFt) = |(cos B - u*tan X)|
|---------------- | *(wFt)
|(cos B + u*tan X)|

where cos B = cos of normal pressure angle
tan X = tan of the worm helix angle
u = coeff of friction.

However looking at the formula you are using and I quote:-
"Then to solve for P, I divide 45in-lbs by 0.5in, the pitch radius of the worm. This gives me 90in-lbs"

If you divide 45in-lbs/ 0.5in then you get 90lbs
not 90in-lbs so I think there is something missing or incorrect with the formula you have been given.

Regards desertfox

 

[windell747]

Thank you desertfox. I'll get my hand on a Mechanical Engineers Data Book and take a look at that equation!

Would that equation be in a mechanical engineers handbook as well?

Ohh desertfox, there was a typo.

What I said was "Then to solve for P, I divide 45in-lbs by 0.5in, the pitch radius of the worm. This gives me 90in-lbs"

What I meant to say was "Then to solve for P, I divide 45in-lbs by 0.5in, the pitch radius of the worm. This gives me 90lbs".

So the units come out correct.

mahalo nui loa!

 

[desertfox]

Hi windell747

I have never seen the formula that you are quoting however
I found this formula for Dynamic loading in a book called
"Machine Design theory and practice"(ISBN 0-02-329000-5)


Fd = ((1200+Vpg)/1200)* Ft

where Vpg = pitch line speed of gear in feet/minute

Ft = transmitted load as determined by the input
horsepower applied to the gear.

best regards

desertfox

 

[windell747]

Thank you very much desertfox. I went to my local library and found the "Mechanical Engineer's Data Handbook" which contains both the efficiency and thrust force equations that i've been looking for. Your suggestion has been very helpful! should've looked for this text from the beginning...haha

 

[stephenweinstein]

1. Either the worm gear diameter, gear ratio, lead angle, pitch radius of worm, or some combination of these is wrong.

The correct values will satisfy

gear ratio * tan(lead angle) * worm pitch radius = worm gear pitch diameter / 2

2. The formula trust force = input torque / worm pitch radius / tan(lead angle) is only valid where efficiency is 100%. Otherwise, the formula is trust force = efficiency * input torque / worm pitch radius / tan(lead angle).