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Crowning Calculation on Spur Gear

Crowning Calculation on Spur Gear

Crowning Calculation on Spur Gear

Hi Everyone,

Is there anyone who can mathematically show the correlation between misalignment value and crowning radius for spur gear. I have a drawing of one spur gear which contains crowning modifications not only on the flank but also on the tip.
Drawing has the distance between the outside diameter and the top of crowning for the tip. The question is how to calculate the radius of crowning? (Center point also is an unknown for me)
Another question is flank diameter. I have value of the distance between the top of the flank point and the top of the crowning radius when we look at the section of pitch circle. I could not find any true calculation of these diameters.
On the other hand , this crowning modification is using for misalignment but i could not find any mathematically correlation between the misalignment (°) and crowning radius. When I searched on this website I found this topic and they sent calculated pdf file. Is there any chance to get this calculation spreadsheet or does anyone teach me how to calculate it.

ref: thread406-309426: crowning
Thanks in advanced.

RE: Crowning Calculation on Spur Gear

The machinist hand book has a formula for calculating the radius on the tip.


here is a link https://planetcalc.com/1421/

The crown on a gear or spline is at the Pitch Diameter
I have a formula, but I have my notes in storage.
It will be a while before I can grab it, but yes
the crown drop as Terry said is done on a basic dimension for the TIP and the Tooth Flank.
as far as the crown drop & Radius for the misalignment I don't have that.
but I have seen .0003 up to .0025 in. crown drop.
the spline tip can be turned or ground, it is manufactured to the radius, but inspected with the crown drop.
a radius is reference because there is a wide band of radius tolerance change to crown drop.

PS I do remember the change of root (Minor diameter on External) is calculated by the above formula
then it is translated to tooth profile change using the pressure angle.

sorry this stuff was passed on as a young engineer and I don't have any data to prove it.
I do remember one of the USA AGMA spec's that defines what your asking for.
would have go through them

RE: Crowning Calculation on Spur Gear


I know the formula which are r2=power(Facewitdh,2)/(8*Crowning Drop) and r1=r2*tan(pressure_angle)
The question is how can i decide how much crown drop I need? In my opinion it must depend on my misalignment requirement. I have searched lots of AGMA standarts, everyone of them mentioned about crowned spline but none of them is telling how to calculate them. If you find it please share with me.

RE: Crowning Calculation on Spur Gear

it is not a straight forward answer, it's complicated.
AGMA 927, 2001, 6002
from 6002

6.2.2 Load distribution factor, Km
The load distribution factor, Km, is defined as the peak load intensity divided by the average or uniformly
distributed load intensity; i.e., the ratio of peak to mean loading. The basic method of calculating the load
distribution factor is described in clause 15 of ANSI/AGMA 2001-D04. When determining the mesh
alignment factor, Cma, use the values for the precision enclosed gear units shown as Curve 3 in Figure 7.
While this method is generally satisfactory for stationary applications, marine propulsion gear elements
are subjected to changing load distributions due to foundation flexure caused by variations in vessel
ballasting and draft, variations in sea state, variations in load, and variations in power plant component
temperature. These all potentially affect load distribution in the reduction gear.
To offset this potential variation, marine propulsion gear housings and gear elements must be designed to
withstand forces caused by the previously mentioned variations in addition to those from the gearing and
propeller thrust loads. Therefore, either end relief or crowning is recommended.
This method of calculating the load distribution factor becomes questionable as the value of Km
approaches 2.0. In such cases, an alternate method for calculating Km is recommended. Alternative methods for calculating Km
Using the alternative analytical method described in AGMA 927-A01 allows the engineer or designer to
determine the effects of support movements as well as the effects of lead modification. This is a more
encompassing method of calculating the load distribution factor as it allows for the inclusion of the
additional factors listed above. Variations in these factors should be considered. Limiting values of Km
If the load distribution factor is confirmed to be in excess of 1.6, lead modification and end relief should be
employed to minimize the possibility of end loading of the gear teeth under maximum load considerations.
The previous version of this standard, in agreement with the ABS Rules in effect at that time,
recommended consideration of lead modification whenever the calculated deflection across the face
width of the pinion exceeded 0.001 inches. While this limit is appropriate for finer pitch through hardened
designs, a higher limit could be applied for coarser pitch carburized designs. Marine drive manufacturers
should follow sound engineering practice in this regard.
Since it is impossible to accurately quantify all the potential variations in tooth contact, allowances must
be made to take these variations into consideration. In order to maintain a reasonable degree of
conservatism, the minimum value of Km for marine gearing shall be 1.2.
6.2.3 Stress cycle factor, ZN
The stress cycle factor, ZN, adjusts the pitting resistance of mating gear elements based on the
anticipated number of loaded mesh contacts (cycles) that individual teeth will experience during their
design life. It should not be construed to imply a fixed life. The number of cycles shall be based on the
recommended life given in Table 6 for the appropriate class of vessel.
ZN shall be determined by clause 17 of ANSI/AGMA 2001-D04. In figure 17, the upper curve shall be
used for stress cycle factors above 10 million cycles.
6.2.4 Hardness ratio factor, CH
If the pinion hardness is significantly higher than the mating gear hardness, a “work hardening” effect can
increase the pitting resistance of the gear. The hardness ratio factor, CH, is used to modify the allowable
contact stress number, sac, of the gear to account for this effect. Variables that affect the hardness ratio
factor are tooth hardness, gear ratio, pinion surface finish, and he

RE: Crowning Calculation on Spur Gear

I am really grateful. Thank you, I tried it and works quite good. Thank you again.

RE: Crowning Calculation on Spur Gear

you are welcome
this has been a question over the years and there was no definite answer, until now.
I am happy this helped


RE: Crowning Calculation on Spur Gear


Here is a Gear Technology article that provides a method to calculate your spur gear face crown profile based on axial misalignment. Once you establish the face crown profile required, the article suggests using equations from Roark's to calculate contact stress based on your operating loads.

Should not need tooth tip crowning unless the angular misalignment is significant and/or the gear has a high L/D ratio. Sometimes tooth tip crowning is used to remove very narrow/knife edge top lands that would be prone to cracking.


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