RACK AND PINION, HOW TO MAKE SURE THE SET IS GOING TO BE ENGAGED UNDER LOAD ?

[JJAV1983]

Hello All,
Is there a way to calculate the maximum separation distance between rack and pinion under load?

Total load on Rack:

L= 85000 lb
PD= 6.928 Pitch Diameter of Pinion
No.Teeth=22
n= 6 number of pinions
PA= 20 pressure angle
ho= distance from back face to pitch line of rack = 2.81 in

Force per pinion Ft=L/n = 14166.667 lb (tangential)
Torque required at pinion: (Ft*PD/12)= 8178 ft-lb
Separating Force= Ft*tan= 5156.245 lb

Taking into account that the Diametral Pith is 3.175 in, from

http://www.engineersedge.com/gears/gear_backlash.htm

we have that:

For a 20 degree pressure angle: The change in center distance= 1.374 x change in backlash= 1.374 x .012475 (value interpolated from link above) = .017 in"

I have determined the pinion and gear center distance as; 5.959 in. HOW DO WE DETERMINE THE MAXIMUM SEPARATING DISTANCE WHEN THE PINION IS UNDER LOAD? (in order to keep the set engaged)

Your help will be much appreciated.

Thank you,

JJAV

 

[tbuelna]

I am a bit confused about what you are asking for. Do you want to know the displacement between the pinion pitch center and the rack pitch line under load?

If so, the radial force acting thru the pinion shaft is the resultant of the tangential and separating forces at the gear mesh contact (Fr = [Ft^2 + Fs^2]^1/2). Since you have six pinions you will need to determine the radial force at each one, taking into account factors such unequal load distribution between the pinions, and apply these forces along the rack. To determine each mesh displacement under load, you will need to calculate local deflections in the pinion shaft, rack, and housing structures.

As for backlash, it does not have any effect since the rack and pinion gear teeth are only loaded on one side at any given time. Of course the clearance between the unloaded side of the pinion tooth in mesh and the adjacent face of the rack tooth trailing it will increase as the gear/rack pitch centers displace under load. But this increased clearance goes away when the forces at the gear mesh are relieved.

In regards to the maximum amount of mesh displacement it would require for the mating pinion and rack teeth to become "disengaged" under load, it would have to be quite substantial. At least enough to reduce the operating contact ratio below 1.0. One attractive characteristic of involute geometry gears is their ability to tolerate changes in pitch center distance. A displacement of .017" in the 3.464" PCD of your 3.176DP gears would probably still be tolerable, but you might have to de-rate your gears somewhat to compensate for it.

Hope that helps.
Terry