What pressure angle does F1 use in their gearbox

[Batman]

I've been playing around with some GearCAD software and I had a look at what a gear would look like with a 30 degree pressure angle and it reminded me of an F1 pinion from a McLaren F1 car. Does anyone know for sure what pressure angle they run? I know that 30 degree teeth are the strongest due to their thick base and it would make sense that they would use it for this.

[tok-tokkie]

Does the power transmission efficiency not decrease as the pressure angle increases? The force separating the shafts increases so it means a stronger casing is required = additional weight.

[riff_raff]

Does the power transmission efficiency not decrease as the pressure angle increases? The force separating the shafts increases so it means a stronger casing is required = additional weight.

tok-tokkie,

With regards to spur gears, you are mostly correct. But F1 transmissions use many different configurations of gears. External spur gears for the primary & layshaft shift gears, spiral bevels for final drives or for changing the angle of input shaft rotation, spur gears for oil/hydraulic pumps, and spur or helical gears for differentials.

Like most things mechanical, there is a compromise between strength, efficiency, weight, package size, producibility, and fatigue life when it comes to establishing the optimum gear tooth pressure angle for a particular application.

The spur gears used for shifting would likely have pressure angles around 25deg. This would be the best compromise given the limited fatigue life and high bending load requirements needed in F1 shift gears.


Higher pressure angles tend to result in gear teeth with greater bending strength, lower efficiency, and lower contact ratios. But when the number of teeth becomes very small, like in an 11 tooth pump gear, the pressure angle must be increased to prevent undercutting during manufacture.

And finally, with spiral bevel gears, a more typical operating pressure angle would be about 20deg.

[buffs]

Batman, I do believe F1 driveline gears are direct generated, therefore the pressure angle does not really make sense in a 'traditional way of thinking'.
Read this:

http://www.thermotech.com/pdf/Gears_Pow ... _Paper.pdf

You can see asymmetrical teeth here indeed:

http://www.ptiltd.co.uk/transmission_gears.htm

tok-tokkie, the gearbox is actually a frame structural part, I do not think the shafts forces are an issue.

[riff_raff]

buffs,

Race transmission spurs gears probably don't use "direct generated" geometry, but they do definitely employ lots of non-standard profile mods, profile shift, and face geometry mods. The reason for this is so that they can get various combinations of tooth counts to mesh satisfactorily with a fixed pitch center distance.

http://www.hewland.com/svga/dg.htm

riff_raff

[woody3says]

You are correct about the PA of the shifting gears Riff_raff. I work with VERY similar gears every day and on the same equipment that, at one time, half the grid was and mostly still is produced on. I know a factory engineer that has been inside several team shops. They are direct generated as well.

[ringo]

Batman, I do believe F1 driveline gears are direct generated, therefore the pressure angle does not really make sense in a 'traditional way of thinking'.
Read this:

http://www.thermotech.com/pdf/Gears_Pow ... _Paper.pdf

You can see asymmetrical teeth here indeed:

http://www.ptiltd.co.uk/transmission_gears.htm

tok-tokkie, the gearbox is actually a frame structural part, I do not think the shafts forces are an issue.

good post.

[yky5192]

i hav a query???
why is that nowdays pressure angle in automobiles is around 20-22 degrees...as it was around 14.5 degrees in automobiles manugactured before???????????
and why the pressure angle is decreased instead acc. to the theory it should hav increased ....as FORCE cos(angle)....iz responsible to transmit the force...?????

[strad]

I was under the impression that they were square cut and so narrow you'd never believe they withstand the power.

[riff_raff]

i hav a query???
why is that nowdays pressure angle in automobiles is around 20-22 degrees...as it was around 14.5 degrees in automobiles manugactured before???????????
and why the pressure angle is decreased instead acc. to the theory it should hav increased ....as FORCE cos(angle)....iz responsible to transmit the force...?????

yky5192,

With conjugate involute gear tooth meshes, there is usually a compromise between variables such as contact ratio and bending. Gear sets with lower pressure angles (such as 14.5deg) will have a higher contact ratio and less bending strength than a gear set with a greater pressure angle (such as 20 or 25deg). The higher profile contact ratios tend to produce less gear mesh noise in spur gears. But if helical gears are used, they have more favorable face contact ratios which spur gears don't. So a helical gear combined with the greater bending strength of a 20 or 25deg pressure angle is a better compromise.

riff_raff

[tok-tokkie]

Please excuse an off topic diversion.

Buffs, many thanks for that link. I suspect I have actually unwittingly used Direct Design myself!

I have been making a pendulum clock for years. I have a decent industrial cnc machining center (Haas VF2) and CAD/CAM of my own. I make the clock gears by profile cutting with a 1mm diameter slot drill. Laminate them together is I need wider (thicker) gears. Only 4 pairs of gears required for clock hrs -> mins is 12:1 set but mins -> secs is 60:1 set which is the difficulty. Original gears were involute though I have replaced the 60:1 with cycloidal. Since the gears are profile cut I use whatever module results from the shaft center distance (chosen to fit clock) and number of teeth (minimum set by cutter diameter). The profile was mathematical involute profile generated in Excel & plotted as a spline in CAD through the cordinates from Excel.

Clocks are fascinating. The target is MAXIMUM efficiency as all losses are reflected in the size of the drive weight - good clocks have small drive weights. Clocks are speed increasers - drive on hour shaft (in my case but usually another shaft alongside it) transmitting to escape on seconds shaft which runs 720x faster. Finally it is an intermittant drive mechanism - it stops & starts every second. Power transmission is insignificant but long life is measured in centuries.

I became aware of your specialisation riff_raff & intended contacting you for advice on minimising gear torque losses as that is the target. I have 2 grandchildren; clock for the first is comitted but I would like advice for the next one. Project is just a retirement occupation & I am busy on something else right now.

[xpensive]

In a mechanically perfect world, there is no relative surface-movement between the interacting gear-teeth as they are in a continuous rolling contact along their involute profiles. There would be no metal-to-metal contact either, as the hydraulic "squeeze-effect" is creating an oil-film between the surfaces due to the high contact pressure, just like in a roller bearing.

Still in the perfect world, with that oil-fim the lateral friction between the gears is xtremely low, why a steep angle generates an axially separating load, which at the end of the day has to be supported by a bearing fixed to something stationary, unless you have twin-gears with opposite angles of course.

[riff_raff]

xpensive,

You make some excellent points about basic gear design, and also one of the reasons the direct design approach is attractive. As you noted, having gear mesh contacts that operate in the hydrodynamic regime is very important for good efficiency and resistance to scoring/scuffing. With simple gear sets (ie. external spur gears with low ratios and tooth counts above 20), involute geometry produces conjugate action with very little relative contact sliding. However, when the ratios get large (small pinion & large gear), the tooth counts get low (<20), or where there is a small external pinion and large internal ring gear, then the gear geometries must be modified to minimize contact sliding and equalize bending stresses.

These types of geometry modifications (profile shift, addendum modifications, tip mods, etc.) have been used for many years, and are a similar approach to the direct design technique. However, where the direct design approach differs is that it takes geometry modifications to the extreme, with things like asymmetrical tooth profiles. The asymmetrical direct design tooth profiles have some benefits, mostly with regards to bending strength, but the process also has some drawbacks with regards to production costs. Of course, production costs are not an issue in F1 gearboxes.

Finally, the reason that involute geometry was adopted for gear teeth has to do with the flexibility of involute gears. Gears with common dp/module and pressure angles, but different numbers of teeth, will readily mesh if spaced properly. And involute gears are also relatively tolerant to the changes in mounting center distance that invariably occurs with gear/housing materials (ie. steel gears & magnesium housings) that have a thermal CTE mismatch as the gearbox gets hot during operation.

riff_raff

[xpensive]

Thanks riff_raff, now back to the resulting axial load on the gear, where the same (Fa) will be a function of torque (T), gear-radius (r) and tooth-angle (Alfa), given that the oil-film is perfect and friction zero;

Fa = T/r * tan Alfa

If torque is 300 Nm, radius 30 mm and tooth-angle is 26.7 degrees, then Fa = 5000 N

5000 N (500 kg) is not a load to ignore when it comes to the life-xpectancy of an 18 000 Rpm bearing of the matching size.

A tooth-angle of 14 degrees would cut Fa in half to 2500 N, increasing life-xpectancy of the same bearing with a factor of 10.

[riff_raff]

xpensive,

In your last post I believe you mean Fn and not Fa. A spur gear mesh would not have any appreciable axial forces.

With spur gears, the tooth contact normal force relationship is Fn = Ft/cos alfa, where Ft is the pitch line tangential force and alfa is the pressure angle. The contact normal force (Fn)is usually resolved into a pitch line tangential force vector (Ft)and a separating force vector (Fs). These vectors can be transposed onto the gear shaft axis to determine bearing radial loads.

But as you note, a lower pressure angle reduces the separating force component for a given Ft. And of course, you will need to take into account the load distribution between multiple teeth (contact ratio) if you want an accurate vector analysis.

Finally, as you also noted, the fatigue life of a rolling element bearing for your gear example, operated at 18,000rpm and a 500kg radial load, would need to be carefully evaluated. For example, if that bearing had 10 rollers and a fixed load relative to the inner race, the loaded sector of the inner race surface would accumulate fatigue cycles at the rate of 10.8x10^6/hour.

Regards,
riff_raff