Safe limit of twist in a shaft

[strantor]

I want to make a torqe-sensing PTO shaft for my tractor. I don't want a pony brake dyno or anything similar, I want to measure PTO torque and speed while running actual PTO attachments. To do this I think the simplest way is to measure twist of the PTO shaft. This is how it's done in industrial settings:

So contrary to the norm, I want the maximum safe amount of twist. This will make my measurement less challenging. I've calculated some values for hollow tube and solid rod, and for my target maximum torque over a 5ft shaft I can get 20+ degrees of twist, but I have no idea if that's safe, or one the verge of turning into a pretzel. Is there any way to figure the maximum safe amount of twist?

 

[macardoso]

You'd need to look at the material strength and shape of the shaft. A couple of places you might draw the line of "safe"

• Ultimate Strength (derived from shear stress theory). This determines when a ductile material (steel) will fail
• Yield Strength. This is when a permanent deformation has occurred in the part
• Fatigue limit. This is the point below which the part will not fail when exposed to repeated load cycling

There are several stress theories which are used to derive the Ultimate strength of the material and each may be more or less conservative. This gets a bit complicated.

This is all calculated from the stress in the shaft which is in turn calculated from the applied loads and shaft geometry. Simple shapes like rods and tube can be calculated from textbooks, but more complex geometry (like a shaft with keyway) may require Finite Element Analysis (FEA).

You'll also want to apply a safety factor to the load you find. I would shoot for either the Yield Strength or Fatigue Limit as my limit.

I worked for a company which made super high end axle systems for race cars out of a specialty torsion resistant steel (700M grade if I remember correctly). We would laser etch timing marks at each end of the shaft and when those timing marks had taken a permanent deformation of so many degrees, the shafts needed to be replaced. Cool stuff.

 

[strantor]

You'd need to look at the material strength and shape of the shaft. A couple of places you might draw the line of "safe"

• Ultimate Strength (derived from shear stress theory). This determines when a ductile material (steel) will fail
• Yield Strength. This is when a permanent deformation has occurred in the part
• Fatigue limit. This is the point below which the part will not fail when exposed to repeated load cycling

There are several stress theories which are used to derive the Ultimate strength of the material and each may be more or less conservative. This gets a bit complicated.

This is all calculated from the stress in the shaft which is in turn calculated from the applied loads and shaft geometry. Simple shapes like rods and tube can be calculated from textbooks, but more complex geometry (like a shaft with keyway) may require Finite Element Analysis (FEA).

You'll also want to apply a safety factor to the load you find. I would shoot for either the Yield Strength or Fatigue Limit as my limit.

I worked for a company which made super high end axle systems for race cars out of a specialty torsion resistant steel (700M grade if I remember correctly). We would laser etch timing marks at each end of the shaft and when those timing marks had taken a permanent deformation of so many degrees, the shafts needed to be replaced. Cool stuff.

This smells like one of those rabbit holes where you spend a month learning all kinds of exciting technical stuff and only get further away from the answer you were hoping to find. Maybe it would be better to find some way incorporating some kind of spring or rubber cushion that deforms at a known rate (and returns to shape).

 

[extropic]

@strantor
The etched marks mentioned by @macardoso are super simple. Not a rabbit hole at all.
Alternatively, paint a narrow stripe down the length of the shaft.
If the stripe remains straight, unloaded, you have not plastically deformed the shaft.
If the stripe is becoming a spiral, unloaded, you have exceeded the material's yield strength. Failure, at high loads, is imminent.
The value of the stripe assumes that the shaft is the weak link, so will fail before other PTO drive components are damaged.

If you work through the linked calculations, using properties appropriate for your choice of material, the shear stress is the value you're concerned with. Determine the safety factor you're comfortable with and keep your design limits that far below the chosen material properties.

Shafts Torsion

The torsion of solid or hollow shafts - Polar Moment of Inertia of Area.

www.engineeringtoolbox.com

 

[vocatexas]

I'm not an engineer, but I grew up running lots of shaft driven farm equipment. In my experience a twist of ten degrees would lead to catastrophic failure.

 

[FOMOGO]

This is why God created the "Holy shear pin", and the "Sacred clutch". Mike

 

[pdentrem]

Local racers would run a straight line of paint on their driveshaft and axles. Very much the same as punch marks mentioned earlier.
Pierre

 

[strantor]

@strantor
The etched marks mentioned by @macardoso are super simple. Not a rabbit hole at all.
Alternatively, paint a narrow stripe down the length of the shaft.
If the stripe remains straight, unloaded, you have not plastically deformed the shaft.
If the stipe is becoming a spiral, unloaded, you have exceeded the material's yield strength. Failure, at high loads, is imminent.
The value of the stripe assumes that the shaft is the weak link, so will fail before other PTO drive components are damaged.

If you work through the linked calculations, using properties appropriate for your choice of material, the shear stress is the value you're concerned with. Determine the safety factor you're comfortable with and keep your design limits that far below the chosen material properties.

Shafts Torsion

The torsion of solid or hollow shafts - Polar Moment of Inertia of Area.

www.engineeringtoolbox.com

My reply to @mcardoso was too abbreviated; I realize now, an inside joke that only I'm inside of.
I understand the concept of the timing marks he described and the painted line that you describe. That's the concept that I want this to operate under. I'll have a slotted disk at either end of the shaft and an optical fork sensor measuring the phase shift between them. A digital equivalent of the painted line or timing marks. If you connected an engine timing light to a magnet on the spinning shaft, you could see the twist in your line and the offset between my disks equally clear.

The background on my inside joke is that I've already been pounding those equations for a few days and can't seem to arrive at any better understanding of what the critical parameters are. Then I interpreted his reply as basically "all of them." It sounded like a well informed response seemed to confirm my suspicion that the reason I can't find a simple answer, no thumb rules, no tables of permissible shaft torques by material and diameter, no online calculator to tell me exactly what I want to know, is because there is no simple answer to my question. Not what I wanted to hear but appreciated nonetheless.

Now, you say it's as simple as shear stress. I want to believe that, and I promise to spend the next day or two trying to convince myself of it, but I have a lot of mental hurdles to overcome before I get "there."

 

[strantor]

To be clear, I'm not wanting a way to measure whether or not my shaft has a permanent deformation of twist. I want my shaft to twist, (as much as possible without permanently deforming) so that I can measure the twist in operation, and turn it into a running torque value. I just want to know how much torque I can put on any given shaft without damaging it or someone or something.

 

[strantor]

I'm not an engineer, but I grew up running lots of shaft driven farm equipment. In my experience a twist of ten degrees would lead to catastrophic failure.

Are you talking about a permanent deformation of 10 degrees or running with a 10 degree twist that goes away after you turn it off?