# Engineering calculation, fastening 2 gears

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#### petertha

##### Well-Known Member
I need to permanently attach these two 2 idler gears together. I had in my mind to drill a hole centered on the joint line & axially insert a key-like dowel pin (matching drill bit shank cutoff) parallel to the shaft. The axle hole is 5mm ID. The intersecting hub is 7.5mm OD x 4.5mm long. I'm actually not too keen about drilling because the remaining wall thickness gets skinny to the axle hole. The gears are steel, maybe something like 4140. Can someone provide the magic equations to determine shear strength for:

1) No pin, Loctite only on circular hub (specs say 4000 psi if that's the right number). Assume the rear face is not contributing anything because its mostly tooth form. So just the green hub area.
2) key-like axial steel pin as a function of diameter, say 1/32" just as initial guess. For example 1/16" diameter pin leaves only 0.018"
3) just for kicks, a perpendicular pin drilled through the valley of the big gear tooth into the hub (so the circular cross section of pin, maybe larger diameter).

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#### petertha

##### Well-Known Member
I guess I could have inquired about silver soldering too, but I'm not sure if I want to. This is a 1018 scrap of same dimensions. My first go with Harris Safety Silv 56 & white flux. I'm not sure I like the solder fillet on what would be the back of gears, although maybe I used a bit too much. The glassy flux residue mostly came off in hot water but it took some Dremel action to get rid of all the dark crud. That would be PITA on the gear teeth nooks & crannies. Is there a relatively simple recipe I should be aware of to soak the black off? I used a MAPP torch btw. The steel was dull cherry by the time the flux went clear. Would that temp have adverse affect on my gears? I machined them so they were not crazy hard.

The dummy blank assembly held together facing in the lathe at maybe 0.005" cuts if that means anything. I was trying to see if silver solder had flowed in the annulus. If I squint my eyes, maybe? The hub/hole clearance was about 0.001 to 0.002" diameter. My gears fit a bit snugger so maybe 0.001"

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#### Jasonb

##### Project of the Month Winner!!!
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Without knowing what the gears are for and the likely load it's hard to say if just Loctite will do.

Acid pickle will clean off the flux and scale, citric acid is slow and gentle

#### Charles Lamont

##### Well-Known Member
I would try high strength Loctite by itself on carefully cleaned parts. I would say it is very likely to be satisfactory, unless the gears are excessively heavily loaded.

My current project is a starter motor reduction gearbox, and it relies on gears Loctited to their shafts. It has been tried briefly and is OK so far. It is currently at the stage of cosmetic finishing.

Considering the worst case, if the joint were to fail, what would happen?

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#### petertha

##### Well-Known Member
This gear assembly are the idler gears. The 15T large one meshes the 15T crankshaft spur gear. The 10T small gear meshes the 40T internal ring gear, which drives the cam plates. The cam lobes drive pushrods to act on the rockers, ultimately pushing valve springs. I can dig up the spring/deflection data. I haven’t thought this through but maybe 2 valves being open (overlap) at any given time. Mostly I don’t want the gear set to ever let go, that would be a bad thing.

#### Master

##### Well-Known Member
I have used Permatex High Temp Sleeve Retainer with great success. Small tube and inexpensive. Got mine at the local NAPA store. Suggestion, get your parts lined up right the first time.

#### petertha

##### Well-Known Member
Acid pickle will clean off the flux and scale, citric acid is slow and gentle
Are you saying citric acid would do the same, just slower? Something like this? Can it be tap water or needs to be distilled?

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#### Jasonb

##### Project of the Month Winner!!!
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Tends to be the powdered/crystals that get used just add to tap water as much as it will take. Yes it's slower and will need a few hours. I tend to use "brick and patio" cleaner which is hydrochloric acid based and 1/2hr will do just don't forget you put the part in the acid.

As to the joint I would have thought that a good close joint and something like Loctite 648 would do, I use that to bond cam lobes to shafts and make small crankshafts. If you do want to add a pin then if worried how close it comes to the hole you could move it out radially so 0.5mm is in the boss and 1mm in the gear. Also does not need to be full depth so maybe only half gear depth. Final option would be a radial pin between two teeth of the gear and set just below the depth of the valley

#### Drawfiler

##### Member
You can try for a tight press fit and finish ream after. If you use adhesive, check with the data sheet on clearance need for the best result, some types work better with a looser fit.
I would avoid the ‘half and half’ axial pin on gears this small.
silver solder is messy but if the flux is only where you want the solder, ie down the bore and on the little end of the assembly and not in the teeth then you use the minimum solder and quench when hot, the flux will mostly come off.
I would make the large gear and the cylindrical portion of the small one over long, turn a countersink on the large gear bore so you have a gutter to feed the solder into then face off after.
One final option is to soft solder, not popular these days but easier to clean up, tin both parts first, remove excess solder then warm up them both and push together when hot. Make the cylindrical portion a lot too long, taper it down to provide a guide when you fit the two gears together and face off after.

#### Steamchick

##### Well-Known Member
I would have made an interference fit... This then allows for any heat treatment or case hardening of gears without cooking loctite or de-soldering....
But there are many ways to "kill this pig"...
But please do the calcs for torque/shear at the shaft-gear interface. That should help you decide the optimum process.
K2

#### ajoeiam

##### Well-Known Member
I would try high strength Loctite by itself on carefully cleaned parts. I would say it is very likely to be satisfactory, unless the gears are excessively heavily loaded.

My current project is a starter motor reduction gearbox, and it relies on gears Loctited to their shafts. It has been tried briefly and is OK so far. It is currently at the stage of cosmetic finishing.

Considering the worst case, if the joint were to fail, what would happen?
Very nice model.

What did you do it in? (software)

#### Steamchick

##### Well-Known Member
Simple calcs for my steam engine in a boat with a steam engine, I used a bought "computer printer toothed belt and gears" - worked fine for the torque applied to the screw. I.E. 3/4" bore 3/4" stroke steam engine at 20psi, with 3:1 speed reduction from 2000rpm max. => max torque = 8.8lbs (on piston) x 0.38" (crank throw) x 3 (gear ratio)= 10.2lb.in.
If this torque is applied to gear bonded to a 1/4" shaft, at 3/8" long, the shear stress of the gear-shaft joint at 1/8" radius is 81.6lbs/(3.142 x 0.25x 0.38) = 273.4 psi, so look up the permissible shear stress of your loctite equivalent to see if it can handle your calculated shear stress on your shaft-gear interface. I'm sure you'll handle the sums for your starter gear chain. But remember the starter isn't just compressing valve springs, it is accelerating masses too, so I should use the "stall torque" of the electric starter as the max input torque that can be applied to the gear train.
Ask if you need more guidance... and if anyone spots my "deliberate mistakes", then please correct me! (my fingers don't always fit the buttons on the calculator, and my mental arithmetic checks have found one error already!

#### Charles Lamont

##### Well-Known Member
Very nice model.

What did you do it in? (software)
Thank you.

Onshape.

#### petertha

##### Well-Known Member
As to the joint I would have thought that a good close joint and something like Loctite 648 would do, I use that to bond cam lobes to shafts and make small crankshafts. If you do want to add a pin then if worried how close it comes to the hole you could move it out radially so 0.5mm is in the boss and 1mm in the gear. Also does not need to be full depth so maybe only half gear depth. Final option would be a radial pin between two teeth of the gear and set just below the depth of the valley
680 is what I have & had in mind. Specs below.

To answer another question about inter-gear fit, I basically followed the plans (then subsequently got to questioning them later LOL). The gears are purchased at about 2x thickness shown & required subsequent modification to what you see. Part of what is constraining the turned down hub OD of smaller gear is cutting through the troughs of the teeth into full material without making the remaining hub thinner yet. My picture doesn't quite show but even at this diameter, there are actually a hint of what look like splines (remnants of the teeth).

I'm not sure if some of the other posts were pertaining to my gears or not, but to reiterate, the gears are joined together as one & free rotate about the shaft. Not attached to the shaft.

Maybe another idea is to drill 2 axial pin key holes but at shallower depth. Its the drill drifting off & potentially close or breaking through to the axle hole I'm concerned about, especially with the potential presence of intersecting a remnant of the gear tooth trough to misguide it. Hope this makes sense.

Loctite 680 retaining compound is a high strength, high viscosity room temperature curing adhesive used to join fitted cylindrical parts. It fixtures in 10 min and provides a shear strength of 4000 psi. Capable of filling diametral gaps up to 0.015 Inch (0.38 mm). - Loctite 680 is designed for the bonding of cylindrical fitting parts, particularly where low viscosity is required. The product cures when confined in the absence of air between close fitting metal surfaces and prevents loosening and leakage from shock and vibration. read less

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#### Charles Lamont

##### Well-Known Member
I still think you should try it without the pins.

I, for one, am not unclear about your application. Refering to my example of my fixing gears to the shaft with Loctite, the point I meant to make, though I could have explained it more thoroughly, is that the application is more highly loaded than your case, because the radius of the joint is smaller in relation to the gears than yours is. This means that both the shear force is relatively higher and the joint area smaller, so the joint stress is doubly greater.

Based purely on experience, I expected these joints to just work (as they do, so far) without bothering to do any calculations. Prompted by your concerns, I have now done them. The most highly stressed connection is at 140 psi.

#### ajoeiam

##### Well-Known Member
Thank you.

Onshape.
Went a looking - - - cheapest option was \$1500 usd PER YEAR.
For that I would amortize my costs and buy something for \$5k or so.

Good on you though - - - great looking result!

#### Jasonb

##### Project of the Month Winner!!!
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You should have looked harder then you would have found the free version for hobby use

#### ajoeiam

##### Well-Known Member
You should have looked harder then you would have found the free version for hobby use

Thank you - - - - looked at it a bit.
This is SAAS as I see it.
Means that everything I would do someone else has the rights to.

Somehow I have a hard time with that.
I can give up my right to something - - - -but to never even have it - - - that tends to make me grumpy!

#### Bentwings

##### Well-Known Member
Simple calcs for my steam engine in a boat with a steam engine, I used a bought "computer printer toothed belt and gears" - worked fine for the torque applied to the screw. I.E. 3/4" bore 3/4" stroke steam engine at 20psi, with 3:1 speed reduction from 2000rpm max. => max torque = 8.8lbs (on piston) x 0.38" (crank throw) x 3 (gear ratio)= 10.2lb.in.
If this torque is applied to gear bonded to a 1/4" shaft, at 3/8" long, the shear stress of the gear-shaft joint at 1/8" radius is 81.6lbs/(3.142 x 0.25x 0.38) = 273.4 psi, so look up the permissible shear stress of your loctite equivalent to see if it can handle your calculated shear stress on your shaft-gear interface. I'm sure you'll handle the sums for your starter gear chain. But remember the starter isn't just compressing valve springs, it is accelerating masses too, so I should use the "stall torque" of the electric starter as the max input torque that can be applied to the gear train.
Ask if you need more guidance... and if anyone spots my "deliberate mistakes", then please correct me! (my fingers don't always fit the buttons on the calculator, and my mental arithmetic checks have found one error already!
Fingers don’t fit mine don’t fit either plus I see two of everything I use a stylus hunt and peck. Very hard to hit te righ arget.
byron

#### petertha

##### Well-Known Member
Drilling a hole for a round pin key wasn't bad at all, at least in this 1018 test blank assembly. No breakthrough or drift issues. I drilled a shallow 120-deg center drill & tried 2 hole sizes just to evaluate - a #55 & #52 drill which lands me respectively with 0.023" & 0.017" distance tangent to tangent from the pin OD to axle hole. I think this the way I'll proceed, using smaller #55 drill. Seems like the best of both worlds - Loctite adhesion on the hub area & a steel pin acting as a keyway also retained with Loctite.

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