Custom Gear Design for T5 timing belt

[vonfinck]

Hey everyone, 

I am trying to build me a custom gear generator for T5 belt gears. I have no experience with gear design and am struggling since two days with it. 

When the given parameters are the amount of teeth, the pitch, slope of the teeth etc. then the outer diameter of the gear should be "Amount of Teeth * Pitch" correct?

That leaves me only with not-working beltgears though. 

I want to be able to ajust just the amount of teeth and fusion does the rest. Should be super straight forward, but I think my calculations or reference thoughts are wrong. 

Can someone have a look and help a struggling engineer ;D 

here is a quick video about it: https://youtu.be/xVnVJuS_5Cg

The reference: 

Pitch = 5mm

L = 1.8mm

h = 1.2 mm

Teeth= 44

[g-andresen]

Hi,

Please share the file.

File > export > save as f3d on local drive  > attach to post.

günther

[vonfinck]

Hey, 

Here is a share link, there you may download it already. https://a360.co/3U7WCnS

The cloud-processing gets stuck at the moment. Don't know why though ;). The downside of fusion ... 

[MRWakefield]

I think the issue is your assumption that the OD is Pitch x #Of Teeth. If you study the image of the belt you'll see the cord belt inside the elastomeric covering. This cord belt doesn't stretch (well, not significantly) and it's this 'pitch line' that determines the pitch circle of the pulley. Unfortunately the belt graphic doesn't show the distance between the 'neutral line' of the belt and the root of the belt teeth. If you can find out this distance you can then deduct this (x2) from the Pitch Circle Diameter to arrive at the pulley OD.

I did a quick Google search and found this which might be of some help. I'm sure if you do a bit more searching you'll find even more help on how to design these pulleys.

Hope this helps.

EDIT:

Since I posted this last night I've done a bit more digging and found out some more info:

• The flanks of the pulley teeth should be involute in form rather than straight sided (this makes sense if you think of the belt as the rack in a rack & pinion setup, where the rack has straight sides and the pinion has an involute form). If the flanks are not of the correct form I would expect premature wear of the belt at the corner of the root of the belt tooth profile. I've not looked into it but I expect that the involute will be generated from the base circle diameter. Which would be calculated from the tooth flank angle and the Pitch Diameter (PDxCos(Flank_Angle)).
• I found a table of T5 pulleys here which also gives the PD (Pitch Diameter) and the Pulley OD. I brought that into Excel to calculate the difference between the two (see attached). If you open it you'll see that the difference isn't a constant value but ranges between 0.76 to 0.86mm with an average at around 0.826mm. Without access to a copy of DIN 7721 I can't say what formulae they use to calculate the value for any given case.

If I think of anything else out I'll let you know.

[MRWakefield]

Ok, a bit more info...

I thought I'd see if I could get anywhere by looking at this as a rack & pinion problem. The pitch of a T5 belt is set at 5mm and the PA ('Pressure Angle') (the same as the flank angle) is 20°. Using involute gear formulae this gives a constant Module of 5/Pi (1.592). The PCD is therefore equivalent to # of Teeth x Module and the base circle diameter (for generation of the involute curve) is equivalent to PCD x Cos(PA).

To check the theory I took a 20 tooth T5 pulley and plugged the numbers into the PCD formula. The resulting PCD agreed with the table on the page I linked to in an earlier post so I'm confident that's correct. I haven't checked an involute generated from the calculated base circle against an existing pulley or a belt so this would require further testing.

Hope this helps.

[MRWakefield]

Right, here we go... another update!!

It appears that although the involute profile is the correct one, you are allowed to replace this with a simplified profile. This simplified profile has a flank angle of 25° (50° included angle) instead of an involute. I suspect that this gives the required clearance to prevent the premature wear in the root corners that I mentioned in an earlier post. It also agrees with the image that appears on the page I linked to.

I have also found out that in the case of T5 pulleys the difference between the pitch diameter and the OD of the pulley is a constant 0.84mm.

So to recap:

1. The Module is 5/Pi (1.5915)
2. Multiply the Module by the number of teeth to give the PCD
3. Take 0.84mm away from the PCD value to get your pulley OD.
4. The pulley groove profile has an included angle of 50°

Again, I hope this helps.

[HughesTooling]

EDIT. Just noticed this was for an XL pulley not a T5. Shouldn't be too difficult to modify though.

Here's a design I made a long time ago to calculate the pulleys and pitch for a given amount of teeth on a belt. Note the timing of the second pulley will only be correct if both the number of teeth on the belt and pulley are even. The pitch between the pulleys will be correct though. You could do some calculations to rotate the second pulley 1/2 a tooth with a parameter but I don't have time to think about that at the moment. I've only bothered to do this for a setup with both pulleys with the same number of teeth.

[vonfinck]

Hey Mr Waefield, 

THANK YOU for the thorough answer. 

I'm back in the lab on Monday morning and will put it through the CNC Router.  (and 3D printer before that). 

I thought exactly that I need to somehow adjust for the "compression of the pitch in relation to the diameter of the pully or more specifically the radius". But I had no idea how to do that. I'll dive into your calculation and table asap. It looks exactly what I was looking for and I want to understand how to get to the values and so on, so that I can apply it to other gear types as well. 

[MRWakefield]

You're welcome, I hope it all works out ok. I wouldn't bother with the table. At the time of posting this was the only reference I had to determine the offset of the OD to the PD. Since then I have found a quote from ISO 17396 which specifies this to be exactly 0.84mm (for all T5 pulleys).

Don't forget to let us know how you get on with it.

[vonfinck]

Hey there, i have been on it for a few hours today. (i know ...) It seems so freaking simple, yet i always get stuck. 

here is a screen capture... run it with 10x speed 😉 there is no audio in it. 

The teeth to teeth-Gap is assymetrical and i want to build it as good as it is in the shematic. (not only for training purpose but mainly for training purpose). 

I calculated the helper lines by doing these steps: 

1. calculate the modulus: Pitch "5mm" /PI
2. PitchCircleDiameter PCD= M*n (number of teeth "36")
3. BaseCircleDiameter BCD = PCD*Cos(Preassureangle "20°")
4. create a circle for the pitch circle (PCD)
5. create a vertical helper line to mark half of a teeth
6. create an arc with half the length of the teeth width "1.8mm" = ((1.8/2)/(PCD*PI))*360
7. create a vertical helper line to mark the pitch
8. create an arc with half the length of the pitch "5mm/2" = ((5/2)/(PCD*PI))*360 
9. build the slope with preassure angle, create the radiä for the edges etc.
10. Realise something does not fit.

I'll give it one more and see if it fits tomorrow morning in the lab. 

[MRWakefield]

I've sent you a PM in case I get into trouble for posting ISO standards data in a public forum.

[vonfinck]

Hey Marcus,

Thank for the big help. With your help I simplified it and get how to do the involute as well now ;D BUT i am setting up everything strictly as per datasheet of the belts that i have. (sadly a whole box of these belts, so i would like to use these in particular). 

https://www.optibelt.com/fileadmin/extranet/power_transmission/technische_Unterlagen/Datenblaetter/A...

But my design is always to small in comparison to what the manufacturers for t5 belts put out. I have two sample aluminium belt pulleys here but with the wrong amount of teeth. But they are good for testing of course. There, the belt fits perfectly. Mine ... pitch seems to fit but outer diameter not. 

Maybe I just did a wrong formula somewhere? 

I attached the file including the refrerence pulley. 

I am absolutely gratefull for the help. 

[MRWakefield]

I've taken a quick look and compared it to a model I've done (see attached) and there are differences between the two. In your model you have an OD of Ø68.028mm and mine has an OD of Ø69.188 (which agrees with the reference pulley in your design).

Here's yours:

Here's the reference pulley in your design:

Here's mine:

So yes, there is an error in your calculations. If you go back to message #6 you'll see that the OD of the pulley should be 0.84mm smaller than the PCD, your OD is smaller by 2mm (this would agree with what you're observing with your 3D printed pulley(s) being too small). I notice that the included angle of your grooves are set to 40° whereas 50° would prevent premature wear of the belt (as previously mentioned). I also notice that the reference pulley also has an included angle of 40°, however this might be just simplified geometry as is common practice with vendor supplied models. In reality the actual pulley supplied is likely to be of involute form.

Hope this helps.

[MRWakefield]

How are you getting on? Did my last post make sense?