Contact ratio of spur gears with varying centre distance

[OfficialGreenTea]

Hi!

As a side-project I am designing and building a ramen noodle machine. This is similar to a pasta machine, just significantly larger and stronger. For dough sheeting purposes, two press rollers of approximately 120 mm diameter are being rotated by two spur gears, each with an approximately 120 mm pitch circle (this will be slightly adjusted based on hunting ratio's).

I am trying to figure out what module and centre distance makes sense for these gears. Since not all dough requires an equal thickness, the center distance between the two rollers needs to be variable. Ideally the gears should be able to move apart (up to 5 or 6 mm) while the gears still need to remain in a meshed state ready to transfer torque. Therefore, the whole tooth depth of the gears need to be at least 5 to 6 mm. This limits the gears to module 3 or greater:

- Module 3: 6,75 mm whole tooth depth
- Module 4: 9,00 mm whole tooth depth
- Module 5: 11,25 mm whole tooth depth

With spur gears, I’ve read that spur gears are less sensitive to centre distance variation (last comment). It is also mentioned that it is possible to use the contact ratio to figure out the (maximum?) centre distance between two gears. Ideally, the contact ratio should never fall below 1.2 even when the gears are 5 or 6 mm apart. I tried to calculate the contact ratio of three gears, with module 3, 4 and 5 respectively. Each gear has a pitch circle of approximately 120 mm (adjusted to a hunting ratio). The calculations are based on the transverse contact ratio for spur gears, as described here:

- Module 3, 41 teeth, pitch circle of 123 mm, outside diameter of 129 mm, pressure angle of 20°, base circle of 123cos(20°), centre distance of 123 mm: contact ratio of 1,718.
- Module 4, 31 teeth, pitch circle of 124 mm, outside diameter of 132 mm, pressure angle of 20°, base circle of 124cos(20°), centre distance of 124 mm: contact ratio of 1,660
- Module 5, 27 teeth, pitch circle of 115 mm, outside diameter of 125 mm, pressure angle of 20°, base circle of 115cos(20°), centre distance of 115 mm: contact ratio of 1,592

If my calculations are correct, when using a center distance of 2 times the pitch circle (so no spacing between the gears), there is no problem; all ratio's are above 1.2.

However, when increasing the center distance to for example 6 mm, still none of the contact ratio's fall below 1.2, despite the gear 3 module only having 0,75 mm of tooth depth left to work with:

- Module 3, 41 teeth, same as above, centre distance increased to 129 mm: contact ratio of 1,487
- Module 4, 31 teeth, same as above, centre distance increased to 130 mm: contact ratio of 1,487
- Module 5, 27 teeth, same as above, centre distance increased to 121 mm: contact ratio of 1,452

In fact, when increasing the gap to 8 mm (just for the sake of the argument) still all ratio's are above 1.2, despite knowing that the whole tooth depth of the module 3 gear is only 6,75 mm.. In other words, the module 3 gears would not be meshing with a gap of 8 mm, but still the contact ratio is well above 1.2. This makes me believe something is wrong with my calculations.

Therefore, my question is: how do I figure out which module gear I need in order to design a ramen machine which is able to increase the centre distance of the gears with 5 or 6 mm. Is it possible to use the contact ratio formula, and if so, are my calculations correct?

Thanks!

TL;DR: For a noodle machine design I need two spur gears with a 120 mm pitch circle to be able to vary their centre distance with +-6 mm. How do I calculate the minimum module these gear need?

 

[3DDave]

If you use two idler gears in series between the final gears you can rotate the final rollers around the centers of the idler gears and change the spacing of the rollers without affecting the contact ratio. This will allow the maximum fatigue life of the gears. Since the idlers are likely to be smaller, one of them can be the driven part of a gear speed reduction as an input to better match typical motor torques.

Alternatively, since a run of noodles will take some time, it may be worthwhile to just just different diameter rollers - they need to come out sometime for cleaning the machine.

 

[OfficialGreenTea]

Thanks for your reply! I really like both of your suggestions, as they offer new design ideas I haven't thought of.

1. Using idler gears in series is a great idea I need to investigate further. Thank you!
2. Changing the diameter of the rollers will be difficult, as it significantly reduces the amount of possible noodle widths possible. Typically, you'd want to adjust the dough thickness with a 0,1 mm precision. Making 30 to 40 rollers is not feasible.

Could you help me understand if it is feasible to simply use two module 4 gears with a whole tooth depth of 9,00 mm, and increase the centre distance between these gears up to 6,00 mm? What are the risks of such design, where the gears are at worst only meshed 3,00 mm? Could the gears be designed in such a way to minimize these risks?
Thanks!

 

[spigor]

- Module 3, 41 teeth, pitch circle of 123 mm, outside diameter of 129 mm, pressure angle of 20°, base circle of 123cos(20°), centre distance of 123 mm: contact ratio of 1,718.
- Module 4, 31 teeth, pitch circle of 124 mm, outside diameter of 132 mm, pressure angle of 20°, base circle of 124cos(20°), centre distance of 124 mm: contact ratio of 1,660
- Module 5, 27 teeth, pitch circle of 115 mm, outside diameter of 125 mm, pressure angle of 20°, base circle of 115cos(20°), centre distance of 115 mm: contact ratio of 1,592

That is correct, except for the number of teeth in 3-rd: should probably be 23 teeth, not 27 teeth.

- Module 3, 41 teeth, same as above, centre distance increased to 129 mm: contact ratio of 1,487
- Module 4, 31 teeth, same as above, centre distance increased to 130 mm: contact ratio of 1,487
- Module 5, 27 teeth, same as above, centre distance increased to 121 mm: contact ratio of 1,452

That is incorrect as per my calculations.

Module 3, 41 teeth:
A=129: the major diameters touch, no contact between the flanks, contact ratio=0
A=124.64: contact ratio=1.2

Module 4, 31 teeth:
A=130: contact ratio=0.371
A=125.96: contact ratio=1.2

Module 5, 23 teeth:
A=121: contact ratio=0.569
A=117.10: contact ratio=1.2

In your calculations, you are probably mixing the profile angle with the pressure angle. The profile angle stays the same, while the pressure angle increases with the center distance being increased. Reducing the profile angle (and therefore the pressure angle) makes the contact ratio larger, but not to the extent you seem to be looking for. For example:

Module 5, 14.5PA, 23 teeth:
A=121: contact ratio=0.621
A=117.83: contact ratio=1.2

Like 3DDave said - an idler gear setup is something for such applications.

 

[spigor]

One more reference calculation:

Module 20, 20PA, 17 teeth:
A=340: contact ratio=1.51
A=346: contact ratio=1.23

 

[mfgenggear]

OfficialGreenTea
not sure what or how you are trying to accomplish this.
look at sheet metal roll machines. it has on fixed roller connected to a motor.
and one roller that is adjustable.
can you draw a picture.
I do not like your Idea. I believe it will be prone to wear.

 

[Compositepro]

Using two inter-meshing gears on nip or calendar rolls works fine for many applications, and is commonly done. Using two additional idler gears between the rollers allows for a greater range of gap between the rollers, and a smaller, constant backlash in the gears. Sprockets with an s-wrapped roller-chain is another approach, which allows for a wider range of gap without losing mesh. The chain approach requires a chain tensioner that can take up a lot of slack (often a idler sprocket on an air cylinder).

 

[OfficialGreenTea]

Thank you all for the replies! I am now convinced an idler gear setup would work best. I am looking for a variable spacing up to 6 mm. I could see how a setup with a variable centre distance could be prone to wear. As the goal is to design a machine which would produce one hundred portions a day, this is not ideal. I got the variable spacing distance idea from an old manual noodle machine (the ONO type 1) I have. I recorded a short video showing the variable spacing of the gears. Notice how the gears do not mesh at the beginning. With this machine, it is possible to work with a spacing as wide as 6 mm, even though the gears and module are small. This is probably bad for the gears.

Of course, with the ONO type 1 machine, you only make a couple of portions a week at most, which means the gears would take significantly longer to wear down. I simply wanted to explore all options, since the ONO setup is simplified when compared to an idler gear setup.

In your calculations, you are probably mixing the profile angle with the pressure angle. The profile angle stays the same, while the pressure angle increases with the center distance being increased. Reducing the profile angle (and therefore the pressure angle) makes the contact ratio larger, but not to the extent you seem to be looking for.

This is correct. I was not paying close attention to the difference between the profile angle and pressure angle. Thanks for clearing that up.