Gear WB: Backlash resulting in bad profile

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abdullah
Posts: 3583
Joined: Sun May 04, 2014 3:16 pm

Re: Gear WB: Backslash resulting in bad profile

Postby abdullah » Wed Aug 19, 2020 1:04 pm

EduBambu wrote:
Tue Aug 18, 2020 3:07 pm
The detail is that I used a backlash value in microns and turned it backlash in reverse.
Yes, thanks, I realised this worked. My issue was rather this:
looo wrote:
Tue Aug 18, 2020 3:24 pm
Looking at the formula I guess we somehow changed to angular backlash but kept the property-type (length). You should be able to get the correct amount of backlash by using:

<backlash in mm> / dw / 2
Thanks! That was my original issue.
chrisb wrote:
Tue Aug 18, 2020 4:05 pm
This may work, but internal gears are different from a subtracted external gear.
looo wrote:
Tue Aug 18, 2020 4:37 pm
The profile should be the same. So from a kinematic point of view this shouldn't be a problem. Using a negative clearance (-0.25 or smaller) and 0.25 for the head-property should work. Additional fillets would be nice to have, but are not yet available.
I had read in the forum that the profile was the same, but indeed, the "separation" was not same, because clearances and backlash, and "head"/"shift". The documentation is nice:
https://wiki.freecadweb.org/FCGear_InvoluteGear

But I still have the "problem" with differentiating "shift" and "head" at least from a usability point of view.

Yesterday, I ended up setting clearance, backlash and head to 0, and shift to 0.125:
Screenshot_20200819_142646.png
Screenshot_20200819_142646.png (88.88 KiB) Viewed 241 times
Now, with loo's input:
Screenshot_20200819_143037.png
Screenshot_20200819_143037.png (114.55 KiB) Viewed 241 times
The screenshots look rather similar. My guess is that the "shift" version has slightly larger ring profile diameter, while the "clearance+blacklash+head" rather changes the tooth.

Is there any "rule of thumb" or "serious design rule" of when to use "shift"?
EduBambu wrote:
Wed Aug 19, 2020 3:04 am
I tested 3 gear combinations and with one of the gears I chose the backlash value, in the combined view, of 0.010 mm (10 microns).
EduBambu wrote:
Wed Aug 19, 2020 3:04 am
None of them has the numerical value indicated in the combined FreeCAD view. Except when it is "zero".
Nice empirical work.

the formula in your table: B_angular = 6880 * B /D (in arc minutes) = 6880 / 60 * B/D (in degrees) = 6880 / 60 / 180 * pi * B/D (in radians) = 2 * B/D (in radians).

Loo's formula is B_angular = B/D/2

So actually there is a 4 factor between both formulas which I cannot explain (maybe it is a different definition).
EduBambu wrote:
Wed Aug 19, 2020 3:04 am
Where;
J (real) = Backlash measured in gear
J (inf) = Baclash reported in combined view
m = gear module
Z = number of teeth

Therefore, in case you need a specific backlash value, the following function should be used:

J (inf) = J (real) / (m x Z / 4)
If J(inf) is angular backlash and J(real) is linear backslash (mm), following Loo's formula:

J(inf) = J(real)/D/2 = J(real) / (m x Z / 2)

A factor "2" of difference.

I do not know where this differences are coming from, though...
chrisb wrote:
Wed Aug 19, 2020 5:15 am
Can you please edit the first topic and change the subject to Backlash without the s in the middle. Future searchers will be thankful.
sure! :oops: my future searches will thank me :lol:
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looo
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Re: Gear WB: Backlash resulting in bad profile

Postby looo » Wed Aug 19, 2020 5:22 pm

abdullah wrote:
Wed Aug 19, 2020 1:04 pm
Is there any "rule of thumb" or "serious design rule" of when to use "shift"?
if you have a fixed gear ratio (number of teeth) and a fixed axial distance and a given module, you need shifting. shifting is the only way to change the pitch diameter while keeping the module and the number of teeth constant.

abdullah wrote:
Wed Aug 19, 2020 1:04 pm
So actually there is a 4 factor between both formulas which I cannot explain (maybe it is a different definition).

my formula should result in an approximated backlash value (measured) if you use the same value for two gears (backlash in reality is a property of a pair of gears).
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EduBambu
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Location: Minas Gerais, Brasil

Re: Gear WB: Backlash resulting in bad profile

Postby EduBambu » Sun Aug 30, 2020 1:17 am

looo wrote:
Wed Aug 19, 2020 5:22 pm
abdullah Escreveu: ↑
quarta ago 19, 2020 10:04 am
Is there any "rule of thumb" or "serious design rule" of when to use "shift"?
Is there a "rule of thumb" or "serious design rule" of when to use "shift"?

Yes! It has rules and recommendations for using the "shift"!

I recommend the document references again; https://qtcgears.com/tools/catalogs/PDF_Q420/Tech.pdf, observe topic 4.5 on page 20. There it is explained that the "shift" is the displacement of the construction circle of the evolvent that determines the profile of the tooth (involute).

In general, this construction circumference has a diameter of 56/60 to 58/60 of the primitive diameter of the gear. For example; a gear of 10 teeth and module 6 (cylindrical spur gear) would result in a primitive diameter of 60 mm; therefore the construction diameter of the tooth profile would be 56 mm. So the distance between the two circumferences on the gear tooth is; 2 mm.

The value of "shift" is the difference that must be applied to the distance between the two circles, the primitive and the construction. In the example above; 2 mm.

The "shift" value can be positive, in which case the tooth profile is increased in the "foot". Or negative, in which case the profile of the tooth is decreased in the "foot". In the document I indicated above, they are figures 4-6 and 4-7, on page T20.

Attached to this answer is a drawing showing an example: a gear of 20 teeth and module 5 resulted in the tooth width of 8.77 mm. After changing the shift at -0.05, the tooth width decreased to 8.60 mm.

Eng_mot_09.png
Eng_mot_09.png (171.71 KiB) Viewed 173 times

In practice, the gear tooth was moved by 0.25 mm to the center of the gear. Resulting in smaller outer and inner diameters, by 0.25 mm, for the gear. The effect for the backlash of the gear pair is very similar to increasing the distance between centers by 0.25 mm.

In table 1-5 of the cited documentation, and presented earlier in an answer to this topic, we have to; B = 2 (∆C) tanφ. Where;

B = backlash due to increased distance between centers
∆C = increased distance between centers
φ = gear pressure angle


Soon; B = 2 x 0.25 x tanφ => B = 0.18 mm

If the design of the gear profile is correct, we can measure a distance of 0.18 mm between each gear face. This is not at all easy to do on the TechDraw workbench.

That is why I propose to calculate and demonstrate this backlash, and with that the entire design of spur gears from FreeCAD, through the FEM workbench.

The proposed model will consist of a 10-tooth pinion driving a 20-tooth intermediate gear, which will drive a 10-tooth rack. The modulus of all gears
will be 5 mm.

For analysis by FEM the pinion will be fixed in its internal diameter and the rack will receive a load transversal to the teeth of 10 N.

The set built respecting the correct measures must have a backlash of 0.00 mm.

When we try to create a mesh in the set with "zero" clearance, the resulting mesh tends to "leak" from one gear to another at the point of least clearance. In this case it is "zero".

Observe the image obtained from FreeCAD using Gmsh with a maximum element size of 10 and a minimum of 4. It is clear that the sides converge to a single point at the minimum clearance location.

Eng_mot_03r.png
Eng_mot_03r.png (507.91 KiB) Viewed 173 times

When we change the shift value of the intermediate gear by -0.05, the "zero" clearance points have a visible clearance. It is this gap that we want to measure.

Using Gmsh in the set again after changing it, we obtain a clean mesh, without "leaks" from one gear to another.

Eng_mot_05r.png
Eng_mot_05r.png (290.15 KiB) Viewed 173 times

So far we have realized that the construction of the gear by FCGears and FreeCAD is quite accurate (at least spur gears).

The result of the FEM analysis will give us information about the accuracy of the gear construction commands.
Attachments
Engrenagem4.pdf
(646.48 KiB) Downloaded 9 times
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EduBambu
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Re: Gear WB: Backlash resulting in bad profile

Postby EduBambu » Sun Aug 30, 2020 3:37 am

Checking the result of the analysis of the gear clearance by FEM.

It was also convenient to modify the 10-tooth pinion profile, but without changing the backlash, that is, without inserting any "shift" value. In this case, the undercut option was chosen. Although it does not affect the clearance calculation, it is correct to apply the undercut due to the relationship:

Nc = 2 / sin²φ where:
Nc = Minimum number of teeth without undercut
φ = gear pressure angle


Therefore: Nc = 2 / sin² (20º) = 2 / 0.117 = 17.09 => 17 teeth

As the pinion is a 10-tooth gear, the undercut must be adopted.

Eng_mot_01r.png
Eng_mot_01r.png (30.82 KiB) Viewed 157 times

The results of rack displacement clearly show the gap between teeth, resulting from the value adopted for "shift", of -0.05.

Eng_mot_10r.png
Eng_mot_10r.png (316.06 KiB) Viewed 157 times

The values ​​verified directly between the teeth of the gears also indicate, with great approximation, the value of 0.18 mm expected for the backlash.

Eng_mot_12r.png
Eng_mot_12r.png (384.38 KiB) Viewed 157 times

The last figure shows the tension on the side of the gear teeth. The relatively high stress value is due to the low thickness chosen for the gears.

Eng_mot_07r.png
Eng_mot_07r.png (417.16 KiB) Viewed 157 times

The objective was to make the contact evident and to check the clearance without any doubt.
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looo
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Re: Gear WB: Backlash resulting in bad profile

Postby looo » Sun Aug 30, 2020 6:35 am

@EduBambu
In my eyes you are making things too complicated (but the analysis for sure looks quite impressive) In reality it is as simple as: you should not shift a gear-profile for the effect of backlash. Shifting is for:
1. creating more equal teeth's for a pair of gears with a big difference in number of teeth. In this case you use negative shift on the stronger (bigger) gear and positive shift on the weaker (smaller) one.
2. Avoid undercut.
3. find an axial distance for given module + number of teeth.

Attached is a file that shows the usage of shifting.
null-transmission: no shifting
v-null-transmission: reinforcing the smaller gears teeth (1 + 2)
v-transmission: vary distance (3)
Bildschirmfoto von 2020-08-30 10-09-08.png
Bildschirmfoto von 2020-08-30 10-09-08.png (60.93 KiB) Viewed 143 times

edit: we already had a forum discussion about shifting. This resulted in this function which computes the axial distance of two shifted gears:
https://github.com/looooo/freecad.gears ... .py#L26L46
Attachments
gears_shifting_example.FCStd
(380.29 KiB) Downloaded 6 times