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 (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 (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 (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.