helix angle(s) in external helical gears 4

[zanouk]

Hello all,

I work as an application engineer and I have recently taken over a project regarding the construction of gears in general. So I have only a basic understanding of the subject.
I noticed that in the CAD construction the person who was previously responsible of gears has defined more than just one helix angle, i.e. one for each circle: a helix angle for the tip diameter, base diameter and root diameter.
In the actual construction we use only the helix angle at the root diameter (formula = 180/π*rtan(rootØ/referenceØ)*tanß), while in all the other formulas we use the "regular" ß=20° angle. This helix angle at the root diameter actually determines the path of cutting away material from a cylinder with a diameter = the tip diameter (the path of the tool with which we would obtain the gear).
I have read a bit through DIN 3960, but was unable to find a simple explanation of why it is important to use different ß angles.

Can anyone explain as simple as possible the necessity (if there is a real one) of having a different ß angle for each defining circle?

Thank you in advance.

 

[tbuelna]

For purposes of accurately defining helical tooth profile surface geometry in a CAD model you would need to account for the changes in tooth thickness from tip to root. With a helical gear, the point of contact moves in two directions (radial and axial) along the tooth flank. For example, during the approach phase a planar point of contact moves radially from tip (HPSTC) to root (LPSTC), while also moving axially. The continuous increase/decrease in helix angle during this approach phase is due to the decreasing/increasing tooth thickness along the arc of contact. The opposite is true for the recess phase. However, when it comes to the typical drawing data used to describe a helical gear, the helix angle is only defined at the pitch diameter, usually in both the normal and transverse planes.

One other thing to consider with regards to precise helix angle definition is that with high performance gears it is common to use lead correction and/or face crowning. Both of these modifications would have a slight effect on the operating helix angle variation as the planar point of contact shifts axially.

I apologize if my explanation is confusing. I'm not very good at technical writing. Hope it helps anyway.

Terry

 

[spigor]

By definition- the nominal helix angle is measured on the pitch diameter, that's a convention used in the standards. You can then calculate the value of a helix angle on a different diameter if you need it, but you can not select the value freely.
Hope it helps you any.

 

[mfgenggear]

zanouk

what other have said about is excellent responses. General with standard manufacturing methods. Gear Shaping & hobbing, generation gear grinding, form grinding & inspection. the basic helix angle is give & used at the pitch diameter. but data is given in the normal plane & calculated to the transverse plane. It would help to read gear books like Dudleys, Vogel, Earl Buckingham & to understand the calculation & transition from normal plane to Transverse.
it is unnecessary to use the helix angle at the different diameters unless there is a specialized machining process I am not aware of.
It would help on the type of equipment that is used at your facility. maybe then we could help you more.

The basic gear data is given, then that data is used by manufacturing to achieve drawing dimensions. then the Inspection department verifies the lead (parallelism), involute, total, & tooth to tooth errors. These are attributes that determine if the correct diametral pitch, pressure angle & the basic helix angle.

Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[tbuelna]

zanouk-

Attached is a chart showing how the normal plane helix angle changes from tip to root. The example is a 35t/59t external gear set with a 19deg helix angle.

Hope that helps.
Terry

 

[zanouk]

Thank you all for your responses. They are very helpful.

tbuelna, thank you for your great explanation of why it is necessary to compute and use the different ß angles. Now it makes more sense.
I will definitely have to read further on the subject of gears, so thanks mfgenggear for the book recommendations.

We usually have plastic gears which are molded according to the CAD files we provide, so it makes sense to have a model as precise as possible.
I'm good at noticing when something is wrong, but unfortunately I'm not that good at fixing them when it comes to gears..and as I'm quite new to this topic, more questions will follow.

 

[mfgenggear]

zanouk

even tho the model is use to manufacture the plastic gears. the inspection criteria is the same. to make sure the gears have the correct helix angle by inspecting the gear data. drawing a helical gear profile is doable. simply purchase a gear program that has a proven track record. it will draw the profile for you. it is very simple to make a mistake. the program will pay for itself. it is beneficial to understand the mathematics behind it, but then it become tedious & repetitious.

HTH

Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[tbuelna]

zanouk,

I agree with mfgenggear- don't be cheap. For about 1000-1500 bucks you can buy an excellent gear program (like GearTrax) that will output very accurate CAD models for spur, helical or spiral bevel gears. It will pay for itself in one gear design project.

Regards,
Terry

 

[zanouk]

Hello all,

Thank you for your suggestions.
Buying a gear program would seem the better option, but for the moment I have been assigned to do exactly this job...create a working gear model. (actually improve the creation method used so far)
That's why I'm reading and learning and asking for others opinions. For the moment, it's the best that I can do.
So regarding the gear program, I can only propose this solution to my team leader, but it will not be my decision to take.

Have a good weekend!

 

[PeteDB]

The surface of a helical tooth follows a spiral path around the axis of rotation. The pitch of this helical spiral is constant. It is called the lead. It is the distance a point on the profile travels in the axial direction if it were to extend 360°. This is why the helix angle is different at different diameters. The ratio of the circumference divided by the lead equals the tangent of the helix angle. Since the circumference increases with diameter the helix angle also increases. Knowing the helix angle at a given diameter you can calculate the lead. With the calculated lead you can determine the helix angle at any other diameter.

 

[tbuelna]

PeteDB-

I would disagree somewhat with your description. The surface of a helical gear tooth follows an involute profile around the axis of rotation, which would be in the transverse plane. However, any given point on the tooth surface having a constant radial offset would indeed follow a helical path in the axial direction with rotation.

If zanouk truly wishes to create an accurate CAD surface model of a helical gear, I would recommend reading the best technical reference on the subject by Feydor Litvin.

 

[Occupant]

Unless I misunderstand something - the involute realy exits only in the normal plane.

 

[gearguru]

Here is the Litvin's book. Helical gears theory starts on page 377.

http://books.google.com/books?id=XU...Aw#v=onepage&q=wildhaber-novikov gear&f=false

 

[gearguru]

PeteDB' explanation seems to be correct.
If I had to create the 3D CAD model I would create
the profile of the gear tooth in normal plane, and
2 helixes (one could be on the pitch diameter, the other on OD). They have to have different helix angles, as PeteDB mentioned.
Then the tooth profile would be "swept" using those 2 helixes as "guides".
I used UG long time ago, that's the terminology as I remember it.

 

[PeteDB]

Occupant: The involute profile is defined in the transverse plane. (The plane perpendicular to the axis of rotation). It is the path a point on a string takes as it is unwrapped from the base circle.

The involute profile in the transverse plane is swept in a spiral path to create a helical tooth surface. So Gearguru, if you defined the profile in the transverse plane you should only need one helical curve to define the path. The pitch of the helical curve would equal the lead.

 

[gearguru]

PeteDB,
I am sorry, but... you are right.
And when creating the 3D model in UG one also had to use the "spine" - the centerline (axis of rotation) of the gear to constrain the geometry.

 

[Occupant]

To PeteDB: That is not correct - what I mean to say is, you, obviously, can do anything you want, but that's not the way it is generally done. I would have to do some digging to find the right literature. However, suffice it to say that e.g alpha.n (the normal pressure angle - now almost exclusively 20 degrees) defines the involute. In the transverse plane you have alpha.t = atan(tan(alpha.n)/cos(beta)) - the transverse pressure angle. The way these gears are cut, it would require a new cutter for every change in pressure angle if one would follow your suggestion, because the formulas would then have to change to show alpha.t = 20 deg. and alpha.n would then change with the helix angle.

 

[tbuelna]

I've attached the relevant section from Dudley on pressure angle of external helical gears, which may help clarify things.

Regarding choice of pressure angle there are some trade-offs. As Occupant noted, a 20deg pressure angle is probably the most common for stock metal gears. In general, lower pressure angles (such as 14.5deg) will give higher contact ratios, create less noise, and give a bit better efficiency. While higher pressure angles (such as 25deg) will give greater tooth bending strength, which is usually critical for fatigue life in high load, high speed metal gears. I don't have any experience with plastic gears, so I cannot give any advice as to the best choice of pressure angle there.

Since zanouk's application is a molded plastic helical gear I think the issue of availability of standard cutting/shaping tools would not apply. But since the finished tooth profile will be formed by a mold surface there are other things to consider, such as part shrinkage, when designing the mold shape. The mold surface must have precise amounts of compensation for shrinkage as the plastic part cools, and due to variations in section thickness in the gear teeth/rim/hub the shrinkage and distortion is not uniform throughout the gear body.

As a starting point I would highly recommend zanouk purchasing a copy of AGMA 909-A06 and AGMA 1006-A97. These documents discuss how factors such as mold "hang-up" and shrinkage-induced stresses can influence choice of pressure angle in a molded plastic gear.

Hope that helps.
Terry

 

[mfgenggear]

Just seems that trying to draw a correct lead & profile of a helix gear is easier said than done.
It would be interesting to see the results using a CNC gear checker.
Sorry I just don't have the confidence that a correct geometry will result.
Has anyone actually done this?

Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[spigor]

Mfgenggear,
the so called 5-axis milling of gears starts with a NC model, and many reports claim it has been successfuly done (regardless the cost) at least with the cylindrical gears, worm gears and bevels. So, it's been done, I can also confirm that from my personal experience.