# Helical profile when follows a circular path...acute problem

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#### jasmeet11arora

##### New member
Dear friends,

Need your help in this challenging model which I am doing in Pro/E....tried various options...which is basically a spiral (Helical) cut...seems tricky to me but failed to get the required model, Please help

1. There is a frustrum (upper part of cone is cut).

2. There is a tool....circular in shape...having three circular contours...each contours are 120 degrees to each other.

3. Axis of cone and axis of tool is FIXED...27 units.

4. Now just imagine that cone is rotating and tool is also rotating on their axis...hhmm just like worm wheel and worm gear.

our tool is like worm wheel...and our cone is like worm gear...but worm gear use to be cylindrical...but our worm gear...i mean cone...is conical and not cylindrical.

5. If you will concentrate on the helical profile....for ordinary...screws or springs...we use to give profile shape (for helical cut) in pro/E...and normally it use to be a straight line.

BUT here the case is different....here...as both the axis are fixed...the helical profile will follow the circular path.

6. I can say that this helical profile in the cone is helping the contour of the tool to follow circular path because the tool can only rotate on its axis and axis is fixed.

7. Last point to mention.......when the cone take one full rotation......tool take one third of the rotation...it means when cone takes three rotations...tool take one full rotation

8. PROBLEM IS TO GET THE EXACT HELICAL PROFILE OF THE CONE.

please do mention if I am not clear at any point...or any thing which is unclear to you all.

Thanks and waiting for your response.

Regards,

Arora

View attachment 129

#### Huug

##### New member
Hmmmm, not that easy I think!

Do you have a (helical) curve on you conical part?

For example created with an equation.

Maybe you can try a variable section sweep with that curve, with the fixed axis as the pivot direction.

Don't stay to long trying to do it with that helical feature. It's more something for springs or screws. And it makes your part slow and large on filesize.

Huug

#### jasmeet11arora

##### New member
Hej !! Hugo

great..if u got the problem....infact its very much difficult to make anybody understand this problem..unless untill...one is very much proficient n show some interest to understand it. I appreciate ur response.

# Hmmmm, not that easy I think!

## yeah ofcourse...since long i m breaking my head wid dis.

# Do you have a (helical) curve on you conical part?

## yeah exactly...the helical curve is in the conical part.

# Maybe you can try a variable section sweep with that curve, with the fixed axis as the pivot direction.

## Equation ?? will be great..if u can explain a bit...i will certainly try for dat too.

Thanks n Regards,

Arora

#### kvision

##### Moderator
using the curve as a trajectory for a variable section sweep and using a plane parallel to the flat surface of the 3 lobes should give you the shape you want. If the curve can't be used in it's current form then use a formed curve. This will automatically wrap a straight line around the solid in a helical pattern. The pitch etc can be driven with simple sketcher relations.

#### Huug

##### New member
Because I find this an interesting one, I've tried somewhat.

The start is to get a curve from equation that exactly descibes the center of the path of one of the three lobes around the conic.

So I set some dimensions:

Distance between the two axes: 20

Distance of center of lobe to vertical axis: 10

One rotation of conic part is 120 degrees of lobes part.

The cylindrical curve should be something like this

r=15-10*cos((t*120)-60)

theta=180+t*360

z=-sin(60)*10+t*10*sin(60)*2

That should look like this:

View attachment 382

And then a variable section sweep around that one with the diameter of the lobe. Maybe the curve should be extended on both sides to get a complete cut in de conic part.

Maybe you can supply some dimensions.

Huug

#### jasmeet11arora

##### New member
Hej !! Hugo

just now saw your significant logical solution...n couldn't resist myself to re-reply instantly......

# I can feel that variable section sweep can provide us the solution....I will also concentrate on the same. It is to be noted that 'kvision' has also come up with the similar solution, which strengthens our claim of 'variable section sweep'

# enclosing the dimensions

1. Distance between the two axes: 27 (as shown in cone dwg)

2. Distance of center of lobe to vertical axis: If I am right, you mean to say the distance between the centre of lobe (NOT CENTER OF TOOL) to the vertical axis that is cone.

This distance will keep on changing...and will follow the circular path of radius 14 (as shown in tool dwg)....am I right ??

3. One rotation of conic part is 120 degrees of lobes part:

right....its the ratio of 3:1 , when cone takes 360 degrees...tool (lobes) will rotate by 120 degrees.

do tell please, if anything is not clear.

Thanks n Regards,

Arora

View attachment 384

View attachment 385

#### cristelino

##### New member
Can you send me the models

Unique the worm gear?

In my opinion whats wrong is variable dimension of the worm

So finally what you try to solve with this solution

Of course if is not confidential

[email protected]

#### Huug

##### New member
Arora, thanks for the drawing, that will help to define the part better.

So let me try to explain one more time. It's a little bit of mathematics, I do not need that often either, but it isn't hard.

Something you should have learned in highschool.

So what we need is a helical curve around a conical worm.

Problem is: the depth of the path varies, while the lobe is rotating.

How much does this vary? It moves over 120 degrees, or two times 60 degrees.

So the depth varies the cosinus of 60 degrees (0,5) with a radius of 14, so 7.

In one single turn of the worm the R of the spline varies from 20 to 13 and back to 20.

Makes the r of the equation: r=27-14*cos((t*120)-60)

The theta makes one turn, 360 degrees, but starts with this csys at 180,

so theta=180+t*360

The length of the curve in z-direction is two times the sinus of 60 degrees, and starts with a negative value.

so z=14*sin((t*120)-60)

As we do a variable section sweep cut with R10.5 along this curve, we see that it does not cut enough material of the conical worm. So we have to extend the curve with 90 degrees on both ends. Which makes the equation:

r=27-14*cos((t*180)-90)

theta=90+t*360*1.5

z=14*sin((t*180)-90)

At this point we have a nice worm which matches almost perfectly

View attachment 383

But the size at the end of the worm makes it neccesary that the curve at the end runs a little further.

But at this point the z value should decrease. But I've spended enough time so far.

Huug

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