Catia Dişli tasarımı ingilizce

Welcome to my HomepageWritten by Gildas TrébaolPublished at http://gtrebaol.free.fr/Last update on August 28, 2008

SVG stuff

SVG (Scalable Vector Graphics) is a XML format for displaying figures in 2 dimensions.

It is an official format of the W3C (World Wide Web Consortium). SVG is widely used for the user interface of mobile phones (in 2008, about 600

million handsets). SVG can also be used on desktop computers, for embedding vector graphics in HTML

documents.

Title Description

SVG to Flash compiler

A paper and some SVG or Flash/SWF animationspresented in August  2008 at the SVG Open  2008conference, at Nuremberg in Germany.

SVG control panelsA paper and some SVG animations presentedin August  2005 at the SVG Open  2005conference, at Enschede in the Netherlands.

Simple SVG viewer A small Java Applet that I developed in 2001.

Parametric gears designed with Catia V5

What is Catia?

Catia is a mechanical CAD system invented in the seventies by the"Avions Marcel Dassault - Bréguet Aviation" company, a military aircraft manufacturer.

Despite its venerable age, CatiaV5 is probably the most powerful 3D CAD system available today.

Once written in Fortran and running on IBM mainframes, it has become a C++ sofwarethat runs perfectly on any PC having 1GB RAM and hardware-accelerated 3D graphics.

The gear tutorial

In May and June 2005, I attended a training session for learning how to use Catia V5. After that, I tried to design spur gears controlled by a few parameters (diameter, pitch,

etc). I started with a good Catia tutorial devoted to the same subject,

then I wrote my own tutorial for designing other kinds of gears. I hope that the geometric model of my gears is close to the design of real gears,

so let me know if you notice some mistake.

Title Description

Spur gears How to design a parametric spur gear.

Bevel gear That parametric part can produce bevel gearsvarying from the spur gear to a "flattened gear".

Worm A screw-shaped gear.

Helical gear An helical gear, used with a worm for making a toy gearbox.

Internal gear

This tutorial explains how to use internalgears for making an epicyclic gearbox.

Les moteurs de Marius Lavet

Here are some pages about the patent and designs created in 1936 by Marius Lavet,absolutely unrelated to the movies filmed by Marcel Pagnol at the same time.

Who is that guy?

For quite a long time, I wondered about the origins of the stepper motor,but in 2005 I learned that it is a creation of Marius Lavet, a French engineer.

Currently, Marius Lavet is considered as the inventor of the pulse motorminiaturized and integrated in most of the quartz watches.

But he has also nearly invented the permanent magnet stepper motor.

A variant of the permanent magnet motor

When you examine the Lavet patent FR823395,you can notice many other devices than the miniature pulse motor.

So I tried to extrapolate the different mechanisms proposed in the patentin order to make an archaic pre-WW2 stepper motor.

You can compare it with the current design of "can stack" permanent magnet motors.

Title Description

Marius Lavet The inventor of the stepper motor used in quartz watches

FR823395

A fac-simile of the original patent, extracted from theEuropean patent database and converted to HTMLwith an OCR tool.

The patent includes 78 figures

pm_36 (500 KB)

Catia assembly showing a variant of the patented devices.

pm_42 (950 KB)

Catia assembly of a real permanent magnet stepper motor.

Designing parametricspur gears with Catia V5Published at http://gtrebaol.free.fr/doc/catia/spur_gear.htmlCreated by Gildas Trébaol on June 10, 2005.Part design rebuilt on October 31, 2005.Tutorial rewritten on April 9, 2007.Zipped part: spur_gear.zip (100 KB).Zipped demo: spur_gears.zip (800 KB).VRML gear: spur_gear.wrl (330 KB).

  The powerful CAD system Catia version 5 has nobuilt-in tool for designing gears. When you are makinga realistic design, you may need a template spur gear.

Since the geometry of a spur gear is controlled by a few parameters,we can design a generic gear controlled by the following parameters:

The pressure angle a. The modulus m. The number of teeth Z.

This tutorial shows how to make a basic gear that you can freely re-use in your assemblies.

1. Gears theory and standards

1.1 Sources, credits and links

Most of my tutorial is based on a nice tutorial on helical gearsin English at http://ggajic.sbb.co.yu/pub/catia/.

I improved it a little for making an exactly symmetric tooth. The mathematic description of the involute curve is visually explained

in French at http://serge.mehl.free.fr/courbes/developC.html. The formulas of the involute curve can also be found

in French at http://www.mathcurve.com/courbes2d/developpantedecercle/developpantedecercle.shtml.

The gear technology is explainedin French at http://casm.insa-lyon.fr/engrenag/.

The conventional formulas and their names in Frenchcome from the pocket catalog Engrenages H.P.C, June 1999 edition.

1.2 Table of useful parameters and formulas

Here is a table containing the parameters and formulas used later in this tutorial:

The table is given first so that you can use it for further copy/paste operations.

All the units are defined in the metric system. This figure shows the a, ra, rb, rf, rp parameters defined in the table:

# Parameter Type or unit Formula Description Name in French

1 a angulardegree 20deg

Pressure angle: technologic constant(10deg ≤ a ≤ 20deg)

Angle de pression.

2 m millimeter — Modulus. Module.

3 Z integer — Number of teeth (5 ≤ Z ≤ 200). Nombre de dents.

4 p millimeter m * πPitch of the teethon a straight generative rack.

Pas de la denture sur unecrémaillère génératrice rectiligne.

5 e millimeter p / 2Circular tooth thickness,measured on the pitch circle.

Epaisseur d'une dentmesurée sur le cercle primitif.

6 ha millimeter m Addendum = height of a tooth

Saillie d'une dent.

above the pitch circle.

7 hf millimeter

if            m > 1.25       hf = m * 1.25else hf = m * 1.4

Dedendum = depth of a tooth belowthe pitch circle. Proportionnally greaterfor a small modulus (≤ 1.25 mm).

Creux d'une dent. Plus granden proportion pour unpetit module (≤ 1.25 mm).

8 rp millimeter m * Z / 2 Radius of the pitch circle. Rayon du cercle primitif.9 ra millimeter rp + ha Radius of the outer circle. Rayon du cercle de tête.10 rf millimeter rp - hf Radius of the root circle. Rayon du cercle de fond.11 rb millimeter rp * cos( a ) Radius of the base circle. Rayon du cercle de base.

12 rc millimeter m * 0.38

Radius of the root concave corner.(m * 0.38) is a normative formula.

Congé de raccordement à la racined'une dent. (m * 0.38) vient de la norme.

13 tfloating pointnumber

0 ≤ t ≤ 1 Sweep parameterof the involute curve.

Paramètre de balayagede la courbe en développante.

14 yd millimeter

rb * ( sin(t * π) -cos(t * π) * t * π )

Y coordinateof the involute tooth profile,generated by the t parameter.

Coordonnée Y du profil de denten développante de cercle,généré par le paramètre t.

15 zd millimeter

rb * ( cos(t * π) +sin(t * π) * t * π )

Z coordinateof the involute tooth profile.

Coordonnée Z du profil de denten développante de cercle.

16 ro millimeter rb * a * π / 180deg

Radius of the osculating circle ofthe involute curve, on the pitch circle.

Rayon du cercle osculateur à la courbeen développante, sur le cercle primitif.

17 c angulardegree

sqrt( 1 / cos( a )2 - 1 ) /PI * 180deg

Angle of the point of the involutethat intersects the pitch circle.

Angle du point de la développante àl'intersection avec le cercle primitif

18 phi angulardegree

atan(  yd(c) / zd(c) ) +90deg / Z

Rotation angle used for making agear symetric to the ZX plane

Angle de rotation pour obtenir unroue symétrique par rapport au plan ZX

1.3 Notes about the formulas (in French)

Formule N°11: explication de l'équation rb = rp * cos( a ):

La crémaillère de taillage est tangente au cercle primitif. Au point de contact, a définit l'angle de pression de la ligne d'action. La ligne d'action est tangente au cerce de base. On a donc un triangle rectangle à résoudre.

Formule N°12:

Entre le cercle de pied et les flancs des dents,prévoir un petit congé de raccordement pour atténuer l'usure en fatigue.

Formules N°14 et N°15:  explication de zd = rb * cos( t ) + rb * t * sin( t ):

La développante est tracée sur le plan YZ, qui correspond à la vue de face dans Catia. Le premier terme rb * cos( t ) correspond à une rotation suivant le cercle de base. Le second terme rb * t * sin( t ) correspond au déroulement de la développante. Cette expression rappelle que le rayon de coubure de la développante vaut rb * t.

Formule N°16:

Pour simplifier le dessin d'un engrenage, on peut éventuellementremplacer la développante de cercle par un arc de cercle.

A good approximation of a curveat a given point is the osculating circle.

The osculating circle of a curve at a pointshares with the curve at that point:

A common tangent line(continuity of the 1stderivative).

A common radius of curvature(continuity of the 2nd derivative).

Une bonne approximation d'une courbeen un point donné est le cercle osculateur.

Le cercle osculateur à une courbe en un pointpartage avec la courbe en ce point:

Une même tangente(continuité au 1erdegré).

Un même rayon de courbure(continuité au 2nd degré).

Cercle osculateur à la courbe développante au niveau du diamètre primitif:o L'angle de la dévelopante est égal à l'angle de pression a.o Le rayon du cercle osculateur est donc:  ro = rb * a * π / 180.

Formule N°17:

En réalité, la développante est déphasée par rapport à la figure ci dessus. Pour exprimer ce déphasage, on calcule le paramètre angulaire c au point où la

développante coupe le cercle primitif. On a alors:

o zd(c)2 + yd(c)2 = rp2

o rb2 * ( 1 + c2 ) = rp2

o cos(a)2 * ( 1 + c2 ) = 1o c2 = 1/cos(a)2 -  1

2. Start and configure the generative shape design workshop

The part design workshop is not sufficient for designing parametric curves.

So, we switch to the generative shape design workshop:

Next, we configure the environment for showing parameters and formulas:

We set the 2 highlighted check boxes:

Now the tree of your part should look like this:

3 Enter the parameters and formulas

3.1 Define the primary generation parameters

Switch to the Generative Shape Design workshop and click on the f(x) button:

Then you can create the gear generation parameters:1. Select the unit (integer, real, length, angle, …).2. Press the create parameter button.3. Enter the parameter's name.4. Set the initial value, used only if the parameter has a fixed value.

Now your tree should look like this:

3.2 Define dependent parameters

Most of the geometric parameters are related to a, m, and Z. You don't need to assign them a value, because Catia can compute them for you. So, instead of filling the initial value, you can press the add formula button.

Then you can edit the formula:

3.3 Check the primary and computed parameters

Set the following option in order to display the values and formulas of each parameter:

Now your tree should display the following parameters and their formulas:

3.4 Parametric laws of the involute curve

Up to now, we have defined formulas for computing parameters.Now we need to define the formulas defining the {Y,Z} cartesian position of the points on the involute curve of a tooth.

We could as well define a set of parameters Y0, Z0, Y1, Z1, … for the coordinates of the involute's points.However, Catia provides a more convenient tool for doing that: the parametric laws.

In order to create a parametric law:  click on the fog button:

Enter the formulas #14 and #15 of the 2 laws used for the Y and Z coordinates of the involute curve:

o yd = rb * ( sin( t * PI * 1rad ) - cos( t * PI * 1rad ) * t * PI )

o zd = rb * ( cos( t * PI * 1rad ) + sin( t * PI * 1rad ) * t * PI )

Notes about the formula editor of Catia:

The trigonometric functions expect angles, not numbers,so we must use angular constants like 1rad or 1deg.

PI stands for the π number.

4. Create a geometric body and start inserting geometric elementsIn Catia, the PartBody is intended for mechanical surfaces.For geometric constructions, you need to work in a geometric body:

 Create it with the Insert / Open Body top menu:

Then, you can use the buttons on the right toolbar for inserting different geometric elements.

Catia assigns a default name to each geometric element, but you can rename it with a contextual dialog

opened with the right button / properties menu of the mouse:

5. Make the geometric profile of the first tooth

The following steps explain how to design a single tooth.The whole gear is a circular repetition of that first tooth.

5.1 Define the parameters, constants and formulas

Already done in the section related to parameters and formulas.

5.2 Insert a set of 5 constructive points and connect them with a spline

The position of each point is defined by the yd(t) and zd(t) parametric laws:

Define 5 points on the YZ plane.

In order to apply the involute formulas, edit the Y and Z coordinate of each pointand enter the values of the parameter from t = 0 to t = 0.4(most gears do not use the involute spiral beyond 0.4)

For example, for the Y coordinate of the involute's point corresponding to t = 0.2:

Make a spline curve connecting the 5 constructive points:

5.4 Extrapolate the spline toward the center of the gear

Why do we need an extrapolation ?

The involute curve ends on the base circle of radius rb = rp * cos(20) ≈ rp * 0.94.

When Z < 42, the root circle is smaller than the base circle. For example, when Z = 25:rf = rp - hf = rp - 1.25 * m = rp * (1 - 2.5 / Z) = rp * 0.9.

So the involute curve must be extrapolated for joining the root circle.

Extrapolate the spline:

Start from the 1st involute point.

The length to extrapolate is empirically defined by the formula f(x) = 2 * m:

5.5 Rotate the involute curve for the symmetry relative to the ZX plane

Why do we need a rotation ?RED On the extrapolated involute curve designed in the Y, Z coordinate system …

the contact point on the pitch circle has an unconvenient position. It is more convenient to draw a tooth that is symmetric on the ZX plane,because it makes it easier to control the angular position of a gear in a mechanism :

LIME On the rotated involute curve … the two contact points of the tooth …

CYAN that are located on the pitch circle at ± 90deg / Z …MAGENTA are symmetric relative to the ZX plane.

The colors above correspond to the following geometric elements:

For computing the rotation angle, we need first to compute the involute parameter or the pitch circle (formula #17):

Is it true ? In order to check it, you can build two temporary elements:

Insert another point and apply the involute formula with the c parameter:

Then, insert a half-circle having the radius of the pich circle rp.

Check that the involute point with the c parameter is actually located on theintersection of the pitch circle and the extrapolated spline curve:

Once the c parameter is checked, the temporary point and the temporary circle can be deleted.

Now, we can rotate the extrapolated curve, so that the first gear tooth is symetric relative to the ZX plane:

We use the formula #18 for computing the phi rotation angle in 2 steps:1. The curve is rotated by atan( yd(c) / zd(c) ) so that the intersection

between the involuteand the pitch circle (the red point on the figure) is moved to the ZX plane.

2. Then, curve is rotated by ¼ of the gear period: 90deg / Z (the left lime point on the figure),

so that the ZX plane corresponds to the median plane of the first tooth.

A rotation operation is applied to the extrapolated spline, using the phi rotation angle:

5.6 Draw the outer circle and the root circle

We insert two half circles having a radius equal to ra and rf, respectively.

The figure below shows how to configure the outer circle:

5.7 Insert a rounded corner near the root circle

The corner between the extrapolated involute curve and the root circle has a radius defined by the rc parameter.

Catia asks you to select an arc (in red) out of 4 possible geometric solutions (in blue):

5.8 Create the rounded corner of the next tooth

Why are we going up to the next tooth ?

Initially, I designed a symmetric profile for the first tooth and I duplicated it Z times:

But then, the generated profile was interrupted between each tooth by a fake edge:

For preventing that, I build now the whole profile between consecutive teeth on the root circle:

Now we can build the symmetric corner:

On the figure above, you can see:o A vertical line tracing the ZX plane.o An oblique line tracing the median plane between consecutive teeth.o This plane corresponds to the ZX plane rotated by 180deg / Z around theX

axis.

The following figure shows how to define that median plane:

Now, this plane is used for defining a symmetric rounded corner on the root circle:

5.9 Assemble the different elements of the first tooth

Now, we have to cut, fill and join the different elements of the 1st tooth:

Cut the segment of the extrapolated spline between the outer circle and the rounded corner.

Define a symmetric profile relative to the ZX plane, for the other side of the 1st tooth:

We could cut the root circle and the outer circle,but instead we define two arcs having a radius equal to rf and ra, respectively:

The last operation consists in joining all the elements of the 1st tooth:

6. Build the whole gear profile and extrude itThe gear profile is just a circular repetition of the tooth:

We define a repetition around the X axis. The number of instances is controlled by the Z parameter (number of teeth):

The first tooth and the duplicated teeth are joined for making the whole gear profile:

Now, we can switch back to the part design workshop (see the green arrow) and extrude the gear profile:

7. Cut the gear wheel

The gear wheel is cut after the extrusion, because each application requires a specific wheel thickness:

In a real factory, the teeth of the gear would be machined after the gear wheel is cut on a lathe.

In a CAD design, it is simpler to make the gear wheel with a groove, after the extrusion of the teeth.

That wheel design is semi-parametric: the external diameter and the 20deg chamfer are dependent of ra,

but the bore diameter and the thickness are adjusted manually on the sketch:

Now, you can add pocket(s) for transmitting the torque between the gear wheel and a key or a splined shaft.

8. Check the parametric generation

Now you can play with the Z and m parameters and generate any spur gear:

If Z is equal to 13:

If Z is equal to 15:

Designing parametricbevel gears with Catia V5Published at http://gtrebaol.free.fr/doc/catia/bevel_gear.htmlWritten by Gildas Trébaol on June 25, 2005.Zipped parts: bevel_gear.zip (340 KB).VRML97 model: bevel_gear.wrl (58 KB).The knowledge used for designing spur gears can be reused for making bevel gears

This tutorial shows how to make a basic bevel gear that you can freely re-use in your assemblies.

1 Sources, credits and links The conventional formulas and their names in French come from the page 100 of the

book"Précis de construction mécanique" by R. Quatremer and J.P. Trotignon, Nathan publisher, 1983 edition.

I found a clear explanation of bevel gears in the pages 258 to 280 of the book"Les mécanismes des machines y compris les automobiles" by H. Leblanc, Garnier publisher, 1930 edition.

For an exhaustive analysis, we could also use the famous old book "Les engrenages" written by Mr Henriot.

The principle for designing a bevel gear consists in drawing two primitive conical surfaces: The front cone, parallel to the edges of the teeth.

The rear cone, used for designing the profile of a tooth.

The half angle delta of the front cone depends on: The module m. The number of teeth of the gear Z1. The number of teeth of the other gear Z2. The angle between the axis of the two gears.

In most applications using bevel gears, the angle between the axis of the two gears is equal to π/2.In that case, the half angle delta of the front cone is defined by the formula:delta = atan( Z1 / Z2 )

2 Table of gear parameters and formulasThe following table contains:

The parameters and formulas used for standard spur gears. The specific parameters and formulas added for bevel gears (in the cells colored in

pink).

# Parameter Type or unit Formula Description Name in French

1 a angulardegree 20deg

Pressure angle: technologic constant(10deg ≤ a ≤ 20deg)

Angle de pression.

2 m millimeter — Modulus. Module.

3 Z1 integer — Number of teeth (11 ≤ Z1 ≤ 200). Nombre de dents.

4 Z2 integer —

Number of teeth of thecomplementary bevel gear.

Nombre de dents de la roueconique complémentaire.

5 delta angulardegree

atan( Z1 / Z2 )

Half angle of the front primitive cone.

Demi angle au sommet ducône primitif avant

6 ld millimeter —Length of the teethon the front primitive cone.

Longueur des dentssur le cone primitif avant.

7 ratio1 - ld /( lc * cos( delta ) )

pour calculer les homothéties du flanc intérieur

8 dZ millimeter 0mm Translation offset of the generative

Décalage des constructions

geometry on the Z axis.

géométriques suivant l'axe Z.

9 p millimeter m * πPitch of the teethon a straight generative rack.

Pas de la denture sur unecrémaillère génératrice rectiligne.

10 e millimeter p / 2

Circular tooth thickness,measured on the pitch circle.

Epaisseur d'une dentmesurée sur le cercle primitif.

11 ha millimeter mAddendum = height of a toothabove the pitch circle.

Saillie d'une dent.

12 hf millimeter m * 1.25Dedendum = depth of a toothbelow the pitch circle.

Creux d'une dent.

13 rp millimeter m * Z / 2 Radius of the pitch circle. Rayon du cercle primitif.

14 rc millimeter rp / cos( delta )

Rayon du cône primitif arrière

15 ra millimeter rp + ha Radius of the outer circle. Rayon du cercle de tête.

16 rf millimeter rp - hf Radius of the root circle. Rayon du cercle de fond.

17 rb millimeter rc * cos( a ) Radius of the base circle. Rayon du cercle de base.

18 rr millimeter

m * 0.38 = "arccercle fond" * 0.7763

Radius of the root concave corner.(m * 0.38) is a normative formula.

Congé de raccordement à la racined'une dent. (m * 0.38) vient de la norme.

19 tfloating pointnumber

0 ≤ t ≤ 1 Sweep parameterof the involute curve.

Paramètre de balayagede la courbe en développante.

20 tc angulardegree

-atan( yd( a / 180deg )/ xd( a / 180deg ) )

Trim angle used to put thecontact point in the ZX plane.

Angle d'ajustement pour placer lepoint de contact dans le plan ZX.

21 xd millimeter

rb * ( cos(t * π) +sin(t * π) * t * π )

X coordinateof the involute tooth profile,generated by the t parameter.

Coordonnée X du profil de denten développante de cercle,généré par le paramètre t.

22 yd millimeter

rb * ( sin(t * π) -cos(t * π) * t * π )

Y coordinateof the involute tooth profile.

Coordonnée Y du profil de denten développante de cercle.

1 First attempt: a simple projection on the rear primitive coneThis view shows that the whole geometry must be rebuilt, because the simple projection on a cone implies interferences between the root circles:

2 Projection of the involute on the rear primitive coneNow, the tooth is actually designed on a cone:

The involute is still designed on the XY plane. Then it is projected on the rear primitive cone. The root circle and outer circle are defined in planes orthogonal to the axis of the cone.

The tooth profile is made with "cut and assemble" operations on the root circle,the projection of the involute curve on the cone, and the outer circle.

The whole profile is a circular repetition around axis of the cone. The profile is good, but it has a major drawback: the axis of the cone (in red) is not

parallel to X, Y or Z (in green).

3 Designing the involute curve on an inclined plane

In order to make the gear aligned with the Z axis (shown in green), the involute curves is designed on an inclined plane (shown in red):

4 Making the tooth profile The inner tooth profile is generated by a scale operation on the outer tooth profile. The scale factor is computed by the ratio between the length of the front cone and the

length of the teeth:ratio = 1 - teeth_length / front_cone_length.

The tooth is generated by a multi-section surface, guided by 2 line segmentsconnected to the end points of the outer tooth profile and innner tooth profile.

The whole profile is a circular repetition of the tooth profile around the Z axis. Now the teeth surface is ready, but the generation parameters are not well defined yet.

5 Making the outer and inner side conesOn most bevel gears, the teeth are delimited by an exterior cone and an interior cone. In order to build these cones:

The tooth profile is duplicated on the whole circle. That profile is then used for cutting the rear cone. The remaining part of the rear cone makes the outer side of the teeth. The inner side is made by a scale-down operation on the outer side surface. Then we can merge the inner side cone, the teeth surfcaces and the outer side cone. The resulting surface can be converted to a solid body in the Mechanical Part

workshop.

6 Checking and improving the robustness of the theet surfaceThe parametric gear show in the previous section fails when the delta angle is greater than 70degrees.After hacking some parameters, the following image shows an improved extreme geometry:

Minimal number of teeth Z1 = 11. Maximal delta angle = 79degrees.

7 Checking the generation of the side surface We do the same work on the generation of the side surfaces. Of course, this geometry should never be used in a real mechanism.

8 Putting the primitive cones in a separate group of surfacesNow that the gear design is completed, we can put the fundamental geometric elements in a separate group and display them in green.

The following image show the rotation axis, the primitive circle, the front and rear primitive cones.

These elements can be are useful for checking the position of the bevel gears in the mechanical assembly workshop.

9 Flat gear

This figure shows a gear generated with the widest front cone:

10 Normal gear

On the opposite, we can check that we go back to the ordinary spur gear when the delta angle tends to zero:

11 Check if the curved surfaces could be simplified The final bevel gear file is large: 950 KB for 13 teeth. So we can wonder if the file could be smaller with simpler surfaces. In order to check that, I replace all the surfaces generated by circles, arcs or involute

curves with surfaces generated by straight lines. The file size only decreased to 890KB, so the curved surfaces of the bevel gear are not

worth being simplified.

Designing parametricworms with Catia V5Published at http://gtrebaol.free.fr/doc/catia/worm.htmlWritten by Gildas Trébaol on June 26, 2005.Zipped part: worm.zip (306 KB).VRML97 model: worm.wrl (304 KB).

The worm is a part of a worm / worm wheel reduction gear

This tutorial shows how to make a basic worm that you can freely re-use in your assemblies.

1 Sources, credits and links The worm can be coupled with a worm gear or with an helical gear. The principle for designing a worm consists in drawing a thread helix that cuts a

cylinder. The worm dimension is taken from the part catalog Engrenages H.P.C, June 1999

edition. The worm above corresponds to the part ref. W1,5-1 page 358.

2 Table of worm parameters and formulas

# Parameter Type or unit Formula Description Name in French

1 a angulardegree 20deg

Pressure angle: technologic constant(10deg ≤ a ≤ 20deg)

Angle de pression.

2 m millimeter — Modulus. Module.

3 N real —Number of turns of the thread(3 ≤ N ≤ 15).

Nombre de tours du filet de la vis.

4 D millimeter — Diameter of the pitch cylinder.

Diamètre du cylindre primitif.

5 L millimeter p * (N + 1)

Length of the thread. Longueur du filetage.

6 ψ (psi) angulardegree

atan( m / D )

Angle of the worm helix. Must matchthe angle of the worm wheel helix.

Angle d'hélice de la vis. Doit être égal àl'angle d'hélice de la roue correspondante.

7 dZ millimeter -L/2Translation offset of the wormsurface on the Z axis.

Décalage de la surface de la vissuivant l'axe Z.

8 p millimeter m * πPitch of the teethon a straight generative rack.

Pas de la denture sur unecrémaillère génératrice rectiligne.

9 e millimeter p / 2Tooth thickness,measured on the pitch circle.

Epaisseur d'une dentmesurée sur le cercle primitif.

10 ha millimeter mAddendum = height of a toothabove the pitch circle.

Saillie d'une dent.

11 hf millimeter m * 1.25Dedendum = depth of a toothbelow the pitch circle.

Creux d'une dent.

12 rr millimeter m * 0.38

Radius of the root concave corner.(m * 0.38) is a normative formula.

Congé de raccordement à la racined'une dent. (m * 0.38) vient de la norme.

1 Make the pitch helix

2 Add straight segments at each end of the thread

3 Draw the thread profile

4 Make the helical thread

5 Make the thread extremities

6 Insert a cylinder tangent to the outside circle

7 Intersect both surfaces

8 Fill the worm surface and add a hub

ψ angle of t

Designing parametrichelical gears with Catia V5Published at http://gtrebaol.free.fr/doc/catia/helical_gear.htmlWritten by Gildas Trébaol on July 1st, 2005.Zipped part: gearbox.zip (728 KB).VRML97 model: helical_gear.wrl (414 KB).

A helical gear can be used  with a worm,in a worm / worm wheel gearbox

This tutorial shows how to make a basic helical gear that you can freely re-use in your assemblies.

1 Sources, credits and links The helical gear can be coupled with a worm part. The helical gear is close to the standard spur gear part. The main difference is the inclination angle of the teeth relative to the rotation axis:

o On a spur gear, the tooth is parallel to the gear axis.o On an helical gear, the angle between the teeth and the axis is named ψ. (i.e.

the Greek letter "psi").o The ψ angle of the helical wheel must match the ψ angle of the worm.

The lead L of the helix screw corresponds to the formula:  L = π * D / tan( ψ ). The dimension of the helical gear and the worm shown in this tutorial are taken

from the page #358 of the part catalog Engrenages H.P.C, June 1999 edition.

2 How to use the same parametric part for spur gears and helical gears

The standard spur gear coresponds to a ψ = 0. In that case, L = π * D / tan( 0 ) = ∞.

So we cannot use the helix curve provided by Catia when ψ = 0. However, whe can use a zero angle when the helix is replaced by a straight line:

o For ψ = 4.50deg we have L/D = π / tan( 4.50deg ) ≈ 39.o For ψ = 20.0deg we have L/D = π / tan( 20.0deg ) ≈ 9.

Since the L/D ratio is large, a straight line is a good approximation of the helix. Then the spur gear and the helical gear can be generated both by the same parametric

part.

3 Make the tooth profileThe tooth profile is built using the Catia part shown in the spur_gear.html tutorial:

4 Make the rotated tooth section and the inclined guidesThe tooth template is a multi-section surface:

The first section is the tooth profile built previously in the spur_gear.html tutorial. The second section is a translation and a rotation of the first section on the Z axis. The translation length corresponds to the wheel thickness e. The rotation angle φ corresponds to a fraction of the helical lead L:

φ = 360deg * e/L = 360deg/π * tan( ψ ) * e/D. The inclined guides are two line segments connected to the ends of the tooth sections.

5 Make the gear surface with a circular repetition of the tooth

6 Make a part body with a filled teeth surface

7 Assemble or intersect it with the main part body

The intesection of the second part body with the main body is advantageouswhen the main part body is a beveled cylinder.

8 Check that we can generate a spur gear

When ψ = 0deg, the helical gear becomes a standard spur gear.

9 Make a toy gearboxWith the worm shown in the worm.html tutorial, you can make a reduction gearbox:

I theory, we should use a worm wheel instead of an helical wheel,but I don't know how to design a worm wheel...

So I use an helical wheel having the same ψ angle as the worm. The distance between the two shafts is the sum of the pitch radius of the worm and the

worm gear. For a pitch m = 1.5mm, a worm pitch diameter D = 20mm and an helical wheel having

Z = 22 teeth,that distance is (D + m * Z) / 2 = (20 + 1.5 * 22) / 2 = 26.5 mm.

Using internal gearsin an epicyclic gearboxPublished at http://gtrebaol.free.fr/doc/catia/epicyclic.htmlWritten by Gildas Trébaol on September 18, 2005.Zipped part: gearbox.zip (1.4MB).

This tutorial shows how to make an epicyclic gearbox based on spur gears, internal gears and a "planet carrier".

1 Sources, credits and links

An epicyclic gearbox has the advantage of providing a high speed ratio in minimal dimensions.

Compared to a wheel/worm wheel system, it has a reduced wear because it contains only gears rolling on each other.

It is also a differential mechanical system, sometimes used in steering systems and powertrains.

A whole chapter is devoted to eplicyclic gears in the book "Les mécanismes des machines" by H. Leblanc.

At the page 327, he gives a general definition of the epiclyclic gearboxes:

le train épicycloïdal est un dispositif de roues dentées,dont la première a un axe fixe et dont les autres ont leurs axes entraînéspar un levier ou un châssis tournant autour de cet axe fixe de la première.

The dimensions of the two internal gears shown in this tutorial are takenfrom the page 235 of the part catalog Engrenages H.P.C, June 1999 edition.

2 Design of the gearbox

The first step consists in designing an internal gear.The principle is the same as for a classic spur gear.The main difference is that the metal is outside of the teeth.

Internal gears are less frequentlyused than spur gears, andmore complex to produce.So their cost is usually twicethe cost of a spur gear.

The second step consists in designing a planet carrierfor the spur gears that will roll in the internal gears.

Here is a simple carrier,machined in a single part.

At the third step, the first internal gear is duplicated for makinga second internal gear having different parameters:

blue internal gear: Z=42 m=0.8mm green internal gear: Z=41 m=0.8mm

The green gear is fastened on a carter.The blue gear is the output of the gearbox.

The planet carrier in the input of the gearbox.

At the fourth step, we add the planet gears and their shafts:a second internal gear having different parameters:

blue planet gear: Z=17 m=0.8mm green planet gear: Z=16 m=0.8mm

That combination gives a gearbox ratio equal to:1 - ZA/ZB * ZD/ZC = 1 – 42/17 * 16/41 ≈ 1 : 28

At the fifth step, the 3 shafts are pressed against the 3 couples of spur gears.The pressure between the 3 shafts and the spur gears must be high enoughfor transmitting the torquebetween the green spur gearsand the blue spur gears.

Note that the parts are simple enough forallowing a fully automated manufacturingwithout requiring any manual operation.

Now the gearbox is completed.The output internal gear (in blue)is pressed against the output shaft.

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