**2. Mechanical transmissions parameter modelling**

Modelling of selected mechanical transmissions was done in *Sketcher*, *Part Design* and *Generative Shape Design* modules of CATIA V5 system. As prerequisite for this way of modelling, it is necessary to know modelling methodology in modules *Wireframe and Surface Design* and *Assembly Design* of CATIA V5 system. (Karam & Kleismit, 2004; Dassault Systemes, 2007a, 2007b; Zamani & Weaver, 2007)

After finished modelling procedure, mechanical transmissions can be independently used in assemblies in complex way.

Parameter marks and conventional formulas (Table 1. and 5.) used in mechanical transmissions modelling can be found in references (Repcic & et al., 1998; Repcic & Muminovic, 2007, pgs. 139, 154-155, 160-161). Clear explanations for transmissions gear and belt transmissions can be found in references (Repcic & et al., 1998, pgs. 54-106, 118-151).

### **2.1 Transmissions gear parameter modelling**

Next paragraph is shows 3D geometric parameter modelling of characteristic standard catalogue gears: spur gears, bevel gears and worms.

Gears were selected as characteristic example, either because of their frequency as mechanical elements or because exceptionally complex geometry of cog side for modelling.

Every user of software system for designing is interested in creation of complex plane curve *Spline* which defined geometry of cog side profile.

The control of 3D parameterised model geometry is done by created parameters, formulas and parameter laws shown in the tree in Fig. 1. (Cozzens, 2006) Parameters review, formulas and parameter laws in the *Part* documents tree activating is done through the main select menu (*Tools* → *Options* → *Part Infrastructure* → *Display*).


Mechanical Transmissions Parameter Modelling 7

To define fixed parameters (Fig. 2.), we select command *Formula* from tools palette

1. choose desired parameter type (*Real*, *Integer*, *Length*, *Angle*) and press the button *New* 

**3** 

**1 3** 

**4** 

3. assign a parameter value (only in the case if parameter has fixed value) and

4. press the button *Apply* to confirm a new parameter creation.

**1** 

**2.1.1 Spur gears parameter modelling** 

*Parameter of type*,

2. type in a new parameter name,

**2** 

Fig. 2. Fixed parameters defining

**2** 

Fig. 3. Changeable parameters defining

*Knowledge* or from main select menu. Then, we:


Table 1. Parameters and formulas

Fig. 1. Gear geometry control

#### **2.1.1 Spur gears parameter modelling**

6 Mechanical Engineering

**Spur gear Bevel gear Worm** 

*xd*=*rb*\*(cos(*t*\**PI*)+sin(*t*\**PI*)\**t*\**PI*) *N*=6,5 *yd*=*rb*\*(sin(*t*\**PI*)-cos(*t*\**PI*)\**t*\**PI*) *L*=(*N*+1)\**p*

> *rc=r*/cos(*delta*) *lc*=*rc*/sin(*delta*)

*b*=0.3\**rc*

*dZ*=0 mm

Table 1. Parameters and formulas

Fig. 1. Gear geometry control

0≤*t*≤1 *gama*=*a*tan(*m*\**z*1/*d*)

*tc*=-*a*tan(Re*lations*\*yd*.*Evaluate*(*a*/180deg)/

Re*lations*\*xd*.*Evaluate*(*a*/180deg))

*ratio*=1-*b*/*lc*/cos(*delta*)

*delta*=*a*tan(*z*1/*z*2) *dZ*=-*L*/2

*ra=r+m ra*=*d*/2+*ha*

*rf*=*r*-1.2\**m*

*rr*=0.38\**m ha*=*m hf*=1.2\**m*

To define fixed parameters (Fig. 2.), we select command *Formula* from tools palette *Knowledge* or from main select menu. Then, we:



Fig. 2. Fixed parameters defining


Fig. 3. Changeable parameters defining

Mechanical Transmissions Parameter Modelling 9


For the purpose of accuracy checking of previously conducted activities, review of formulas, parameter laws and values of all defined fixed and changeable parameters is activated in the

The example of spur gear parameter modelling is shown in the next paragraph. All dimensions, or more precisely, geometric changeable parameters of spur gear are in the function of fixed parameters *m* and *z*. We can generate any spur gear by changing

**Part Number** *m z dg d bz bg bk tk* G2-20 2 20 30 15 20 35 5 2,35 G3-40 3 40 60 25 30 50 8 3,34 G4-60 4 60 120 30 40 60 10 3,34

> 2° G3-40 (*m*=3 mm, *z*=40)

Fig. 6. shows three different standard catalogue spur gears made from the same CATIA V5

The example of bevel gear parameter modelling is shown in the next paragraph. All dimensions, or more precisely, geometric changeable parameters of bevel gear are in the function of fixed parameters *m*, *z*1 and *z*2. We can generate any bevel gear by changing

Fig. 6. Different spur gears are the result of parameter modelling

file, by changing parameters *m* and *z*. (Saric et al., 2009, 2010)

3° G4-60 (*m*=4 mm, *z*=60)

While we use law editor, we have to take into account the following:

.

of that angle constants like 1*rad* or 1deg must be used,

tree of *Part* document (*Tools* → *Options* → *Knowledge*).


Table 2. Selected spur gears parameters

1° G2-20 (*m*=2 mm, *z*=20)

parameters *m*, *z*1 and *z*2.

**2.1.2 Bevel gears parameter modelling** 

parameters *m* and *z*.

*yd rb t PI rad t PI rad t PI* \* (sin( \* \* 1 ) cos( \* \* 1 ) \* \* ) (2)

Most geometrical gear parameters are changeable and are in the function of fixed parameters *m* and *z* (Fig. 3.). We do not need to set values for these parameters, because CATIA V5 system calculates them itself. So, instead of values setting, formulas are defined by choosing the command *Formula* (Fig. 4.). When formula has been created, it is possible to manipulate with it by the tree, similar as with any other model feature.


Fig. 4. Formula setting


Fig. 5. Setting of parameter laws for calculation of *x* and *y* coordinates of involute points

Position of the points on involutes profile of cog side is defined in the form of parameter laws (Fig. 5.). For coordinate points of involute (*x*0,*y*0), (*x*1,*y*1), .... , (*x*4,*y*4) we most frequently define a set of parameters. To create parameter laws, we choose the command *Law* from tools palette *Knowledge*. Then, we give two laws in parameter form, which we are going to be used for calculation of *x* and *y* coordinate points of involute

$$r\!dxd = r b \, ^\ast \left( \cos(t \, ^\ast PI \, ^\ast 1 \, rad) + \sin(t \, ^\ast PI \, ^\ast 1 \, rad) \, ^\ast t \, ^\ast PI \right) \tag{1}$$

Most geometrical gear parameters are changeable and are in the function of fixed parameters *m* and *z* (Fig. 3.). We do not need to set values for these parameters, because CATIA V5 system calculates them itself. So, instead of values setting, formulas are defined by choosing the command *Formula* (Fig. 4.). When formula has been created, it is

possible to manipulate with it by the tree, similar as with any other model feature.

Fig. 5. Setting of parameter laws for calculation of *x* and *y* coordinates of involute points

are going to be used for calculation of *x* and *y* coordinate points of involute

Position of the points on involutes profile of cog side is defined in the form of parameter laws (Fig. 5.). For coordinate points of involute (*x*0,*y*0), (*x*1,*y*1), .... , (*x*4,*y*4) we most frequently define a set of parameters. To create parameter laws, we choose the command *Law* from tools palette *Knowledge*. Then, we give two laws in parameter form, which we

*xd rb t PI rad t PI rad t PI* \* (cos( \* \* 1 ) sin( \* \* 1 ) \* \* ) (1)

Fig. 4. Formula setting

$$yd = rb \, ^\ast \left( \sin(t \, ^\ast PI \, ^\ast 1 \, rad) - \cos(t \, ^\ast PI \, ^\ast 1 \, rad) \, ^\ast t \, ^\ast PI \right) \tag{2}$$

While we use law editor, we have to take into account the following:


For the purpose of accuracy checking of previously conducted activities, review of formulas, parameter laws and values of all defined fixed and changeable parameters is activated in the tree of *Part* document (*Tools* → *Options* → *Knowledge*).

The example of spur gear parameter modelling is shown in the next paragraph. All dimensions, or more precisely, geometric changeable parameters of spur gear are in the function of fixed parameters *m* and *z*. We can generate any spur gear by changing parameters *m* and *z*.


Table 2. Selected spur gears parameters

Fig. 6. Different spur gears are the result of parameter modelling

Fig. 6. shows three different standard catalogue spur gears made from the same CATIA V5 file, by changing parameters *m* and *z*. (Saric et al., 2009, 2010)

#### **2.1.2 Bevel gears parameter modelling**

The example of bevel gear parameter modelling is shown in the next paragraph. All dimensions, or more precisely, geometric changeable parameters of bevel gear are in the function of fixed parameters *m*, *z*1 and *z*2. We can generate any bevel gear by changing parameters *m*, *z*1 and *z*2.

Mechanical Transmissions Parameter Modelling 11

Fig. 8. shows three different standard catalogue worms made from the same CATIA V5 file,

This application includes wide area of the industry for the fact that belt transmitting is often required. Generally, belt transmitting designing process consists of needed drive power estimate, choice of belt pulley, length and width of belt, factor of safety, etc. Final design quality can be estimated by efficiency, compactness and possibilities of service. If engineer does not use parameter modelling, he/she must pass through exhausting phase of design, based on learning from the previous done mistakes, in order to have standard parts like belt pulleys and belts, mounted on preferred construction. This process is automatized by parameter modelling. In such process, characteristics that registered distance between belt pulleys, belts length, etc., are also created. Such characteristics, also, register links, belt angle speeds and exit angle speed. The results for given belts length can be obtained by the feasibility study. Few independent feasibility studies for the different belts lengths are compared with demands for compactness. In such a way, several constructions of belt transmitting can be tested, and then it is possible to find the best final construction solution. The example of belt pulley parameter modelling is shown in the next paragraph. The belt pulley *K* is shown in the Fig. 9., and it consists of several mutual welded components: hub *G*, pulley rim *V*, plate *P* and twelve side ribs *BR*. All dimensions, or more precisely, geometric changeable parameters of belt pulley are in function of fixed parameters *d*, *Bk*, *dv* and *s*. We can generate any belt pulley with cylindrical external surface by changing

*CYL2 CYL1*

Dimensions of hub depends from diameter of shaft *dv*, on which hub is set. Shaft diameter is

Hub shape can be obtained by adding and subtraction of cylinders and cones shown in the

*CYL4*

*CYL7*

*CYL8*

*CYL9*

*P BR*

*BOX*

*CYL5CYL6*

*KON6 KON5*

*V*

*CYL3*

*KON4 KON3*

*KON2 KON1*

*G*

by changing parameters *m*, *z*1 and *N*. (Saric et al., 2009, 2010)

**2.2 Belt transmissions parameter modelling** 

parameters *d*, *Bk*, *dv* and *s*.

*dv*

*do*

*d*

Fig. 9.

*s*

*K*

*Bk*

*dop*

Fig. 9. Modelling of belt pulley parts with cylindrical external surface

the input value through which the other hub dimension are expressed.


Table 3. Selected bevel gears parameters

Fig. 7. shows three different standard catalogue bevel gears made from the same CATIA V5 file, by changing parameters *m*, *z*1 and *z*2. (Saric et al., 2009, 2010)

Fig. 7. Different bevel gears are the result of parameter modelling
