**2.1.3 Worms parameter modelling**

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


Table 4. Selected worms parameters

Fig. 8. Different worms are the result of parameter modelling

Fig. 7. shows three different standard catalogue bevel gears made from the same CATIA V5

2° DB3-15 (*m*=3 mm, *z*1=15, z2=30)

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

**Part Number** *m z*<sup>1</sup> *dg d L Lg* **Connection between hub and shaft** 

2° W2,5-2 (*m*=2,5 mm, *z*1=2, *N*=5)

W1,5-1 1,5 1 23 10 35 45 M5 W2,5-2 2,5 2 35 15 45 60 M6 W3-3 3 3 41 20 55 70 M8

B2-25 2 25 25 40 12 10,6 25,52 M5 DB3-15 3 15 30 36 18 17 36,26 M6 FB4-15 4 15 60 48 20 34 59,9 M8

**Connection between hub and shaft** 

> 3° FB4-15 (*m*=4 mm, *z*1=15, z2=60)

3° W3-3 (*m*=3 mm, *z*1=3, *N*=5)

**Part** 

**Number** *<sup>m</sup> <sup>z</sup>*<sup>1</sup> *<sup>z</sup>*<sup>2</sup> *dg d bz bg*

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

Table 3. Selected bevel gears parameters

1° B2-25 (*m*=2 mm, *z*1=25, z2=25)

**2.1.3 Worms parameter modelling** 

Table 4. Selected worms parameters

1° W1,5-1 (*m*=1,5 mm, *z*1=1, *N*=6,5)

Fig. 8. Different worms are the result of parameter modelling

Fig. 8. shows three different standard catalogue worms made from the same CATIA V5 file, by changing parameters *m*, *z*1 and *N*. (Saric et al., 2009, 2010)

#### **2.2 Belt transmissions parameter modelling**

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

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

Dimensions of hub depends from diameter of shaft *dv*, on which hub is set. Shaft diameter is the input value through which the other hub dimension are expressed.

Hub shape can be obtained by adding and subtraction of cylinders and cones shown in the Fig. 9.

Mechanical Transmissions Parameter Modelling 13

Fig. 10. shows three different standard belt pulleys with cylindrical external surface made from the same CATIA V5 file, by changing parameters *d*, *Bk*, *dv* and *s*. (Saric et al., 2009)

Use of side ribs that are posed between holes on the plate is recommended during

Rotary parts of belt pulley shown in the Fig. 9., can be modelled in a much more easier way. More complex contours, instead of their forming by adding and subtraction, they can be formed by rotation. In the first case, computer is loaded with data about points inside primitive which, in total sum, do not belong inside volume of component. In the second case, rotary contour (bolded line in the Fig. 11.) is first defined, and, then, primitive of

For primitives, shown in the Fig. 11., final form is obtained after the following operations

*ROT2*

*CYL*

Designer must be significantly engaged into the forming of the component shape. Because of that reason, once formed algorithm for the modelling of the component shape is saved in computer memory and it is used when there is need for the modelling of the same or similar

Parts which are not suitable for interactive modelling are modelled by parameters. In the process of geometric mechanical transmission modelling in CATIA V5 system, we do not have to create shape directly, but, instead of that, we can put parameters integrated in geometric and/or dimensional constraints. Changing of characteristic fixed parameters gives us a 3D solid model of mechanical transmission. This way, designer can generate more alternative designing samples, concentrating his attention on design functional aspects,

For the purpose of final goal achieving and faster presentation of the product on the market, time spent for the development of the product is marked as the key factor for more profit gaining. Time spent for process of mechanical transmissions designing can be reduced even

by 50% by parameter modelling use with focus on the preparatory phase (Fig. 12.).

*K ROT ROT CYL BOX* 1 2 6· U 6· (8)

*BOX*

modelling of belt pulleys with longer diameter (Fig. 10.).

desired shape is obtained by rotation around rotate axis.

*ROT1*

Fig. 11. Modelling of rotary forms

shape with similar dimensions. (Saric et al., 2009)

without special focus on details of elements shape. (Saric et al., 2010)

**3. Conclusion** 

$$\mathbf{G} = \mathbf{C}\mathbf{Y}\mathbf{L}\mathbf{1} + \mathbf{C}\mathbf{Y}\mathbf{L}\mathbf{2} - \mathbf{C}\mathbf{Y}\mathbf{L}\mathbf{3} - \mathbf{K}\text{ON}\mathbf{1} - \mathbf{K}\text{ON}\mathbf{2} - \mathbf{K}\text{ON}\mathbf{3} - \mathbf{K}\text{ON}\mathbf{4} \tag{3}$$

Pulley rim of belt pulley depends from diameter of belt pulley *d*, pulley rim width *Bk*, diameter of shaft *dv* and minimal pulley rim thickness *s*.

$$V = \text{CYL4} - \text{CYL5} - \text{CYL6} - \text{KON5} - \text{KON6} \tag{4}$$

Plate dimensions depend from diameter of belt pulley *d*, minimal pulley rim thickness *s* and diameter of shaft *dv*.

$$P = \text{CYL7} - \text{CYL8} - 6\text{CYL9} \tag{5}$$

Side ribs are side set rectangular plates which can be shown by primitive in the form of prism.

$$BR = BOX \tag{6}$$

Whole belt pulley is obtained by adding of formed forms.

$$K = G + V + P + \dots \text{(\$\bullet\$BR\$)}\tag{7}$$


Table 5. Parameters and formulas

Fig. 10. Different belt pulleys with cylindrical external surface are the results of parameter modelling

Pulley rim of belt pulley depends from diameter of belt pulley *d*, pulley rim width *Bk*,

Plate dimensions depend from diameter of belt pulley *d*, minimal pulley rim thickness *s* and

Side ribs are side set rectangular plates which can be shown by primitive in the form of

**Belt pulley with cylindrical external surface**  *CYL*1: *D*=1,6·*dv*, *H*=0,75·*dv CYL*9: *H*= 0,1·*dv CYL*2: *D*=1,7·*dv*, *H*=0,65·*dv*+2 mm *KON*1: *D*=1,6·*dv*, *H*=1 mm, angle 45° *CYL*3: *D*=*dv*, *H*=1,4·*dv*+2 mm *KON*2: *D*=1,7·*dv*, *H*=1 mm, angle 45° *CYL*4: *D*=*d*, *H*=*Bk KON*3: *D*=*dv*, *H*=1 mm, angle 45°

*CYL*5: *D*=*d*-2·*s*, *H*=*Bk*/2+0,05·*dv*+1 mm *KON*4: *D*=*dv*, *H*=1 mm, angle 45° *CYL*6: *D*=*d*-2·*s*-0,1·*dv*, *H*=*Bk*/2-0,05·*dv*-1 mm *KON*5: *D*=*d*-2·*s*-0,1·*dv*, *H*=1 mm, angle 45° *CYL*7: *D*=*d*-2·*s*, *H*=0,1·*dv KON*6: *D*=*d*-2·*s*, *H*=1 mm, angle 45°

> 2° K315 (*d*=315 mm, *Bk*=63 mm, *dv*=60 mm, *s*=4,5 mm, *dop*=204 mm, *do*=60 mm)

Fig. 10. Different belt pulleys with cylindrical external surface are the results of parameter

diameter of shaft *dv* and minimal pulley rim thickness *s*.

Whole belt pulley is obtained by adding of formed forms.

*CYL*8: *D*=1,6·*dv*, *H*=0,1·*dv*

Table 5. Parameters and formulas

1° K200 (*d*=200 mm, *Bk*=50 mm, *dv*=50 mm, *s*=4 mm)

modelling

diameter of shaft *dv*.

prism.

*G CYL CYL CYL KON KON KON KON* 123 1 2 3 4 (3)

*V CYL CYL CYL KON KON* 456 5 6 (4)

*P CYL CYL CYL* 7 8 6· 9 (5)

*BR BOX* (6)

*BOX*: *A*=[(*d*-2·*s*)-1,8·*dv*]/2, *B*=0,35·*Bk*, *C*=0,1·*dv*

> 3° K400 (*d*=400 mm, *Bk*=71 mm, *dv*=70 mm, *s*=5 mm, *dop*=250 mm, *do*=70 mm)

*K G V P BR* 6· (7)

Fig. 10. shows three different standard belt pulleys with cylindrical external surface made from the same CATIA V5 file, by changing parameters *d*, *Bk*, *dv* and *s*. (Saric et al., 2009)

Use of side ribs that are posed between holes on the plate is recommended during modelling of belt pulleys with longer diameter (Fig. 10.).

Rotary parts of belt pulley shown in the Fig. 9., can be modelled in a much more easier way. More complex contours, instead of their forming by adding and subtraction, they can be formed by rotation. In the first case, computer is loaded with data about points inside primitive which, in total sum, do not belong inside volume of component. In the second case, rotary contour (bolded line in the Fig. 11.) is first defined, and, then, primitive of desired shape is obtained by rotation around rotate axis.

Fig. 11. Modelling of rotary forms

For primitives, shown in the Fig. 11., final form is obtained after the following operations

$$K = \begin{pmatrix} ROT1 \ -ROT2 \ -6CYL \end{pmatrix} \mathbf{U} \ 6 \cdot \mathbf{BOX} \tag{8}$$
