## Influence of forced material in roller compactor parameters II.

31. August, 2009, Autor článku: Krok Alexander, Elektrotechnika, Strojárstvo
Ročník 2, číslo 8 Pridať príspevok

In the chemical, pharmaceutical and food industry, many problems in transport, storage and handling of pulverised products are caused by formation of dust. Using roll-type presses to compact such materials, dust-free products can be realised. In the first part of this paper we described the model of compaction process in the roller press. In this part we show some of our results.

Summary

If the equipment is designed, we can adjust Johanson theory. The role of contribution is to show the interdependence between the parameters which describe the compacting process. Our equipment has the technological conditions to withstand measurements in higher pressures. It is very interesting for us the effects of the forced material into roll gab, roll diameter, roll force and so on. In the figure 4 there is possible to understand the change of the roll force according the roll diameter. In figure 5 is shown the change of the roll diameter according the nip angle.

Figure 4 The graphical behaviour roll force into roll diametere

Figure 5 The graphical behaviour roll diameter into nip angle

Influence of forced material /filling/ into gab size, roll sizes and coefficient of compressibility is shown in the figures 6, 7, 8.

Figure 6 The Graphical behaviour pm/p0 into gab size

Figure 7 The Graphical behaviour pm/p0 into coefficient of compressibility

To calculate influence of forced material according to nip angle is necessary to change the ratio pm/p0.

Figure 8 The Graphical behaviour pm/p0 from roll (D)

Figure 9 The Graphical behaviour pm/p0 from nip angle $\alpha_{N}$

By the simplification of the equation 11 after is possible to get the equation 15

 $\displaystyle \frac{p_m}{p_0} \frac{1 + \sin \delta}{1 - \sin \delta} = R_{1} (\alpha_{N}) \frac{\sigma_{\theta}}{\sigma_{\alpha}} (\alpha_{N}, K) = const.$ (15)

 $\frac{p_m}{p_0} = value \hspace{1 mm} X \hspace{1 mm} angle (\theta)$ (16)

In the equation 15 the left member is constant so the right member is a function according αN.. The solution of that equation is too difficult that is why we suppose the ratio pm/p0 has lineal relation with the angle $\theta$. By the simplification of the equation number 15 we will get the equation number 17 and in the figure 9 is shown the graphical solution of this equation .

 $\displaystyle \frac{d}{d \theta} \Bigg [ \ln \Bigg ( \frac{const.}{\frac{\sigma_{\theta}}{\sigma_{\alpha}} (\alpha_{N}, K)} \Bigg ) \theta \Bigg ] = \frac{d \frac{1}{R_1 (\alpha_N)}}{d \theta} = \ln \frac{d \sigma_{\theta}}{d \theta}$ (17)

Other possibilities in order to focus this problem is creating simulation programs which will be able to generate the results by auto run applications (*.exe).The results, graphs and more were obtained by using the computational program Matlab [7], but is necessary emphasize that program is running by license that is why is better to use a free software ( GNU license). In this case we were using the code C in order to create our algorithms which are object – oriented . programming. For example to calculate the integral of a function in Matlab we can use the command QUAD(FUN,A,B), but in the programming language C is necessary to create this function.

Figure 10 Calculation of the roll diameter using C++

Conclusions

The presented work deals the theoretical design of the roll compactor using the mathematical model proposed by Johanson which express the relation between the material properties, the compactor dimensions and the operation conditions. It was interesting for us to analyze the effects of the forced material into roll gab, roll diameter, roll force and so on. The obtained results using Matlab after we recalculated using C++ due to the advantages which have been descript before.

References

1. BALCASKI, M. : Numerical methods for predicting roll press powder compaction parameter. Ecole. : Des Mines D’Albi- Carmaux. : France, 2003
2. HUBERT, M. : Aplikácia rovníc stlačiteľnosti v teórii návrhu kompaktora. : STU, 2000
3. CUNNINGHAM, J. C. : Experimental Studies and Modeling of the Roller Compaction of Pharmaceutical Powders. : Drexel Univerzity, 2005
4. JENIKE, A. W. – SHIELD, R. T. : On the plastic flow of coulomb solids beyond original failure. : Journal of Applied Mechanics, 1959, 26 s
5. JOHANSON, J. R. : A Rolling Theory for Granular Solids. : Journal of Applied Mechanics, Transactions of ASME, 1965, s. 842-848
6. JOHANSON, J. R. : Factors Influencing the Design of Roll-Type Briquetting Presses. Proceedings of the 9th Biennial Conference : The International Briquetting Association : 1965, s. 17-31
7. Matlab Online Manual version 6.1.0.450 Release 12.1

Index symbol

 A substitution relation (1) B width roll (m) D roll diameter (m) d average gravity canal on the surface roll (m) F spacing force (N) K compressibility constant for granular solid (1) M torque (N∙m) Pm max. horizontal pressure (Pa) P0 input pressure (Pa) s roll gap (m) $P_{\theta}$ pressure on axis x (Pa) $\alpha_N$ nip angle (rad) $\beta$ help angle (rad) $\theta$ angular position at the surface of a roll (rad) $\sigma$ normal stress (Pa) $\sigma _m$ max. general stress between of the rolls (Pa) $\sigma _{\theta}$ medium general stress by $\theta$ (Pa) $\delta$ effective angle internal friction (rad) $\varphi _w$ effective angle external friction (rad) $\lambda$ between a tangent of the surface and the tangent of a main stress (rad) $\rho$ material density (kg.m-3) $\rho _s$ shoot density (kg.m-3) $\rho _A$ compacting slip density (kg.m-3)

Co-author of this paper is Marián Peciar, Slovak University of Technology, Faculty of Mechanical Engineering, Námestie slobody 17, 812 31 Bratislava 1.

### 2 príspevky(ov) k článku “Influence of forced material in roller compactor parameters II.”

1. Influence of forced material in roller compactor " napísal:

kindly send me the a copy of the article part -1 & 2 .
I found this interesting.
” Influence of forced material in roller compactor ”

Thanks & Regards,
Anurag Vyas
India.

2. Evandro Godoy napísal:

Hello,

I need your help with calculation of a roller press and ask for a quotation to know about payment for this job.

I have two motor reducers each 9 kw, final speed 2,1 rpm and 32000 N/m torque. I intend to use both, one each roller, in the same machine.

To obtain a compression force of 130 Mpa on the briquet, and considering above restrictions, I need to know the correct roller diameter I could use.

Thanks,

Evandro Godoy
Rua da Palmeiras, 325 – Limoeiro
Minas Gerais/MG
Brazil

Fone : 55 31 8892-4031