# Analytical Model of a Machining Centre Vertical Axis with Dynamic Weight Counterbalancing by a Pneumatic Proportional Valve

Analytical Model of a Machining Centre Vertical Axis with Dynamic Weight Counterbalancing by a Pneumatic Proportional Valve

Giorgio Olmi

Dcpartment of Industrial Engincering (DIN), University of Bologna, Vialc del Risorgimento 2, 40136 Bologna, Italy

Page:
205-212
|
DOI:
https://doi.org/10.18280/ijht.320130
N/A
|
Accepted:
N/A
|
Published:
31 December 2014
| Citation

OPEN ACCESS

Abstract:

High Speed Machining is getting more and more important in order to fulfill the goal of a reduction of manufacturing times and costs, togcther with an increase of quality. The design of modern Machining Centres is quite a difficult task, as high forces of incritia arise from high specds. Thus, the development of simulative mathematical models can be of a great support for the designer. This paper deals with the development of a Simulink model of the vertical axis of a machining centre. Full details arc provided on the mechanical and pneumatic devices it is composed of, in particular regarding the architecture and the operative behaviour of a pneumatic proportional valve. This is important device has the basic role of dynamically counterbalancing the spindle head weight, maintaining the resulting force at a constant value, independently of the applied motion. Full details on the algchraic and differential equations to be implemented are provided throughout the paper. The results proved the efficicncy of the pneumatic device and its short response time. Processing the simulative outcomes led to the identification of an equivalent second-order dynamic system. A simplified Simulink model could therefore be developed accordingly and used to simulate the response to whatever motion law applied to the head.

Keywords:

machining centre, pneumatic proportional valvc, pneumatic cylinders, weight counterbalancing, dynamic response

1. Introduction
2. The Pneumatic-Mechanical System and the Proportional Valve
3. Development of a Simulative Model
4. Simulation Results
5. Discussion
6. Conclusions
References

1. Y. Altintas, C. Brecher, M. Weck and S. Witt, Virtual machine tool, Annals of CIRP, vol. 53(2), pp.  619-642, 2005.

2. M.F. Zaeh and T. Oertli, Finite element modeling of ball screw feed drive systems, Annals of CIRP, vol. 53(1), pp. 289-293, 2004.

3. J.S. Chen and W.Y. Hsu, Dynamic and compliant characteristics of a cartesian-guided tripod machine, Journal of Manufacturing Science and Engineering, vol. 128(2), pp.  494-502, 2006.

4. H. Zhang, W. Zhao, J. Zhang and H. Liu, Research on the modeling of dynamics for vertical axis ball screw feed system, Proc. International Symposium on Assembly and Manufacturing, ISAM 2013 (Xi'an, China), Category number: CFP13ATP-ART, Code: 101457, 2013.

5. W.Z. Ding, X.D. Huang, M.L. Wang and B.S. Wang, Effect of trajectory-controlled algorithm  on the mechatronical performance of high-speed machining, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 227(9), pp. 1277-1286, 2013.

6. Y. Yang, W.-M. Zhang, Q. Zhou and T. Yang, Dynamic characteristic study of ball screw feed drive systems based on multi-flexible body model, Journal of Donghua University (English Edition), vol. 30(2), pp. 118-124, 2013.

7. G. Olmi and G. Vassura, Modelling pneumatic circuits with variable-geometry nozzles: A hybrid approach, Proc. 2006 SEM Annual Conference and Exposition on Experimental and Applied Mechanics (Saint Louis, MO, United States), vol. 1, pp. 447-457, Code 68397, 2006.

8. D. Croccolo, M. De Agostinis and N. Vincenzi, Structural analysis of an articulated urban bus chassis via FEM: A methodology applied to a case study, Strojniski Vestnik/Journal of Mechanical Engineering, vol. 57(11), pp. 799-809, 2011.

9. D. Croccolo, M. De Agostinis, G. Olmi and A. Tizzanini, Analysis of the stress state in brake caliper mounts of front motorbike suspensions, Advances in Mechanical Engineering, vol. 2013 , article number: 525010, 2013.

10. M. Comandini, G. Olmi and A. Freddi, Fatigue performance of shot-peened gears investigated by experimental and numerical methods, Transactions of Famena, vol. 31(2), pp. 1-10, 2007.

11. G. Olmi, M. Comandini and A. Freddi, Fatigue on shotpeened gears: Experimentation, simulation and sensitivity analyses, Strain, vol. 46(4), pp. 382-395, 2010.

12. G. Olmi, Low cycle fatigue experiments on turbogenerator steels and a new method for defining confidence bands, Journal of Testing and Evaluation, vol. 40(4), pp. 539-552, 2012.

13. D. Croccolo, M. De Agostinis and G. Olmi, Fatigue life improvement of holed plates by interference fitted pins, Proc.

2012 ASME International Mechanical Engineering Congress and Exposition, IMECE 2012 (Houston, TX, United States), vol. 8, pp. 65-71, DOI: 10.1115 / 1 \mathrm{MECE} 2012-86118,2012

14. D. Croccolo, M. De Agostinis and G. Olmi, Fatigue life characterisation of interference fitted joints, Proc. 2013 ASME International Mechanical Engineering Congress and Exposition, IMECE 2013 (San Diego, CA, United States), vol. 2B, pp. V02BT02A015 (10 pages), DOI:10.1115 / \mathrm{IMECE} 2013-63515,2013

15. G. Olmi and A. Freddi, A new method for modelling the support effect under rotating bending fatigue: Application to Ti-6V alloy, with and without shot peening, Fatigue and Fracture of Engineering Materials and Structures, vol. 36(10), pp. 981-993, 2013。

16. G. Olmi, A. Freddi, M. Bandini, M. Lanzoni and B. Riccò, Calibration and performance evaluation of hydrogenated amorphous silicon stress sensors, Proc. 2006 SEM Annual Conference and Exposition on Experimental and Applied Mechanics (Saint Louis, MO, United States), vol. 3, pp. 1616-1626, Code 68397, 2006。

17. G. Olmi, A. Freddi and D. Croccolo, In-field measurement of forces and deformations at the rear end of a motorcycle and structural optimisation: Experimental-numerical approach aimed at structural optimization, Strain, vol. 44(6), pp. 453-461, 2008.

18. G. Olmi, Investigation on the influence of temperature variation on the response of miniaturised piezoresistive sensors, Strain, vol. 45(1), pp. 63-76, 2009.

19. G. Olmi, A new loading-constraining device for mechanical testing with misalignment autocompensation, Experimental Techniques, vol. 35(6), pp. 61-70, 2011.

20. G. Olmi, A Novel Method for Strain Controlled Tests, Experimental Mechanics, vol. 52(4), pp. 379-393, 2012.

21. G. Olmi, An efficient method for the determination of the probability of failure on the basis of LCF data: Application to turbogenerator design, SDHM Structural Durability and Health Monitoring, vol. 8(1), pp. 61-89, 2012.

22. D. Croccolo, M. De Agostinis and G. Olmi, Experimental characterization and analytical modelling of the mechanical behaviour of fused deposition processed parts made of ABS-M30, Computational Materials Science, vol. 79, pp. 506-518, 2013.

23. G. Olmi and A. Freddi, Reliability assessment of a Turbogenerator Coil Retaining Ring based on Low Cycle Fatigue data, Archive of Mechanical Engineering, vol. 61(1), pp. 5-34, DOI: \$10.2478/meceng-2014-0001 2014.

24. D. Croccolo, M. De Agostinis, P. Mauri and G. Olmi, Influence of the engagement ratio on the joint strength of press fitted and adhesively bonded specimens, International Journal of Adhesion and Adhesives, DOI:10.1016/j.ijadhadh.2014.01.017, In Press.

25. G. Olmi, An experimental investigation on a crack propagating from a geartrain housing in an asphalt milling machine, Engineering Failure Analysis, vol. 38 pp. 38-48, 2014.

26. International Organization for Standardization, ISO 6358: 1989 Pneumatic Fluid Power - Components Using Compressible Fluids - Determination of FlowRate Characteristics First Edition, Geneva, Switzerland, 1989.

27. International Organization for Standardization, ISO 6358-1: 2013 Pneumatic fluid power - Determination of flow-rate characteristics of components using compressible fluids - Part 1: General rules and test methods for steady-state flow - First Edition, Geneva, Switzerland, 2013.

28. International Organization for Standardization, ISO 6358-2: 2013 Pneumatic fluid power - Determination of flow-rate characteristics of components using compressible fluids - Part 2: Alternative test methods First Edition, Geneva, Switzerland, 2013.

29. G. Belforte, Manuale di Pneumatica - II Edizione, Tecniche Nuove, Milan, 2005.

30. S. Doughty, Mechanics of Machines, John-Wiley Sons, New York, 1988.