Öz, Vacuum-related variables of milking systems Milchwissenschaft 66 (2) 2011 119 Mathematical modelling and optimization of vacuum related vari- ables in conventional and quarter individual milking systems using response surface methodology By H. ÖZ 1 , S. ROSE-MEIERHÖFER 2 , A. DEĞIRMENCIOĞLU 3 , U. STRÖBEL 2 , R. BRUNSCH 2 , H. BILGEN 3 and U. ERDOĞAN 4 1 Ege University, Ege Vocational Training School, Department of Agricultural Machinery, 35100 Bornova-Izmir, Turkey 2 Leibniz Institute for Agricultural Engineering e.V., Department of Engineering for Livestock Management, Max-Eyth Allee 100, 14469 Potsdam, Germany. 3 Ege University, Faculty of Agriculture, Department of Agricultural Machinery, 35100 Bornova-Izmir, Turkey 4 Ege University, Faculty of Science, Department of Mathematics, 35100 Bornova-Izmir, Turkey Mention of trademarks or company names are for scientific purposes only and do not imply the endorsement of these products by the au- thors or their institutions they represent. The objective of this study was to develop empirical functions in order to predict vacuum fluctuations in b and d-phase and in claw using response surface methodology (RSM) and to verify the optimum points and the mathematical models for both, conventional and quarter individual milking system. The independent variables considered in the study included the system working vacuum, the pulsation rate and ratio and the milk flow rate. Experiments based on the central com- posite design (CCD), one of the designs in RSM, were conducted in the laboratory using water and artificial teats. The data obtained were then used to develop functions in polynomial form that allowed predicting the vacuum fluctuations in claw for conventional system and junction point in quarter individual milking system, b and d-phase for both systems. Op- timum point for system working vacuum was obtained for both systems and it was found to be 38.9 and 39.7 kPa for con- ventional and quarter individual milking systems, respectively. The fluctuation models obtained from the study indicated the complexity of the fluctuation phenomena in milking systems. But, it is believed that the models developed may be used for the design of conventional and quarter individual milking system for a better performance. Mathematische Modellierung und Optimierung der vakuumbezogenen Variablen in konventionellen und viertel- individuellen Melksystemen unter Verwendung der Response Surface Methodik Das Ziel der Studie war es, empirische Funktionen zu entwickeln, um Vakuumfluktuationen in der b- und d-Phase im Sammelstück unter Verwendung der response surface-methodology (RSM) vorauszusagen und die optimalen Punkte und die mathematischen Modelle in beiden Melksystemen (konventionell und viertelindividuell) zu überprüfen. Die un- abhängigen Variablen, die in der Studie betrachtet wurden, bestanden aus dem Anlagenvakuum, der Pulsrate, dem Saug-/Druckverhältnis und dem Milchfluss. Die Experimente, die auf dem central composite-Design (CCD) basierten, einem der Entwürfe in RSM, wurden mit Wasser und künstlicher Zitze im Labor durchgeführt. Die im Labor gemessenen Daten wurden dann verwendet, um polynomische Funktionen zu entwickeln, welche die Vakuumfluktuationen im Sam- melstück für konventionelle und viertelindividuelle Melksysteme in der b- und in der d-Phase voraussagen können. Für beide Systeme wurde nur ein optimaler Punkt für das Vakuum erreicht. Dieser lag jeweils bei 38,9 kPa und 39,7 kPa für die konventionellen bzw. viertelindividuellen Melksysteme. Die Fluktuationsmodelle, die aus der Studie erhalten wurden, zeigten die Komplexität der Fluktuationsphänomene in Melksystemen auf. Dennoch kann angenommen werden, dass die entwickelten Modelle zu einer Steigerung der Leistung in der konventionellen und viertelindividuellen Melktechnik beitragen können. 04 Milking systems (vacuum related variables, response 04 Melksysteme (vakuumbezogene Variable, Response surface methodology Surface-Methodik) 1. Introduction Milking systems have evolved over the years with the introduction of new technology and automation, and the objective of evolutions was to obtain the whole milk from the animal teat in the shortest time without causing any detrimental effect on udder health while increasing the productivity by reducing the labour. As a new system that allows milking each teat indi- vidually, MultiLactor ® (MULTI) has been developed in order to eliminate the detrimental effects that induced by conventional milking systems such as teat damage, teat irritation/pain. This system includes periodic air inlet at the teat end that can be adapted for the use at milking parlour. It has a sequential pulsation and clus- ter is adapted by milking person (10,14). As an advan- tage of this system using quarter individual milking in conventional milking parlours- it is expected to reduce SCC as an indicator of udder health (13). This new system can also be used at milking parlours and intro- duced by Automatic Milking Systems (AMS). The studies using automated milking systems mostly focused on udder health. But the number of bulk-milk somatic cells increased when AMS was used (12,16). This shows the necessity of having an additional method to detect clinically infected cows and measuring the milk composition especially SCC per each udder quarter is important (2). The use of real time tests like wet and dynamic tests in order to determine the vacuum behaviour in milking clusters is useful, but factorial type tests require time and effort. On the other hand, mathematical functions are helpful in order to predict the variables considered in a study for a better system design and use. Vacuum fluctuations are of importance for the evaluation of milking equipment and for the evaluation of a milking system along with the mean vacuum in