Mathematical models for the prediction of vacuum dynamics of a milking system with four-way milking cluster

Abstract

Objective: The objective of this study was to determine the effects of system vacuum, pulsation rate and ratio and flow rate on vacuum dynamics of a milking system with four-way cluster. In order to meet this objective, empirical functions were developed to predict vacuum related dependent variables. These dependent variables were considered to be vacuum drops and fluctuations in b and d-phase and in claw along with average claw vacuum and teat end vacuum for four-way milking cluster. Material and Methods: Experiments based on the central composite design, one of the designs in Response Surface Methodology (RSM), and using water and artificial teat were conducted in the laboratory. The data obtained from the experiments were then used to develop functions in polynomial form that allowed predicting the vacuum related variables. Results: Eight different functions were developed. The coefficient of the determination (R2) for all the models was above 0.9. It is believed that the models developed in this study can be used to design the milking system equipped with four-way milking cluster. Conclusion: The simplest models are the ones that are developed for the average claw vacuum and the models developed for the vacuum drops in d-phase and claw. The common point of these three models along with the average vacuum prediction function is that there is no quadratic or cubic term entered into the model. The highest vacuum drops in b-phase for four-way milking cluster occurs when the pulsation ratio of 62:38. The system behavior for vacuum drops in d-phase is different than b-phase and a linear surface is valid. It only consists of flow rate and pulsation ratio.