Models of adaptation of the milking machines systems

Two systems of milking machines were considered - biotechnical and vacuum. Methodology for estimation of efficiency of the "machine-animal" biotechnical system was worked out. The dependences of the efficiency parameters of the technical system operation were analyzed. The KMMO operator load factor of the milking machine was proposed. The factor characterizes the technological process of the machine milking. The analytical dependences were worked out for the simulation of the productivity of milking machines and oscillation of the vacuum-gage pressure. As to the simulation results, when the vacuum pipeline diameter was increased the oscillation of the vacuum-gage pressure decreased. The results of analysis and theoretical researches on technological process of the cow machine milking gave a possibility to define the requirements to the improvement of technological process and technical equipment, which will provide the increase of efficiency of the milking systems. Usage of the developed cyber-physical system of the machine milking of cows will increase the productivity of the milking machine in 1.26…1.85 times. At the vacuum gage pressure oscillation of ΔPvp = 2500 Pa the suction ability of milking machine will be E=4.093 m/s accordingly. The defined index of efficiency of the adapted systems functioning of the milking machine is KBTS2 = 55.3.


Introduction
We will consider the process of cows milking as a biotechnical system of the "person-machine-animal", that does possible the functional ensuring of realization of the genetic potential of the cow productivity with the interaction of objects of this system. Efficiency of functioning of the biotechnical system depends on the parameters of its objects that ensure the quality and efficiency of technological functions.
As a basic performer of the technological process of milking, the milking machine provides adaptation of the technical system to physiology of milk ejection of the cow through vacuum gage pressure with preset parameter and possibility of its adjusting. The milking machine provides also the parameters control and maintenance at the set level during milking of cows. Pulsating air system of milking machine is the peculiarity of unit arrangement that changes the configuration and functional possibilities. Pulsating air system gives an opportunity also to work autonomically, or in composition of the automatic control system of technological process (Industrial Control -IC) of the machine milking. To operate in the composition of IС the milking machine was additionally completed by the measuring device of milk ejection intensity, microprocessor control unit and other elements of electronics [1,2]. However, the vacuum gage pressure forming is still one of important factors of the parameters forming directly that does possible adaptation of the "machine-cow" system. The question of parameters adaptation of the milking machine systems was examined by Dmytriv V.Т. and other [3][4][5], where influence of the technological and construction parameters on work mode of systems is analyzed. Also, the stability of vacuum gage pressure was estimated directly by the group of researchers consisting of Pazzona A., Murgia L., Zanini L. et al., depending on the method of adjusting in the vacuum pipeline or in a milking machine. They set that stabilizing of vacuum by the regulator of gravitational type is more dynamic, and the permanent to time is twice more lower from the computer-based system [6]. An analogical conclusion is also in accordance with research results of the regulators of pulsating vacuum gage pressure [7]. In particular Reinemann D.J., Schuring N. and Bade1 R.D. investigated the vacuum gage pressure oscillation depending on: а) configuration of the vacuum and milk hose systems (length of pipelines, hose diameter and other parameters influencing the losses of pressure); b) flowrates of milk in the milk pipeline; c) rates of air movement in the vacuum pipeline. They set that the vacuum gage pressure was raised up as in a vacuum-and milk pipeline, so in the under-teat chamber of the teat cup in the process of diminishing of the intensity of milk ejection [8].
The analysis of research works shows that the grounding of parameters of the effective functioning of the cows milking bioengineering system requires the development of conception and methodology of optimization of the mentioned system parameters and the same for the technical constituent of this system. Optimization of the bioengineering system parameters is also important for the increase of efficiency of milking machines.

Effectiveness of the "operator-machineanimal" bioengineering system
The effectiveness of work of the machine milking operator (MMО) was determined by the productivity for the maximum system load. This parameter depends on the n mu quantity of the milking units and the t m duration of the milking of one cow (with consideration of the preparation and final operations t m = t mm + t p-f ), and also the Z li labour inputs: where: W mmthe productivity of the milking machine, cows/h., n muquantity of the milking units, pcs., t mduration of the milking of one cow, h., Z lilabour inputs, MJ. Effectiveness of functioning of the technical system of milking was estimated by the quality parameter of functioning of the vacuum system, namely the ∆р VP amplitude of pressure oscillation of the vacuum system of milking machine. The vacuum gage pressure oscillation depends on the П es parameters of the mentioned technical system elements, the K fes quality of its interaction and the Z ТS energy expense for the system functioning: where ∆р VPthe amplitude of vacuum gage pressure oscillation, Pa, П еsparameters of technical system elements, К festhe quality coefficient of the interaction of technical system elements, Z ТSthe energy expense for the technical system functioning, MJ. Effectiveness of the bioengineering system depends on the cow milk ejection that is limited by the pressure oscillation in the vacuum system of the milking machine. The milk yield decrease can be described by the function as a result of the vacuum gage pressure oscillation [9]: where ∆Q Mthe loss of cow milk yield as a result of the pressure oscillation, MJ, Q pthe potential of the cow milk yield, MJ, εthe ratio of the pressure oscillation duration to the total milking duration, Е 1 ,Е 2the suction ability of the milking machine with the modes accordingly p 1 =p+Δp VP /2 і p 1 =p -Δp VP /2, рthe vacuum gage pressure in the under teat chamber of the teat cup, Pа, Еthe suction ability of the milking machine for the vacuum gage pressure р in the under teat chamber of the teat cup, J=E·2/3parameter of the milk ejection.
The suction ability of the milking machine was determined according to the described procedure [9]: where K fthe proportion of phases of the milking machine, K μflow coefficient, ρ мmilk density, kg/м 3 .
On the basis of the above mentioned parameter the effectiveness of the milking machine system is expressed by the formula: where Z BTSthe energy expense for the functioning of the milking machine system, The demonstrated formula (5) presents that effectiveness depends of the parameters of the technical system. The mentioned technical system has to ensure the conditions of the milk ejection from the cow udder according to the lactogenesis physiology demand with the reduction of the MMО labour inputs and also total energy expense lowering for the functioning of the milking machine systems.
Taking into account the order of the preparation and final operations of machine milking one can determine the K оп load factor of the milking machine operator by the formula [10]: where t mduration of the one cow milking, t m =t mm +t p-f , s [11], t fduration of the final operations, s. If the K MMO > 1operator is underloaded, accordingly the milking machine is not overdone on the udder teats, if the K MMO < 1the machine milking operator is overloaded and the schedule of preparation and final operations is not kept, or the milking machine is overdone on the udder teats of cow.
From the equation (6) we shall derive the formula for determining the optimal quantity of the milking machines, taking into account that t p- where t pthe duration of the preparation operations by the MMО, s. Taking into account the average distribution of the duration of preparation and final operations ( ) the equation of the productivity of milking machine will have the appearance: the average value of the duration of preparation and final operations of the cow machine milking accordingly, s, S(t p ), S(t f )the root-mean-square deviation of the duration of preparation and final operations of the cow machine milking accordingly, s.

Amplitude of the pressure oscillation of vacuum system of the milking machine
The construction of the milking machine can be presented as the functionally finished elements, which are the constituents of the vacuum system of the milking machine ( Fig. 1) [12].
Taking into account the law of mass conservation for the gas in the controlled volume by way of equation of the air motion mechanical energy and work for overcoming of the frictional force, the second airflow during the pumping-out of the vacuum system will be [13]:  Taking into account that , the equation (10) will have the appearance: Also taking into account that dM = Vdρ i , we will have: After the dependences of (11) and (12) were equated, the sign was accounted and formula was reduced , the differential equation of air pumping out from the V volume will have the appearance: The (13) formula is transformed and integrated with the limitations from 1 to р i /р А and from 0 to τ: The integration results define the duration of air pumping out of the V volume from the pressure р А to the vacuum gage pressure р і, and will be determined in series by the formula: To simulate the characteristic of the vacuum gage pressure changes in the vacuum system of the milking machine one has to know the time parameters of the vacuum pressurethe time interval of the air pumping out from the volumes of the variable vacuum gage pressure. From the equation (16)  where Vthe volume of chambers of the variable vacuum gage pressure of the milking machine, м 3 , S csathe cross-sectional area of the pulsator drain port, м 2 , ψvelocity aspect ratio defines the pressure relation, m 1/2 /s, ρ Аthe air density in the V volume for the atmospheric pressure, kg/м 3 , р Аthe air atmospheric pressure in the V volume, kg/м 2 , р іthe value of the vacuum gage pressure in the і-th point of time, kg/м 2 , npolytropic coefficient, n = 1,41.
Thus, the quantity of pumped out air will be: where Vthe volume of chambers of the variable pressure, м 3 , R пgas constant of the air, R п = 287,72 J/(kg·ºС), Θ -air temperature, ºС.
For connection of the і chambers with the given volume one can determine the volume, pressure and the air quantity accordingly [12]: The amplitude of the vacuum gage pressure oscillation in the vacuum pipeline is determined by the formula: where G VP , Gthe air quantity in vacuum pipeline and volumes of the variable vacuum gage pressure accordingly, kg, V VPthe volume of the vacuum pipeline of the specific milking machine, м 3 , P(N пmu )the probability of simultaneity and coincidence of the phase and work times of the specific milking machines:

Results
The productivity of the milking machine (equation 8) depends on the duration of preparation t p and final t f operations, duration of machine milking t mm and the cow productivity. Also the productivity of the milking machine depends of the quantity of the milking units, which are operated by the MMO with the regulated load factor K MMO . The results of the modelling are shown in Fig. 2 and 3.  The analysis of dependence of the productivity of the milking machine from the duration t mm of machine milking of cow and ratio of t f /t p (Fig.3) demonstrates when t f →max, t p →max, the productivity of the MMO work is not submitted to the specific law. The area on the 3-D graph of the 26...34 cows/hour productivity fits with the milking machine for the bucket milking, 34...50 cows/hourpipeline milking in the barn, from 51 cows/hourparlor milking.
The analysis of dependence of the productivity of the milking machine from the time t mm of machine milking of cow and ratio of t f /t p (Fig.2) demonstrates when t f →min, t p →min, the productivity of the MMO work is submitted to the second-order equation.
The area on the 3-D graph of the 29...36 cows/hour productivity fits with the milking machine for the bucket milking, 37...50 cows/hour with the pipeline milking in the barn, from the 51 cows/hour and high with the parlor milking.
Modelling of the pressure oscillation amplitude in the vacuum pipeline is demonstrated in Fig. 4. Graphic dependence of the vacuum pressure oscillation amplitude changes Δр vp from the number of simultaneously working milking machines  nmu N with coincidence in time of the cycles and phases of pulsator work with probability Р(N nmu ) and the vacuum pipeline D diameter was shown in Fig. 5.
The analysis of simulation results shows that with an increase of the number of milking machines the vacuum pressure amplitude is increased.

Discussion and conclusion
The dependences (1)(2)(3)(4)(5) show that efficiency depends on the parameters of the technical system which have to provide the conditions for the milk take out from the cow udder in accordance with the physiology of milk lactogenesis and ejection with reduction of both the МMО labor inputs and energy expense in the process of milking machine system functioning.
The requirements of the machine milking process were fulfilled for the K MMO ≥ 1. The milking duration in