THE ANALYSIS OF THE EFFECT OF CHANGING THE VOLUME OF THE UNDER-TEAT CHAMBER, RUBBER ELASTICITY AND PULSATION TYPE ON THE SIZE OF THE RETURN FLOW IN A SHORT MILK TUBE

Tomasz Pawlak, Józef Szlachta, Adam Luberański
Institute of Agricultural Engineering, Agricultural University of Wrocław, Poland

ABSTRACT

The purpose of the paper was to show the effect of changing the volume of the chamber under the teat and the elasticity of the teat rubber on the intensity of the return flow in a short milk tube. The studies analyzed the return flow with the use of simultaneous and alternate pulsation. Three levels of working sub-pressure were applied (50, 46, 42 kPa), four sizes of teat penetration (100, 75, 62 and 50 mm) as well as four types of teat rubber. The measurements were made in a laboratory with the simulation of the flow stream of the milk-replacing liquid 2, 4, 6 and 8 kg·min^-1. A mathematical formula was worked out on the basis of the results of studies to describe the return flow for alternate and simultaneous pulsation at a satisfactory value of determination coefficient R² of over 0.6.

Key words: simultaneous pulsation, alternate pulsation, return flow.

INTRODUCTION

The return flow can have two forms: one when a big amount of liquid raised by the air at small velocity (1-2 mˇs^-1) is withdrawn – stream flow – or the other, when a small amount of liquid carried by the air at big velocity (10-20 m·s^-1) is replaced [12, 16]. The withdrawing stream of milk hits the teat and additionally causes its washing. Besides, at the speed of more than 10 m·s^-1 aerosol may penetrate into the teat channel [8, 9, 10].

The principle of the mechanism of transferring microbes between the quarters results first of all from the increase of the volume of the chamber under the teat when the teat rubber opens [6, 7]. A short-lasting increase of the sub-pressure at the end of the teat, with insufficient permeability of the milk tube, creates conditions for the return flow to appear. The studies showed that the strengthening of the phenomenon of return flow (and transmitting mastitis infection) takes place at the simultaneous appearance of cyclic and irregular fluctuations [3, 13]. A number of papers showed the relation between the sub-pressure fluctuations below the teat channel and a growing number of mastitis cases [3, 10, 11]. Nordegren [4] and Danielson [2] claim that high cyclic fluctuations of the pressure cause a high stream return flow and the stroke, whereas Cleasson et al [1] are of the opinion that the situation is reverse – high sub-pressure fluctuations counteract the return flow of milk and the strokes in the teat.

A systematic increase of the milking efficiency of cows set high requirements to the milking machines, mainly regarding the milking parameters with big intensities of the milk flow. The intensity of the milk flow of about 8 kg per minute in high-milking cows is frequent, which causes that the dynamics of the return flow grows especially in the machines the construction of which is not suited to secure transportation of big portions of milk (small diameters of short milk tubes and small volume of collectors) [14, 17]. However, O’Callaghan and Gleeson [5] claim that increasing the diameter of the short milk tube from 8.5 mm to 13.5 mm has a minimal effect on the drop of sub-pressure fluctuations, but they do not provide any theoretical justification of this thesis.

The purpose of the paper was to conduct a comparative analysis of the effect of the volume of the chamber under the teat and the elasticity of the teat rubber expressed by means of the difference between the touch pressures on the phenomenon of the return flow in milking machines. Besides, the study was meant to show the effect of pulsation type, the length of teats, intensity of the milk-replacing liquid outflow on the return flow as well as to establish a generalized mathematical model describing the above-discussed parameters on the return flows in a short milk tube.

METHODS

In order to ensure realization of the purpose, a measurement stand (fig. 1) was constructed on the basis of a pipeline milking machine. The sub-pressure system was made up of a pipeline with the cross-section of 50 mm, which cooperated with a pump RPA 21 with the efficiency of 51 m³·h^-1, a valve regulating the sub-pressure VACUREX 5000 and which was equipped with a retarding reservoir with the volume of 20 l.

Figure 1. Scheme of the stand for measuring the pressure and flow conditions in a milking machine: 1 – vacuummeter , 2 – sub-pressure pipeline, 3 – sub-pressure regulator, 4 – pulsator, 5 – milk-replacing liquid tube, 6 – collector, 7 – milking mug, 8 – artificial teat, 9 – acquisitor, 10 – sub-pressure sensors, 11 – a reservoir with a milk-replacing liquid, 12 – rotameter, 13 – return flow sensor

The studies used distilled water as a milk-replacing liquid, which – according to literature – can replace warm milk [15, 16]. The intensity of the stream of liquid mass flowing through the milking machine for all teats was changed in the range between 0 and 8 l·min^-1 every 2 l·min^-1 by means of a rotameter.

Figure 2. Exemplary course of sub-pressure: 9 – in the collector, 10 – in the teat chamber, 11 – in the inter-wall chamber, 12 – at the end of the teat, 14 – course of the dynamics of the return flow in a short milk tube of the machine operating at the working sub-pressure of 50 kPa, the intensity of the liquid flow of 8 kg/min and simultaneous pulsation

Three working sub-pressures were used during the studies, i.e. 42, 46 and 50 kPa, and the length of the teat of 100, 75, 62 and 50 mm. The measurements of sub-pressure changes in the milk chamber of the collector, the short pulsation tube, the teat chamber and at the end of the teat were performed using the sub-pressure sensors PS-SM-100. The studies made use of simultaneous and alternate pulsators with a similar coefficient of the pulsator and the relation between the phase and the massage. A 15-channel recorder was used to register the measured values, which ensures a simultaneous recording of signals from all sensors with the frequency of 100 trials. Then, by means of proper software, the registered data were processed into pressure parameters characterizing the course of the milking process (fig. 2).

Figure 3. Experimental sensor for measuring the return flow: 1 – lower trunk, 2 – tensometric sensor, 3 – main trunk, 4 – inflow connecting pipe

A return flow sensor was developed to measure the return flows in the short milk tube (fig. 3).The principle of marking the return flow is based on the measurement of the velocity of the flowing liquid in the short milk tube and it is expressed in Nˇs. The flowing liquid (medium) in the short tube affects the open-work screen (tensometric beam), causing its bending under the pressure of the flowing mixture of liquid and air. The active area of the screen constitutes 33% of the total cross-section of the connecting pipe of the teat rubber. Tensometers stuck on the tensometric beam (open-work screen) transmit the signal to the acquisitor, which is adequate to the velocity of the retreating medium. A graphic picture of the signal transmitted to the acquisitor is the graph in figure 4, which shows the pulsation curve (4) and the curve (5) characterizing the flows of the media in the short milk tube.

Figure 4. Scheme of the measurement of the return flow 1 – area of the return flow, 2 – area of the normal flow of the liquid (milk), 3 – zero line of the flow, 4 – sub-pressure in the inter-wall chamber, 5 – reverse flow in the connecting pipe of the teat rubber

In the presented graph (fig. 4), curve 5 depicts the flows in the short milk tube both in the direction of the collector (principal flow) and the return flow (in the direction of the teat). The principle of marking the line of zero flow 3 (fig. 4) is included in the paper [14]. In order to obtain the size of the flow in the required units it was necessary to graduate the scale of the sensor of the flow-measurer according to the principle of the impulse of the force by means of modes masses, which were, successively: m₁ = 0.45 g, m₂ = 1.8 g, m₃ = 3.9 g, m₄ = 4.5 g. The above model masses were converted into the unit of the force expressed in Newtons. Calibration of the sensor consisted of recording the signals coming from the flow sensor for a given model force operating during the period of one second. In this way the fields characterizing the dynamics of inclination of the tensometric beam of the sensor were obtained in the period of 1 second. Then the area of the obtained field, which for particular velocities of model forces were: A₁ = 5.76 mm², A₂ = 27 mm², A₃ = 54.4 mm², A₄ = 65.8 mm², was integrated. The obtained areas for particular model masses made it possible to calculate the regression in the form y = 14.407x – 0.0942, at the correlation coefficient R₂ = 0.9983. In this way the calibration line of the sensor of the return flow of the medium was achieved in the short milk tube.

Because of no possibility of far-reaching changes of the working parameters of a specific teat rubber (construction dimensions of the trunk – diameter, length, elasticity, size of deformation of the chamber under the teat and the short milk tube), it was necessary to consider different teat rubbers in the studies. This allowed for broadening the range of changes in the parameters considered in the studies and determining the level of basic pressure parameters of the milking machine.

The next stage established the elasticity of the teat rubbers on the principle of differences in the touch pressures (TPD) through the registration of the sub-pressure values at which the contact of the walls of the trunk part of the rubber took place.

Measurements ∆Vs were performed by means of an indirect method, i.e. assuming that the increase of the inter-wall chamber is accompanied by the same drop of the volume of the chamber under the teat.

Elasticity measurements TPD were realized for the teat penetration of 50, 62, 75 and 100 mm, and for changes of the volume of the chamber under the teat ΔVs with the earlier enumerated lengths of the teat and at the sub-pressure of 42, 46 and 50 kPa.

Table 1. Elasticity of the teat rubbers TPD for varying teat lengths

Rubber type	Elasticity of teat rubbers (difference of touch sub-pressures TPD) (kPa), for particular penetrations
	50 mm	62 mm	75 mm	100 mm
1	10.8	11.2	13.3	19.5
2	12.1	13.3	16.6	24.3
3	16.2	19.2	23	40.2
4	16.9	20.4	24.1	41.1

Table 2. Volume changes of the chamber under the teat of the examined teat rubbers for different teat lengths and values of system sub-pressures

Rubber type	Sub-pressure kPa	Changes of the volume of the chamber under the teat ∆Vs (cm3) for particular penetrations
		50 mm	62 mm	75 mm	100 mm
1	42	40.07	37.74	33.85	23.31
	46	40.52	38.52	34.41	23.87
	50	41.07	39.07	38.8	23.87
2	42	39.96	37.74	33.3	23.2
	46	40.52	38.3	33.86	23.53
	50	41.07	38.85	37.82	23.86
3	42	20.98	19.31	15.54	6.33
	46	21.2	19.65	15.76	6.44
	50	21.31	19.76	17.69	6.88
4	42	19.98	17.76	14.43	4.88
	46	20.2	18.09	14.65	5.42
	50	20.54	18.32	16.47	5.55

RESULTS

According to the methods and research assumptions for the measurement of the return flow, the studies used the method of the measurement of velocity. Correctness of the assumption is confirmed in the results of studies [14], which proved the relationship between velocity (intensity) of the return flow and the real return flow reaching the level of the teat measured in the short milk tube.

The phenomenon of the return flow stays in a close relation to the changes in the volume of the chamber under the teat and the speed of these changes. Greater changes of the volume of the under-teat chamber increase a tendency to suck in the milk or the mixture of milk and air towards the teat, strike the teat or even a tendency for the milk (with pathogenic bacteria) to get inside the teat chamber. This can lead to the infection of the teats with all its consequences. This phenomenon is even enhanced with high values of the flow intensity (ranging 8-10 kg milk per minute), which can cause (with small diameters of the short milk tubes) blocking of the milk pipes as a result of too slow collection of milk from the teat chamber.

Figure 5. Return flow Pp in the function of volume changes of the under-teat chamber dvs with the sub-pressure of 50 kPa, the streams of the mass of the milk-replacing liquid Qm = 2-8 kg·min-1, simultaneous and alternate milking for four lengths of the teat 50, 62,75 and 100 mm

In all the considered cases the studies found out higher values of the dynamics of the return flow with alternate pulsation (fig. 5). Values of the return flow Pp change proportionally to the increase of the under-teat chamber and they significantly depend on the intensity flow of the milk-replacing liquid Qm. A change of value Qm from 2 to 8 kg·min^-1 generates an increase of the value of the return flow from 0.03N·s to 0.68N·s for simultaneous milking and from 0.06 N·s to 0.99 N·s, respectively, for alternate milking. At the same time it can be observed that increased lengths of the teats are followed by correspondingly lower values of Pp for both pulsation types.

The next part of the paper analyzes the effect of the elasticity of the teat rubber on the return flow, considering the fact that the greater elasticity of the teat rubber, the less rapid its movement (in the phase of the rubber opening) is, which should have an influence on decreasing the fluctuations of the sub-pressure in the under-teat chamber and in this way create better conditions for stabilization of the milk outflow to the collector (without return flows). However, decreasing the elasticity below a certain limit can have a very negative effect on the relation between the phase of sucking and the phase of massage (shortening the phase of sucking), which can cause considerably longer time of milking.

The lowest intensities of the return flows took place with the greatest elasticity of the teat rubbers (fig. 6). An increase of the teat length is followed by a drop of the values of the return flows Pp for all considered measurement variants. The values of the return flows for the teat length of 50 mm with simultaneous pulsation ranged from 0.09 to 0.68 N·s, and with alternate pulsation these values stayed within the range of between 0.11 and 0.99 N·s. When the teats with the length of 100mm were used, the values of PP from 0.03 to 0.53 Nˇs for simultaneous pulsation and from 0.06 to 0.57 Nˇs for alternate pulsation were obtained. The studies showed a decisive increase of the value of the return flow together with the increase of the intensity of liquid flow Qm.

Figure 6. Return flow Pp in the function of differences of touch pressures TPD with the sub-pressure of 50 kPa, streams of the mass of the milk-relating liquid Qm = 2-8 kgˇmin-1, simultaneous and alternate pulsation for four teat lengths 50, 62, 75 and 100 mm

In order to prove the significance of the effect of the analyzed parameters, the results were subjected to a multivariate analysis of variance (table 3), which showed that a significant influence on the values of the return flow Pp (at the significance level of α = 0.05) is exerted by the intensity of the liquid outflow Qm, difference of the touch pressures TPD, teat length Pe and changes of the volume of the under-teat chamber dvs.

Table 3. Results of multivariate analysis of variancev

Parameter	Source of variation	Outflow intensity Qm	Difference of touch pressures TPD	Teat length Pe	Deformation of under-teat chamber dvs
	number of freedom degrees	3	10	3	18
Dynamics of return flow Ppp for alternate pulsation	level of significance	0.0000	0.0000	0.0000	0.0000
	value of test F	216.747	8.454	10.485	6.030
Dynamics of return flow Ppj for simultaneous pulsation	level of significance	0.0000	0.0000	0.0000	0.0000
	value of test F	114.162	10.881	12.486	6.347

An attempt was made to give a mathematical description of the studied parameter Pp on the basis of the analyzed factors. The following general form of the function for the return flow was adopted:

Pp = (Qm) (dvs, TPD, Pe)

The method of multiple regression with step elimination of independent variables from the mathematical model was used to obtain a quantitative description of the effect of the disturbing parameter Qm (intensity of the milk-replacing liquid) and the parameters connected with the teat rubber – dvs (deformation of the under-teat chamber), TPD (differences of the touch pressures) and Pe (length of the teat) on the intensity of the return flow Pp.

Table 4. Results of multiple regression with step elimination of the variables for Pp and simultaneous pulsation

Independent variable	Coefficient	Standard error	Test value - t	Level of significance
Constant a	-0.349278	0.039868	-8.7608	0.0000
Milk flow Qm	0.08631	0.026193	3.2951	0.0011
Milk flow Qm2	-0.044643	0.008315	-5.3689	0.0000
Milk flow Qm3	0.005208	0.000683	7.6230	0.0000
Deformation of the under-teat chamber dvs	0.01043	0.000971	10.7427	0.0000
Length of teat Pe3	1.896774E-7	3.271686E-8	5.7975	0.0000

Finally, the mathematical model describing return flows in the short milk tube with simultaneous pulsation assumes the form of the empirical equation:

Ppj = 0.349278 + 0.08631Qm – 0.044643Qm² + 0.005208Qm³ + 0.01043dvs + 1.896774E-7Pe³

with the satisfactory coefficient of determination R² = 0.64.

Table 5. Results of multiple regression with step elimination of the variables for Pp and alternate pulsation

Independent variable	Coefficient	Standard error	Test value – t	Level of significance
Constant a	-0.432428	0.132133	-3.2727	0.0011
Milk flow Qm	0.113281	0.025702	4.4075	0.0000
Milk flow Qm2	-0.058594	0.008159	-7.1813	0.0000
Milk flow Qm3	0.006836	0.00067	10.1965	0.0000
Deformation of the under-teat chamber dvs	0.031909	0.006132	5.2034	0.0000
Deformation of the under-teat chamber dvs3	-0.000011	2.40009E-6	-4.7781	0.0000
Difference of the touch pressures TPD2	-0.000738	0.000294	-2.5143	0.0123
Difference of the touch pressures TPD3	0.00002	6.412762E-6	3.0838	0.0022

Finally, the mathematical model describing return flows in the short milk tube with simultaneous pulsation assumes the form of the empirical equation:

Ppp = 0.432428 + 0.113281Q – 0.058594Qm² + 0.031909dvs – 0.000011dvs³ – 0.000738TPD² + 0.00002TPD³

with the satisfactory coefficient of determination R² = 0.66.

CONCLUSIONS

1. The model suggested in the paper makes it possible to consider jointly the effect of parameters characterizing the teat rubber in the conditions of the changing momentary outflow of the milk from the teat.

2. The lowest intensity of return flows are achieved with the greatest elasticity of the teat rubbers; for rubber 1 – 0.13-0.99 N·s, for rubber 2 – 0.12- 0.8 N·s, for rubber 3 – 0.04-0.52 Nˇs and for rubber 4 – 0.03-0. 51 N·s.

3. Changing the volume of the chamber under the teat (5.5-41 cm³) causes a change of the value of the return flow 0.03-0.41 Nˇs for the teat rubber of the smallest volume, and 0.15-0.99 Nˇs for the greatest volume, depending on the intensity of the outflow of the milk-replacing liquid, kind of pulsation and length of teats.

REFERENCES

1. Cleasson C.O., 1978. Personal information. Agric. University, Uppsala.

2. Danielsson U., 1978. Calculation of the jet flow velocity in the short milk tube of milking machine. Personal Information.

3. Hamann J., 1989. Maschineller Milchentzung und Mastitis. Rozprawa habilitacyjna, Stuttgart.

4. Nordegren S. A., 1980. Cyclic Vacuum Fluctuations in Milking Machines. Diss. Hohenheim.

5. O’Callaghan E. J., Gleeson D. E., 2000. Ocena systemów doju w odniesieniu do nowego ryzyka mastitis, reakcji tkanki strzyka i wydajnoœci doju. Raport końcowy projektu nr 4505 Funduszu Strukturalnego UE. Teagasc AFD Authority. Ballsbridge – Dublin.

6. O`Shea J., O’Callaghan E., Meaney W., 1975. Liner slips impacts and infection. Ir. J. Agric. Res. 14, 372.

7. O’Shea J., O’Callaghan E., 1980. Effect of vacuum fluctations and liner slip on new infection rates. Proc. Int. Wkp. Mach. and Mastitis, Moorepark 6.

8. O’Shea J. et al., 1987. Relationship between machine milking an the incidence of mastitis of dairy cows. Ir. J. Agric. Res. 18, 3, 225-235.

9. Thiel C.C. et al., 1973. The influence of some physical characteristics of milking machine on rate of new mastitis infections. J. Dairy Res. 40, 117-119.

10. Thiel C.C., 1974. Bienn. Rep. Nat. Inst. Res. Dairying. 35-38.

11. Whittlestone W. G., 1968. The principes of mechanical milking. Verlag Blackwood and Paul LTD. Auckland.

12. Wiercioch M., 1992. Badania prędkoœci przepływu cieczy w króćcu gumy strzykowej kubka udojowego [The investigation of speed of flow liquid in short milk tubes]. Zesz. Nauk. AR Wrocław. Mechanizacja Rolnictwa II 219, 125-132 [in Polish].

13. Wiercioch M., Szlachta J., Łuczycka D., 1993. Pęd przepływu powrotnego w niektórych aparatach udojowych [The speed of back flow in some milking units]. Zesz. Probl. Post. Nauk Rol. 410, 59-67 [in Polish].

14. Wiercioch M., Szlachta J., 1995. Przepływ powrotny w zmodyfikowanych aparatach udojowych [Back flow in modified milking units]. Rocz. Akademii Rolniczej w Poznaniu – CCLXXIV, 101-106 [in Polish].

15. Wiercioch M., 1998. Ocena intensywnosci wypływu mleka ze strzyka krowy w poszczególnych cyklach przy użyciu różnych systemów (aparatów) udojowych [The opinion in the intensity of milk outflow from a cow’s teat in individual cycles near use the different milking units]. Maszynopis, IIR AR Wrocław, 2-12 [in Polish].

16. Worstorff H., 1977. Experimentelle Untersuchung zur Stabilisierung das Vacuums in der Melkeinheit. Aus den Arbeiten das Sonderverschungebereiches 141.

17. Woyke W., Hamman J., Osteras O., Mayntz M., 1993. Wpływ parametrów pracy dojarek mechanicznych na tkanki strzyków [The influence of parameters of work milking units on tissue the teat]. Zesz. Probl. Post. Nauk Rol. 410, 93-98 [in Polish].

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Tomasz Pawlak
Institute of Agricultural Engineering,
Agricultural University of Wrocław, Poland
37/41 Chełmonskiego Street; 51-630 Wrocław, Poland
phone: (+48 71) 32 05 715
fax: (+48 71) 348 24 86
email: pawlak@imr.ar.wroc.pl

Józef Szlachta
Institute of Agricultural Engineering,
Agricultural University of Wrocław, Poland
37/41 Chełmonskiego Street; 51-630 Wrocław, Poland
phone: (+48 71) 32 05 731
fax: (+48 71) 348 24 86
email: szlachta@imr.ar.wroc.pl

Adam Luberański
Institute of Agricultural Engineering,
Agricultural University of Wrocław, Poland
37/41 Chełmonskiego Street; 51-630 Wrocław, Poland
phone: (+48 71) 32 05 735
fax: (+48 71) 348 24 86
email: luberanski@imr.ar.wroc.pl

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