EFFECT OF THE DIAMETER OF THE LONG-PULSE TUBE ON THE PULSATOR CURVE. M.A. v.d. Brandt and W. Rossing

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1 EFFECT F TE DIAMETER F TE LNG-PULSE TUBE N TE PULSATR CURVE M.A. v.d. Brandt and W. Rssing INTRDUCTIN Different makes f milking machines use lng-pulse tubes with varius inside diameters. At the request f the IS Technical Cmmittee 23/SC ll/wgv2 "Milking Machine Installatin", we examined the effect f the diameter f the lng-pulse tube n the pulsatr curve. The measurements were carried ut in a labratry n an artificial udder with bth pipeline and bucket installatins. TERETICAL Theretically we can sider the vacuum variatin in the pulsatin chamber as fllws: Increasing vacuum phase P R i i R x- P2 c P = vacuum in vacuum line PI = vacuum in pulsatr P2 = vacuum between teat cup and liner Rl = resistance f tube between vacuum line and pulsatr R2 = resistance f pulsatr and pulse tube C = capacity f rm between teat cup and liner + capacity f pulse tubes. * Student f the Technical igh Schl at Zwlle ** Institute f Agricultural Engineering

2 T ensure that there wuld be n variatin in P, we used a vacuum pump with a large capacity. We can make the fllwing equatins: 0 = Pl-P Rl P2-P1 R2 dp2 -C dt (1) (Pl--P)R2 = (P2-P1)R1 r P2 Rl R1+R2 + R2 R1+R2 PI... (2) P2 - PI = dp2 -CR2 dt (3) Substitude (2) in (3), dp2 P2 = P - C(R1 + R2)... (4) dt If we accept that the sliding valve f the pulsatr pens in a very shrt time, then P changes as a step functin -t_ P2 = P(l - e T )... (5) This frmula shws that the time it takes fr P2 t reach the value f P depends n the resistance Rl and R2 and the capacity C. DECREASING VACUUM PASE The air under atmspheric pressure can flw a the pulsatr and the pulse tubes in the space between the teat cup and the liner. Pb x- p2^

3 Pb = atmspheric pressure 0 = Pb - P2 R2 dp2 dt... (6) P2 = Pb - CR2 dp2 dt (7) This frmula shws that the time taken fr P2 t reach the atmspheric pressure Pb depends n the resistance R2 and the capacity C. MEASUREMENTS Fr the measurements the fllwing variables were intrduced. MILKING PIPELINE MACINE Pulsatr A B C D E Alternative pi IT Simultaneus it Pulse tube diameter 6 mm 7 mm 8 mm 9 mm, all 2400 mm lng Capacity teat cup large small

4 We can cmbine the variables as fllws: A 6 small 7 small 8 small 9 small 6 large 7 large 8 large 9 large B 6 small 7 small 8 small 9 small 6 large 7 large 8 large 9 large 6 small 7 small 8 small 9 small 6 large 7 large 8 large 9 large D 6 small 7 small 8 small 9 small 6 large 7 large 8 large 9 large E This pulsatr is placed n the claw s that n lng-pulse tubes can be used E large E small E withut teat cups BUCKET MILKING MACINE Pulsatr Pulse tubes alternative pulsatin simultaneus pulsatin Capacity diameters 6 mm, 920 mm lng 7 mm, " " teat cups: large small We can cmbine the variables as fllws: A B C D 6 small 7 small 6 small 7 small 6 small 7 small 6 small 7 small 6 large 7 large 6 large 7 large 6 large 7 large 6 large 7 large

5 During the measurements the teat cups were nected t an artificial udder. The pressure variatin was measured with pressure transducers and recrded with a recrder which had a satisfactry frequency respnse (0-100 z). The air sumptin was measured with a gas vlume meter (Drawings 1 and 2). The results f the measurements are presented in Tables 1, 2 and 3 and in the Figs Frm the graphs the fllwing data can be btained: ttal pulsatin cycle a. increasing vacuum phase b. maximum vacuum phase c. decreasing vacuum phase d. minimum vacuum phase 50 kpa Pulsatin cycle kpa

6 These data are expressed in % f the ttal pulsatin cycle (tables 1, 2 and 3). These tables als shw the pulsatr rate, air sumptin in litres f expanded air per min, and the air sumptin in 1 expanded air per 60 cycles. CAPACITY C The capacity f the installatin: - capacity f space between teat cup and liner (4 x by simultaneus and 2 x by alternative) - capacity f lng pulse tube - capacity f shrt pulse tubes (4 x by simultaneus and 2 x by alternative pulsatin). The capacity f the pulsatin chamber was measured by puring water int the chamber with a vacuum inside the liner. Capacity f small teat cup: 105 cm 3 (by alternative) 135 cm 3 (by simultaneus) Capacity f large teat cup: 165 cm 3 Capacity f pulse tubes diameter 1 = 2400 mm 1 = 920 mm 1 = 25 mm 6 mm 7 mm 8 mm 9 mm 67.0 cm cm cm cm 3 26 cm cm cm 3 Ttal capacity and teat cups in litres with different tube diameters, pulsatr s

7 Milking pipeline machine diameter f pulse tube small alt. small sim. large alt. large sim. 6 mm 7 mm 8 mm 9 mm Bucket milkin ç machine diameter f pulse tube small alt. small sim. large alt. large sim. 6 mm 7 mm We can clude that the teat cups have mre influence n the ttal capacity than the diameter f the pulse tubes.

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9 -9- a r ni e a r r dl ft ft M C r 0),a rö hfl r Pu 10 \ 0) r r r CJ e 1 ai (U g r 14 3 ' >, <D - 0 ft -> c 1 C r +J 3 - rd ft +> fn dp -> v 13 l+j X dp l+j X dp I-P v /a l+j X dp l+j v rti 0 I-P X dp jal+j V + 0 ifl +J X ) 6 ja ) 3 - g +J T3 E (11 ft a> 3 +J u 1 <D r +J ft 3 rfl >, ft +J v c d- d- c CsJ ^ CX) *-\ c c c D ^ [^ ' C v C C C C rf tû v C L CT) L L C C [-- ~ C C C v C L c [-- CÛ r C c v C v L "- c r al c C 00 C C [-- v C C T L L L C v C t-^ L C C- C zj- v C v zj- L c c C-- CÛ 7t c- c- zx L C v v c CÛ v C r r C C C- C zf L C L C v zf L c C c (1) hn tl rd n- c c c c c C"- ^ L C C v L c v t' en L C L c c - ~ L L L L L L L _j. C c c [-- CJD c L c- L L L L L v C C c L C r m c c L v C c C L ç C C L T L L L zien f- zien r L =1 C L L L L L zien C C v v L [ " C t> 00 L en zï zf C-- c L 0) bü U C L < v c L c L L zj- C L L c c rd C c l L c - L C c L QJ bü U m C L L L C"» L C-- 1 0) G 0

10 -1 0- b L C (X) C c c c D c j- c j- L c c L in 1/ 60 cycles L L C L CT) L C-» c c c c c c UD 00 c c L L L - l C L L c LD L - c L c \ - L L L L c L-~ C L L c j- LD LD LD L L LD LD L LD L L L ri 00 =t L time f pulsatin cycle, sec - V Zf en en C"- - L pulsatr rate L L L L c-» L L - L L LD J" L Cû C =r L C L L l- v l-p X [-- L L en C C. C C en c c C L en c C C C C c c c c l- - X L Zt C C zr c C en C C L en c c C C dp P Xi - X C C L L L L L L L J=f L L en C L L L J" LD L L L [>- CÛ LD t' en C Ü n) M C l- m - X a+b tt x 100% C C C v C C C - t~ r~- LD cû en LD L c J3- en L L L L LD C C L c r~~ L L 00 C C C c~~ [> v C C- t> t"^ v c C~~ L C c C L L e p a) >! D «tube diam. mm teat cup f- t-t S C c r r r C b fd 1 f L C t^~ CÛ F- a) b r L r^ -M r L - CTJ b U C X3 i v C -P < CQ c J Q

11 CNCLUSINS The values f (a) and (c) are affected by the resistance in the system and the capacity f this system (this is als shwn by the frmulas). Althugh we d nt knw the effect f these factrs n the milking, we assume that the effect f the diameter f the pulse tubes must be small. Frm the tables the effect f the capacity seems fairly great cmpared with that f the tube diameter. Fr a pipeline milking machine with an alternative pulsatr and teat cups f nt t large capacity, a lng-pulse tube with a diameter f 6 mm is sufficient: with teat cups f a larger capacity this diameter slightly lengthens the increasing and decreasing vacuum phase s that a tube with an inside diameter f 7 mm gives a better result. With a simultaneus pulsatr it is clear that an inside diameter f 6 mm is t small and the diameter must be at least 7 mm. Fr a bucket milking machine with an alternative pulsatr and a pulse tube 920 mm lng, a diameter f 6 mm is sufficient. Fr a simultaneus pulsatr a pulse tube with an inside diameter f 7 mm gives better results.

12 vacuum trller vacuum- J C J * * -jzh4 gasmeter mercury gauge clawartificial teat ilk tube I pulse tube- ^12- pressure transducer ' teat cup 1 = 920 c r -pulsatr bucket 1 recrder Drawing 1 Diagram f the labratry installatin fr measuring the pressure drp in the lng-pulse tube by bucket installatins.

13 vacuum trller vacuum pulsat *! * 1 Z) C 7 Agasmeter mercury gauge pulse tube, -,= I = 2400 artificial teat ^17- teat cup pressure transducer milk tube I -claw recrder Drawing 2 Diagram f the labratry installatin fr measuring the pressure drp in the lng-pulse tube by pipeline installatins.

Fig. 1-50 shw the pressure variatins in the different situatins between teatcup and liner. ssssss :::: asss :ui :SI [rj ;:. wax ::.is»«' ' ::!::; is :i ss! :: :'.:: ; Ë li 1?! SI! SS! is sssi is.

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