MODEL OF HYDROPNEUMATIC THREE POINT HITCH

Transcription

1 ENINEERIN FR RUR DEVEPMENT Jelgava, MDE F YDRPNEUMTI TREE PINT IT Jans acekls-bertmans, Erks Kronbergs atva Unversty of grculture jans.lacekls@llu.lv, erks.kronbergs@llu.lv bstract. Ths paper presents a model of a hydropneumatc three pont htch system for farm tractors. model of hydropneumatc three pont htch s derved to sut the control task of oscllatons dampng of the tractor aggregate. The reacton forces of the tractor htch system hydraulc cylnder were determned, correspondng to dfferent weght postons of the mplement. The htch mechansm s dvded n three knematc groups (unt of upper lnk and mplement, unt of lft arm and unt of lower lnk) for calculatons. From the smulaton wth the program Workng Model t was establshed that the tractor htch system lower lnk and mounted sol cultvaton tool at low ampltude oscllatons durng transport can be smplfed as a sngle beam. The necessary stffness characterstcs for beam suspenson, dependng on the mplement weght and ts poston, were determned. Uses of hydraulc accumulators were provded for obtanng dfferent stffness characterstcs of suspenson. The volume and necessary charge pressure were determned for hydraulc accumulators. Keywords: hydropneumatc htch, hydraulc accumulators. Introducton Durng tractor movement, wth attached to the htch-system workng equpment (plough, harrow), over rough road surfaces oscllaton of the machne takes place. These oscllatons are a reason of pressure pulsatons n the hydraulc htch-system. The prevous experment [] presents results of pressure oscllaton nvestgaton n the hydraulc htch-system of the tractor laas res TX 557 durng the moton around an artfcal roughness test road. Durng the experments oscllatons at the dfferent drvng speed, dfferent tre pressure, loadng weght poston and htch-system oscllaton dampng (turned on/off) were nvestgated. The results of the experments present maxmum pressure peaks of 70 bar n the tractor hydraulc system. The hydraulc htch-system wth hydropneumatc accumulators allows adjustng the stffness and dampng characterstcs of the hydraulc cylnder, lmtng the pressure oscllaton ampltude. In order to reduce the pressure maxmal values durng oscllatons, a mathematcal model of tractor hydraulc htch system wth hydropneumatc accumulators was developed. The mathematcal model for the mplement on the htch system was smplfed to the model of a sngle beam wth dfferent weght and moment of nerta. The results of calculatons were compared wth the results of the experments. Materals and methods The three-pont htch mechansm was consdered as a planar system. The system was modelled n two dmensons to represent the force n the orgnal geometrcal confguraton between the tractor and the mplement. In order to evaluate the vertcal force of tllage tools a two dmensonal study of tractor lnkage mechansm s needed. The mechansms consst of seven artculated beams. To make the force calculaton smpler, the three-pont htch-system mechansm was descrbed by tes and pn jonts. The coordnates of each jont are calculated n a coordnate system and the three-pont htch mechansm s shown n (Fg. ). The Workng Model software [] for the tractor three pont htch-system small ampltude oscllaton smulatons was used. In the Workng Model software dynamc model wth the same parameters of the tractor and attached equpment weght, road roughness and movement speed as n the expermental nvestgaton had been used [3]. The smulaton model n the prevous experment s expressed n the sde-vew. Ths sde vew of the three-pont htch mechansm model was created and descrbed on transportaton poston. The mplement dsplacement and oscllatons are dependng on the tractor drvng speed, road roughness and tractor htch-system stffness, and dampng parameters. The tractor htch-system actuator conssts of two hydraulc cylnders and t was used for mounted mplement lft up or down. The parameters of the hydraulc cylnder and tyres are doubled n the sde-vew smulaton model. From the smulaton wth the program Workng Model t was establshed that the tractor htch system lower lnk and mounted sol cultvaton tool at low ampltude oscllatons can be smplfed as 49

2 ENINEERIN FR RUR DEVEPMENT Jelgava, a sngle beam. To determne the hydraulc cylnder arm for a sngle beam smplfed htch-system t s necessary to calculate the equlbrum of a common htch-system mechansm. Results and dscusson For calculaton the htch mechansm s dvded n three knematc groups: unt of upper lnk and mplement, unt of lft arm; unt of lower lnk. The common hydraulc htch-system mechansm and loadng aggregate knematc scheme are shown n (Fg. ). F 3 B 7 D E Fg.. Sde vew of three-pont htch mechansm: lft arm (changeable); upper lnk (changeable); 3 smplfed mplement; 4 lft rod; 5 lower lnk; 6 tractor hydraulc htch-system hydraulc cylnder; 7 support. s the frst the upper lnk and the mplement unt are descrbed. The mplement was descrbed on transportaton poston (Fg. ). F φ F F θ l5 l4 Fx γ l α F l l3 F y F x F x F y Fy Fg.. Unt of upper lnk and mplement Fg. 3. tch-system lower lnk unt The projectons of forces and moment of the unt of the upper lnk and mplement gve the followng system of equatons: y = 0 ; FF snϕ + Fy = 0 () x = 0 ; F cosϕ + F = 0 () F M = 0; FF cosϕ 4 cosθ + FF snϕ 5 snθ 4 cosθ = 0 (3) The F F, F x and F y are the lft rod reacton forces at the pont F and, but s the weght of the mplement. These values depend on the tractor hydraulc htch-system poston. The lower lnk unt s descrbed as the second. The lower lnk one sde s connected to the tractor frame, but another sde s connected wth the mplement lower support (Fg. 3). The projectons of forces and moment of the lower lnk gve the followng system of equatons: x y = 0 ; F + sn γ F = 0, (4) y y x = 0 ; F F cosα F = 0, (5) x x 50

3 ENINEERIN FR RUR DEVEPMENT Jelgava, M = 0; F F snα y cos γ + F cos γ + F x cosα sn γ = 0 sn γ, (6) where F x and F y s the reacton force at the pont, but F s the reacton at the pont. The values of angles depend on the tractor htch-system hydraulc cylnder poston. The lft arm unt s descrbed as the last. ne sde of the lft arm s connected to the tractor frame wth the pvot B, but another sde s connected wth the lft rod (Fg. 4). The poston of the lft arm s changed by the hydraulc cylnder. The htch-system lftng arm unt s located n the transport poston when the hydraulc cylnder s at stretched poston. l 6 F Bx β l 7 F By B ε F λ F Fg. 4. tch-system mechansm unt Fg. 5. Physcal mplement and weght poston on three pont htch-system of tractor: weght; physcal mplement; 3 three pont hydraulc htchsystem; 4 tractor laas res 557 TX;, B and poston of weght The projectons of forces and moment of the unt of the upper lnk and mplement gve the followng system of equatons: M B y = 0 ; FBy F snλ + F snε = 0 (7) x = 0 ; F + F cos λ F cosε = 0 (8) = 0; F + F Bx snε 7 sn λ l 6 cos β + F cos β + F cosε 7 cos λ l 6 sn β + sn β = 0 where F Bx and F By s the reacton force at the pont B, but F s the reacton of the hydraulc cylnder at the pont. F = F D are the reactons of the lft arm at the ponts and D. The values of the angles depend on the tractor htch-system hydraulc cylnder poston. The force reacton of the tractor hydraulc htch-system cylnder was calculated from the equlbrum equaton. The pressure values n the hydraulc cylnder f the frcton s neglected can be calculated by the followng expresson: where p hydraulc cylnder pressure n chamber, Pa; F c force of hydraulc cylnder, N; pston area of hydraulc cylnder, m. (9) Fc p =, (0) The prevous experment [] presents the results of pressure n the hydraulc htch-system of the tractor laas res TX 557 f the loadng weght (Fg. 5) s stuated on the postons, B, and fxed on transportaton poston. t poston the ntal average pressure s 50 bar but at poston B t reaches tll 0 bar and at poston tll 45 bar. Puttng the force reactons F, F B and F n to the equaton (0) at poston the ntal pressure s 46.7 bar but at poston B t reaches tll 09.7 bar and at poston tll 56.9 bar were calculated. 5

4 ENINEERIN FR RUR DEVEPMENT Jelgava, For creatng of a smplfed model of the htch system and mounted mplement (Fg. 6) t s necessary to determne the coordnate of the hydraulc cylnder l 9 at dfferent weght postons (, B and ) on condton f F = F, (Fg. 3, 4) then: where l 8 coordnate of loadng weght, m. l 9 l8 = () The calculated l 9 for poston of the hydraulc cylnder coordnate s 0.9 m but for poston B t reaches 0.3 m and for poston t s 0.33 m. In further calculatons the average hydraulc cylnder coordnate (l 9 = 0.3 m) was used. In order to study the dynamc oscllaton of the tractor hydraulc htch-system n the experments an artfcal roughness test road was used. hangng the drvng speed from 3 km h - tll 3.7 km h - the forced oscllaton frequency changes from.65 z to.95 z. The results of the experments have shown that the resonance of oscllatons occurs at the drvng speed 7.8 km h - and the forced oscllaton angular frequency s 6.8 z. F N Z l 8 Z m, I l V l 9 N δ m, I F N l cl. 3 l V N K Fg. 6. Smplfed sde vew of three-pont htch mechansm: smplfed lftng lever; support; 3 hydraulc cylnder Fg. 8. Smplfed sde vew model of fscal three-pont htch mechansm ssumng that the tractor s equpped wth a tllage tool, the average transport speed ranges from 0 km h - to 5 km h -. If the tractor s movng through the road surface roughness 0.05 m - the angular frequency wll range from 8.73 z to 3.9 z. The free oscllaton frequency of the mplement aganst the tractor frame should be at least four tmes less than the forced oscllaton frequency, then the mounted tllage tools could be used [4] as oscllaton suppressors. Then the physcal model (Fg. 6) of the free oscllaton frequency wll be.8 to 3.7 z, expressed n the formula: λ = l V k, I where l V dstance to hydraulc cylnder, m; I Ʃ summary loadng tool moment of nerta, kg m ; k hydraulc cylnder stffness coeffcent, N m -. ssumng that the physcal model of the free oscllaton frequency s 3 z, then from the equaton () we can fnd the three-pont system hydraulc cylnder stffness coeffcent k at dfferent loadng weght postons (, B and ): Σ Σ l V () I k = λ, (3) The overall nerta moment of the physcal model at certan weght postons (, B and ) s obtaned (I = 37.4 kg m, I B = kg m, I = kg m ). The overall system sprng stffness coeffcent value at certan weght poston s (k = N m -, k B = N m -, k = 3376 N m - ). Knowng the statc pressure p of the tractor hydraulc system, when the 5

5 ENINEERIN FR RUR DEVEPMENT Jelgava, hydraulc htch loadng tool s at transport poston and the pressure peak values durng transport p, then dsplacement of the hydraulc cylnder s expressed wth the followng equaton: x = ( p p ) k, where p average pressure at statc mode, Pa; p pressure maxmum value at transport mode, Pa; cross-sectonal area of hydraulc cylnder, m. Sgnfcant pressure changes n the hydraulc htch system (wthout accumulators) occurred when the loadng weght was placed n postons B (45-75 bar) and (80-0 bar), but f the weght was placed at poston, the pressure values were n the range of bar, whch does not sgnfcantly affect the handlng of the tractor aggregate and the hydraulc system lfetme. For further calculatons the pressure values at the weght adjustment B and are used. Then the tractor hydraulc cylnder rod dsplacement of the reduced stffness wll be x B = 0.08 m, x = 0.0 m f the statc pressure of the tractor hydraulc htch system p B = 30 bar and p = 45 bar, but the pressure to whch the hydraulc systems are desgned to lmt p B = 50 bar and p c = 60 bar. Then the volume changes of the tractor hydraulc system at weght poston B ( V B = m 4 ) and ( V = m 4 ) are expressed as the equaton: V = x (5) From the calculatons the requred number of hydraulc accumulators was determned at ther fxed constructve volume, the hydraulc accumulators adabatc volume change graph was used (Fg. 9). (4) V, l p 0, bar p B p p B p p, p bar ydroaccumulator volume, l Fg. 9. dabatc characterstcs volume changes of hydraulc accumulators The dagram shows that at the hydraulc accumulator constructve volume 0.75 l and the loadng weght at poston B, where p B = 30 bar, but p B = 50 bar, the average volume changes are V l, but f the loadng weght s at poston, where p = 45 bar, but p c = 60 bar, the average volume changes are V 0038 l. s a result, to ensure that equaton (5), the calculated volume change would requre three hydraulc accumulators whch were loaded n to 30 bar. If there s extreme roughness of the road hydraulc accumulators would be loaded at hgher pressure, such as 50 bar. 53

6 ENINEERIN FR RUR DEVEPMENT Jelgava, onclusons. The free oscllaton frequency of the mplement aganst the tractor frame should be at least four tmes less than the forced oscllaton frequency, then the mounted tllage tools could be used as oscllaton suppressors.. Knowng the statc pressure of the tractor hydraulc system, when the hydraulc htch loadng tool s at transport poston and the permssble pressure peak values durng transport, the dsplacement and stffness of the hydraulc cylnder can be determned. 3. orrespondng to the stffness of the hydraulc cylnder the requred number of hydraulc accumulators at ther fxed constructve volume and chargng pressure s determned usng adabatc volume changes graphs. cknowledgement Paper was wrtten by fnancal support of European Structural Fund Support for Realzaton of Doctoral Studes n atva Unversty of grculture - realzed by Project Department of atva Unversty of grculture (contract no. 009/080/DP/.../09/IPI/VI/07). References. acekls-bertmans J., Prs V., Kronbergs E., Metla-Rozentals., Metla M. Physcal model of tractor mplement. In: Proceedng of the 8 th Internatonal Scentfc onference Research for Rural Development. Jelgava: U, 0, pp MS.Software orporaton. Workng Model D software, User s Manual (000). 3. acekls-bertmans J., Prs V., Jesko Z. Investgaton of Pressure scllaton n ydraulc tch-system. In: Proceedngs of the 6th Internatonal Scentfc onference Research for Rural Development. Jelgava: U, Николаи Е.Л. Теоретитеская механика, часть II. Государственное издательтво техникотеоретической литературы, Москава, с. 54