Pneumatic driven high pressure pumps (PDHPPs), having a number of considerable advantages in comparison to other types of high pressure pumps, are widely used in different sectors of modern industry. However, estimating the performance characteristics of a PDHPP is complicated due to the specifics of physical processes taking place during its operation. A mathematical model was developed to solve this problem. Two main operating modes are considered: for constant load and for constant volume, which cover the most common uses of the PDHPPs. The solution of the model made it possible to estimate how various parameters affect the operation of the pump. Thus, with an increasing pressure of compressed air, the volume flow grows at the pump outlet; with a higher pressure of the pumped liquid due to compressibility and a higher load on the drive cylinder, the flow, on the contrary, reduces. In case the PDHPP operates for the constant volume, the time of pressure increase grows with an increase of the required pressure and the value of this volume. The mathematical model and computational data can be used in the development of new and modification of the existing pumps.
Ñòàòüÿ ïîñâÿùåíà ìàòåìàòè÷åñêîìó ìîäåëèðîâàíèþ äèíàìè÷åñêèõ õàðàêòåðèñòèê ïðîìûøëåííîãî ïíåâìàòè÷åñêîãî ìàíèïóëÿòîðà-ïàíòîãðàôà ñ ëèíåéíûì äâèãàòåëåì îáîëî÷êîâîãî òèïàïíåâìîìóñêóëà. Ãëàâíîé ÷àñòüþ ïíåâìîìóñêóëà ÿâëÿåòñÿ àðìèðîâàííàÿ íåðàñòÿaeèìûìè íèòÿìè öèëèíäðè÷åñêàÿ îáîëî÷êà. Ïíåâìîìóñêóë îáëàäàåò âàaeíûìè ïðåèìóùåñòâàìè ïåðåä ïíåâìàòè÷åñêèì öèëèíäðîì-âîçìîaeíîñòüþ ïëàâíîãî ðåãóëèðîâàíèÿ ñêîðîñòè, áîëüøåé óäåëüíîé ìîùíîñòüþ è áîëüøèì ðåñóðñîì ðàáîòû. Ìàíèïóëÿòîðû ìóñêóëüíîãî òèïà áëàãîäàðÿ ñâîéñòâàì ïðèâîäà îáëàäàþò îáëåã÷åííîé êîíñòðóêöèåé ïî ñðàâíåíèþ ñ ìàíèïóëÿòîðàìè íà ïíåâìîöèëèíäðàõ, à òàêaeå ÿâëÿþòñÿ áîëåå áåçîïàñíûìè äëÿ îêðóaeàþùåé ñðåäû è ÷åëîâåêà. Òàêèå ìàíèïóëÿòîðû ìîãóò ïðèìåíÿòüñÿ â çàãðÿçíåííûõ è ýêñòðåìàëüíûõ ñðåäàõ, â îáëàñòÿõ ïðîèçâîäñòâà, ãäå íå òðåáóåòñÿ âûñîêîé òî÷íîñòè îïåðàöèé.  êà÷åñòâå ïðèâîäà ïíåâìàòè÷åñêîãî ìàíèïóëÿòîðà áûë ïðèìåíåí ïíåâìîìóñêóë ôèðìû FESTO. Íà ñåãîäíÿøíèé äåíü ìíîãèìè àâòîðàìè áûëè ðàçðàáîòàíû ìîäåëè ïîäîáíûõ ìàíèïóëÿòîðîâ ñ âûðàaeåíèÿìè äëÿ ñòàòè÷åñêèõ õàðàêòåðèñòèê ïíåâìîìóñêóëîâ FESTO, ñîäåðaeàùèìè áîëüøîå êîëè÷åñòâî ýìïèðè÷åñêèõ êîýôôèöèåíòîâ. Öåëüþ äàííîé ñòàòüè ÿâëÿåòñÿ ðàçðàáîòêà ìàòåìàòè÷åñêîé ìîäåëè äëÿ ïîëó÷åíèÿ äèíàìè÷åñêèõ õàðàêòåðèñòèê ïðîìûøëåííîãî ìàíèïóëÿòîðà ïðè ïîäúåìå è îïóñêàíèè ãðóçà ñ ïðèìåíåíèåì íîâîãî óòî÷íåííîãî âûðàaeåíèÿ äëÿ ñòàòè÷åñêèõ õàðàêòåðèñòèê ïíåâìîìóñêóëà. Íîâîå âûðàaeåíèå ñîäåðaeèò ìèíèìóì êîððåêòèðîâî÷íûõ êîýôôèöèåíòîâ, îòðàaeàåò ïðèíöèï ðàáîòû ïíåâìîìóñêóëà è îáåñïå÷èâàåò ñõîäèìîñòü ñ ýêñïåðèìåíòîì â ïðåäåëàõ 10 %. Ðàçðàáîòàííàÿ ìàòåìàòè÷åñêàÿ ìîäåëü äëÿ ïíåâìàòè÷åñêîãî ìàíèïóëÿòîðà ìóñêóëüíîãî òèïà òàêaeå ñîäåðaeèò äèôôåðåíöèàëüíûå óðàâíåíèÿ äâèaeåíèÿ ïðèâîäà ìàíèïóëÿòîðà, óðàâíåíèÿ èçìåíåíèÿ äàâëåíèÿ â ïîëîñòè ïðèâîäà, óðàâíåíèÿ èçìåíåíèÿ äèàìåòðà îáîëî÷êè è óãëà óêëàäêè íèòåé îáîëî÷êè. Ìîäåëü ïîçâîëÿåò îöåíèòü õàðàêòåð ïåðåõîäíûõ ïðîöåññîâ è âàaeíûå ïàðàìåòðû ïíåâìàòè÷åñêîãî ìàíèïóëÿòîðà, òàêèå êàê âðåìÿ è ñêîðîñòü ïîäúåìà è ñïóñêà ãðóçà, è ìîaeåò â äàëüíåéøåì ïðèìåíÿòüñÿ äëÿ ìàíèïóëÿòîðîâ àíàëîãè÷íûõ êîíñòðóêöèé.
Ñòàòüÿ ïîñâÿùåíà èññëåäîâàíèþ âîçìîaeíîñòè êîððåêòèðîâêè ïîëîaeåíèÿ âûõîäíîãî çâåíà ïíåâìîïðèâîäà ìóñêóëüíîãî òèïà óñèëèåì îïåðàòîðà â òî÷êå ïîçèöèîíèðîâàíèÿ. Ìíîãèå ðàáîòû äðóãèõ àâòîðîâ ïîñâÿùåíû ðàçðàáîòêå ïîçèöèîííûõ è êîíòóðíûõ ñèñòåì äëÿ óïðàâëåíèÿ ïíåâìîìóñêóëîì. Äëÿ ïðîìûøëåííûõ ìàíèïóëÿòîðîâ, èñïîëüçóåìûõ äëÿ ïîãðóçî÷íûõ èëè ðàçãðóçî÷íûõ ðàáîò, íå òðåáóåòñÿ ñîçäàíèÿ ñëîaeíûõ àâòîìàòè÷åñêèõ ñèñòåì óïðàâëåíèÿ. Ïîýòîìó â ðàáîòå ðàññìàòðèâàåòñÿ ìåòîäèêà âûâîäà ãðóçà â òðåáóåìóþ ïîçèöèþ ñ ïîìîùüþ ïðèëîaeåíèÿ äîïîëíèòåëüíîãî óñèëèÿ îïåðàòîðîì âðó÷íóþ. Äëÿ ðàçðàáîòêè ìåòîäèêè áûëà ïîëó÷åíà ìîäåëü, îñíîâàííàÿ íà ðàíåå ðàçðàáîòàííîé ìîäåëè äëÿ ïîäúåìà/îïóñêàíèÿ ãðóçà ïíåâìîìóñêóëîì.  ðåçóëüòàòå ìîäåëèðîâàíèÿ áûëè ïîëó÷åíû ãðàôèêè çàâèñèìîñòè óñèëèÿ îïåðàòîðà îò âåëè÷èíû äîïîëíèòåëüíîãî ïåðåìåùåíèÿ äëÿ ïíåâìîìóñêóëà DMSP-10 ïðè p M = var, m = const, à òàêaeå çàâèñèìîñòè äëÿ ðÿäà ðàçìåðîâ ïíåâìîìóñêóëà (DMSP-10, DMSP-20, DMSP-40) ïðè p M = const, m = var, è äàíû ðåêîìåíäàöèè. Äëÿ ýêñïåðèìåíòàëüíîé ïðîâåðêè ìåòîäèêè áûë ðàçðàáîòàí ñïåöèàëüíûé ñòåíä. Ýêñïåðèìåíò ïðîâîäèëñÿ äëÿ ïíåâìîìóñêóëà DMSP-10-400N ñ íà÷àëüíûì äèàìåòðîì 0,01 ì è äëèíîé 0,4 ì.  õîäå ýêñïåðèìåíòà áûëè ñíÿòû çàâèñèìîñòè óñèëèÿ îïåðàòîðà îò äîïîëíèòåëüíîãî ïåðåìåùåíèÿ â äèàïàçîíå îò 0,001 ì äî 0,01 ì ïðè ðàçíîì ìàãèñòðàëüíîì äàâëåíèè, p M = var è ïîñòîÿííîé ìàññå ãðóçà, m = const. Ðàñõîaeäåíèå ñ ðåçóëüòàòàìè ìîäåëèðîâàíèÿ íàõîäèòñÿ â ïðåäåëàõ 11 %. Ðàçðàáîòàííàÿ ìîäåëü è ïîëó÷åííûå çàâèñèìîñòè ïîçâîëÿþò îöåíèòü óñèëèÿ îïåðàòîðà íà ýòàïå ïðîåêòèðîâàíèÿ ïðèâîäà èëè ìàíèïóëÿòîðà è ïîäîáðàòü êîíñòðóêòèâíûå ïàðàìåòðû ïíåâìîìóñêóëà äëÿ îáåñïå÷åíèÿ òðåáóåìîãî äèàïàçîíà ïîçèöèîíèðîâàíèÿ.
 ñòàòüå ðàññìîòðåí âîïðîñ ìàòåìàòè÷åñêîãî ìîäåëèðîâàíèÿ ðàáî÷åãî ïðîöåññà ïíåâìîïðèâîäíûõ íàñîñîâ âûñîêîãî äàâëåíèÿ.  êà÷åñòâå îáúåêòà èññëåäîâàíèÿ ðàññìîòðåí íàèáîëåå ðàñïðîñòðàíåííûé è ïðîñòîé êîíñòðóêòèâíûé âàðèàíò ïîäîáíûõ íàñîñîâ-îäíîïîðøíåâîé íàñîñ îäíîêðàòíîãî äåéñòâèÿ, äëÿ êîòîðîãî ïðèâåäåíà ñõåìà è îïèñàí ïðèíöèï ðàáîòû.  ñîîòâåòñòâèè ñ ïðèíöèïèàëüíîé ñõåìîé ðàçðàáîòàíà ðàñ÷åòíàÿ ñõåìà, íà îñíîâàíèè êîòîðîé ñ ðÿäîì äîïóùåíèé ñîñòàâëåíà ìàòåìàòè÷åñêàÿ ìîäåëü, îïèñûâàþùàÿ ôèçè÷åñêèå ïðîöåññû, ïðîèñõîäÿùèå ïðè ðàáîòå íàñîñà. Äëÿ èññëåäîâàíèÿ íàñîñîâ ðàçëè÷íûõ òèïîðàçìåðîâ çà õàðàêòåðíûé ðàçìåð ïðèíÿò äèàìåòð ïëóíaeåðà íàñîñíîé ñåêöèè, à òàêaeå ââåäåíû êîýôôèöèåíòû ïðîïîðöèîíàëüíîñòè, ÷åðåç êîòîðûå âûðàaeåíû äèàìåòð ïîðøíÿ ïðèâîäíîé ñåêöèè è ðàáî÷èé õîä ïîðøíÿ. Èç ðåçóëüòàòîâ ìà-òåìàòè÷åñêîãî ìîäåëèðîâàíèÿ ñëåäóåò, ÷òî ñ óâåëè÷åíèåì õàðàêòåðíîãî ðàçìåðà íàñîñà ïîäà÷à åãî ðàñòåò, ÷òî ñîîòâåòñòâóåò õàðàêòåðèñòèêàì ñåðèéíî âûïóñêàåìûõ íàñîñîâ è ïîäòâåðaeäàåò àäåêâàòíîñòü ìàòåìàòè÷åñêîé ìîäåëè. Ïðè ýòîì ðîñò ïîäà÷è ñ ðîñòîì õàðàêòåðíîãî ðàçìåðà íîñèò íåëèíåéíûé õàðàêòåð. Íàèáîëüøåå âëèÿíèå íà ïîäà÷ó íàñîñà õàðàêòåðíûé ðàçìåð îêàçûâàåò ïðè ðàáîòå íàñîñà íà õîëîñòîì õîäó. Ñ ðîñòîì äàâëåíèÿ ïåðåêà÷èâàåìîé aeèäêîñòè íà âûõîäå íàñîñà âëèÿíèå õàðàêòåðíîãî ðàçìåðà ñíèaeàåòñÿ, òî åñòü åãî óâåëè÷åíèå íå ïðèâîäèò ê ñóùåñòâåííîìó ïîâûøåíèþ ïîäà÷è. Èññëåäîâàíèå âëèÿíèÿ äèàìåòðà ïîðøíÿ è åãî õîäà íà õàðàêòåðèñòèêè íàñîñà ïîçâîëèëî óñòàíîâèòü, ÷òî óâåëè÷åíèå õîäà íåñóùåñòâåííî âëèÿåò íà ïîäà÷ó, óâåëè÷åíèå äèàìåòðà ïîðøíÿ ïðèâîäíîé ñåêöèè ïðèâîäèò ê ñíèaeåíèþ ïîäà÷è ïðè ïðî÷èõ ðàâíûõ óñëîâèÿõ. Èç ïîëó÷åííûõ ðåçóëüòàòîâ ñëåäóåò, ÷òî ïðè ïðîåêòèðîâàíèè íîâûõ èëè âûáîðå ñåðèéíûõ íàñîñîâ ñëåäóåò òùàòåëüíî àíàëèçèðîâàòü âîçìîaeíûå óñëîâèÿ èõ ðàáîòû ñ öåëüþ îïðåäåëåíèÿ ðàöèîíàëüíûõ ïàðàìåòðîâ êàê ñàìèõ íàñîñîâ, òàê è ãèäðîñèñòåì â öåëîì. Ðàçðàáîòàííàÿ ìîäåëü ìîaeåò ïðèìåíÿòüñÿ ïðè ïðîåêòèðîâàíèè íîâûõ íàñîñîâ, à òàêaeå ïðè èññëåäîâàíèè ðàáîòû ñóùåñòâóþùèõ. Ïîëó÷åííûìè õàðàêòåðíûìè çàâèñèìîñòÿìè ìîaeíî ðóêîâîäñòâîâàòüñÿ ïðè âûáîðå ñåðèéíî âûïóñêàåìûõ îáðàçöîâ íàñîñîâ.
The article considers the issue of mathematical modeling of tandem pneumatic cylinders. Despite the fact that the mathematical description of the operation of drives with single-piston cylinders is considered in sufficient detail in the literature, the peculiarity of drives with tandem cylinders, namely the commutation of their working cavities with pneumatic discharge and exhaust lines through one pneumatic distributor, requires the formation of a certain approach to their mathematical description. The paper shows two developed versions of mathematical models that describe their work. The first option involves taking into account some conventional intermediate chambers behind the pneumatic distributor, where the division and combination of compressed air flows between the pneumatic distributor and the working cavities of the tandem pneumatic cylinder takes place. The second one (the simplified) considers the working cavities of the cylinder independently. Comparison of the results of mathematical modeling for two options showed a fairly significant difference in the time of movement of the piston of the cylinder. Moreover, it can be seen from the results that this difference is primarily associated with the distribution of air pressure between the intermediate chambers and the working cavities of the cylinder. According to the obtained results, it follows that when developing pneumatic drives and pneumatic actuators with tandem pneumatic cylinders, despite the complexity of the calculation, it is preferable to take into account in the mathematical model the intermediate chambers, where the division and combination of compressed air flows takes place. The developed model can be used in the design of pneumatic drives of various machines and mechanisms that use tandem pneumatic cylinders. This modeling approach can be used in the study of other multi-piston pneumatic engines or drives with several engines controlled by a single pneumatic switchgear.
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