Analysis of operating characteristics and internal power flows of compound cycloid transmissions

[T. P. Mačkić]

XII, 176 listova

U ovom radu predstavljen je matematički model koji omogućuje procenu osnovnog stepena iskorišćenja za dve varijante jednostepenog cikloprenosnika, od kojih je jedna sasvim nova koncepcija sa stepenastim ciklozupčanicima. Radi jednostavnije analize, klasična varijanta je nazvana „VD“, dok je varijanta sa stepenastim ciklozupčanicima nazvana „2V“. Objašnjeni su uslovi pri kojima može nastupiti samokočivost prenosnika. Prikazan je način određivanja toka relativne snage i izrazi za računanje stepena iskorišćenja svih radnih režima. Pokazano je da vratilo venca, za tip „VD“ i vratilo venca 1 (venca sa manjim brojem valjčića) za tip „2V“, predstavljaju zbirna vratila, a da su ostala dva vratila diferencijalna. Izvedeni su izrazi za intenzitete relativnih brzina spregnutih profila, u tački dodira, i intenzitete brzine klizanja i zbirne brzine kotrljanja. Definisani su obrtni momenti i sile koje deluju na elemente prostog cikloprenosnika i izvedeni izrazi za određivanje intenziteta sila. Sagledan je uticaj zazora i deformacija na veličinu i promenu kontaktnih sila. Predstavljen je teorijski model koji određuje gubitke usled postojanja relativne snage, kako za ograničene, tako i za diferencijalne jednostepene cikloprenosnike. Izrađen je algoritam i program, koji se bazira na predstavljenom modelu i izrazima za određivanje geometrijskih, kinematičkih, statičkih i triboloških veličina i urađena je analiza uticaja ovih veličina na osnovni stepen iskorišćenja. Uočene su mnogo bolje karakteristike, ako cikloprenosnici koriste igličaste ležajeve kao valjčiće na vencima. Prikazani su mogući režimi toka unutrašnje snage diferencijalnog cikloprenosnika i zavisnost ovih tokova od položaja zbirnog vratila i vratila ukupne snage. Uočeno je postojanje tzv. „beskorisne snage“, koja predstavlja manju parcijalnu snagu, koja je usmerena suprotno od efektivne snage. Definisane su strukture dvostepenih cikloprenosnika i način označavanja strukturnih slogova i vratila, uz korišćenje Volfovog simbola. Detaljno su sagledani mogući tokovi snage kroz ograničeni dvostepeni cikloprenosnik i objašnjen je uslov pojave podele i cirkulacije unutrašnje snage. Izdvojeno je ukupno 8 šema gde dolazi do podele snage i 13 šema u kojima se javlja cirkulacija snage. Definisana je metodologija za određivanje radnih karakteristika, gubitaka i unutrašnjih tokova snage složenih cikloprenosnika. Kreiran je program koji omogućava izbor varijante i vanjskog toka snage, unos ulaznih parametara, određivanje toka relativne snage kroz strukturne slogove i procenu vrednosti stepena iskorišćenja cikloprenosnika. Izvršena je analiza 21 varijante ograničenog dvostepenog cikloprenosnika. Izrađeni su fizički modeli cikloprenosnika i eksperimentalno provereni, kako bi se potvrdili matematički modeli i verifikovala definisana metodologija. Konstatovana je veoma dobra korelacija između teorijskih i eksperimentalnih rezultata, pri čemu faktor srednjih gubitaka ne prelazi 3%, za sva merenja.

In this paper, a mathematical model is presented that enables the assessment of the basic efficiency for two types of simple cycloid drive train, one of which is a completely new concept with stepped cycloid gears. To simplify the analysis, the classical type is named "VD", while the type with stepped cycloid gears is named "2V". The conditions under which self-locking can occur are explained. The method of determining the internal power flow and expressions for calculating the efficiency of all operating modes are presented. It is shown that the central gear shaft, for the type "VD" and the central gear shaft 1 (the central gear with a smaller number of rollers) for the "2V" type, are summation shaft, and the other two are differential shafts. Expressions were derived for the intensities of the relative speeds at the point of contact of the coupled profiles and the intensities of the sliding speed and the total rolling speed. Torques and forces acting on the elements of a simple cycloid drive train are defined and expressions for determining the intensity of forces are derived. The influence of clearances and deformations on the size and change of contact forces is shown. A theoretical model is presented that determines losses due to the existence of rolling power, both for simple and differential cycloid drive trains. An algorithm and program based on the presented model and expressions for determining geometric, kinematic, static and tribological parameters were developed and the influence of these parameters on the basic efficiency was analyzed. Much better characteristics have been observed if the cycloid drive trains use needle bearings as rollers on the central gears. The possible modes of the internal power flow of the differential cycloid drive train and the dependence of these flows on the position of the summation shaft and the total power shaft are shown. It was observed the existence of the so-called "futile power", which represents a smaller partial power, which is directed opposite to the effective power. The structures of bicoupled cycloid transmmisions and the way of denotation of a simple cycloid drive train and shafts are defined, using the Wolf symbol. Possible internal power flows through the constrained bicoupled cycloid drive trains are reviewed in detail and the condition for the appearance of division and circulation of internal power flow is explained. A total of 8 schemes where power division occures and 13 schemes in which power circulation occurs were singled out. A methodology for determining the operating characteristics, losses and internal power flows of compound cycloid transmissions is defined. A program was created that enables selection of the variant and external power flow, entry of input parameters, determination of the flow of rolling power through the structural cycloid drives and evaluation of the efficiency of the bicoupled cycloid drive train. An analysis of 21 variants of the constrained bicoupled cycloid drive trainс was performed. Physical models of bicoupled cycloid drive trains were created and experimentally verified, in order to confirm the mathematical models and verify the defined methodology. A very good correlation between theoretical and experimental results was established, with the average loss factor not exceeding 3% for all measurements.

složeni cikloprenosnici, stepen iskorišćenja, samokočivost, beskorisna snaga, Volfov simbol, cirkulacija snage, relativna snaga.

compound cycloid transmission, efficiency, self-locking, futile power, Wolf symbol, circulating power, rolling power.

621.83/.85 (043.3)

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