OPTIMAL ADDENDUM COEFFICIENTS OF CYLINDRICAL INVOLUTE GEARING FROM POINT OF VIEW ITS EFFICIENCY

The optimisation of gearboxes, namely of teethed wheels is still valid subject of scientific research. The development of software products for multiparametrical optimisation at Machine Engineering Faculty University of Technology Bratislava was concluded into successful solutions of arbitrary defined objective functions. In the article are given the results of teeth gears optimisation with involute gearing from point of view of its efficiency. The calculation included the complete geometrical and strength check of gearing according to DIN 3990 level B / ISO 6336 as the restriction conditions in original way.The optimisation of gearboxes, namely of teethed wheels is still valid subject of scientific research. The development of software products for multiparametrical optimisation at Machine Engineering Faculty University of Technology Bratislava was concluded into successful solutions of arbitrary defined objective functions. In the article are given the results of teeth gears optimisation with involute gearing from point of view of its efficiency. The calculation included the complete geometrical and strength check of gearing according to DIN 3990 level B / ISO 6336 as the restriction conditions in original way

Possible Ways of Reducing the Number of Gears in Universal Gear Units

This paper analyzes possibilities of reducing the number of necessary gears in the family of universal motor gear reducers with helical gears, since both the production and storage of a large number of different gears cost a lot and impose a great burden for any gear manufacturer, as it can be seen from literature [1,2] that focuses on this problem. The paper particularly emphasizes the necessity of narrowing down the assortment of gear reducers and the possibility of changing the design solution between the pinion and the electric motor as they represent the basic possibilities for reducing the number of necessary gears. The paper also points out the need for a special selection of preferred gear ratios and corresponding gears as one of the possibilities for reducing the total number of gears. This can certainly result in faster delivery of a gearbox with the preferred gear ratio

Tooth flanks scoring resistance of non-involute teeth profiles in plane toothed cylindrical gears

Rad prikazuje rezultate teorijskih i eksperimentalnih istraživanja otpornosti na zaribavanje bokova zubaca cilindričnih zupčanika sa konveksno-konkavnim oblicima profila zubaca. Postoje opšti osnovni izrazi, zasnovani na temperaturnom kriterijumu, koji su primenljivi za sve zadate oblike kontaktnih površina bokova zubaca cilindričnih zupčanika. Izrazi koji su dobijeni na osnovu teorije su ilustrovani rezultatima ispitivanja na zaribavanje prema FZG metodi ispitivanja zupčanika na uređaju sa zatvorenim kolom snage (DIN 51354).The paper presents results of theoretical and experimental research into the scoring resistance of plane convex-concave gears. There are generalized basic relations of the integral temperature criterion for all kinds of path of contact in defined plane cylindrical gears given. Theoretically obtained relations are illustrated by the results of the scoring tests according to the FZG method (DIN 51354)

Determinističke i probabilističke metode u određivanju pravilno spregnutih čelnih profila zubi cilindričnih zupčanika

Currently design and clasification of gearing comes almost exclusively from a so-called “technological method”. Its means that for a known form of one wheel (mostly a hob tool), a correctly mating form of a tooth flank of a mating wheel is determined. This commonly known and simple method positively describes also the path of contact of mating profiles. Such method defined already by Buckingham [1], when he wrote “The simplest way has been to define any definite conjugate gear-tooth system is to specify the form and size of its basic rack. There is a definite relation between a gear-tooth profile and its path of contact so that if either one is given, the other is fixed.” In the article, the authors from a given shape of path of contact by design and classification of cylindrical gearing. There are two totally different methods introduced to solve this task, namely deterministic and stochastic one.Suvremeno oblikovanje i podjela ozubljenja temelje se gotovo isključivo na takozvanoj “tehnološkoj metodi’’. To znači da se za poznati oblik zuba jednog zupčanika (najčešće alata u obliku odvalnog pužnog glodala) određuje oblik zuba pravilno spregnutog profila drugog zupčanika. Ova opće poznata jednostavna procedura određuje istovremeno i zahvatnu crtu spregnutih profila. Istu metodu definirao je Buckingham [1], kada je napisao “Najjednostavniji način za definiranje proizvoljnog pravilno spregnutog zupčastog para je da se definira oblik i veličina njegove osnovne ozubnice. Postoji jednoznačan odnos između oblika profila zuba zupčanika i oblika njegove zahvatne crte, što znači da ako je jedan od njih zadan, drugi je jednoznačno određen.” Autori u članku prikazuju način oblikovanja i podjelu ozubljenja cilindričnih zupčanika na osnovi poznatog oblika zahvatne crte. Predstavljene su dvije u potpunosti različite metode za rješavanje ovog zadatka, i to jedna deterministička, a druga stohastička

Optimization of HCR gearing geometry using generalized particle swarm optimization algorithm

Posebna vrsta osnovnog evolventnog profila nestandardnog ozubljenja zove se ozubljenje s visokim stupnjem prekrivanja (HCR-ozubljenje), kada je stupanj prekrivanja veći uvijek su barem dva para zubi u dodiru (εα ≥ 2) i gdje jedinica dopune visine nije jednaka onoj za standardno ozubljenje, tako da se visina zuba povećava i veća je od jedan ha* > 1. Kada se rabi HCR-ozubljenje, nije potrebno postići veći kapacitet opterećenja zupčanika, ali ipak postoji veći rizik od smetnji zbog veće visine zuba. Prednost HCR-ozubljenja je veća otpornost (razdioba opterećenja se dijele na više parova zuba u isto vrijeme) i niža razina relativne buke ozubljenja, koja se može značajno smanjiti uporabom stupnja prekrivanja εα koji je cijeli broj. HCR profili su složeniji od standardnih evolventnih profila, oni imaju veću sklonost za pojavu smetnji, istaknut vrh debljine, ali i potkopavju zub tijekom proizvodnje (primarna proizvodna smetnja). Zbog povećanog dodatka visine, postoji veća mogućnost da se javljaju neke smetnje ili zašiljeni vrh zuba. Zato treba spriječiti ove pogreške i provjeriti jesu li sve jednadžbe i ograničenja zadovoljeni. Dana metoda pronalaženja optimalnih rješenja za h*a1, h*a2 i x1 koristi generalizirani algoritam optimizacije roja čestica (GPSO algoritam) i MATLAB kao program za optimizaciju. Ova optimizacija roja čestica je vrlo brz i pouzdan način.Special kind of basic involute profile of non-standard gearing is called high contact ratio (HCR) gearing, when the contact ratio is higher and there are always at least two pairs of teeth in contact (εα ≥ 2) and where unit addendum height is not equal one like for standard gearing, so the tooth height is increased and it is bigger than one ha* > 1. When HCR gearing is used, it is not necessary to achieve a greater gear load capacity, but nevertheless there is a greater risk of interference due to a greater height of tooth. Advantage of the HCR gearing is also a higher resistance (load distribution is shared on the more pairs of teeth at the same time) and lower relative noise level of gearing, which can be significantly reduced by using integer HCR factor εα. HCR profiles are more complicated than standard involute profiles, they have greater predisposition for occurring interference, pointed tip thickness, but also undercut of teeth during the production (primary production interference). Due to increased addendum height, there is larger possibility of occurring some interference or pointed tooth tip. Therefore it should prevent these errors and check if all equation and constraints are satisfied. The given method of finding optimal solutions for h*a1, h*a2 and x1 uses Generalized Particle Swarm Optimization Algorithm and MATLAB as a program for optimization. This GPS optimization is a very fast and reliable method