the influence of overhung and axial loads at output shaft of universal ...

So, the choice of gear reducer with solid input shaft isbased on its load torque (T N ), or motor service factor(equat.5), as well as the permissive values of radial(F Ri perm ) and axial (F Ai perm ) loads of the free inputshaft of gearbox (for gearboxes with solid input shaft)and radial (F Ro perm ) and axial (F Ao perm ) loads of theoutput shaft (for both types of gear units), Fig.2.EMRFig.2. Schematic review of a loading of the output shaft ofgeared motor (EM – electric motor,R – reducer,F R – overhung load, F A – axial load)Additionally, the choice of gear reducer is also basedon thermal capacity (equation 2), where it should takeinto account that thermal capacity depends on theambient temperature, as well as on the size (andsometimes the shape and position of mounting) ofgear reducer. Its values can be obtained as a table ora diagram (Fig.3).P, kWΘΘ, °CFig.3. Graphic display of thermal capacity for particular sizeof gear reducerThermal capacity is a little different for geared motorand gear reducer with solid shaft (with classic input orwith input for IEC motors), because the fan of electricmotor of geared reducer provides some greater aircirculation and thus better cooling of reducer, while,due to the heating of electric motor, gearbox issubjected to somewhat larger heating from themotor. Sometimes these cooling and heatingquantities can be canceled, and sometimesunfortunately not, so they should be separately shownin the diagram (or table).In order to reduce the production cost of electricmotors, it is going on a maximum reduction ofmaterial consumption, which causes faster heating ofthe motor, so that today insulation material of class Fis installed in motors (which allows their heating up to150°C). Of course, the fan of electric motor does notallow reaching this temperature, but certainlybecause of higher temperatures of motor it comes to astronger heating of gear unit, especially if the motorhas bigger number of starting during an hour, andparticularly if it is a motor with a brake whichadditionally heats the reducer.Manufacturers of gear reducers are aware of thisproblem and take into account the thermal capacity oftheir gearboxes and try to increase it. They usuallymanage this by increasing the surface area of housing(i.e. by placing ribs on the surface of housing of gearP QTF RF Аunit), or by increasing the coefficient of heattransmission by defining of such forms of housing thatwill provide better air circulation around it, which isdriven by a fan of electric motor (this is only appliedfor geared motor), or by placing a special fan (bymanufacturers) on the worm shaft of worm andhelical-worm gear reducer.Operating regime of gear units has also major impacton their thermal capacity. For example, servicenature, operating time and number of starting canstrongly affect on the heating and thus the thermalcapacity of gear reducer. Especially differentcombinations of these parameters can strongly affecton the heating which is considered by service factor.The calculation of their actual impact is quite complexand can not be accurately described by mathematics,but very accurate values can be obtained by concretemeasurements.In the case that condition is not satisfied (equation 2),it is necessary to adopt a larger (stronger) gearbox,with a larger surface area participating in theexchange of heat, or it is need to use the system forcooling oil. For smaller sizes of gear reducers it ischeaper to select larger gearbox, while in medium andlarge size of reducer it is rational to use oil coolingsystem. The system consists of filter, circulatingpumps, overflow and several classic valves, piping andheat exchanger with fan and electric motors.The existence of an external overhung and axial loadon the output shaft, which permissive limit values canbe found in the catalogs of manufacturers of gearreducers, causes additional load of bearings of gearboxand the occurrence of additional friction in them(whose approximate value amounts F μR = μ F Rperm –friction in the bearing due to the external overhungforce, F μA = μ F Aperm = 0.4 μ F Rperm – friction in thebearing due to the external axial force) and it causesadditional heating of gear unit. Since there areoverhung and axial loads simultaneously acting,bearing load must not exceed 0.4, so there is F Aperm =0.4 F Rperm .Additional losses of power in the bearing (P L ) can becalculated by the equation:P L = 1.05 x 10 -4 M n (5)where:n – number of revolution of output shaft, min -1M – total frictional moment of bearingTotal frictional moment of bearing depends on severalfrictional moments as follows:M = M 0 + M 1 + M 2 + M 3 (6)where:M 0 – load independent frictional moment, NmmM 1 – load-dependent frictional moment, NmmM 2 – axial load-dependent frictional moment, NmmM 3 – frictional moment of seals, NmmThe frictional moment (M 0 ) is not influenced bybearing load but by the hydrodynamic losses in thelubricant and depends on the viscosity and quantity ofthe lubricant and also the rolling velocity. Itdominates in high-speed, lightly loaded bearings and iscalculated using:57

2 / 3 3( ν n) d−7M0 = 10 f0m(7) P 1 – the load determining the frictional moment, N forparticular bearing and load:if ν n ≥ 2000 or usingP 1 = 3 F Aa perm – 0.1 F R perm (11)−73M0 = 160 × 10 f0dm(8) Frictional moment (M 2 ) which depends mostly on theif ν n < 2000, where:axial load can be calculated as follows:d m – mean diameter of bearing (for particular bearingM 2 = f 2 F Aa perm d m (12)d m = 0.5 (d + D) = 0.5 (30 + 72) = 51 mm)where:f 0 – a factor depending on bearing type and lubrication f 2 – a factor depending on bearing design and(for particular bearing f 0 = 1)lubrication (for particular bearing design andν – kinematic viscosity of the lubricant at the lubrication f 2 =0.006)operating temperature, mm 2 /s (for usual operating The frictional moment (M 3 ) of the seals for a sealedtemperature Θ = 40°C)bearing can be estimated and for particular bearing itTable 1. Results of calculation of a typical worm gearreducer without a fan with shaft height 80 mmThermal capacity – P Q , W 1500 920 280Permissive overhung forceof output shaft – F R perm , N3260 5370 5300Permissive axial force ofoutput shaft – F A perm , N5520 7800 7800Actual permissive axialforce when overhung andaxial loads simultaneously 1304 2148 2120acting on output shaft – F Aaperm, NSpeed ratio – u 5.4 26 79Revolution number ofoutput shaft – n, min -1 259 54 18Mean diameter of bearing –d m , mm51 51 51Kinematic viscosity of thelubricant at the operating 53,6 210 544temperature – ν, mm 2 /sLoad independentfrictional moment – M 0 , 7.66 6.7 6.07NmmLoad-dependent frictionalmoment – M 1 , Nmm68.62 148.73 145.74Axial load-dependentfrictional moment – M 2 , 399.02 657.29 648.72NmmFrictional moment of seals– M 3 , Nmm18 18 18Total frictional moment ofbearing – M, Nmm493.3 830.71 818.53Additional power losses ingear reducer – P L , W13.41 4.71 1.55Percent ratio of powerPLlosses – ⋅100, %0.89 0.51 0.55PQThe load dependent frictional moment (M 1 ) arisesfrom elastic deformations and partial sliding in thecontacts and predominates in slowly rotating, heavilyloaded bearings. It can be calculated from:M 1 = f 1 P 1 d m (9)where:f 1 – a factor depending on bearing type and load forparticular bearing and load:0.55⎛ FRperm ⎞f1 = ( 0.0006K 0. 0009)⎜ ⎟(10)⎝ C0⎠is calculated as M 3 = 18 Nmm.For a smaller size of gear reducer (with shaft height h= 80 mm) orientation values of frictional moments andadditional losses of power in worm and helical-wormreducer are calculated and shown in Table. 1.Based on carried out calculation it follows that theadditional power losses in the gearbox, with themaximum permissive overhung and axial loads of theoutput shaft, amounts about 1%, so that they can becompletely ignored. On the basis of this, it is quitejustified that manufacturers of gear reducers, whenmake the instruction for selecting gearbox, ignore theinfluence of external loads on the thermal capacity ofgear unit and thus considerably simplify their selectionof gear reducer.CONCLUSIONBased on the conducted analysis it can be seen that theexternal overhung and axial loads of the output shaftof worm and helical-worm gear reducers have a smallinfluence on the change of thermal capacity, about 1%,so that manufacturers of gear reducers ignore it with afull right, i.e. they do not take external forces intoaccount when selecting gearbox and do not makecorrection in thermal capacity. Also, it would beinteresting to see what influence has only axial forceat the output shaft, because in this analysis axial loadis 0.4 of permissive overhung load, but when just axialforce is applied, it can be much bigger.REFERENCES[1] KUZMANOVIĆ, S., Universal Gear Reducers withCylindrical Gears, University of Novi Sad, Faculty ofTechnical Sciences, Novi Sad, 2009. (in Serbian)[2] Catalog SEW Eurodrive, Movimot Gearmotors, Edition04/2004[3] SKF General Catalogue, 2007[4] Catalog Nord, Constant speeds, G1000/2008,Getriebebau Nord, Hamburg[5] Catalog Siemens, Flender Gear Units, Catalog MD 20.1-2009AUTHORS & AFFILIATION1. Siniša KUZMANOVIĆ,2. Milan RACKOV1-2. UNIVERSITY OF NOVI SAD, FACULTY OF TECHNICAL SCIENCES,NOVI SAD, SERBIA58