1、12FTM01AGMA Technical PaperBalancing NoLonger Smoke andMirrorsBy R. Hines Mifsud, HinesIndustries, Inc.Balancing No Longer Smoke and MirrorsRobin Hines Mifsud, Hines Industries, Inc.The statements and opinions contained herein are those of the author and should not be construed as anofficial action
2、or opinion of the American Gear Manufacturers Association.AbstractWe all experience unbalance and balancing in everyday life:S washing machine on “spin dry” vibrating due to unevenly distributed clothes;S ceiling fan swaying back and forth as it spins;S getting new tires and you are asked if you wou
3、ld like your wheels “balanced”.Picture or imagine:S spinning a Frisbee with a 1” sphere of clay stuck to one side;S swinging a stone around, overhead, on a string.In all the above examples,S the mass center and geometric center are misaligned;S there is an out of balance condition;S the object is no
4、t balanced or has unbalance.Whenanunbalancedobjectisspun,itvibratesinrhythmwiththerotationandtheforcescausedbyunbalanceare relative to the square of the rotational speed. Two key equations are:Unbalance = Mass (or Weight) x RadiusDisplacement = Unbalance/Total Mass (or Weight)Inthepagesthatfollow,th
5、roughstories,equationsandproblemsolving,balancingisdiscussedasmoremathand common sense and less smoke and mirrors.Copyright 2012American Gear Manufacturers Association1001 N. Fairfax Street, Suite 500Alexandria, Virginia 22314October 2012ISBN: 978-1-61481-032-23 12FTM01Balancing No Longer Smoke and
6、MirrorsRobin Hines Mifsud, Hines Industries, Inc.Introductory story Balancing is smoke and mirrorsIn the late 1970s a balancing machine salesman visited a customers plant who had just received a newbalancer from the salesmans competitor. The plant manager saidthey werevery happywith theirautomaticba
7、lancingmachineandofferedtoshowittothesalesman. Themanagerwalkedthesalesmanoutonthefloorand the two of them watched the operator and balancer in action.Theoperatorplacedapartonthebalancerandclosedthedoor. Thebalancerspunthepart,stopped,weldedonaweight,spunupagain,stopped,anddisplayed“goodpart”. Theop
8、eratorremovedthebalancedpart,putin a new part, and closed the door. The balancer spun up the part, stopped, welded on a weight, spun upagain, stopped, and displayed “good part”. This scenario was repeated several more times as the salesmanand the manager watched.The manager commented, “We just love
9、our new machine. All day long it balances parts by welding onweightsandputsoutgoodparts”. Thesalesmansuggestedhavingthe operatorplace a“balanced part”backinthebalanceragainjusttoseewhatwouldhappen. Sotheoperatorplacedthepreviouslybalancedpartbackin the balancer again and closed the door. The balance
10、r spun up the part, stopped, welded on a secondweight, spun up again, stopped, and displayed “good part”. The manager had the operator take anotherpreviously “balanced part”and putit intothe balanceragain. Again, thebalancer spunup thepart, weldedonanother weight, spun up again, and displayed “good
11、part”. Suddenly the manager was not so happy with hisbalancingmachine. Ithadbecomeclear;thismachinewasnotbalancingthepartsatall. Theyhadpurchasedan expensive welding machine to weld weights on their parts.Balancing Shedding some lightProductionManagerswhohavejustaddedanewbalancertotheirshoporproduct
12、ionlineoftenask“HowdoIknow if my part is balanced?” This question is usually asked after the person has had some basic training inbalancing and has started balancing some parts. They quickly realize that visually, there is no measurabledifference between a “balanced” part and an “unbalanced” part. T
13、hey can see the “balanced” part has someholes (or other correction) and the “unbalanced” part has no holes (or other correction.) The balancingmachine says, “Good part,” but they still feel a need to ask “How do I know if the part is REALLY balanced?”and“Whatifthebalanceriswrong?” Iwillattempttoansw
14、erthesequestionsinthepagesthatfollow,suchthat“if you can fog a mirror” you can probably understand balancing.Basic balancing principalsThe simplest form of unbalance iscalled “Forceunbalance”, “Staticunbalance”, or“Single planeunbalance”.Theseareallwordsforthesamething. Ifyoutakeanunbalancedgear,mou
15、ntitonashaft,andsetitbetweentwoknifeedges;theheavyspotwillrolltothebottom. Whenthispartisspunupandtheheavyspotisspinningaround,theforcesgeneratedbytheheavyspot,pullthegearinthedirection ofthe heavyspot. This issimilartospinningastoneonastring. Theforcescausedbytheunbalanceincreaseordecreaseasthesqua
16、reofthechangeintherotationalspeed. Unbalanceisusuallymeasuredandspecifiedinunitsofounce-inches,gram-centimeters, or gram-millimeters. Roughly, 1 oz-in = 72 g-cm = 720 g-mm. See Figure 1 and Figure 2.4 12FTM01Figure 1. Part with unbalanceFigure 2. Part with unbalanceSingle plane unbalanceThe equation
17、 for calculating the amount of single plane unbalance is:Unbalance = Mass (or Weight)RadiusThis is the mass of the heavy spot multiplied by the gear radius to the center of the heavy spot.Getsomeoilbasedmodelingclay,andweigha1grampiece.Addthe1grammassofclaytoabalancedgear,so the clay is located at a
18、 radius of 200 mm. The gear now has an unbalance of:Unbalance = 1 g200 mm = 200 g-mm(0.035 oz8 in = 0.28 oz-in)Reflecting on balancing machinesThe following is a very brief synopsis of balancing machines, past and present:Balancingways. A gear assembly (or a gear mounted on a shaft) is placed on two
19、 knife edges. The heavyside rolls to the bottom to show the unbalance.Bubblebalancers. Theaxisofthepartisheldverticallyandloosely. Thepartdoesnotrotateandabubbleisused to show the location of the unbalance or heavy spot.Soft suspension balancing machines. Hold the part suspended on a fine wire. The
20、part is spun at highspeeds (above the resonant frequency of the suspension) and the machine measures the displacement.5 12FTM01Partsofdifferentweightsrequireadifferentcalibration. Partswithlarge initialunbalance mustbe balancedinsteps at gradually increasing speeds.Hard suspension balancing machines
21、. Hold the part on a stiff suspension. The part is spun at relativelylow speeds (below the resonant frequency) and the machine measures the force caused by the unbalance.Calibration is the same for the full range of part weights. This suspension readily allows for on-machine cor-rectionandevenpartsw
22、ithlargeamountsofunbalancecanbebalancedonthefirstspin. Nonrotatingbalan-cing machines with a hard suspension use what is called a stiff pivot.Forces generated by the unbalance SmokescreenTo calculate the amount of force caused by unbalance in a rotating object, use the following equation:Funb= 1.77
23、(RPM/1000)2(oz-in)orFunb= 127.41(RPM/1000)2(g-cm)where:Funbis the centrifugal force generated by unbalance in a rotating object, in pounds oz-in is the amount ofunbalance in the residual heavy spot, in ounce-inches.In a gear assembly, operating at 1500 rpm, with 1 oz-in of unbalance:Funb= 1.77 (RPM/
24、1000)2(oz-in) = 1.77(1500/1000)21oz-in=4lbforceIn another gear assembly, with 4X the amount of unbalance, the Force is 4larger:Funb= 1.77 (RPM/1000)2(oz-in) = 1.77(1500/1000)24oz-in=16lbforceIn the first gear assembly, operating at 4X the original speed, the Force is 16X larger:Funb= 1.77 (RPM/1000)
25、2(oz-in) = 1.77(6000/1000)21oz-in=64lbforceThe problems caused by the unbalance are relative to the overall weight, age, and use of the gear assembly.Displacement = Distance between geometric axis and mass axisOn a balanced gear the geometric axis and mass axis are the same. The geometric axis is th
26、e axisdeterminedduringmanufacture;itisthecenteroftheshaftthatthegearismountedontospin. Themassaxisis the line or axis thatthe gearwill naturallyrotate aroundif itis tossedup intothe airand spun. SeeFigure 3.Figure 3. Balancing is alignment mass axis to geometric axis6 12FTM01Ifyouaddsomemasstothegea
27、rononeside,thecenterofmassormassaxisofthegearshiftsinthedirectionof the added mass. The distance between the mass axis and the geometric axis is called displacement.Displacement = Amount of unbalance/Total mass (or weight)Tocalculatethedisplacement,youtaketheamountofunbalance,200g-mm,anddivideitbyth
28、etotalmassofthe gear or gear assembly, 50 kg or 50,000 g.Displacement = 200 g-mm/50,000 g = 0.004 mm of displacement0.28 oz-in /1764 oz = 0.00016” (1.610- 4) of displacementBalancing = Alignment of geometric axis and mass axisGearsmaybebalancedbyaddingweight,180fromtheheavyspot,bywelding, riveting,a
29、dding epoxyputty,etc.,seeFigure 4. Whenwebalancethegearfromtheaboveexample,weremovematerialattheangleoftheheavy spot, either by drilling, milling, or grinding. If we precisely remove 1 gram of mass, at a radius of 200mm,attheangleoftheheavyspot;themassaxisandgeometricaxisarerealignedandthegearis“bal
30、anced”,see Figure 5. We could also remove 2 gram at a 100 mm radius or 20 gram at a 10 mm radius. Thesmallestcorrections for unbalance are made as close to the outer diameter of the part as possible.Figure 4. Welding on a weight to correct unbalanceFigure 5. Drilling holes to correct unbalance7 12FT
31、M01Balance toleranceOne method of setting a balance tolerance is using the API equation:Balance tolerance = 4W/N = 4Weight in pounds per stanchion/rpmUsing a 50,000g (110 lb) gear assembly, that rotates at 5000 rpm in use:455 lb/5000 rpm = 0.044 oz-in /stanchion = 32 g-mm/stanchionItisimportanttonot
32、ethatalthoughtherpmisusedintheequationtodeterminetheamountofunbalance;thisdoes not mean the part must be spun at5000 rpmto measurethe unbalance. Somebalancers donot spinatall; they measure the weight on all sides of the geometric center of the part.Unbalance = (1 g32 mm)/stanchion2 stanchions = 64 g
33、-mm = 0.088 oz-inThegearassemblywillhave64g-mmofunbalance,whetheritissittingstill,spinningat100rpm,3500rpm,or10,000rpm. Theforcescausedbytheunbalancewillbevastlydifferent,buttheamountofunbalanceremainsthe same. It is important to list the rpm assumed for a particular balance tolerance. Thebalance to
34、leranceisoften listed as “32 g-mm at 5000 rpm”. Again,the “5000rpm” isspecifying theoperating speedand doesnotrefer to the balancing speed. If the part will spin faster or slower than 5000 rpm in use, a different balancetolerance should be calculated.Theonlyreasontobalanceattheoperatingspeedisifpart
35、sorcomponentsof theassembly swingout orshiftatahigherspeed. Manyturbinesandcombineshavebladesorhammersthatshiftoutwardasthepartisspunuptotheoperatingspeed,sotheyshouldbebalanced atthat speed. Whencomponents areshifting atdiffer-entspeeds,theunbalanceisalsochanging. Forultraprecisionbalancing,replica
36、tingtheoperatingtemperat-ure and pressure for the part in use, should be considered. See Figure 6.Two plane unbalanceIn the case of two gears mounted on a shaft, one gear may have unbalance, caused by a heavy spot at oneangle, and the second gear may have a different amount of unbalance at a differe
37、nt angle. Thisis called“dy-namic unbalance”, “two plane unbalance”, or “a combination of couple unbalance and force unbalance”. Inthis case, the mass axis and geometric axis are no longer parallel but skewed. To correct the unbalance, theheavy spot on each gear will need to be removed.Figure 6. Crad
38、le style balancer with 2 stanchions to support the part8 12FTM01As the two correction planes are moved closer together, along the geometric axis, the amount of correctionrequired increases to infinity. The smallest corrections are made closest to the part outer diameter and withthe correction planes
39、 the furthest apart. See Figure 7.Importance of small variations where theres smoke.If a balanced gear with a mass of 50 Kg (110 lb) is mounted on a balanced shaft and the clearance, oreccentricity, is such that the gear is held off center by 0.00006” (or 610- 5inch) it will cause the assembly tobe
40、unbalanced.110 lb16 oz/lb610- 5= 0.106 oz-in (63 g-mm), 0.053 oz-in/stanchionComparethistoourbalancetoleranceof0.04oz-in/stanchion. Theassemblyisoutoftolerance,notbecauseof any unbalance in the gear but because the gear is held off center in the assembly. The shaft may haverunout (TIR) or clearance
41、of 0.00012” (1.210- 4)or0.003mm.Dontletyourtimespentbalancing“goupinsmoke”. Itisinefficienttobalancecomponentstotighttolerancesunless part dimensions, clearance, and runout are held to equally tight tolerances in the final assembly.Wherepossible,itisoftenbesttobalancethefullassemblyinitsownbearings;
42、radialorpreloadedaxial. SeeFigure 8 and Figure 9.Figure 7. Two plane unbalanceFigure 8. Small variations (exaggerated view)9 12FTM01Figure 9. Small variations (exaggerated view)Problem solvingProduction line gears mirror imagesWhen balancing gears in a production environment, it is important to cont
43、inually monitor the final “balanced”product. Are they actually balanced? Is the machine still calibrated and set up correctly? And how do youknow? Toconfirmthatthe“balanced”gears,inyourcrate,areactuallybalanced,youshouldtake5or10fromeach lot, back to the balancer and run the following tests:S Measur
44、e unbalance. Is it below tolerance?S Turn the part 180 on the tooling and measure unbalance again. Is it still below tolerance?S Measure each of the parts in this manner. If they are not all clearly below tolerance, you should run theentire lot through the balancer again. The moral check early and o
45、ften until you gain confidence in thebalancer.S Add a test weight, either to the spindle or a master part. Is the balancer calibrated? = does the balancerdisplay the amount of unbalance expected for the test weight?S Check the rest of the set up related to your part and correction methodIt is import
46、ant to keep “scrap” parts from getting accidentally mixed in with the “good” parts. There are manystandard, balancing machine features available to help with this, including:S password required to remove scrap parts from the balancerS locked scrap binsS ink marking only good parts or only scrap part
47、sS automatic transfer of parts to conveyors for good or scrap partsProblem solving gear assembly blowing smokeWhen balancing gears that will be assembled later, it makes sense to balance the assembly as well. Eventhough the individual gearsand shaftare balanced,the finalassembly mayhave unbalancedue
48、 toclearanceandrunout. See“ImportanceofSmallVariations”. Totestthatthegearsorassembliesaretrulybalanced,youcan use the list given in “Production line gears” = measure, turn 180 to measure again, and test calibration.Sometimes a gear assembly is balanced, the machine setup is changed and another part
49、 or assembly isbalanced, then the setup is changed again and the first assembly is put back into the balancer. Thereadingsmaybequitedifferentwhy? See“Importanceofsmallvariations”. Whenyouarereadingfinelevelsofunbal-ance,smallchangescanmakeabigdifference. Ifthebalancerbearingslocateinonelocationontheshaftone10 12FTM01timeandanotherlocationthenexttime,andthereisrunoutintheshaft,thenthegeometriccenterlinechangesandsodotheunbalancereadings. Forthisreason,itisoftenbesttobalancetheassemblyinitsownbearings;
