3.! Lateral a nd Tor sional Vibrations: An elastic system that is

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3.! Lateral a nd Tor sional Vibrations: An elastic system that is subject to ext ernally appl ied forces and the periodic motion that results from s uch f orces is forced vibrations.

1 3.! Lateral a nd Tor sional Vibrations: An elastic system that is subject to ext ernally appl ied forces and the periodic motion that results from s uch f orces is forced vibrations. These systems a re evaluated in two ways: One is t orsio nally for analyzing the eff ects of torsional v ibrat i o ns, the other is late r ally f or determining the infl uence o f lateral vibrations. In the case of a torsional system, t he system vibratory motion occurs as a result o f e ach s pring ma ss system coupled to each other. Thus a coupled system has to be analyze6 in its entirety by first separating its properties into a s eries of discrete s prings and masses. This method is k nown when appl ied to a multimass system a s using lumped parameters. These parameters are developed into a model in order to a nalyze the system as a whole and solve its tors i onal mechanical vibr ations. It is i mportant to note that this result is only as good as its model. In f act, t he process of lumping parameters could be t he l argest source of errors. Sinc e the gearbox itself is only one of several e l ements in a coupled train, it is clearly not wi thin the gear manufac t urer 's control as to the result of t he system a nalysis torsionally nor be an influenc e on e ither the modeling data for which results can be concluded. For this reason, torsiona l vibration problems cannot be the responsibility of the gear manutacturer. Coupled machinery for l a teral analysis deals with equations of motion that are completely separate f rom each other. Each principa l mode respond s independently to a freque nc y e q uation. As a resul t, e ach coupled element c a n i ndependently be anal y zed and a deter mination o f t h e inf luence o f critical s peeds with r espect to running s ~ e ed s can be determined. If a potential speed problem exists, chang e s in mass, mass distribut i on, stiffness and allowable unbalance c an be adj usted. An undamped lateral critical speed anal ysis s hould be cond uc ted f i rst to determine if a po t ential res onance problem exists. If necessary, a damped analysis c a n be conducted f o r a closer predicti on of true responsiveness. A f orce d r o tor response analysis may be req uired when a very accurate result i s necessary where critical s peeds cannot be avoided wi t h r espect to running speeds or when design restraints limi t the a b i lity to change phys ical parameters. Refe r e nce Appendix C for information on evaluation of lateral d ynamics.

3. 8 Tors i onal and Lat e ral Vibrations : An elast ic system that is s ub j ect to ext ernally applied forces and t he perlodic ruo t ion t hat r esults from s uch forces is f orced vibrations.

2 3. 8 Tors i onal and Lat e ral Vibrations : An elast ic system that is s ub j ect to ext ernally applied forces and t he perlodic ruo t ion t hat r esults from s uch forces is f orced vibrations. These system s a re evaluated in t wo ways: One i s t orsionally tor analyzing the effects of torsional v ibrations, t h e o ther is lat erally for determining the inf l uence of late ral v ibrati ons. Because of the wide vari ation of gear driven systems, Section 6 o f this standard outlines areas where proper assessment o f t he system may be necessary and appropri a te responsibility between the gear manufacturer a nd customer clearly assigned.

6. Vibration and Sound : 6.1 Vibrat ion Analysis. Vibrat i on of any component of the gear unit c an result i n additional d y namic loads being superi mpose d on the no rmal o perating load.

3 6. Vibration and Sound : 6.1 Vibrat ion Analysis. Vibrat i on of any component of the gear unit c an result i n additional d y namic loads being superi mpose d on the no rmal o perating load. Vibrat ion of sufficient amp l itude may result in i mpact loading of t he gear teeth, i n terfere n c~ in the gear me sh or damage to close clearance parts of the gea r unit. Whe r e unusual torque variati o ns develop peak loads whicn exceed the applica t ion hors epower by a rat io grea t er t han the tactor Ca or Ka t specified for the application, t he magnitude and frequency of s uch torque variat10ns should be evaluated wi th r egard to the e ndurance and yiel d properties of t he ma ter i als used to ensure p r oper selection. The types o f vibrati on wh ich are g ener ally of concern f or gear units are the t orsio nal, l ateral and axial modes of t he rotating elements s ince the se can have a d irect influence on tne tooth load. Of these, the t wo t h a t are normally rev iewed analytic a lly during design are t h e lateral critical speeds of t he gear unit r otat1ng shafts and t he torsional critical f req uencies ot the powe r transmission system. b.2 TorSIonal Vi bration Analysis. Any tors i onal vibr ation analysis must consider the c omplete sys t em includ ing p r ime mover, gear unit, driven equipment, ana co uplings. Dynamic loads Imposed on a gear un i t from t o r s i onal vibrations are the result o f t he dynamic behavior of the entire system and not the gear unit alo ne. Tnus a co u~le d system has to be analy zed In its enti re t y by first separating its propert i e s into a series of discrete springs and ma s s e s. This me t hod is known when applied to a multimass system as us ing l ump e d par ameters. These parameters are developed i nto a mode l in ord e r to analyze the system as a who l e and solve i ts t orsional mechani cal vibrations. I t is i mport ant t o not e tha t this result i s o nly as good as its model. In f act, the p r ocess ot l umping parameters c o uld be the largest source of errors. SInce the gearbox i t s e lf is only one of several elements in a coupled train, it i s c learl y no t within the gea r manuf actur er' s control as t o the resul t of the system a na lysis torsionally nor be an i n f l uence on either the model ing data for wh ich r e s ults can be concluded. For this reason, torsional vibration problems cannot be t he responsibility of the gear manufacturer. The gear unit manufacturer is seldom the system des igner and i n normal c ases t he g e a r uni t manufacturer is responsible only f or provid i ng mass elastic data to the system designer.

4 6.3 Lateral Vi bration Analysis. Hi gh s p e ed gear arives should have the rotors analyzed for lateral critical speeds. Lateral critical speeds are defined as rotative speeds where an actual peak in dynamic vibrations of the rotor o c curs. Critical speeds can occur when any harmonic forcing f unct i on of the system, such as rotating unbal ance, i s equal to o r near a responsive natural frequency of t he r o tor-bearing system. Coupled machinery for lateral analysis deals with equations of motion that are completely separate from each other. Each principal mode responds independently to a frequency equation. As a result, each coupled element can independently be analyzed and a determination of the influence of cri t ica l speeds with respect to running speeds can be determined. If a potential speed problem exists, changes in mass, mass distribution, stiffness and allowable unbalance can be adjusted. An undamped later al critical speed analysis should be conducted first to determine if a potential resonance problem exists. If necessary, a damped analysis can be conducted for a closer prediction of true respons iveness. A forced rotor response analysis may be r equired when a ver y accurate result is necessary wher e critical speeds cannot be avo i ded with respect to running speeds or when design restraint s limit the ability to change physical parameters. Reference Append ix C for information on evaluation of lateral dynamics Analysis Requirements. Most h igh s peed g e ar drives will have their rotors s upported by fluid film type bearings. This bearing type has spri ng and d amping characteristics in the X and Y axis and XY and YX c ross coupled spring a nd damp i ng coefficients. These spring and damp ing coefficients, wh e ther tor oil film or r oller type bearings must be accurately d e termine d as a function of applied load a nd speed as a first step in rotor dynamics analysis. An accurate rotor mass elastic mode l is essential, including mass, center of gravity, and polar and transvers e moments of inertia of any mounted couplings on the rotor.

5 6.4. Vibration Measurement. The filtered vibration amplitude l evels shall not exce ed the r e commended l i mits give n in AGMA 6000-A88, unless otherwise agreed to between the purchaser a nd manufacturer Sound Measurement. The sound level measure ments and limits shall be in accordance with AGMA 295 unless othe rw is~ ag r eea upon uy the p urchaser and manufact urer.

Structural Dynamics Lecture 2. Outline of Lecture 2. Single-Degree-of-Freedom Systems (cont.)

Structural Dynamics Lecture 2. Outline of Lecture 2. Single-Degree-of-Freedom Systems (cont.) Outline of Single-Degree-of-Freedom Systems (cont.) Linear Viscous Damped Eigenvibrations. Logarithmic decrement. Response to Harmonic and Periodic Loads. 1 Single-Degreee-of-Freedom Systems (cont.). Linear