ROTA­TION­AL AND TOR­SION­AL VIBRA­TION ANALY­SIS

WHAT ARE ROTA­TION­AL AND TOR­SION­AL VIBRA­TIONS?

Tor­sion­al vibra­tions are mechan­i­cal vibra­tions that occur due to peri­od­ic torque fluc­tu­a­tions on a rotat­ing shaft. The torque fluc­tu­a­tion leads to a speed fluc­tu­a­tion which is super­im­posed on the aver­age rota­tion­al speed. A char­ac­ter­is­tic fea­ture of tor­sion­al vibra­tions is that the fre­quen­cies of the speed and torque fluc­tu­a­tions are usu­al­ly syn­chro­nous with the rev­o­lu­tions of the shaft. Instead of fre­quen­cies, one then speaks of rota­tion­al har­mon­ics — also called orders.

WHAT CAUS­ES TOR­SION­AL VIBRA­TIONS ?

Tor­sion­al vibra­tions are caused by non-uni­for­mi­ties:

• Non-uni­form dri­ve torque
fluc­tu­a­tions on the dri­ve side e.g. in the case of the inter­nal com­bus­tion engine due to the non-con­tin­u­ous com­bus­tion and the crank­shaft geom­e­try.

• Non-uni­form brak­ing torque
fluc­tu­a­tions on the dri­ven side e.g. in rec­i­p­ro­cat­ing com­pres­sors due to non-uni­form forces dur­ing com­pres­sion.

• Trans­mis­sion error
A non-uni­form trans­mis­sion occurs, among oth­er things, in the uni­ver­sal joint due to the geom­e­try when the shafts are not par­al­lel. Or due to back­lash in the dri­ve train when the direc­tion of rota­tion changes or the pow­er flow changes when the input and out­put sides change. In gears (gear and belt), geo­met­ri­cal devi­a­tions (such as eccen­tric­i­ty and tooth pro­files) as well as defor­ma­tions under load cause torque and speed fluc­tu­a­tions. In addi­tion, the stick-slip effect (fric­tion­al vibra­tion), for exam­ple, can cause non-uni­form trans­mis­sion.

HOW CAN SPEED FLUC­TU­A­TIONS AND THE COR­RE­SPOND­ING VIBRA­TION ANGLES BE VISU­AL­IZED?

NO SPEED FLUC­TU­A­TION
img. 1
img. 2

With peri­od­ic, sinu­soidal speed fluc­tu­a­tion, the gear does not run at a con­stant speed dur­ing one rev­o­lu­tion. On one half of the rev­o­lu­tion it is slow­er than the aver­age speed and on the oth­er half it is faster.

SPEED FLUC­TU­A­TION
img. 3
img. 4

The speed fluc­tu­a­tion itself is not vis­i­ble in the trick shot, but its effect is. Math­e­mat­i­cal­ly, this effect is the inte­gral over the speed vari­a­tion and is called the vibra­tion angle. The vibra­tion angle (red line in img. 4) is the peri­od­ic advance and delay of the non-uni­form­ly rotat­ing shaft in rela­tion to a uni­form motion. This vibra­tion angle is clear­ly vis­i­ble in the trick shot as the swing­ing motion of the gear. Here it is a vibra­tion angle of 6 degrees, which cor­re­sponds exact­ly to one tooth pitch.

WHAT SHOULD BE CON­SID­ERED IN THE CASE OF TOR­SION­AL VIBRA­TIONS?

Elas­tic­i­ty of the involved ele­ments
The elas­tic­i­ty of com­po­nents always leads to tor­sion­al vibra­tions when torque and speed fluc­tu­ate.
In this process, the shafts twist or warp in them­selves. When the nat­ur­al fre­quen­cies are excit­ed,
there is a risk of res­o­nance over­shoot.

Vibra­tion prop­a­ga­tion
The vibra­tions are trans­mit­ted to oth­er struc­tures via the bear­ings of the shafts.

Tor­sion­al vibra­tions depend on :
- Tem­per­a­ture (oil, damp­ing, ther­mal expan­sion)
- Aging and degree of wear  
- Load con­di­tion and rota­tion­al speed

WHAT ARE THE EFFECTS OF TOR­SION­AL VIBRA­TIONS?

Tor­sion­al vibra­tions cause prob­lems in terms of:

Com­fort issues
All types of noise and vibra­tion (NVH) prob­lems

Safe­ty 
Wear and com­po­nent fail­ure due to aging (fatigue) or over­stress­ing

Accu­ra­cy 
Trans­mis­sion errors of rotary motion; shafts do not run per­fect­ly syn­chro­nized

Effi­cien­cy 
Addi­tion­al ener­gy input that does not con­tribute to the dri­ve

WHY DO TOR­SION­AL VIBRA­TIONS HAVE TO BE MEA­SURED?

Accu­rate mea­sure­ment and analy­sis of tor­sion­al vibra­tions is a require­ment in engi­neer­ing and vehi­cle devel­op­ment depart­ments. In recent years, tor­sion­al exci­ta­tion sources have increased in pow­er and com­plex­i­ty. In addi­tion, the use of lighter mate­ri­als in engines and dri­v­e­lines makes them more sus­cep­ti­ble to tor­sion­al exci­ta­tions. Con­tin­u­ous opti­miza­tion of the engine, dri­ve­train, and rotat­ing com­po­nents is required to mit­i­gate the result­ing com­fort and dura­bil­i­ty issues in new vehi­cle and rotat­ing com­po­nent devel­op­ment. Dri­ve­train sim­u­la­tion mod­els can help devel­op­ment engi­neers pre­dict and iden­ti­fy tor­sion­al res­o­nance sce­nar­ios, for exam­ple, and design out the prob­lems dur­ing the devel­op­ment phase. Detailed and accu­rate data is essen­tial for fine-tun­ing, check­ing and con­firm­ing all vehi­cle improve­ment mea­sures. With­out appro­pri­ate data, accu­rate and mean­ing­ful mod­el­ing is not pos­si­ble, as dynam­ic test data is a pre­req­ui­site for para­me­ter­i­za­tion and ver­i­fi­ca­tion of mod­el­ing assump­tions.

WHERE DO TOR­SION­AL VIBRA­TIONS OCCUR?

Tor­sion­al vibra­tions occur in rotat­ing com­po­nents, motors and pow­er­trains.

WHICH SEN­SORS ARE USED TO MEA­SURE SPEED?

The mea­sure­ment of the rota­tion­al speed or angu­lar veloc­i­ty is usu­al­ly car­ried out by means of

  • mag­net­ic scan­ning of an exist­ing gear or an eas­i­ly mount­ed toothed disk
  • Using an opti­cal or mag­net­ic incre­men­tal encoder on the shaft
  • Scan­ning of black and white mark­ings by means of laser optics.

The use of the respec­tive sen­sor depends on the par­tic­u­lar appli­ca­tion, the envi­ron­men­tal con­di­tions as well as the required res­o­lu­tion.

ROTA­TION­AL AND TOR­SION­AL VIBRA­TIONS ANALY­SIS PRIN­CI­PLES AND MEA­SURE­MENT

We pro­vide spe­cial­ist equip­ment for the mea­sure­ment and analy­sis of tor­sion­al vibra­tion. The company‘s core prod­uct is the Rota­tion Analy­sis Sys­tem (ROTEC-RAS), a pc-based sig­nal acqui­si­tion and analy­sis sys­tem [8]. Tor­sion­al vibra­tion mea­sure­ment re-quires detec­tion of the times of occur­rence of equal­ly spaced angu­lar posi­tions around a rotat­ing shaft (e.g. mea­sure­ment of gear tooth or encoder pulse pas­sage fre­quen­cies). Sev­er­al types of trans­duc­ers can be used to pro­vide pulse sig­nals which are pro­por­tion­al to a shaft‘s rota­tion­al fre­quen­cy. The RAS speed chan­nels use dig­i­tal coun­ters with a high-fre­quen­cy clock (12 GHz, 40 bit) to record the time inter­vals between puls­es. This angu­lar sam­pling pro­vides a fixed num­ber of data points per rev­o­lu­tion which is inde­pen­dent of the rota­tion­al speed. The momen­tary angu­lar veloc­i­ty of rotat­ing shafts is thus mea­sured, i.e. the mean veloc­i­ty from pulse to pulse. The vibra­tion angle and the angu­lar accel­er­a­tion are obtained by inte­gra­tion and dif­fer­en­ti­a­tion of the mea­sured angu­lar veloc­i­ty respec­tive­ly. These two cal­cu­la­tions are impor­tant when inves­ti­gat­ing tor­sion­al vibra­tion prob­lems. Anoth­er impor­tant cal­cu­la­tion is the angle between two speed chan­nels (angle of twist of a shaft, trans­mis­sion error between two cou­pled shafts). The RAS analy­sis soft­ware, work­ing pri­mar­i­ly in the angle domain, pro­vides com­pre­hen­sive analy­ses in the time and spec­tral domain (FFT order and fre­quen­cy analy­sis). The RAS‘s near real-time capa­bil­i­ty with dis­play and analy­sis of all chan­nels allows adjust­ment of test para­me­ters dur­ing the mea­sure­ment. Apart from dig­i­tal, 10GHz speed chan­nels, RAS sys­tems are also fit­ted with addi­tion­al mea­sur­ing chan­nels which facil­i­tate con­di­tion­ing and cap-ture of a vari­ety of ana­logue sig­nals with sam­pling rates up to 400kHz. The dis­tinc­tive fea­ture of ROTEC-RAS is the phase-matched acqui­si­tion of all sig­nals: speed sig­nal acqui­si­tion with vari­able dis­cretiza­tion of time (angle-equidis­tant sam­pling) and acqui­si­tion of ana­logue sig­nals – accel­er­a­tion, force, pres­sure, torque, etc. – at con­stant time inter­vals (time-equidis­tant sam­pling).

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