Rota­tion­al Vibra­tions - Tor­sion­al Ana­lys­is

Rota­tion­al vi­bra­tions in ro­tat­ing com­pon­ents under al­tern­at­ing tor­sion­al loads, such as in gas tur­bines or in the drive shafts of com­bus­tion en­gines, place high de­mands on pro­tec­tion and dia­gnost­ic sys­tems:

  • High sampling rates in the MHz range
  • Time-syn­chron­ous re­cord­ing of all meas­ured vi­bra­tion para­met­ers
  • In­teg­ra­tion of ma­chine op­er­at­ing data into the  meas­ure­ment data stream

Moreover, tor­sion­al vi­bra­tions are often not, or only weakly trans­mit­ted to the ma­chine hous­ing, es­pe­cially if the ma­chine has no gear­box. This means that in order to de­tect tor­sion­al vi­bra­tions one should not rely on ac­cel­er­o­met­ers/vi­bra­tion sensors po­si­tioned on the hous­ing. Only dir­ect meas­ure­ment of the tor­sion­al vi­bra­tions helps to ac­cur­ately de­term­ine the ac­tu­al com­pon­ent stress.

This is ex­actly where the IfTA ap­plic­a­tion for ro­ta­tion­al and an­gu­lar vi­bra­tions and tor­sion ana­lyses comes in. We offer a com­bin­a­tion of per­fectly matched hard­ware and soft­ware com­pon­ents for high-res­ol­u­tion and real-time ana­lyses in an ex­clus­ive bundle with our IfTA Dyn­aMaster and IfTA Ar­gusOMDS sys­tem solu­tions. The tor­sion­al vi­bra­tion data is seam­lessly in­teg­rated into our eco­sys­tem, dir­ectly of­fer­ing all of our proven func­tion­al­it­ies - in­clud­ing pro­tec­tion logic, re­li­able 24/7 data stor­age and in­tu­it­ive visu­al­iz­a­tion.

The core ele­ments of this ap­plic­a­tion are the fiber-optic sensor IfTA LMM2, the High Speed Timer AT2 and the IfTA DSP, which per­forms the ana­lys­is in real-time. To­geth­er with the ana­lys­is soft­ware IfTA TrendView­er, this en­ables the pre­cise iden­ti­fic­a­tion of dan­ger­ous tor­sion­al vi­bra­tion con­di­tions in order to en­sure safe ma­chine op­er­a­tion as well as an in­crease of the re­li­ab­il­ity and longev­ity of your sys­tem.

Rota­tion­al Vibra­tion
  • Meas­ure­ment
  • Ana­lys­is
  • Mon­it­or­ing
  • Pro­tec­tion

Ex­tens­ive and high-pre­ci­sion angle-re­lated eval­u­ation of ro­ta­tion­al and an­gu­lar vi­bra­tions:

  • Identi­fy tor­sion­al and an­gu­lar vi­bra­tions
  • Com­bined soft­ware and hard­ware mod­ule con­sist­ing of the fiber-optic sensor LMM2, the award-win­ning high speed timer  AT2 & the ana­lys­is soft­ware IfTA TrendView­er
  • Flex­ible design and com­pat­ib­il­ity with com­mon sensor prin­ciples

Avail­able as hard- & soft­ware bundle in com­bin­a­tion with our sys­tem solu­tions Dyn­aMaster and IfTA Ar­gusOMDS.

Tor­sion­al Vibra­tions

One speaks of tor­sion­al vi­bra­tions when a ro­tat­ing sys­tem os­cil­lates about one of its axes. In doing so, a part of the ro­ta­tion­al en­ergy usu­ally leads to the peri­od­ic­al twist­ing - or tor­sion - of a com­pon­ent in the os­cil­lat­ing sys­tem.

Hands-on Know­ledge Tor­sion­al Vibra­tions

You are op­er­at­ing a ma­chine where you ex­pect or have even ob­served tor­sion­al vi­bra­tions. Ini­tial model cal­cu­la­tions or meas­ure­ments at the ma­chine hous­ing were able to de­term­ine the tor­sion­al vi­bra­tions' char­ac­ter­ist­ic fre­quen­cies with­in an ap­prox­im­ate range. Now you want to meas­ure these vi­bra­tions and mon­it­or their amp­litudes dur­ing op­er­a­tion. In the fol­low­ing, we will show you how to pro­ceed ef­fi­ciently and give an­swers to the most im­port­ant ques­tions:

  • What does a typ­ic­al meas­ure­ment setup look like?
  • What should I pay at­ten­tion to when se­lect­ing a sensor?
  • How do I choose a suit­able rotary en­coder for my ap­plic­a­tion?
  • Which spe­cific­a­tion of my meas­ure­ment sys­tem de­term­ines the achiev­able meas­ur­ing ac­cur­acy?

Meas­ure­ment Setup

what be­longs where? How are the in­di­vidu­al com­pon­ents called?

In order to meas­ure tor­sion­al vi­bra­tions, you es­sen­tially need two com­pon­ents, as shown in Fig­ure 1: (1) A rotary en­coder and (2) a rotary de­coder. The en­coder codes the tor­sion­al vi­bra­tion in­form­a­tion into a spe­cif­ic out­put sig­nal, which is de­coded by the rotary de­coder and con­ver­ted into the de­sired out­put quant­ity ( ro­ta­tion­al speed, an­gu­lar/speed or ac­cel­er­a­tion vari­ations). Since such a sys­tem eval­u­ates not only the tor­sion­al vi­bra­tion com­pon­ent but also the sta­tion­ary ro­ta­tion­al speed, it is re­ferred to as ta­cho­met­er.

The rotary en­coder usu­ally con­sists of a gear wheel at­tached to the shaft to be meas­ured, which is scanned by a dis­tance sensor (the en­coder sensor). In doing so, a sig­nal is gen­er­ated that shows the gear wheel's char­ac­ter­ist­ic con­tour - con­sist­ing of val­leys and plat­eaus. In order to gen­er­ate an an­gu­lar ref­er­ence, often an­oth­er wheel is used, which has only one tooth or groove and thus defines a zero angle. By means of these two gear wheels, the shaft's cur­rent po­s­i­tion can then be de­scribed uniquely and pre­cisely at any point of time. As an al­tern­at­ive to a gear wheel, de­pend­ing on the ap­plic­a­tion, so-called zebra tape or a per­for­ated disc is often used. If you are un­cer­tain which meth­od is ap­pro­pri­ate for you, we will be happy to as­sist you.

The sig­nals gen­er­ated by the rotary en­coder are trans­mit­ted to the rotary de­coder. In IfTA meas­ure­ment sys­tems, the de­coder con­sists of the timer mod­ule IfTA AT2 and a di­git­al sig­nal pro­cessor, the IfTA DSP. The AT2 mod­ule de­term­ines the tim­ing of the val­leys/plat­eaus with high pre­ci­sion and, based on this, the DSP cal­cu­lates the cur­rent shaft speed as well as the an­gu­lar speed vi­bra­tions (or the de­sired out­put para­met­er). A spe­cial fea­ture of our sys­tems is that they sup­port an angle ref­er­ence in­teg­rated in the de­coder. This elim­in­ates the need for a ded­ic­ated gear wheel to define a ref­er­ence angle: the meas­ure­ment setup gets sim­pler and saves space. In­stead of an ad­di­tion­al gear wheel, the ex­ist­ing one is, for ex­ample, provided with one wider tooth or groove. Our de­coder can de­tect this spe­cial po­s­i­tion and use it as an angle ref­er­ence.

Sensor Selec­tion

Laser, Hall ef­fect or eddy cur­rent?

As de­scribed above, in the en­coder a prox­im­ity sensor scans a gear wheel. Depend­ing on the en­vir­on­ment­al con­di­tions and ac­cur­acy re­quire­ments, an ap­pro­pri­ate sensor must be se­lec­ted spe­cific­ally for each ap­plic­a­tion. Laser-based sensors, such as our LMM2 mod­ule, offer high focus and pre­ci­sion, but have re­l­at­ively high re­quire­ments on the gear wheel's sur­face con­di­tion. In ad­di­tion, they can only op­er­ate in clean en­vir­on­ments that are free of oil, dust and the like.  Sensors based on the Hall ef­fect or eddy cur­rent prin­ciple are less sens­it­ive in this re­gard. They, how­ever, do not have such a nar­row focus. This means that they can de­tect sharp con­tours less pre­cisely, but - be­cause of that - are less sus­cept­ible to noise. We will again be happy to ad­vise you on this sub­ject if re­quired.

En­coder Selec­tion

Max­im­um res­ol­u­tion of the tor­sion­al vi­bra­tion fre­quency de­term­ines Basic en­coder Prop­er­ties

Let us as­sume that you have as part of your pre­lim­in­ary ana­lys­is de­term­ined a max­im­um ex­pec­ted tor­sion­al vi­bra­tion fre­quency of 800 Hz. To be on the safe side, you there­fore want to se­lect a de­coder that can eval­u­ate tor­sion­al vi­bra­tions up to 1 kHz. Your shaft ro­tates con­stantly at 50 Hz. Based on this spe­cific­a­tion we will show you in the fol­low­ing, how to se­lect a suit­able en­coder.

Be­fore we pro­ceed with the prac­tic­al steps, we should first cla­ri­fy some fun­da­ment­al con­cepts. The basic unit of the meas­ur­ing prin­ciple presen­ted here cor­res­ponds to a com­plete ro­ta­tion of the shaft to be meas­ured. There­fore, all rel­ev­ant pro­cesses are re­ferred to a full shaft ro­ta­tion . In par­tic­u­lar, this means that vi­bra­tions are no longer spe­cified in cycles per time (fre­quency do­main) but in cycles per shaft ro­ta­tion (order do­main). As shown in Fig. 2, a vi­bra­tion mode of order 1 has ex­actly one cycle per ro­ta­tion. The same ap­plies to os­cil­la­tions of high­er fre­quency. In order to con­vert quant­it­ies from the order to the fre­quency do­main, it is there­fore ne­ces­sary to mul­tiply them by the ro­ta­tion­al speed.


The en­coder sampling rate N de­scribes how many meas­ur­ing points per ro­ta­tion are re­cor­ded by the en­coder. In the case of the gear wheel, it cor­res­ponds ex­actly to the num­ber of teeth. It is im­port­ant to un­der­stand that the sampling rate in the order do­main ("meas­ur­ing points per ro­ta­tion") has a fixed value, namely N. In the time do­main, how­ever, the sampling rate ("meas­ur­ing points per time") scales with the ro­ta­tion­al speed, namely ro­ta­tion­al speed mul­ti­plied by N. High-fre­quency phe­nom­ena can there­fore only be in­vest­ig­ated at suf­fi­ciently high ro­ta­tion­al speeds.

Just as in the time do­main, the Nyquist-Shan­non sampling the­or­em ap­plies in the order do­main, as well: A sig­nal of order O can be re­con­struc­ted ex­actly from a se­quence of equidistant samples if it was sampled with an en­coder res­ol­u­tion of N > 2 * O. In Fig. 2, right column, this cri­terion is eval­u­ated for three dif­fer­ent mode or­ders as an ex­ample. Since tor­sion­al vi­bra­tions are not ne­ces­sar­ily re­lated to the meas­ure­ment prin­ciple's basic unit, they gen­er­ally occur at a non-in­teger order, e.g., 3.42. In such a case, round­ing up to the nearest whole num­ber is re­com­men­ded for de­term­in­ing the min­im­um en­coder res­ol­u­tion, i.e., 4 in this case.

Equipped with this know­ledge, the en­coder re­quire­ments for the afore­men­tioned ex­ample can be cal­cu­lated as fol­lows:

  • A vi­bra­tion of 1 kHz at a speed of 50 Hz cor­res­ponds ex­actly to a mode of order O = 1000/50 = 20.
  • As a res­ult, ac­cord­ing to Nyquist-Shan­non, an en­coder with a res­ol­u­tion of N > 2 * 20 = 40 is re­quired.
  • In prac­tice, it has been proven to add ap­prox. 25 % to this num­ber. Ac­cord­ingly, an en­coder with at least N = 50 teeth/slots should be se­lec­ted.

Meas­ur­ing Ac­cur­acy

Ac­cur­acy is de­term­ined by sampling rate - not bit depth

A vari­ety of factors in­flu­ence the ac­cur­acy dur­ing a meas­ure­ment, for ex­ample, the sig­nal-to-noise ratio or the se­lec­tion and mount­ing of the en­coder. In the fol­low­ing, how­ever, we will deal spe­cific­ally with the in­flu­ence of the di­git­iz­a­tion of the ana­log sensor sig­nal.

By defin­i­tion, the res­ol­u­tion of a meas­ure­ment cor­res­ponds to the smal­lest change that can be de­tec­ted in the para­met­er being meas­ured. For voltage meas­ure­ments, the res­ol­u­tion is de­term­ined by the bit depth of the ana­log-to-di­git­al con­vert­er. An 8-bit con­vert­er can en­code 256 dif­fer­ent voltage val­ues, while a 12-bit con­vert­er can en­code 4096. This means that the 12-bit con­vert­er has a high­er res­ol­u­tion than the 8-bit con­vert­er, be­cause the former can de­tect smal­ler changes in the voltage sig­nal. As a res­ult, the meas­ur­ing ac­cur­acy in­creases with the bit depth of the con­vert­er - at least if other factors are neg­lected.

However, in the con­text of tor­sion­al vi­bra­tion meas­ure­ments, it is not the amp­litude in­form­a­tion of a voltage sig­nal that is to be di­git­ized, but the exact times at which the sig­nal amp­litude falls below or ex­ceeds a pre­vi­ously defined threshold value (trig­ger event). This is il­lus­trated in Fig. 3: Whenev­er the ana­log input sig­nal crosses the threshold value, the di­git­al out­put sig­nal changes its state from "high" to "low" or vice versa. Based on the di­git­al sig­nal gen­er­ated in this pro­cess, the point of time of these trig­ger events can sub­sequently be de­term­ined with an ac­cur­acy of Δt. The value of Δt is de­rived from the sampling fre­quency. Our IfTA AT2 timer mod­ule samples at a fre­quency of 100 MHz, al­low­ing trig­ger events to be de­tec­ted with an ac­cur­acy of 10 ns.


The trig­ger res­ol­u­tion defines which voltage val­ues can be set for the trig­ger threshold. Our IfTA AT2 timer mod­ule of­fers 12 bits here, i.e. 4096 pos­sib­il­it­ies in the range from -25 V to +25 V. It is im­port­ant to un­der­stand that this value does not say any­thing sig­ni­fic­ant about the ac­cur­acy of a tor­sion­al vi­bra­tion meas­ure­ment. The time res­ol­u­tion de­scribed above is the rel­ev­ant factor here.




Ad­vant­ages of the IfTA Ap­plic­a­tion for Tor­sion­al Meas­ure­ment

High pre­ci­sion

The core mod­ule of this ap­plic­a­tion, the IfTA High Speed Timer AT2, provides a tem­por­al res­ol­u­tion of 10ns. This cor­res­ponds to a fre­quency of 100 MHz and al­lows us to identi­fy and ana­lyze dif­fi­cult to de­tect vi­bra­tions such as ro­ta­tion­al, an­gu­lar and tor­sion­al vi­bra­tions.

Reli­able pro­tec­tion

In com­bin­a­tion with the IfTA Dyn­aMaster or IfTA Ar­gusOMDS, e.g. long-term re­cord­ing, triggered data stor­age with pre- and post-trig­ger as well as pro­tec­tion shut­downs are pos­sible.

Flex­ib­il­ity & Com­pat­ib­il­ity

Fa­cil­it­ated and flex­ible design and com­pat­ib­il­ity with com­mon sensor prin­ciples. High input im­ped­ance (e.g. pho­to­di­odes can be con­nec­ted dir­ectly). Eas­ily and quickly ad­justable trig­ger threshold en­ables auto­mat­ic track­ing under changed meas­ure­ment con­di­tions.

Save costs

An­a­log sig­nals, e.g. from com­mon dis­tance sensors, can be fed in dir­ectly and can be re­solved in the pi­co­second range via threshold value-defined trig­gers, i.e. there is no need for ex­tern­al pro­cessing elec­tron­ics for ana­log in­com­ing sig­nals. This res­ults in cost sav­ings and high­er sig­nal qual­ity.

The Ap­plic­a­tion's core, the High Speed Timer AT2

The out­stand­ing pre­ci­sion and ver­sat­il­ity of the input card res­ul­ted in the award of the messtec + sensor mas­ters (2nd place) in 2017.

Ana­lys­is of Rota­tion­al Vibra­tions - Us­ab­il­ity Example

At first, the High Speed Timer AT2 meas­ures im­pulses with high tem­por­al res­ol­u­tion (top left in the fig­ure).

Depend­ing on the spe­cif­ic con­fig­ur­a­tion, this raw data can be used to cal­cu­late sig­nals for speed, vi­bra­tion angle, vi­bra­tion speed or vi­bra­tion ac­cel­er­a­tion, for ex­ample. Like any other input sig­nal, these can be used for fur­ther ana­lyses, e.g. FFT. For sub­sequent ana­lys­is pur­poses, these quant­it­ies are cor­rel­ated in char­ac­ter­ist­ic plots.

In the ex­ample we have chosen, the high-res­ol­u­tion raw data (top left) is used to cal­cu­late the vi­bra­tion angle (top right). From this, for ex­ample, har­mon­ics can be de­term­ined, in this case with a strong amp­litude of the 4th order (bot­tom left). A Camp­bell plot also il­lus­trates the res­ults of the fre­quency ana­lys­is (bot­tom right: spec­trum plot­ted over the ro­ta­tion­al speed).

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