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 mod­ule 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).

Rec­om­mend­ed Prod­ucts

High Speed Timer AT2

Input mod­ule timer AT2 to record tor­sion­al vi­bra­tions.


Pro­tec­tion sys­tem with di­ag­nos­tic and mon­i­tor­ing func­tion­al­i­ty.


Di­ag­nos­tic tool for high-speed anal­y­sis & in­tel­li­gent vi­su­al­iza­tion.


Fast & in­­­tu­it­ive on­­line/of­f­­line ana­lys­is soft­­ware for ef­­fi­­cient vi­su­al­iz­a­­tion.