High web speeds of present papermaking and finishing processes set extremely high demands for control systems by means of which the movement of the paper web is controlled on a path formed of drums, cylinders, rolls and other corresponding rotating members. To avoid web breaks and/or to adjust the properties of the paper web, the con- trol system requires specific measurement information on the rotating speeds of the members that are in contact with the paper web. In many cases it is significant to know especially the accurate mutual difference between the angular speeds of the rotating members as well as their peripheral speeds, which speed difference affects the forces exerted on the paper web by said members.

Precise control of the rotating speeds is especially important in the reeling up process of a paper web. In the reeling up process a continu- ous paper web of several meters in width, which is passed directly from a paper machine or from a finishing treatment apparatus connected thereto in a continuous, on-line type manner, or from a separate off-line type finishing treatment apparatus, is reeled to form successive machine reels around reeling cores, so-called reel spools. These large machine reels, which substantially comply with the width of production of paper, function as some kind of intermediate storages for the paper web between off-line type finishing processes. Successful reeling up process is essential to maintain the quality of the paper web stored on the machine reels as high as possible for further processing.

There are various known reel-up solutions, of which a reel-up type generally used at present in the reeling up of large-sized, large-mass machine reels is a so-called centre drive assisted reel-up. The afore-

mentioned reel-up type utilizes either a stationary or moving reeling cylinder equipped with a centre drive and a growing machine reel, which is in a so-called nip contact with said reeling cylinder in the reeling station. The paper web is guided on the machine reel via a nip formed between said reeling cylinder and the machine reel that is being formed. To improve the control of the reeling process in centre drive assisted reel-ups the reel spool functioning as a reeling core for the machine reel is provided with a separate centre drive of its own in addi- tion to the fact that the aforementioned reeling cylinder is rotated with a centre drive.

In centre drive assisted reel-ups the properties of the machine reel formed in the reeling process are affected during the reeling process in a known manner by means of control variables, which are, for example the web tension of the paper web determined before the nip and the reeling cylinder, the nip force of the reeling nip (linear load) and the pe- ripheral force exerted on the paper web by the centre drive of the machine reel.

The earlier patent application WO 99/37567 by the applicant discloses a method for controlling the reeling up in centre-drive assisted reel-ups, in which method the radial density of the machine reel that is being formed is determined constantly or at specific intervals, and said den- sity value of the machine reel is utilized in the feedback adjustment of the reeling up process, thus aiming at an optimal radial density profile determined beforehand for each paper grade.

To determine the radial density of the machine reel, information on the change in the mass of the machine reel as a function of time is re- quired. The change in the mass can be calculated when the width and grammage of the paper web as well as the speed of the web reeled on the machine reel are known. The speed of the web is attained in a known manner for example by measuring the speed of rotation of the reeling cylinder having a standard diameter. In view of determining the mass of the machine reel, the width of the web can be considered con- stant and known. It can also often be assumed that the grammage of the web that is reeled is constant and known, but it is also possible to

measure the grammage by means of known methods, if necessary, for example by means of a sensor positioned before the reeling cylinder in the travel direction of the web.

In addition to the change in the mass of the machine reel, information on a concurrent change in the volume of the machine reel is also necessary for determining the density of the machine reel.

One method that is known as such and disclosed for example in the aforementioned patent application WO/9337567 of the applicant for determining the volume of a machine reel is based on the accurate determination of the speed of rotation of the machine reel when the speed of the paper web entering on the machine reel is known. This method is based on the fact that when the diameter and radius of the machine reel grows, the length of the periphery of the machine reel also changes, which change can be detected as a slow deceleration of the speed of rotation of the machine reel.

One known method for determining the mutual difference in the speed of the rotating members is based oh the comparison of the number of pulses of pulse sensors installed on the rotating shafts of said mem- bers in the above-described manner. In the following, the measurement of the difference in the speed of rotation of the machine reel and the reeling cylinder is by way of example described in a manner that is dis- closed for example in the article"Measurement of Paper Roll Density during Winding", L. G. Eriksson, C. Lydig, J. A. Viglund, TAPPI Journal, January 1983, pp. 63-66.

The reeling cylinder is equipped with a first high resolution pulse sen- sor, said first pulse sensor producing for example 5000 pulses per each full revolution of the reeling cylinder. The machine reel that is being formed is equipped with a second pulse sensor, said second pulse sensor producing for example one pulse per each full revolution of the machine reel. By determining the number of pulses obtained from said first pulse sensor during the time between every two succes- sive pulses by the second pulse sensor, it is possible to detect and determine the changes in the speeds of rotation of the machine reel

and the reeling cylinder with respect to each other. The absolute speeds of rotation can be determined by calculating the number of pulses during a specific known period of time.

In such a situation in which the machine reel and the reeling cylinder that are in nip contact with each other have an equal peripheral speed, the pulses obtained from said first pulse sensor during the time between two successive pulses of said second pulse sensor illustrate the length of the periphery of the machine reel that is being formed in relation to the known peripheral length of the reeling cylinder, wherein the measurement can be utilized for determining the radius/diameter of the machine reel, and thereby for determining the volume as well. This information can be utilized further in a known manner to determine the density of the machine reel, and to adjust the reeling up process thereby.

The accuracy of the measurement utilizing pulse sensors in the above- described known manner is, however, always restricted by the number of pulses produced by said second sensor per one revolution, said number of pulses being typically in the order of 5000 pulses/revolution in sensor types suitable for industrial conditions. Because it is not pos- sible to limitlessly increase the number of pulses, i. e. the resolution of the pulse sensors, attempts have been made to avoid this problem by increasing the measurement time, i. e. calculating the number of pulses given by the pulse sensor per several revolutions of the machine reel, thus calculating an average value for the measurement result over several revolutions to improve the measurement accuracy. This of course results in that the real-time quality of the adjustment system utilizing the measurement result suffers, because the measurement result is thus obtained after a delay.

The main purpose of the present invention is to produce a new method for measuring the mutual rotating movement of rotating members, by means of which method it is possible to obtain a significantly better measurement accuracy when compared to the above-described so- lution according to the state of the art, and that in contrast to the state of the art the accuracy of said method is not restricted by the maximum

number of pulses produced by the pulse sensors per revolution.

Furthermore, it is an aim of the invention to provide simple measuring equipment that implements the method and is easy to use.

To attain this purpose, the measuring method according to the inven- tion is primarily characterized in what will be presented in the charac- terizing part of the independent claim 1.

The measuring equipment according to the invention, in turn, is pri- marily characterized in what will be presented in the characterizing part of the independent claim 15.

The other dependent claims will present some preferred embodiments of the invention.

It can be said that the basic idea of the invention is the insight that the accuracy of the measurement can be significantly improved by shifting from the calculation of the number of pulses to determination of the ac- curate event time of the pulses. Thus, the improved measuring accu- racy is not at all based on increasing the number of pulses given by the pulse sensors per one revolution, but good measurement accuracy can now be achieved by means of sensors producing only one pulse per revolution.

According to the method, the first rotating member that is under exami- nation is equipped with a first pulse sensor to produce pulses in pro- portion to the angular position of said first rotating member and the second rotating member is in a corresponding manner equipped with a second pulse sensor to produce pulses in proportion to the angular po- sition of said second rotating member. The aforementioned pulse sen- sors can produce one or more pulses per each full revolution of the member that is being measured.

The specific event times of the pulses produced by the first and the second pulse sensor are registered and they are compared with each other at intervals of one full revolution of the first rotating member used as a reference in a manner described hereinbelow.

A fit and interpolation parameters are determined for each last measured pulse of the pulse sequence produced by the first pulse sen- sor over one or more successive intervals preceding said last pulse, said intervals being formed between those successive pulses regis- tered by the first pulse sensor that correspond to the same angular po- sition in the successive revolutions of the first rotating member. Said fit and interpolation parameters further enable an accurate determination of the angular position of the first rotating member at any moment of time within said interval/intervals.

A position is now determined by means of the fit and the interpolation parameters for each pulse of the second pulse sensor that is detected during the interval last determined for the first rotating member, said position indicating the angular value of the first rotating member func- tioning as a reference during the event time of said pulse.

By means of the positions corresponding to the same angular position in the successive revolutions of the second pulse sensor and in the successive revolutions of the second rotating member it is further pos- sible to determine a progression (difference between the positions i. e. angular values) in relation to the first rotating member used as a reference. In other words by means of the invention it is possible to ac- curately determine the angle/distance revolved by the second rotating member per each revolution, or several revolutions, if necessary, of the first rotating member functioning as a reference.

In the simplest embodiment of the invention the first and second pulse sensor installed in connection with the first and second rotating mem- ber both produce one pulse per each revolution of the member that is being measured.

The invention is not, however, restricted solely to said embodiment, but in connection with both rotating members it is possible to install pulse sensors producing one or more pulses per revolution. In such embodi- ments of the invention, a fit and interpolation parameters are separately determined for each pulse corresponding to a different angular position

and being produced by the first pulse sensor functioning as a reference for each revolution, and each pulse produced by the second pulse sen- sor per one revolution, and corresponding to the different angular posi- tion is separately compared with each aforementioned fit. Thus, a number of n x m values are attained for the angular speed difference, in which n is the number of pulses produced by the first pulse sensor per one full revolution of the first rotating member, and m correspondingly the number of pulses produced by the second pulse sensor per one full revolution of the second rotating member. By means of said values it is possible to further calculate an average value. It is an advantage of this embodiment especially in slow rotating speeds producing a small number of pulses per time unit that the real time quality of the measurement result is improved, and when average values are utilized, the measurement accuracy is also improved.

In a preferred embodiment of the invention the measuring method is applied for measurement of the rotating speed of the machine reel formed in the reeling up process in relation to the speed of the reeling cylinder, i. e. for the measurement of the angular speed difference of said members. This makes it possible to determine the length of the periphery of the machine reel in relation to the length of the periphery of the reeling cylinder, and thereby to determine the change in the ra- dius and volume of the machine reel as a function of time. This infor- mation can be utilized to determine the density of the machine reel, and to adjust the reeling up process by means of the density infor- mation.

The most important advantages of the invention when compared to solutions of related art include significant improvement of the measure- ment accuracy as well as production of accurate measurement results with a slight delay, which improves the usability of the measurement result in real-time adjustment. Furthermore, the invention enables a wide freedom of choice in the selection of the type of pulse sensors necessary in the measurement, because the maximum number of pulses received per one revolution is not significant in view of the accu- racy. Moreover, the measurement device implementing the method according to the invention has a simple structure and can be easily in-

stalled. The measurement device is suitable to be used either as a fixed installation, or it can also be utilized in mobile maintenance and test use.

The following more detailed description of the invention will more clearly illustrate for anyone skilled in the art possible embodiments of the invention as well as advantages to be achieved with the invention in relation to prior art.

In the following, the invention will be described in more detail with ref- erence to the appended drawings, in which Fig. 1 shows, in principle, a mutual arrangement of a machine reel and a reeling cylinder in reeling up, Fig. 2 illustrates the state of the art use of pulse sensors to deter- mine the angular speed difference of a machine reel and a reeling cylinder, Fig. 3 illustrates an embodiment of the invention to determine the angular speed difference of a machine reel and a reeling cylinder, Fig. 4 illustrates an embodiment of the invention that utilizes linear fit, Fig. 5 illustrates an embodiment of the invention that utilizes second order polynomial fit, Fig. 6 illustrates a placement of the trigger means of pulse sen- sors according to the invention in the first and the second rotating member, Fig. 7 illustrates another placement of the trigger means of the pulse sensors according to the invention in the first and the second rotating member, and

Fig. 8 illustrates a preferred embodiment of the measuring equip- ment according to the invention when applied in the adjust- ment of the reeling up process.

Figs 1 and 2 illustrate in principle a mutual arrangement of the machine reel R and the reeling cylinder D in a reeling up process, as well as the state of the art use of pulse sensors S1, S2 to determine the angular speed difference of the reeling cylinder D and the machine reel R.

The reeling cylinder D rotates at a peripheral speed corresponding to the speed of the paper web W, and it is mounted on bearings in the frame of the reel-up or to a stable or moving structure attached to the frame by means of shafts located at the ends. The reeling cylinder D is coupled to a centre drive device M1 via the other end of said cylinder, which centre drive device, in turn, is connected to the drive of another apparatus that feeds the paper web W, in such a manner that the pe- ripheral speed of the reeling cylinder D can be adjusted to correspond to the speed of the web W fed to the reel-up. For this adjustment of the centre drive M1 of the reeling cylinder D it is, according to related art, possible to use a tension measurement member before the reeling cylinder D in the travel direction of the paper web W, to measure the tension of the paper web W.

The paper web W is accumulated on a reeling core T to form a machine reel R, and the machine reel R is loaded at the same time in a known manner against the reeling cylinder D to form a so-called nip and to attain a desired nip force. To the reeling core T, which may be a so-called reel spool with a metal frame and which is journalled pivo- table on bearing housings at its ends, a separate centre drive M2 is connected via the other end of the roll. By adjusting the torque of said centre drive M2 it is possible to affect the peripheral force exerted on the paper web W that is being reeled up in a known manner. By ad- justing the peripheral force, nip force and the tension of the web W preceding the nip, it is possible to affect the radial density profile of the machine reel R.

To control the aforementioned reeling up process, the adjustment sys- tem controlling the reeling up process requires information on the speeds of rotation of the reeling cylinder D and accurate information especially on the mutual difference in the rotating/angular speeds of said members to determine the density of the machine reel R.

In Fig. 1 the reeling cylinder D is according to the state of the art equipped with a first pulse sensor S1, said first pulse sensor producing for example 5000 pulses per each full revolution of the reeling cylinder D. The machine reel R (reel spool T), in turn, is equipped with a second pulse sensor S2, said second pulse sensor S2 producing one pulse per each full revolution of the machine reel R.

By determining the number of pulses (in the drawing m,, m, +i, etc. ) ob- tained by the second pulse sensor S2 during the time between every two successive pulse (marked in the drawing with ni, ni,,, etc. ) from said first pulse sensor S1 in accordance with Fig. 2, it is possible to determine the changes in the angular speeds of the machine reel R and the reeling cylinder D with respect to each other, i. e. the difference between the angular speeds. Absolute rotating speeds can be deter- mined by calculating the number of pulses S1, S2 during a specific known period of time.

In the situation of Fig. 2 the absolute measurement accuracy of the reeling cylinder D and the machine reel R can be improved only by in- creasing the number of pulses given by the first pulse sensor S1 per one revolution of the reeling cylinder D, and/or by calculating the measurement result over several revolutions of the machine reel R (intervals ni, ni+,, etc. ). The latter method, however, significantly weakens the real-time quality of the measurement result.

Fig. 3 shows in principle one embodiment of the method according to the invention for determining the angular speed difference between the machine reel R and the reeling cylinder D.

According to the invention, and deviating from the state of the art, the reeling cylinder D is equipped with a first pulse sensor S1, said first

pulse sensor S1 producing now only one pulse per each revolution of the reeling cylinder D functioning as a reference. The machine reel R is equipped with a second pulse sensor S2, said second pulse sensor S2 producing one pulse per each full revolution of the machine reel R.

According to the invention, the accurate event times of the pulses pro- duced by the first S1 and the second pulse sensor S2 are registered for example in the accuracy of approximately 1 Zs.

In the graph shown in the upper part of Fig. 3, the pulses produced by the pulse sensor S1 are shown in a system of coordinates in which the horizontal axis shows in radians the time t and the y-axis shows the angular position of the reeling cylinder D functioning as a reference.

The moments in time corresponding to the pulses of the first pulse sensor S1 given at intervals of one full revolution of the reeling cylinder D are in Fig. 3 shown with tn, tn+1, tn+2, etc. The event times of said pulses are marked with spherical symbols in the system of coordinates of Fig. 3.

According to the invention, a fit F and interpolation parameters cor- responding to the fit F are now determined for each pulse given by the first pulse sensor S1 over one or more successive intervals preceding said pulse, said intervals being formed between these successive pulses registered by the first pulse sensor S1 that correspond to the same angular position of the reeling cylinder in the successive revolu- tions of the reeling cylinder D.

Fig. 3 shows an interval in+5 preceding the pulse occurring at a moment of time tn+5, said interval being in this case formed between the succes- sive pulses tn+4 and tn+5 of the first pulse sensor S1. In a corresponding manner an interval in+4 etc. is formed between the pulses tn+3 and tn+4.

The fit F and the interpolation parameters further make it possible to determine the accurate angular position of the first rotating member, i. e. the reeling cylinder D at any time within said interval/intervals.

In Fig. 3 the fit F is shown in such a manner that it extends over all the pulses of the pulse sensor S1 shown in the drawing and the intervals therebetween, but in practise the fit F is produced according to the in- vention over one or more successive last produced intervals always when the first pulse sensor S1 gives a new pulse. In other words, the fit F is produced and the interpolation parameters related thereto are determined for a continuous process of predetermined duration ex- tending on an area of specific length of one or more intervals, wherein said fit F of predetermined length"proceeds"in time in the pulse se- quence S1 always when a new pulse arrives.

By means of the fit F and the interpolation parameters determining the same it is now possible to determine a position p'for each pulse of the second pulse sensor S2 that is detected during the interval in, 5 last determined for the first rotating member D, said position p'indicating the angular value of the first rotating member functioning as a reference at the event time of said pulse.

By means of the preceding positions p", p"'of the second pulse sensor S2 that correspond to the same angular position in the successive revolutions of the second rotating member R, it is possible to determine a progression (difference between the angular values) in relation to the first rotating member D used as a reference. In Fig. 3 the progression between the positions p'and p"is marked with d'and the progression between the position p"and p"'is marked with d".

In other words, by means of the invention it is possible to accurately determine the angle/distance revolved by the second rotating member R for each revolution (or several revolutions, if necessary), of the first rotating member D functioning as a reference.

In a situation in which no pulses are attained from the second rotating member R during one revolution of the first rotating member D, it is, of course, necessary to examine the progression of the second rotating member R over several revolutions of the first rotating member D. Such a situation can occur when the diameter of the second rotating member R is considerably larger than the diameter of the first rotating member

D and/or the pulse sensor of the second rotating member R produces only one pulse per revolution.

In a situation in which the peripheral speeds of the machine reel R and the reeling cylinder D that are in nip contact with each other are equal, it is now by means of the method possible to determine the accurate length of the periphery of the machine reel R that is being formed in relation to the (known) length of the periphery of the reeling cylinder D.

Thus, the information obtained by means of the measurement ac- cording to the invention can be further utilized to determine the radius/diameter of the machine reel R, and thus to determine the volume of the machine reel R. This information can be utilized in a known manner to determine the density of the machine reel R, and to adjust the reeling up process thereby.

In the situation shown in Fig. 3 the rotating speed of the reeling cylinder D is described in such a manner that it decelerates as a function of time, which becomes evident as a slow reduction in the frequency of occurrence of the pulses given by the first pulse sensor S1 as well as a formation of the fit F into a downward arching curve.

In a normal situation when the speed of the web W remains substan- tially constant, the situation is similar to the one shown by means of broken lines in Fig. 3, in other words the fit curve F'corresponding to the pulses of the first pulse sensor S1 (shown by means of broken lines in the pulse sequence in the lower part of Fig. 3), takes the form of a linear fit, in other words a straight line shown by means of broken lines in Fig. 3. Thus, when the diameter of the machine reel R grows and the amount of web W reeled up thereon is increased, the frequency of occurrence of the pulses of the second pulse sensor S2 slowly de- creases. Correspondingly, in a situation in which the speed of rotation of the reeling cylinder D would accelerate, the fit F would take the form of a upward arching curve.

The most important advantages of the present invention include a sig- nificant improvement in the measurement accuracy when compared to solutions according to the state of art. When the rotating members ro-

tate for example at a speed of 10 revolutions per second, which cor- responds to a peripheral speed of 1884 meters per minute in a member having a diameter of one meter, a resolution of 100000/revolution is at- tained when using a rather moderate time metering resolution of 1 Zs.

When compared for example to the use of a pulse sensor producing 5000 pulses per revolution, it is thus possible to attain a twenty-fold resolution by means of the invention.

The accuracy of the method according to the invention naturally de- pends on the accuracy of the method used in the interpolation i. e. in the production of the fit F, but in practice the interpolation can be easily implemented in such a manner that it does not restrict the measure- ment accuracy attained by means of the method, but the measurement accuracy is primarily determined on the basis of the accuracy of the measurement of time.

Figs 4 and 5 further illustrate the formation of the fit F in different ways over the two last produced intervals. To illustrate the properties of dif- ferent kinds of fits, the speed of rotation of the first rotating member D functioning as a reference is presented in such a manner that it de- celerates exaggeratedly in the aforementioned drawings. To facilitate the comparison, Figs 4 and 5 show a curve F'by means of a broken line, said curve illustrating the"real"change in the angular position as a function of time in the situation to be examined.

In Fig. 4 the fit F is formed as a linear fit over the two intervals pre- ceding the pulse given by the pulse sensor S1 at a moment of time tn+5.

The linear fit is preferably suitable to be used in a situation in which the rotating speed of the first rotating member D, such as a reeling cylinder that is under examination slowly changes and/or it is only necessary to produce a fit F over one interval.

In Fig. 5 the fit F is formed as a second order polynomial fit over the two intervals preceding the pulse given by the pulse sensor S1 at a moment of time tn+5. As it is well known, the second order polynomial can in its conventional form be presented as a function f (t) = at2 + b, in which t in this case represents time and f (t) the angular position as a

function of time and a and b are interpolation parameters that obtain certain constant values when the fit F is formed. The graph of the second order polynomial fit F is a parabola which, in faster changes in the speed of rotation of the rotating member D can be adjusted to comply with the pulses of the first pulse sensor S1 better than a linear fit.

When the second order polynomial fit F is used, the adjustment and the determination of the interpolation parameters is advantageously con- ducted over two or more intervals in such a manner that the fit F is forced to travel via the pulse sensor time-angular position coordinates that form the outermost measurement points. In other words in Fig. 5 the second order polynomial fit F is formed in such a manner that the curve illustrating the fit F travels via the points measured at moments of time tn+3 and tn+5. In practical experiments conducted by means of the invention, it has been observed that this reduces the inaccuracy caused by the fit F. By extending the fit F over several intervals, the measurement accuracy is also improved, because this effect substan- tially corresponds to the act of calculating an average value for the measurement over several revolutions of the rotating member.

The act of forming a linear or polynomial fit in a specific group of measurements as well as the act of determining the interpolation pa- rameters describing said fit can be considered as a technique known as such that includes in the basic skills of anyone skilled in the art, and thus the production of the fit F will not be described in more detail in this context. If necessary, additional information can be found for example in textbooks in the field of mathematics.

The invention is not, of course, restricted solely to the use of a linear fit or a second order polynomial fit. If necessary, it is also possible to use a multiple order polynomial fit or another fit, which fit F can be formed over one or several successive intervals.

The invention is still not restricted solely to such embodiments in which pulse sensors producing only one pulse per revolution are installed in

connection with the first and the second rotating member, such as a reeling cylinder D and a machine reel R.

Figs 6 and 7 illustrate some embodiments of the invention in which pulse sensors producing several pulses per revolution are installed in connection with the first D and/or the second R rotating member.

Fig. 6 illustrates such an embodiment of the invention in which a second pulse sensor S2 producing two pulses per revolution is in- stalled in connection with the second rotating member R, and a first pulse sensor S1 producing one pulse per revolution is, in turn, installed in connection with the first rotating member D. In Fig. 6 the marks Ri, R2 illustrate the positioning of the pulses produced by the second pulse sensor S2 in different angular positions with respect to each other in the second rotating member R. In practice this is attained for example by means of suitable positioning of the trigger means of the second pulse sensor S2. For example when optical pulse sensors are used, said trigger means can be adhesive reflective tapes or the like that are attached to the rotating member R.

In the situation of Fig. 6 a fit F is determined for the pulse sequence corresponding to the mark D1 in the first pulse sensor S1 functioning as a reference. Each pulse produced by the second pulse sensor S2 per one revolution of the second rotating member R (and corresponding to a different angular position) is compared separately with the afore- mentioned fit. In other words the marks R1 and R2 form in this respect two different pulse sequences, both said pulse sequences being com- pared separately with the fit F. Thus, it is possible to update two new values instead of one for the angular speed difference of the predeter- mined distance revolved by the first rotating member D functioning as a reference, of which values it is possible to calculate an average value.

The advantage of this embodiment especially in slow rotating speeds producing a small number of pulses per time unit, is that the real time quality of the measurement result is improved, and when average values are utilized, the measurement accuracy is also improved.

Fig. 7 illustrates such an embodiment of the invention in a manner cor- responding to Fig. 6 in which the first pulse sensor S1 installed in connection with the first rotating member D produces two pulses per revolution. Now a separate fit F is produced for each pulse sequence corresponding to marks D1 and D2. Each pulse sequence correspond- ing to the different marks R1, R2 and R3 of the second pulse sensor S2 measuring the rotation of the second rotating member is compared separately with both fits F. In the situation of Fig. 7 it is thus possible to update six different values for the angular speed difference of the pre- determined distance revolved by the rotating member D functioning as a reference, of which values it is possible to calculate an average value.

In the situation of Fig. 7, when the marks Ri, R2 and R3, and cor- respondingly, the marks D1 and D2 are not positioned at fixed intervals within one revolution of said rotating members R and D it is possible to automatically determine the number of marks produced per one revo- lution by means of both rotating members R, D. This is possible, be- cause the irregularity in the occurrence of the pulses in time can be detected in the pulse sequences produced by the first pulse sensor S1 and the second pulse sensor S2, respectively. In the situation of Fig. 6, in which the marks R1 and R2 are in the second rotating member R positioned at exact intervals of 180° with respect to each other, the measurement system requires information input by the user regarding the number of the marks, because now the number of the marks can- not be determined on the basis of the pulse sequence produced by the pulse sensor S2.

It is obvious for anyone skilled in the art that when the method ac- cording to the invention is utilized, it is also possible to calculate an average value for the measurement results in a manner complying with the state of the art and even over several revolutions of the rotating members D, R to improve the accuracy.

Furthermore, Fig. 8 shows in principle a preferred embodiment of the measurement apparatus implementing the method according to the

invention when applied in connection with the reeling up of a paper web W.

The measuring equipment of Fig. 8 comprises a first S1 and a second S2 pulse sensor arranged in connection with the machine reel R and the reeling cylinder D. The accurate event times of the pulses produced by said pulse sensors are registered in a data processor CPU, which data processor CPU is arranged to communicate with the control sys- tem controlling the reeling up process.

The data processor CPU can be for example a computer that is en- capsulated in a manner corresponding to the surrounding conditions and equipped with an AD converter card or the like to register the even times of the pulses of the pulse sensors, as well as with a suitable software to perform calculation. A PC computer can be coupled in known manners to communicate with the control systems of the rest of the equipment. It is, of course, obvious for anyone skilled in the art that the data processor CPU can also be contained in the actual adjustment and control system controlling the rotating-members that are under examination, wherein a separate computer or the like is not necessary for the measurement according to the invention.

The data processor CPU is arranged to determine the angular speed difference between the machine reel R and the reeling cylinder D by means of the method according to the invention. In other words, the reeling cylinder R is used as a reference, and after each pulse coming from the first pulse sensor S1, the data processor CPU calculates a fit F and interpolation parameters over the last measured one or more intervals of the pulse sequence of the pulse sensor S1. At the same time the position and progression of the reeling cylinder D are cal- culated as an angular value of a preceding position registered in a similar manner on the basis of the pulse of the second pulse sensor S2 occurring during said last interval. The aforementioned progression now indicates the relative speed of the reeling cylinder D in relation to the machine reel R and at the same time the relative diameter of the machine reel R in relation to the diameter of the reeling cylinder D. The change in the diameter of the machine reel R as a function of time

gives information on the change in the volume of the machine reel R.

This information can be utilized further in a known manner to determine the density of the machine reel, and to adjust the reeling up process thereby.

The invention enables a wide freedom of choice in the selection of the type of the pulse sensors S1, S2 necessary in the measurement. Be- cause the maximum number of pulses obtained per one revolution is not significant in the method according to the invention, it is possible to utilize for example optical, inductive, capacitive, magnetic or any other kind of solution known as such by anyone skilled in the art for the implementation of the pulse sensors installed in the rotating members.

For example when optical sensors are used, it is possible to provide the rotating members with trigger means such as adhesive reflective tapes or the like that move along with the rotating movement, said tapes producing a pulse to be measured when passing by a stationary indicator part. When several trigger means are installed per one ro- tating member, it is not necessary to attach them at fixed angular dis- tances with respect to each other when applying the method according to the invention, which significantly facilitates the installation of the trig- ger means in industrial conditions.

Because of the ease of installation the use of optical sensors of the above kind is advantageous especially in test and maintenance use. In permanent installations it is, however, advantageous to use for example magnetic sensors whose performance is not weakened be- cause of dirt, and which are also otherwise insensitive to external (electric) disturbances.

It is, of course, obvious for anyone skilled in the art that the pulses of the pulse sensors that are being used do not necessarily have to be formed of temporally short pulses that are separate from each other, as shown for example in the lower part of claim 3. To register the angular position of a specific rotating member it is sufficient that at said mo- ment in time, a clear change occurs in the signal of the pulse sensor, for example the signal changes from the stepped value"0"to the value

"1", said values corresponding to predetermined voltage levels or voltage areas. Thus, the registration of"pulses"can take place by using so-called edge sensitive indication in a known manner. For example a pulse sensor producing one"pulse"per one revolution of the rotating member that is under examination can thus give a signal with the value"1"during a predetermined revolution, said signal changing into the value"0"for the duration of the next revolution when passing by the trigger means, and back to the value"1"the next time when passing by the trigger means, etc.

Although the invention is in the examples above described in con- nection with reeling up in particular, it is obvious for anyone skilled in the art, that the invention can also be applied for example in unwinding, calendering or other rotating members that guide and/or treat the paper web in its path. In calendering the invention can be used for example to determine the mutual speed of opposite calender rolls. The invention can also be applied in reel-ups based on king rolls, as well as in king roll slitters or other slitter winders that form customer rolls.

Furthermore, although the examples above mainly concentrate on paper web and its treatment, the same applies in principle for other web-like materials, such as plastic films.

It is thus obvious for anyone skilled in the art that by combining in dif- ferent ways the methods and modes of operation presented above in connection with different embodiments of the invention, it is possible to provide various embodiments of the invention in accordance with the spirit of the invention. Therefore, the above-presented examples must not be interpreted as restrictive to the invention, but the embodiments of the invention can be freely varied within the scope of the inventive features presented in the claims hereinbelow.