Vibration damper for a paper or board machine

FIELD OF INVENTION

The invention relates to a method according to the preamble of claim 1.

The invention also relates to a vibration damper according to the preamble of claim 7.

PRIOR ART

As the widths of paper and board machines are increasing and their speeds rising, the vibration of rolls becomes a problem greater than ever.

A target, in which vibration constitutes a problem, is the calender at the end of the paper or board machine. In calenders, there is at least one nip being formed between two rolls in which the web is treated and the web surfaces are compacted. A problem particularly related to multi-roll calenders is barring. Barring is a vibration problem which is caused by irregularities in the web or by mechanical vibrations which are created by the calender, the drives, the surrounding machines, or the unroundness of the rolls.

Implementing a dynamic damper (in the literature e.g. TMD = tuned mass damper) requires an accurately controlled and adjustable spring constant. Adjustability is only required in commissioning or, in the case of an adaptive damper, also during use. When necessary damper masses increase and when trying to damper high-frequency vibration — e.g. barring 200-800 Hz or a calender frame vibration damper 10 Hz/7,000 kg — high spring constants are required. Providing high spring constants in a limited space is awkward particularly if the spring con-

stant has to be adjustable. This sets limitations for the use of a mechanical damper in such targets of use.

FI patent 94458 describes a method and apparatus for controlling the vibration of the rolls of a paper machine, hi the method, the positions of the critical speed ranges of the roll are changed during run. Critical speed is changed by changing the mass and/or the rigidity of the roll and/or the support point of the roll. As a possibility is presented changing the rigidity of the end bearing of the roll. Between the washer of the bearing housings of the end bearings and the frame, in- termediate pieces of elastic material can be installed. By adjusting the force with which the bearing housing presses the intermediate pieces against the frame, it is possible to adjust the rigidity of the fastening of the bearing housings. Said pressing force can be adjusted by means of a cylinder device or a screw.

JP patent specification 3082843 describes an arrangement for minimising vibrations in a roll. The drive motor of the roll is elastically fastened in the frame. The fastening comprises a rubber intermediate piece enduring vibration between the base plate of the fastening part of the drive motor and the frame. The fastening bolts of the base plate extend through the frame plate into a cylinder fastened on the lower surface of the frame plate in which they are fastened in a piston in the cylinder. There are rubber sleeves below the fastening bolt heads, whereby the fastening of the base plate is provided floating. On the inner surface of the cylinder, there is a projection which limits the upward motion of the piston in the cylinder. Between the cylinder head and the upper surface of the piston, there is a spring and, between the lower surface of the piston and the bottom of the cylinder, there is a pressure space in which the pressure medium is compressed air. The piston is run with compressed air first against the projection of the inner surface of the cylinder, whereby minimum pressing force is applied on the rubber intermediate pieces and sleeves. When the pressure of compressed air below the piston is decreased, the piston moves downwards from the force of the spring being above the piston, whereby greater pressing force is applied on the rubber intermediate

pieces and rubber sleeves. With the pressure of pressure medium being below the piston, it is then possible to adjust the rigidity of the fastening of the roll.

FI patent 101283 describes a method in winding a paper web, in which vibration excitations caused by a paper roll being formed are tried to be avoided by controlling the run speed of the winder. The run speed of the winder is controlled based on the rotational frequency of the paper roll being formed so that, as the rotational frequency of the paper roll being formed approaches the vibration range, the run speed is lowered so that the rotation speed of the paper roll being formed de- creases below the lower frequency of the vibration range. After this, the run speed of the winder is increased so that the rotation speed of the paper roll being formed remains constant until the original run speed of the winder is reached.

FI patent 110333 describes an arrangement for damping the vibrations of a multi- roll calender frame. The arrangement comprises at least one damper which comprises at least one energy-absorbing internal damper element. The damper is fastened at least at one point above the centre line of the shaft of the uppermost roll of the calender. The damper can comprise a creasing bar around which there is a vibrating mass. The free end of the creasing bar is joined to the calender frame with an internal damper and a spring. The internal damper is an energy-absorbing damper, such as a visco damper or a damper manufactured of rubber or viscoelas- tic material. The tuning of the damper is done by changing the distance of the mass from the fastening point of the creasing bar. The tuning can be performed when installing the damper or automatically during run based on a vibration measurement, whereby the distance of the mass is changed until the lowest vibration level is reached.

EP patent specification 1025695 describes a method and apparatus for damping vibrations in a paper machine. In the bearing housing of a rotating roll is fastened a weight by means of a spring i.e. a bar, the distance of which from the bearing housing can be controlled. The weight and the spring constitute a dynamic vibra-

tor. The vibrations of the bearing housing are measured and, by changing the distance of the weight from the bearing housing, the vibration can be compensated by setting the natural frequency of the dynamic vibrator the same as the problematic excitation frequency. The arrangement is at its most advantageous when con- trolling the vibrations of two nip-forming rolls.

SUMMARY OF INVENTION

The arrangement according to the invention provides a vibration damper which is easily and at a wide range adjustable and which has a high spring constant.

The principal characteristic features of the method according to the invention are presented in the characterising part of claim 1.

The principal characteristic features of the vibration damper according to the invention are presented in the characterising part of claim 7.

In the vibration damper according to the invention, the vibrating mass of the damper is affected by gas with the pressure changes of which the vibration fre- quency of the mass is adjusted. By increasing the pressure of gas, the vibration frequency of the mass can be increased and, by decreasing the pressure of gas, the vibration frequency of the mass can be decreased. By choosing the ratio of the volume and the area of the gas space of the damper suitable, adequate rigidity is provided in the damper.

BRIEF DESCRIPTION OF FIGURES

Fig. 1 schematically shows a vibration damper according to the invention.

DESCRIP TION OF ADVANTAGEOUS EMBODIMENTS

Fig. 1 shows a damper according to the invention, based on pressure changes of gas.

The damper 10 comprises a frame structure 11, 12, 13, two diaphragm support elements 21, 22 and a mass 30. The frame structure consists of a cylindrical frame part 13, at a first open end of which is installed a first support element 21 and at an opposite, second end of which is installed a second support element 22. The diaphragm support elements 21, 22 consist of a first expansion ring 21a, 22a forming the outer circle of the support elements 21, 22 and a second expansion ring 21b, 22b forming the inner circle of the support elements 21, 22 and a connecting part 21c, 22c joining these. On top of the first support element 21 is installed a cover part 12 and on top of the second support element 22 is installed a bottom part 11. The bottom part 11, the frame part 13, the cover part 12 and the support elements 21, 22 are fastened to each other by screws 51 extending through the bottom part 11, the first expansion ring 22a of the second support element 22, the frame part 13, the first expansion ring 21a of the first support element 21 into the cover part 12. In a space limited by the support elements 21, 22 and the frame part 13 is arranged a mass 30. The mass 30 is fastened to the support elements 21, 22 by screws 61 extending through the second expansion ring 22b in the inner circle of the second support element 22 and the mass 30 into the second expansion ring 21b in the inner circle of the first support element 21.

The first diaphragm support element 21, the mass 30 and the cover part 12 limit a first pressure space 41 between them in which there is a connection by a first opening 14 extending through the cover part 12. The height of the first pressure space 41 is designated with reference hi. The second diaphragm support element 22, the mass 30 and the bottom part 11 limit a second pressure space 42 between them in which there is a connection by a second opening 15 extending through the bottom part 11. The mass 30 is sealed to the second expansion ring 21b in the in- ner circle of the first support element 21 by means of a first seal 31 and to the sec-

ond expansion ring 22b in the inner circle of the second support element 22 by means of a second seal 32.

The mass 30 is thus suspended in the damper 10 by means of the diaphragm sup- port elements 21, 22, supported by which the mass 30 vibrates. In addition to this, the vibration of the mass 30 is affected by pressure P of gas in the first pressure space 41 above the mass 30 and in the second pressure space 42 below the mass 30.

The operation of the damper 10 is illustrated by means of the following calculation example.

In the calender, barring occurs on frequency range 375 Hz. The problem has been observed to occur randomly also with frequencies 360 and 390 Hz. A dynamic damper to be installed in the bearing housing of the roll is considered able to remove the vibration problem. An adequate vibrating mass is estimated 25 kg. The damper is designed on frequency 375 Hz ± 20%. Then, a lower limiting frequency of the operation of the damper is 0.8*375 = 300 Hz and an upper limiting frequency is 1.2*375 = 450 Hz, whereby the problematic frequency range will be covered.

Equation (1) enables calculating vibration of the damper:

2 - π V m

Equation (1) is an approximation in which the mass of diaphragm springs of the damper is ignored. The equation is still valid, because the mass of the diaphragm springs of the damper is less than 5% from the whole vibrating mass of the damper.

Solving the spring constant ks from Equation (1) results in Equation (2):

k _s = 4- f _D ² -π ² - m (2)

The spring constant of the lower limiting frequency 300 Hz is obtained by means of Equation (2):

h∞ _Hz = 4 - 300 ² - π ² - 25 = 9 - π ² -XQ ⁶ NIm

The spring constant of the upper limiting frequency 450 Hz is obtained by means of Equation (2):

k. _S0H = 4 - 45Q ² -π ² - 25 = 2Q,25 -π ² λtf NIm

The operation idea of the damper is to use gas in a diaphragm type cylinder i.e. the first 41 and the second 42 pressure space as an adjustable spring. It is possible to adjust the spring constant of the gas simply by changing the pressure level of the gas. No mechanical changes, such as motions, actuators etc. are required.

For the adiabatic process, Equation (3) is applicable:

P ₁ - Vf = P ₂ - V ₂ " (3)

In Equation (3), p is pressure in the diaphragm type cylinder, V is volume of the pressure space, n is almost equal to 1.4 for diatomic gas. Lower index 1 relates to the static state of the diaphragm type cylinder (undeflected situation) and lower index 2 relates to the deflected state of the diaphragm type cylinder.

Substituting the pressure space volume V in Equation (3) by operational area A of the pressure space and height h of the gas column results in Equation (4):

p, -(A-h _x )" =p ₂ -(A-h ₂ )" (4)

Solving p ₂ from Equation (4) results in Equation (5):

By means of Equation (6), it is again possible to calculate the spring constant k of gas in the pressure space:

_ AF _ Ap-A _ (p ₂ -p _x )- A k = (6)

Ah Ah A ₂ -A ₁

Inserting Equation (5) to Equation (6) and substituting height λ ₂ of the deflected state of the gas column with h _\ +A result in Equation (7):

According to the above Equation (7), the gas spring constant k is dependent on pre-charge pressure p _\ of the gas and this property is utilised in the invention.

For the damper shown in Fig.1 is obtained:

P ₁ =M0 ⁵ NIm ²

P ₂ =100-10 ⁵ NIm ² h _λ =4-l(T ³ m

/i = l,4

δ = 10 ^~12 m

Z) ₁ =0,12w

D ₂ = 0,25 m

_{A =} π-D] ^-(D ₂ -D ₁ ) ² 1 λ-- 0,0457 ₂ m

The effective areaλ of the elastic diaphragm formed by the diaphragm spring 21, 22 is thus assumed the rigid centre + half of the elastic diaphragm.

With pre-charge pressure Pi =0.1 MPa, the spring constant of the pressure space 41 above the diaphragm spring 21 is obtained by means of Equation (7):

-6,22738-10 ⁵ N/m

With pre-charge pressure Pi = 10 MPa, the spring constant of the pressure space 41 above the diaphragm spring 21 is obtained by means of Equation (7):

= -6,22738-10 ⁷ N/m

A negative value is obtained for spring constants k _\ and & ₂ , which means that the pressure decreases as the volume increases. Therefore, it is a question of choosing the direction of the positive co-ordinates.

The spring constant of the above pressure space 41 and the spring constant of the below pressure space 42 are equal in the embodiment of Fig. 1, because the pressure spaces 41, 42 are identical. In pressure p _\ , the vibration frequency of the mass 30 can be calculated by means of Equation (8) based on Equation (1) as fol- lows:

1 μ -k. +k 3 30000H Wzz

J \bar ~ \\ (8)

2 - π V m

In pressure p ₂ , the vibration frequency of the mass 30 can again be calculated by means of Equation (9) based on Equation (1):

f - _!_ P ^k 2 ^{+ k} 100Hz /<y>

J \bar - ~ "I \ ^y )

2 - π V m

A _^ --^f- ⁶ ' ^{2ml λ0} 2 ^{+ (9} - ^π' ' ^ -465ft

That is, for reaching the frequency range 375 Hz ± 20% (300-450 Hz) mentioned at the beginning, it has to be possible to adjust the pressure of the pressure space in the range of about 0.1-10 MPa.

The diaphragm springs 21, 22 set the basic frequency of the system. The final tuning frequency is then adjusted by the pressure i.e. the basic adjustment is per- formed with the diaphragm springs 21, 22 and the fine adjustment is performed with the pressure. Equations (8) and (9) utilise the same mechanical spring con-

stant calculated on the frequency of 300 Hz, because the pressure does not affect the rigidity of the diaphragm spring 21, 22.

In the embodiment shown in the figure, the frame part 13 is cylindrical which is the most advantageous shape from the viewpoint of sealing. However, the frame part 13 could also be of some other shape, e.g. the shape of a rectangle.

The first pressure space 41 and the second pressure space 42 are advantageously identical, whereby the behaviour of the damper 10 is linear at a wide operating range. With small vibratory motions, the operation of the damper 10 is still linear accurately enough, even though the first pressure space 41 and the second pressure space 42 are not identical. The height h _\ of the first pressure space 41 (and the second pressure space 42) does not have to be constant at the whole range of the first pressure space 41 but the determining factor is the relative change AV/ V.

On both sides of the diaphragm springs 21, 22, the same static pressures prevail i.e. also the state of the mass 30 is in the same pressure. After filling, the first 41 and the second 42 pressure space are closed, whereby vibration creates a pressure difference. The mass 30 vibrates in the vertical direction.

The damper 10 can be used e.g. in connection with a roll nip. Then, the resonance frequency of the roll nip is measured from the machine and the rotational frequency of the roll is calculated from the run speed. The frequency of the damper 10 is adjusted to the multiple of the rotational frequency of the roll which is clos- est to the resonance frequency. Then, the roll will not be adapted, but the vibration transfers to the damper 10.

Above were described only some advantageous embodiments of the invention and it is evident to those skilled in the art that several modifications can be made to them within the scope of the enclosed claims.