Automatic regulation of clearance in a tilting pad journal bearing/Automatinis tarpelio reguliavimas atraminiu ideklu veleno guolyje.

Marcinkevicius, A.H.

1. Introduction

Hydrodynamic tilting pad journal bearings are widely used in turbines, compressors, pumps, machine tools and other machines where rotors are revolving for a long time without frequent start and stoppage. Their advantage is in smooth and accurate revolving motion, good vibration damping properties, high stiffness, service durability. But the main problem of such bearings is the value of clearance between the journal and pad. First of all, at assembly of such bearings in many cases there are not adequate means to measure the clearance, the second, at operation of different bearings, the temperature in different cases after starting from 18-20[degrees]C at longer work increases (in researched bearings [1] up to 41-43[degrees]C, at other experiments [2]--up to 55-65[degrees]C; at approach to failure the temperature may increase up to 85[degrees]C). Thermal deformation of different elements of bearings is different, it may hardly influence on clearance value, and at absence of means for clearance control it is necessary at assembly to set the maximal clearance for the worse expected work conditions of the bearing. Increased clearance increases shaft eccentricity at revolving and decreases bearing stiffness, decreases dynamic stability of the system. Influence of clearance on properties of bearings also is analyzed in works [3, 4]. One can come to conclusion that without knowledge of clearance between the journal and pad, though accuracy of journal rotation is measured, it is difficulty to solve about work quality possibilities of bearings [5, 6].

2. System of automatic regulation

For solving the problem of clearance control the patent application of multi pad self-aligning automatically regulated bearing was proposed by us [7]. Fig. 1 shows the scheme of automatically controlled three pad bearing. The self-aligning pads 1 are placed on pins around the revolving journal 2 in a body 3. Pin 4 is conventional, fixed in body 3 by the screw and counter nut. Pin 5 is assembled on balls 6 with possibility of axial motion in body 7. For that purpose from lower side pin 5 supports to dish type spring 8, from the upper side it by rolls 9 supports to wedge 10, from the other side wedge 10 by rolls 11 is rested on self-aligning support 12. The wedge 10 is driven by servo drive 13 (e.g. by pjezoelectric or other actuators, which are widely used as driving elements [8, 9]). At forward motion of wedge pin 5 moves down decreasing the clearance between pads 1 and journal 2, and tightening the spring 8, at backward motion of wedge spring 8 picks up the pin 5 increasing clearance between pins and journal. The hydrodynamic force acting in the bearing is measured by pin 14 which by thread is connected with bushing 15 by thread assembled in body 3. For measuring purpose the pin 14 is hollow inside, and the measuring stick 16 is assembled in it. The stick 16 is riveted in the head of pin 14, the head is connected with the pin body by the neck eccentric to axis of pin by value e (Fig. 1). Because of eccentricity the neck at action of axial force bends, the bending displacement is enlarged by stick 16 and transmitted to transducer 17. Transducer 17 is electronically connected with the clearance control system, which by control the axial position of pin 5 keeps the set value of hydrodynamic force acting between the pads and journal. Assembly of pin 14 in additional bushing 15 is necessary for the reason that at assembly of journal 2 in two bearings (one in the front part of body 3, the other in the rear part of body) it is necessary to keep together an accurate position of journal axis in the body 3 and to keep accurate position direction of eccentricity e: it must be in the imaginable plane of action of resulting hydrodynamic radial and tangent forces loading the pad, it is perpendicular to the journal axis. If eccentricity e will be turned in accordance with that plane, the radial force will be measured with an error. For this case the pin 14 at its upper side has two cut plane sides 18, direction of eccentricity e and axis of transducer 17 are parallel to these sides (Fig. 1).

Meaning of other parts of bearing design (Fig. 1) there are not explained because it is understandable from the drawing: there are counter nuts for fixing of set position of pins, connecting elements of servo drive 13 with the wedge 10, etc. Only one support with the pin 5 is used for regulation because at three pads 1 the self centering of pads is achieved.

[FIGURE 1 OMITTED]

3. Analysis of bearing properties

At design of the bearing it is desirable to find the more sensitive one which would give the biggest elastic displacement of stick 16 measured by transducer 17 and together with it would guaranty enough strength of the pin which could keep the load of hydrodynamic force produced at revolving of the journal 2. For that reason it is necessary to know the maximal load which can be created by the hydrodynamic force and strength of pin neck. The hydrodynamic radial force of oil film wedge [F.sub.0] is expressed by equation [10, 11]

[F.sub.0] = 5.1 x [10.sup.-11] [mu]nD[B.sup.2]L[C.sub.L]/[[DELTA].sup.2], N (1)

where [mu] is oil viscosity coefficient in centipoises (cP); n is revolving frequency of the journal rev/min; D, B, L are diameter of the journal, width and length of the pad accordingly; [C.sub.L] is coefficient, [C.sub.L] = 1.25/[1 + [(B/L).sup.2]]; [DELTA] is value of clearance between the journal and the pad, in mm. Diameter of the pin head sphere of such a bearing is [d.sub.s] = 24 mm.

Lubrication oil for three pad journal bearings at large revolving frequency of a journal in common is accepted with very small viscosity, approximately 4 cP at temperature 55[degrees]C. It coincides with the lubricant viscosity ISO 6, a little below the Shell Tellus oils Do 10 lubricant. Such is the oil [??]5A produced in Ukraine. Further calculations we will do on the ground of that oil. Let for calculations we will accept the bearings of cylindrical grinder which has three pad bearing with journal diameter D = 70 mm and pad dimensions B = 36, L = 55 mm, number of journal revolutions 3000 rev/min. Fig. 2 shows dependence of force [F.sub.0] on clearance [DELTA] for such a bearing. Calculated value of force [F.sub.0] at clearance [DELTA] = 10 [micro]m is 26722 N.

[FIGURE 2 OMITTED]

Fig. 3 shows the scheme of cross-section of the neck eccentric to internal hole of the pin (stick 16 is not shown there).

[FIGURE 3 OMITTED]

At eccentric position of an external diameter [d.sub.1] of the neck according to an internal hole [d.sub.2] the neutral axis x-x of inertia moment of the neck cross-section will be displaced upward to value [e.sub.1] from axis of symmetry of external diameter [d.sub.1] and to value [e.sub.2] from the axis of symmetry of internal diameter [d.sub.2]. Eccentricity of external diameter according to internal diameter is equal e. At marking the area moment of inertia of external diameter [d.sub.1] to upper side from axis x-x by letter [I.sub.1], moment of inertia of internal diameter [d.sub.2] by [I.sub.2], moments of inertia of cross-section [d.sub.1] and [d.sub.2] from axis x-x to axis of symmetry of these cross-sections by [I.sub.3] and [I.sub.4] accordingly, and area moments of inertia of lower halves of circles [d.sub.1] and [d.sub.2] by [I.sub.5] and [I.sub.6], one can see that common area moment of inertia of the first part of cross-section placed over the axis x-x is equal [I.sub.c1] = [I.sub.1] - [I.sub.2], while of the cross-section placed under the axis x-x is equal [I.sub.c2] = [I.sub.3] + [I.sub.5] - [I.sub.4] - [I.sub.6]. Diameters [d.sub.1] and [d.sub.2] and eccentricity e are known from the pin design. Eccentricity [e.sub.2] is equal [e.sub.2] = [e.sub.1] + e, so there is left not known eccentricity [e.sub.1]. Because

[I.sub.c1] = [I.sub.c2] (2)

by insertion of values from [I.sub.1] to [I.sub.6] into Eq. (1) it is possible to find the value [e.sub.1], necessary for the calculation of area moment of inertia of the neck cross-section.

It is possible to write that moments of inertia from [I.sub.1] to [I.sub.6] are equal

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

there [r.sub.1(2)] are radiuses of diameters [d.sub.1] or [d.sub.2] respectively; [e.sub.1(2)] are their eccentricities according to axis x-x.

Common area moment of inertia [I.sub.c] of the neck cross-section according to axis x-x is equal

[I.sub.c] = [[pi]/4]([r.sup.4.sub.1] + [e.sub.1][r.sup.3.sub.1] + 2[e.sup.2.sub.1][r.sup.2.sub.1] - [r.sup.4.sub.2] [e.sub.2][r.sup.3.sub.2] - 2[e.sup.2.sub.2][r.sup.2.sub.2]) (4)

Because the pin is loaded by the load going through the pin axis and this axis coincides with the hole axis it is necessary to find not coincidence of axial load going through [e.sub.2] with the neutral axis x-x. Inertia moments from [I.sub.1] to [I.sub.4] are expressed by complicated equations, for that reason value e1 was calculated by the method of approximation.

The maximal strain [sigma] received in the neck of a pin and angular deflection of the pin head are evaluated accordingly by the equations

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

there [l.sub.k] is the neck length.

Displacement [delta] at the point measured by transducer 17 will be proportional to length ratio of measuring stick [l.sub.s] to neck length [l.sub.k], it is [l.sub.s]/[l.sub.k]. Because [theta] is proportional to [l.sub.k] and deflection measured by the transducer depends on [l.sub.k] one can go to conclusion that length of the neck [l.sub.k] does not influent on deflection measured by the transducer, but length [l.sub.s].

Table shows dependence between neck diameters [d.sub.1], [d.sub.2], [e.sub.1], strain [sigma] at eccentricity e = 2 mm and load of the pin with force [F.sub.0] = 26722 N, cross-section area A in [mm.sup.2], and neck stiffness c, N/[micro]m; displacement [delta] is for load 1 N.

As it is seen, such diameters of the neck assure necessary strength of the neck. Apart of that, modern sensors can measure displacements in nanometer limits. In such a case the measurement method enables to measure load on a pin 14 (Fig. 1) in limits of 1-10 N. At increase of diameter [d.sub.1] measurement sensitivity decreases, for that reason for proposed dimensions of the bearing Fig. 1 the neck diameters and eccentricity e should be got of that kind.

Force [F.sub.0] shows the hydrodynamic force which acts on the pins at journal rotation. If the journal is at center of the bearing, it is from all pad directions is acted by the same force and is in equilibrium state, the load carrying force ([F.sub.3]) comprises only at dislocation of the journal from its equilibrium (centered) position to eccentricity [e.sub.j]. This force for a three-pad journal bearing is expressed by the equation

[F.sub.3] = [F.sub.0](1/[(1 - 0.5[chi]).sup.2] - 1/[(1 + [chi]).sup.2]) (6)

or stiffness [c.sub.j] of lubricant hydrodynamic wedge film is [c.sub.j] = [F.sub.3]/[e.sub.j], N/[micro]m. There [chi] = 2[e.sub.j]/[DELTA], where [DELTA] at this case is in [micro]m.

Fig. 4 shows the dependence of force [F.sub.3] on value [DELTA] at the eccentricity [e.sub.j] = 1 [micro]m. It is seen that at smaller values of [DELTA] carrying force of the bearing smartly increases. The stiffness cc of the contact between the spherical pin head and the pad sphere can be expressed by the equation

[c.sub.c] = 9.81[d.sup.2.sub.s]/16[k.sub.s] (7)

where [d.sub.s] is diameter of the sphere; [k.sub.s] is a coefficient, [k.sub.s] = 0.5 [mm.sup.2][micro]m/N. Assuming [d.sub.s] = 24 mm, we obtain [c.sub.c] = 706 N/[micro]m.

[FIGURE 4 OMITTED]

The common stiffness [c.sub.com] of the pin head contact and the head neck can be found from the equation 1/[c.sub.com] = [1/[c.sub.c]] + [1/[c.sub.p]] and for the neck with [d.sub.1] = 16, [d.sub.2] = 11 because of its high stiffness the common stiffness leaves practically the same, in the limits [c.sub.com] = 705 N/[micro]m. At not automatically controlled bearing the third pin would also be of the same stiffness. At load with the force [F.sub.0] = 26722 N elastic deflection in mechanical contacts of the bearing would be 37.9 [micro]m. If to assemble the bearing with such interference (that at revolving it could work with the clearance 0.01 mm), after stoppage of rotation the pins will remain prestressed with interference of 27.9 [micro]m, or the interference force will be [F.sub.in] = 19670 N, the journal could not start revolving for such interference. For that reason the bearing could not work with the clearance of 0.01 mm at rotation.

Fig. 5 shows the minimal value of set clearance [DELTA] with which the bearing at revolving of the journal could work keeping initial interference force after stoppage (the same--at starting) equal zero ([F.sub.in] = 0). This force is defined by the equation

[F.sub.in] = [F.sub.0] - [c.sub.com][DELTA] = 0 (8)

[FIGURE 5 OMITTED]

The minimal clearance which is possible to achieve without initial interference at not revolving journal is [DELTA] = 0.0156 mm. One must keep in mind that this clearance must be kept at cold bearing. At its heat, e.g. if temperature between the bearing body and the journal would change to 1 [degrees]C, at the radius of external diameter of the body equal to 90 mm, the clearance would change to 1.1 [micro]m. After stoppage of heated system a new start of it would be with an interference force. It influences hardly on the bearing wear.

The use of automatically controlled bearing enables to set necessary clearance between the pads and the journal at its start and at work and in such a way to achieve necessary working conditions of the bearing. Research of the bearing with controlled work conditions would give better illustration of its work accuracy dependencies (revolving accuracy, damping and vibrations properties, etc.) than at "blind" research, when the hydrodynamic force conditions in the bearing are not known. Apart of that, it is possible to show, that control of the clearance in a bearing at start, at idle run of the journal and at work enables to control power losses and heat of the bearing.

3. Conclusion

Analysis of the possibilities of a new design of hydrodynamic tilting pad journal bearing with self-aligning pads shows that by control of the clearance between the journal and pads it is possible to keep in front defined conditions of the bearing operation, increase its stiffness and at its research to receive the picture, better showing dependencies of functioning quality of the bearing on its real state.

Received April 15, 2011

Accepted April 05, 2012

References

[1.] Marcinkevicius, A.H. 1995. Stabilization of Grinding Processes and Machine Tool Work, Vilnius, Technika. 312 p. (in Lithuanian).

[2.] Hargreaves, D.J.; Fillon, M. 2007. Analysis of a tilting pad journal bearing to avoid pad fluttering, Tribology International 4 (40): 607-612. http://dx.doi.org/10.1016/j.triboint.2005.11.019.

[3.] Reddy, D.S.K.; Swarnamani, S.; Prabhu, B.S. 2000. Thermoelastohydrodynamic analysis of tilting pad journal bearing--theory and experiments, Tribology Transactions 1(43): 82-90.

[4.] Hori, Y. 2006. Hydrodynamic Lubrication, Tokio, Springer Verlag, 360 p.

[5.] Vekteris, V.; Cereska, A.: Jurevicius, M. 2010. Diagnostic research of adaptive hydrodynamic segmental bearings with elastic ring in a rotor system, Mechanika 2(82): 58-62.

[6.] Vekteris, V.; Moksin, V. 2010. The modular principle of design of adaptive film lubrication bearings, Mechanika 4(84): 53-57.

[7.] Marcinkevicius, A.H. 2010. Multi-pad self aligning automatically regulated bearing, Patent Application No 2010107, Vilnius, 6 p. (in Lithuanian).

[8.] Minchenia, V.T.; Stepanenko, D.A.; Zimmerman, C.K.; Bansevicius, R.; Bubulis, A.; Kundu, P.; Gishkeliuk, I.A. 2010. Simulation of vibrational piezoelectric actuators of the micro-robot using the finite element method, JVE Journal of Vibroengineering 12(3): 314-319.

[9.] Patasiene, L.; Ragulskis, K.; Federavicius, A. 2010. Development and experimental analysis of layered actuators, JVE Journal of Vibroengineering 12(3): 333-339.

[10.] Marcinkevicius, A.H. 2010. Hydrodynamic tilting pad journal bearing with automatic control, Warshaw, The Archive of Mechanical Engineering 4(57): 343-354.

[11.] Reshetov, D.N. 1972. Parts and Mechanisms of Metal Cutting Machine Tools, Vol. 2, Moscow, Maschi

A.H. Marcinkevicius

Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania, E-mail: andma@vgtu.lt

http://dx.doi.org/ 10.5755/j01.mech.18.2.1567

Table

Dependence of [e.sub.1], strain [sigma], and measurement displacement
on neck diameters

[d.sub.1], mm    [d.sub.2], mm   [e.sub.1], mm   [sigma], MPa

16                    11             3.19            261
15                    10             2.84            283
14                     9             2.48            310

[d.sub.1], mm    [delta], [micro]m   A, [mm.sup.2]     c, N/[micro]m

16               4.8 x [10.sup.-4]        106        2.25 x [10.sup.7]
15               5.4 x [10.sup.-4]        98         2.43 x [10.sup.7]
14               6.1 x [10.sup.-4]        90         2.65 x [10.sup.7]