Research on coupling theory and its experiments between torque turbulence and bearing load of multi-support-rotor systems

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1 Available online Journal of Cheical and Pharaceutical Research, 04, 6(4): Research Article ISSN : CODEN(USA) : JCPRC5 Research on coupling theory and its experients between torque turbulence and bearing load of ulti-support-rotor systes Xinyu Pang and Zhaojian Yang College of Mechanical Engineering, Taiyuan University of Technology, Taiyuan, Shanxi, China ABSTRACT The bearing load(bl)governs the stability of axes set in the ulti-support-rotor systes(msrs). The torque turbulence (TT) would change BL, which could cause instability of axes set. In order to discern the torque turbulence, the theoretical analysis about the TT effecting on the BL had been done, as well as the coupled odel about TT and BL had been established, and the experiental study was presented in the paper. The two-directions bearing load sensor was introduced and its dynaic characteristic was analyzed as well according to its easuring principle and structure feature. Indirectly easuring the load of bearing bracket in radial and axle direction, the sliding bearing load could be acquired. An eight-support rotor test rig which is a MSRS with sensor was established, and its dynaics character was analyzed. The coupled odel about TT and BL was set up. Finally, the experient about BL in different support positions with two typical TT had been done. With the experiental results, it was anifested that the bearing load sensor has the characteristics of highly sensitivity, and the bearing load value could be onitored online when the TT exerted on the rotor syste. The coupled odel is verified, which provided the theoretical foundation and test data for the torque turbulence recognition. Keywords: Multi-support-rotor syste, bearing load, torque turbulence, sensor, dynaic characteristic INTRODUCTION MSRS is the key coponent for the large-scale rotation equipents such as the stea turbine and the copressor, etc. For calculating the bearing load of MSRS, the ethod of transission atrix has been applied in a long period [], and the result is just a reference function for installing the set of axes. There is little effect on the elevation adjustent and the failure predication. Besides the support position oveent, the bearing load is affected by the oent of torque turbulence which is caused due to the load change in electrical wire netting, the defect in steaer blade and so on. Then the rotational speed of the rotor is disturbed. The stability of the syste is finally destroyed []. Therefore, testing the bearing load with the ost effective exaining instruent directly and catching the feedback inforation real-tie are very great significance for keeping the set stability and avoiding the pernicious accident. Generally, there are four kinds of ethods which would be adopted in discerning the load of utility-type unit[3]. ) Dynaoetry. It can be described that a dynaoetric device is installed between the bearing and bearing bracket, and then the load could be easured directly. ) Deflection ethod. It can be explained that the static displaceent between the axle journal and the bearing is tested, and then the load can be calculated by analyzing the characteristic of oil layer. 3) Elevation ethod. It can be interpreted that the dynaic elevation is exained, and then the bearing load is obtained by calculating the value of the elevation. 4) Pressure ethod. The bearing load is discerned by easuring pressure of the oil fil. So, the dynaoetry is the best way aong the. Nevertheless, there is a little difficulty in installing the sensor because of the structure liitation between the bearing and its bracket. The brackets are usually fixed on the base with the bolts when rotor systes work. In this paper, the two-directions bearing load sensor was introduced and fixed between the bracket and its base. The force acted on the sensor by the 807

2 bearing bracket can reflect on the bearing load. The MSRS kinetic odel and the TT-BL coupling odel are established, and the structure of the bearing load sensor was described. Meanwhile, the dynaic characteristic of the sensor was analyzed and the dynaics of the support structure with sensor is analyzed. Furtherore, soe experients about BL in the different support positions were done with the entioned sensor. I.BEARING LOAD-SENSOR A. Principal and structure of sensor The bearing load was realized by indirect easureent. The easuring principle is resistance strain. The so-called indirect easureent is that the bearing load transfers to the sensor by the bearing housing. The load-sensor outputs different voltage signals which are converted fro resistance values of the strain gauge through the full bridge circuit. The sensor is ade of hard aluinu alloy aterial, on the one hand because of its good elasticity, on the other hand, because of its high strength. The structure of the load-sensor is shown in Fig.. When the load body of the sensor was bearing the horizontal and vertical loads of bearing bracket, the bea would defor greatly. In the neutral layer of the bea, the shear stress and strain are axiu. However, the shear stress was not easured easily and it could only produce the two perpendicular ain stress and angle of 45 degree to the bea central axis, which caused the axiu tensile stress and copressive stress. Thus, four blind holes were processed respectively in the horizontal and vertical bea segents. The two strain gauges were pasted along two directions perpendicular each other which are angle of 45 degree to the central axis bea, where the bending oent was zero in the botto of the hole. Strain gauges R, R, R3, R4 were pasted onto the botto of blind hole on the left and right horizontal segents of the bea, R5, R6, R7, R8 were pasted onto the botto of blind hole on the vertical segents of the bea. R, R, R3, R4 fored a full-bridge circuit, as shown in Fig.. (a), to easure the bearing loads of Y direction. R5, R6, R7, R8 generated a full-bridge circuit, as shown in Fig.. (b), to easure the bearing loads of X direction. Blind hole R Load body Y X R4 Bea R5 R R6 R3 R7 R8 Base Fig.: The structure of bearing-load sensor R4 R3 R8 R7 R R R5 R6 ~ (a) Y direction ~ (b) X direction Fig.: Full-bridge circuit B. Analyze the dynaic characteristics The dynaic characteristics were analyzed using both transient response and frequency response fro the tie doain and frequency doain [4]. Coonly the response characteristics are obtained through step function in the tie doain and through sine function in frequency doain. Dynaic perforance indexes are ainly natural frequency and daping ratio. Natural frequency of the sensor is deterined ainly by the structure paraeters. The higher the ωn value, the faster the response of the sensor. With the "virtual experient syste on echanical control engineering", the dynaic characteristics were analyzed. The virtual experiental syste was developed on the basis of the echanical control theory, for tie doain response, frequency doain response and stability analysis of typical part. 808

3 According to structural paraeters of the sensors, the vibration ass (), stiffness (K) and equivalent daping 7 coefficient (C ɛ ) were calculated respectively, =.68kg, K = N C 0000, e. Substituting these values into the virtual experiental syste, frequency response curve could be obtained under the step input shown in Fig.3. Fig.3: Frequency response curve To reflect the dynaic perforance of the sensor to certain extent, the signal of linear loading process was sapled by the DASP data collection instruent in this paper. The loading speed of X direction is 0. / s, and that of Y direction is 0.08 /s. The output curves were shown in Fig.4. The Fig.4 reflected the sensor can track the dynaic signal quickly and accurately, and the dynaic characteristics were good. Fig.4: X and Y direction sapled curves C. Dynaic analysis of the support structure with sensor The finite eleent odel of the support structure with the sensor was shown in Fig.5. Structural eleent type was Solid85; aterial property was bearing aterial-q35, linear and isotropic, so its elastic odulus E = 0GPa, Poisson's ratio µ = 0.3, density ρ = 7800g/c3; the sensor aterial is the hard aluinu alloy, so the definition of the elastic odulus E = 70GPa, Poisson's ratio µ = 0.3, density ρ = 700g/c3. After the geoetric odel had been created, the odel was eshed using free esh [4]. Analysis type was the Modal. The ode extraction ethod was the Block Lanczos ethod. Modal extraction nuber was 5. Extracted ode frequency range was the default value. The nuber of odal extended was 5. Modal analysis of the loading only included displaceent constraints. All the nodes of the botto of sensor were selected as constraint point, and its constraint type was "All DOF". The result to illustrate natural frequencies of the st~5th order fro Post- Processor (POST) can be seen in Tab. Tab. The st~5th order natural frequencies of the support structure with the sensor Step Natural frequencies(hz)

4 Fig. 5: The finite eleent odel of the support structure with the sensor II. THE DYNAMICS ANALYSIS ON THE MSRS A. The MSRS test rig The structure of the test rig was shown in Fig. 6. 3D odel was shown in Fig.7. The test stand was a siulation test stand of the Turbo. The axes was fored by the four axis connected by rigid coupling. And each axis was installed with two 50kg round iron plates for siulating the actual quality of the rotor accessory such as the ipeller. The axes was driven by the otor, and its rotation speed could be adjusted by frequency converter up to 3000r/in. Between each bearing housing and the base, 8 sensors were ounted on each support point. The end of the shaft was the agnetic brake that can be used to change the torque. In addition, vibration sensors, torque sensors and data collection instruent were contributed to for a coplete test syste, used for fault identification and diagnosis [5]. Fig. 6: The structure of the test stand Load-sensor Fig.7 3D odel of the test stand B. The dynaics odel for MSRS The MSRS is an elastic syste which has the feature of the ass continuous distribution [6]. In order to analyze the dynaics character, the succinct and reasonable echanics odel ust be established. The ass and the rotation inertia of the shaft were distributed to two ends, which fored the integrated-rigid-disc. The axes itself was siplified to the unifor-section elastic shaft without any ass in Fig.8. The positions at the bearing support were called exterior node, and else were called interior node. Fig.8: The echanics odel for MSRS 80

5 So far as the MSRS be concerned, there are four kinds of forces, the spring force, the daping force, intersectional spring force and intersectional daping force, because of the kinetic lubrication bearing existing at the external nodes. The force at the external nodes, F, consisted of the inertial force, the spring force, the external daping force and the out-of-balance excitation force. However, there are only two kinds of force, the inertial force and the excitation force, at the interior node [7]. In the paper, the axes and the bearing were regarded as one external node. For analyzing ainly the structure fored by the sensor cobined with bearing support, and the external daping force and the intersectional stiffness excitation force were not taken into account. Assuing the base is rigid and the bearing bracket is regarded as elastic support, which was equivalent to an elastic body when the sensor was installed between the node and the base. The ass participating in vibration included bearing bracket ass and the sensor ass. The Fig. 9 shows the structural echanics odel on the XY datu. y 0 kp f yf kf Fig. 9: The structural echanics odel when the bearing load sensor was installed Where, y is the distance-the node center deviated fro its static equilibriu position; y f is the distance-the sensor deviated fro its equilibriu position; k p is the isotropic spring stiffness coefficient of the siplified bearing; k f is the isotropic spring stiffness coefficient of the siplified sensor; is the external node ass participating in vibration which includes the integrated-rigid-disc ass, the bearing ass and the bearing bracket ass; f is the sensor ass participating in vibration. So the echanics equations at the external node could be described as following: && p ( f ) ( ) = && + F = y + k y y k y y y k y p f f f f f () C. The axes dynaics equation The MSRS is a ulti-degree of freedo syste. Besides the oil fil coupled force, there were the coupled effects aong the each bearing support force. Supposed the aount of support position as n, and the coupled effect was taken into account in the MSRS, then dynaics equations () as following could be established based on the forula(). [ M ]{ Y&& } + K p { Y Yf } = [ M ] esin ( Ω t + βt ) + { F} M f Y&& f + K f Yf = K p { Y Yf } { F} = [ Q]{ F} () where: [ M ] = [,,, ] L n is the concentrated ass at different support points. [ M ] = [,, L, ] f f f fn is the K p = k p, k p,, k pn participation vibration ass at different support points. L is the stiffness of the each sliding K,,, f = k k k f f fn bearing. L is the stiffness of support. { Y } = { y, y, L, y } n is the vibration displaceent of the each support point along vertical direction. { Y } = { y, y, L, y } f f f fn is the vibration displaceent of the each participation ass at the support point. { F } = { f, f, L, f } n is the support coupled force at the different support point. { F } = { f, f, L, f } n is the value of the bearing load fluctuation at different support point. { Q} is the sensitive coefficient of BL [8]. 8

6 D. The BL odel under the condition of TT When the position of bearing is defined, the dynaic load of bearing is related to the rotor revolution. The faster of revolution was, then the larger of eccentricity of the axle journal ounted by the bearing was, and the load along Y direction becae less. Obviously, the rotor rotation speed was changed directly by TT. Then the dynaic load of bearing was interfered with TT. For the single-span rotor structure, the rotation speed of the axes becae low transient under the condition of TT. Additional load F was also generated. The apping relationship between the value of the BL fluctuation and the torque was described as following: j= ( j, ) F = α jk T T Where, α K is the torque factor. T is the external torque. ( Tj, T ) j X = { F } Supposed i i = D = { X, } i T i,then i = [ ] discernent as X = α s is the radial base kernel function. (3) represents a set of training data. Supposing the paraeter vector for, and then T could be defined according to the equation (4). L L L J & θ y + k θ y k θ y + α T + L θ y y y Fy = k y Fy = k y = T 0 (4) θ y is tilt angle in the y k direction; k and y are the stiffness at its own support point. y and Where, are the respective vertical displaceent at two support points. L L is the span distance between two support points. T is the Fy F distance fro the TT position to support point. and y are the respective BL at the support point. Then the objective function could be defined as follows: J ( f ) = C L( T, Tsi ) + f, f = C L( f ( T ), Tsi ) + f, f i= i= L( f ( T ), Tsi ) Where, is the loss function. iniu for identification object. T is the easured torque, C J ( f ) is the penalty function. s is the ε was adopted as insensitivity loss function in SVM standard. Then the loss function can be described as follows: ( ) 0 f T Ts < ε L( f ( T ), Tsi ) = f ( T ) Ts ε = ε others Three steps should be taken for finishing the coputational process above entioned [9][0]. The first is constructing the training saple for D = { X, T i i} i =. The second is selecting the odel which supports the vector achine. The regression algorith supporting vector achine odel was deterined by kernel function, loss function and capacity control. The radial base kernel function is adopted because of its stronger ability of generalization. The last step is obtaining the optiization solution. Then the BL odel under the condition of TT with the nuber of support points of n in MSRS was described as follows: n { Fi } = αijk( Tij, Ti ) i= j= (5) 8

7 III. THE EXPERIMENT OF BL UNDER OF THE CONDITION OF TT A. The experient process In order to analyze the relationship between TT and BL, the experiental solution was designed as follows: two different kinds of TT were exerted respectively on MSRS when the rotor ran at acceleration phase, constant-speed phase and deceleration phase. Then the curves of bearing load could be acquired. The infinite variable speed of the rotor was realized by the otor which was controlled by the frequency converter. The axiu rotation speed of rotor was 500r/in. The saple frequency is 5Hz. The experient paraeters were shown in Tab.. Tab. The run status and data of MSRS Run status Acceleration phase Constant-speed phase Deceleration phase Duration(s) The oent of ipact torque working (s) 0 90,30 60 The oent of linear torque working (s) 0~30 00~30 60~70 Under the condition listed in Table., the ipact torque curve and linear torque curve of the rotor were shown respectively in Fig.0 and Fig.. Fig.0: The ipact torque Fig.: The linear torque B. Experient result The results of the BL along X direction and Y direction were shown in Fig., which were the syste response under the condition of ipact torque turbulence. 83

8 (a) The direction of X (b)the direction of Y Fig.:The variation torque contours of the rotor under the condition of ipact torque turbulence exerted The results of the BL along X direction and Y direction were shown in Fig. 3, which were the syste response under the condition of linear torque turbulence. (a) The direction of X (b)the direction of Y Fig.3: The variation torque contours of the rotor under the condition of linear torque turbulence exerted The TT ust lead to the reducing of rotational speed of the rotor and the decline of eccentric rate. It can be seen in Fig. and Fig. 3. The variation tendency of the each support load was exained in the experient when the rotor worked in the turbulence torque exerted. Intervened torque turbulence, the variation contours of the bearing load and the torque was alost in the sae tendency. The bearing load was extreely greater than it without torque turbulence exerted in the sae rotation speed. Torque turbulence being away fro the nearest support point, the variation of bearing load was greater than that of other position. CONCLUSION a) The bearing load sensor was installed between the bearing bracket and base. It could not change the structure of the bearing. So it would not have influence to the bearing. The sensor has the better dynaic characteristic and the higher sensitive. The critical speed of revolution could be derived by analyzing its dynaics property; as a result, the operating rotation speed could be obtained. b) It was anifested in experient that the bearing loading in each support point was generating the rearkable variation when the torque turbulence exerted on the axes set. Its aplitude of variation was even higher than the load caused by changing the position of bearing. It is sure that easuring BL after TT exerted is greatly effective in real-tie testing BL of MSRS. Acknowledgeents This work was supported by National Natural Science Foundation of China (NSFC) (Grants: 50759). REFERENCES []L.X. Xu. Dynaic Design of High-Speed Rotary Shaft, st Edition, National Defense Industry Press, Beijing, 994;

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