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3-D stress analysis generator rotor styudy.pdf

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3D Finite Element Stress Analysis of Two-Pole Turbogenerator Rotor Alexey I. Borovkov Eugeny V. Pereyaslavets Denis V. Shevchenko Igor A. Artamonov Computational Mechanics Laboratory, St.Petersburg State Polytechnical University, Russia Abstract In the current paper the rotor (inductor) of two-pole turbogenerator is analyzed. This is the most loaded joint by mechanical and thermal loading. One of the urgent problems during design and manufacturing processes is the problem of rotor v
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  3D Finite Element Stress Analysis of Two-Pole Turbogenerator Rotor  Alexey I. Borovkov Eugeny V. Pereyaslavets Denis V. Shevchenko Igor A. Artamonov Computational Mechanics Laboratory, St.Petersburg State Polytechnical University, Russia Abstract In the current paper the rotor (inductor) of two-pole turbogenerator is analyzed. This is the most loaded  joint by mechanical and thermal loading. One of the urgent problems during design and manufacturing  processes is the problem of rotor vibrations and balancing. Vibration of the two-pole rotor can be caused by several reasons. Special attention should be paid to the vibration with double rotational frequency that can  be observed in general in rotors with significant l/D relation (relation of the rotor body length to its diameter). This vibration is caused by different rotor body stiffness in two main axes directions: axis of  poles (axis of big tooth ) and neutral normal to the axis of poles. In order to compensate rotor body stiffness anisotropy in the current job the system of regular cross-slots in the zone of big tooth (Laffoon's slots or slits) is used. An integral characteristic is considered to evaluate rotor body stiffness dissymmetry: magnitude proportional to the difference of maximum static sags (located in the middle of rotor body) in the directions of principle moments of inertia. One of the most topical problems after application of such cross-slots is stress concentration at the bottom of slots. In the present paper the results of 3D multi-variant finite element (FE) structural analysis of stress concentration zones at the bottom of cross-slots under gravity and centrifugal loading are presented. Together with the results of finite element analysis analytical estimations after Neuber are quoted for stress concentration coefficients in U-like notches with arbitrary depth. Various statements of the contact problems for rotor under gravity and centrifugal loading were considered in order to analyze the effect of contact interaction consideration between various rotor parts on stressed state. Introduction Double rotational frequency vibration cannot be eliminated by any balancing, and the only method of its reduction is maximum equalization of rotor stiffness in two directions. To equalize two-pole rotor stiffness in main axes directions two methods are known and widely used: regular cross-slots (Laffoon’s slots) on the rotor body poles (“big teeth”) or longitudinal slots on poles filled with ferromagnetic [1-7]. Both methods have their own advantages and weak points. In the current paper turbogenerator rotor with stiffness equalization system in the form of Laffoon’s slots is considered (see Figure 1).    Figure 1. Fragment of the turbogenerator rotor body with cross-slots on “big teeth” System of rotor body cross-section anisotropy elimination by cross-slots suggested by US engineer more then 60 years ago and having been used till present days is extremely easy. On the rotor body poles a number of cross-slots is created by milling cutter of radius R (Figure 1). Bottom of the slot is made round to lower stress concentration. Fillet radius r   is commonly equal to half slot width b , i.e. slot bottom profile is semi-circle. In some cases milling cutter can be specially cloistered to get fillet radius more then b/2 . Rarely due to lower efficiency cross-slots are created as circle segment with rectilinear bottom. Slots depth t and distance between them (spacing)  s  are defined first of all from the condition of equalization system efficiency (extent of rotor body cross-section anisotropy decrease), secondly by safety factor in the cross-section with stress concentrator and thirdly by limitations imposed on conditions of electromagnetic parameters invariance. Slots width is usually equal to 10 − 20 mm, but their influence is obviously spread on much wider zone. One of the most urgent problems at Laffoon’s slots usage for stiffness equalization is stress concentration on the slots bottom. In the current paper the results of 3D multi-variant FE structural analysis of stress concentration zones at the bottom of cross-slots under gravity and centrifugal loading are presented. Together with the results of finite element analysis analytical estimations after Neuber are quoted for stress concentration coefficients in U-like notches with arbitrary depth [8]. Comparison of stress concentration coefficients obtained with use of FE software ANSYS [9] and Neuber’s formulae will help to make conclusions about analytical estimations applicability for this important class if industrial problems. Finite element modeling and stress analysis of turbo-generator rotor with stiffness equalization system in the form of Laffoon’s slots Statement of problem During FE analysis two-pole turbogenerator rotor construction will be considered. 3D solid model and rotor  body cross-section are shown in Figures 2 and 3.    Figure 2. 3D solid model of the two-pole turbogenerator rotor Figure 3. Cross section of the two-pole turbogenerator rotor body Gravity is acting on the rotor as loading. In the zones of bearings rigid hinges constraint condition is applied. System of loads and boundary conditions is presented in Figure 4. By virtue of homogeneity of materials and symmetry of geometry, loadings and boundary conditions only half of the construction is considered. To eliminate rotor rigid body displacements along longitudinal axis Oz   outer point of the rotor  body was fully constrained (marked with “ ã ” in Figure 4).    Figure 4. Scheme of loadings and boundary conditions: a horizontal “big tooth” axis; b vertical “big tooth” axis It should be noted that turbogenerator rotor body is made of medium-carbon steel alloy with yield stress 2.0 σ   ≅  900 MPa. At this point and further FE models are created with use of 3D 20-node solid brick structural elements SOLID95. Rotor FE model (with vertical “big tooth” axis) and its fragment are presented in Figure 5, where  NE = 71268  −  total number of finite elements,  NDF = 741255   −  total number of degrees of freedom. FE model is the case of horizontal “big tooth” axis is similar. Figure 5. 3D FE model of the two-pole turbogenerator rotor (taking into account symmetry plane Oyz  )

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