Position Estimation at Zero Speed for PMSMs Using Artificial Neural Networks

This paper presents a method for shaft position estimation of a synchronous motor with permanent magnets. Zero speed and very low speed range are considered. The method uses the analysis of high-frequency currents induced by the introduction of additional voltage in the control path in the stationary coordinate system associated with the stator. An artificial neural network estimates the sine and cosine values necessary in the Park’s transformation units. This method can achieve satisfactory accuracy in the case of low asymmetry of inductance in the direct and quadrature axes of the coordinate system associated with the rotor. The TensorFlow/Keras package was used for artificial network calculations and the scikit-learn package for preprocessing. Aggregating the outputs of several artificial neural networks provides an opportunity to reduce the resultant estimation error. The use of as few as four networks has enabled the error to be reduced by approximately 20% compared to a single example network.

WRITING OUT OF FORMULAS FOR CALCULATING FORCES IN THE JOINTS OF MANIPULATORS IN STATICS

The problem of bulkiness of mathematical models of manipulative systems of industrial robots is solved. Here we consider formulas for calculating static reactions in joints and formulas for active forces that balance the forces of gravity acting on the manipulator's bodies in its stationary state. The manipulator can be in such a state when it is before capturing the object of manipulation and releasing it, or when it is performing some assembly operations, or it is during spot welding and in slow (quasi-static) arc-welding and painting processes. Aim. The aim is to derive general recur-rence and finite formulas for calculating the reaction forces in joints and their projections to the ax-es of the coordinate system rigidly connected with the selected body. Express the formulas of force projections in terms of guiding cosines and justify their optimality in terms of the minimum of arithmetic operations. Derive general inverse recurrence formulas for writing out the guide cosines of the axes associated with the moving bodies of the coordinate system with respect to the stationary coordinate system. Research methods. The methods of research relate to vector mechanics and sys-tems analysis, and the algorithmization of calculations by reducing them to the use of recurrent formulas. Results. A systematic analysis of general formulas, in which all possible regular expres-sions are highlighted which are corresponding unambiguously to the kinematic parameters of ma-nipulators, is performed. These regular expressions are used in software for analytical modeling of manipulator, in particular, for the analytical solution of problems of statics of a manipulator. The method of analytical verification of the prescribed formulas is described. The tasks of writing out optimal formulas for calculating the projections of static reaction forces in joints have been solved. And the tasks of writing out optimal formulas for calculating active forces in progressive joints of universal manipulators with six degrees of freedom, operating in Cartesian, cylindrical, spherical and angular coordinate systems, have been solved also. Analytical verification of the derived equations of stat-ics is performed. Examples of the reuse of the derived formulas for manipulators with the same kin-ematic schemes of their subsystems. Conclusion. Expressions of the equations of statics of manipu-lators through the guide cosines of the axes of the associated coordinate systems of their bodies al-low us to write these equations through the known parameters of body orientation. The recurrent formulas for calculating directional cosines allows to use recursive functions in their software im-plementation, i.e. to increase the computational efficiency of the software.

Rotordynamic characterization of tilting-pad bearings with eight pads in vertical rotors

It has been documented that stiffness and damping for a four-pad bearing are dependent not only the magnitude of the load but also on the position of the rotor in the bearing. However, 8-pad bearings are not commonly employed on horizontal turbines, and the presence of several pads in the bearing will decisively affect the dynamics of the system. This paper evaluates the stiffness and damping coefficients of tilting-pad bearings with eight pads and explore the main frequencies acting on the forced response of a vertical rotor. The bearing properties were modeled as a function of eccentricity and position in the stationary coordinate system by Navier-Stokes equations whose results are taken from commercial software. The simulated unbalanced response is compared to experimental results; the changing position of the shaft produces a periodic stiffness and damping, which is dependent on the number of pads. Cross-coupled coefficients influence is discussed, showing that their absence makes an accurate model for the mean values. The results indicate that simulation of vertical rotors with 8-pad bearings can be simplified which allow more effective simulations and dynamic analysis.

PROBLEMS OF CONSTRUCTION OF ASYNCHRONOUS ELECTRIC DRIVES WITH STATE OBSERVERS

This paper considers the problems of constructing asynchronous electric drives with state observers and the latest advances in the field of sensorless alternating current drives. The main areas of application of asynchronous electric drives with state observers are determined. A vector sensorless control system using coordinate converters from a natural coordinate system to a stationary and rotating one and a state observer based on a mathematical model of a motor in a two-phase stationary coordinate system was used as a basic one when considering the structures of modern asynchronous electric drives. The main types of flow and speed observers of asynchronous electric drives are considered for the tasks of constructing a high-quality asynchronous electric drive with vector control without using sensors. The problem was formulated for further modernization of control systems based on an electric drive with a flow and speed observer.

Static and Rotordynamic Analysis of a Plain Annular (Liquid) Seal in the Laminar Regime With a Swirl Brake for Three Clearances

Tests are reported for a smooth seal with radial clearances 127 μm, 254 μm, 381 μm (1×, 2×, and 3×); length 45.72 mm, diameter 101.6 mm. An insert induced upstream preswirl. Swirl brakes (SBs), comprising 36 square cuts with axial depth 5.08 mm, radial height 6.35 mm, and circumferential width 6.35 mm each. Static and rotordynamic data were produced at ω = 2, 4, 6, 8 krpm, ΔP = 2.07, 4.14, 6.21, 8.27 bar, and eccentricity ratios ε0 = e0/Cr = 0.00, 0.27, 0.53, and 0.80. ISO VG 46 oil at a range of 46–49 °C was used, netting laminar flow (total Re ≤ 650). Dynamic measurements included components of the following vectors: (a) stator–rotor relative displacements, (b) acceleration, and (c) applied dynamic force in a stationary coordinate system. SBs were effective at the 3× clearance only. With the 3× seal, the cross-coupled stiffness coefficients have the same sign (not destabilizing). However, the seal has a negative direct stiffness K that could potentially “suck” the rotor into contact with the stator wall, along with dropping the pump rotor's natural frequency, further reducing its dynamic stability. Measurements were compared to predictions from a code by Zirkelback and San Andrés. Most predictions agree well with test data. Notable exceptions are the direct and cross-coupled stiffness coefficients for the 3× clearance. Predictions showed positive direct stiffness and opposite signs for the cross-coupled stiffness coefficients.

The definition of the direction of forces arising during the interworking of a car’s steer wheel with chassis dynamometer

The article gives the theoretical substantiation of the forces determination that arise during the steerable vehicle wheel with chassis dynamometer interaction taking into account the wheels angles setting in relation to the longitudinal, vertical and transverse vehicle axes. The transition from mobile to fixed coordinate system using Euler angles is considered. The transitions comparison from the stationary coordinate system to the moving one in the system an aircraft axes and ship axes. It made it possible to move to the fixed coordinate system for a steerable vehicle wheel. A table of transition between moving and stationary reference systems has been made. The table provides an opportunity to determine the projections of forces that arise when the steerable vehicle wheel is interacting with the bearing surface when the angles of its installation are relative to the frame, are changed.

Forced Vibration Analysis of Spinning Disks Subjected to Transverse Loads

Forced vibration of a rotating disk subjected to a stationary transverse load is studied in this paper. Time and frequency responses are obtained and effects of the rotating speed on the natural frequencies are evaluated. Finite element method (FEM) is employed as the solution technique and natural frequencies are obtained for different speeds. Forced vibration is then considered and disk responses are determined using the Galerkin method. The solution is determined in two different coordinate systems. In the first one, the disk is assumed to be rotating in an inertial coordinate system, while in the second coordinate system, a rotating peripheral force is applied on a stationary disk. The objective here in this paper is to compare the two modeling scenarios and is to find limiting range of the rotational speed for employing the stationary coordinate system.