scholarly journals SOME FEATURES OF MILLS OPERATION COLD PILER PIPE ROLLING

2018 ◽  
pp. 30-35
Author(s):  
S.R. Rakhmanov
Keyword(s):  
Differential Equation ◽  
Mechanical System ◽  
Dynamic Model ◽  
Dynamic Instability ◽  
Power Line ◽  
Drive System ◽  
Design Stage ◽  
Dynamic Features ◽  
Pipe Rolling ◽  
Parametric Oscillations

Purpose. The establishment of the essence of many dynamic phenomena and the prediction of peak loads, both during the design or reconstruction stages of HPT mills and their operation using advanced calculation methods remain relevant. Methodology. An engineering technique to simplify a developed dynamic model is proposed, which includes the combination and development of known techniques. In addition, active mechanical connections in the original dynamic model of an HPT mill are identified, causing the pronounced parametric processes in the system under study. Findings. The study of the dynamics of simplified two-mass models of the HPT mill with combined parameters and periodically changing mass characteristics has been carried out. A differential equation of parametric oscillations in the drive power line has been compiled. The solution to the differential equation allows us to estimate the dynamic displacements of the considered drive of the working stand of the HPT mill for the most common modes of vibration of the mechanical system. Since the differential equations (8) are present in the formulation of the basic Cauchy problem, we implement the solution numerically, using the Runge - Kut method in the medium of a standard software product, for the most common first form of oscillations of a mechanical system. Originality. Dynamic features of the operation of the drive of the working stand of the HPT mill are presented in the form of angular displacements of the drive shaft of the mechanical system. The dynamics of the drive drive of the working stand of the HPT, 32-3 mill are calculated (pipe rolling along the route 38×3.8 → 19.1×2.1, material – steel Х18Н10Т). Practical value. The causes of the appearance of parametric oscillations in the drive system are identified and dynamic instability zones of the mechanical drive system of the HPT mill is installed, which allows for the selection of optimal rolling conditions at the design stage of technological processes. Keywords: cold rolling, pipe, mill, power line, main drive, dynamic model, simplified design scheme, mathematical model, parametric oscillations, differential equation, angular oscillations, dynamic instability.

scholarly journals CONSTRUCTION OF DYNAMIC INSTABILITY ZONES FOR HIGH STUCTURES UNDER SEISMIC IMPACT

2020 ◽  
Vol 2 (2) ◽  
pp. 42-50
Author(s):  
V Fomin ◽  
◽  
І Fomina ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Coordinate System ◽  
Mechanical System ◽  
Dynamic Instability ◽  
Vertical Component ◽  
System Of Differential Equations ◽  
High Rise ◽  
Concentrated Masses ◽  
Seismic Impact

Seismic impacts create the possibility of parametric resonances, i.e. the possibility of the appearance of intense transverse vibrations of structure elements (in particular, of high-rise structures) from the action of periodic longitudinal forces. As a design model of a high-rise structure, a model is used which adopted in the calculation of high-rise structures for seismic effects, - a weightless vertical rod (column) rigidly restrained at the base with a system of concentrated masses (loads) located on it (Fig. 1). By solving the differential equation of the curved axis influence function for a rod is constructed by means of which influence coefficients are determined for the rod points, in which the concentrated masses are situated. These coefficients are elements of the compliance matrix . Next, the elements of the stiffness matrix are determined by inverting the matrix . Using a diagonal matrix of the load masses and matrix a system of differential equations of free vibrations of a mechanical system, consisting of concentrated masses, is constructed, and the frequencies and forms of these vibrations are determined. From the vertical component of the seismic impact, its most significant part is picked out in the form of harmonic vibrations with the predominant frequency of the impact. Column vibrations are considered in a moving coordinate system, the origin of which is at the base of the column. The forces acting on the points of the mechanical system (concentrated masses) are added by the forces of inertia of their masses associated with the translational motion of the coordinate system. The forces of the load weights and forces of inertia create longitudinal forces in the column, periodically depending on time. Further, the integro-differential equation of the dynamic stability of the rod, proposed by V. V. Bolotin in [8], is written. The solution to this equation is sought in the form of a linear combination of free vibration forms with time-dependent factors. Substitution of this solution into the integro-differential equation of dynamic stability allows it to be reduced to a system of differential equations with respect to the mentioned above factors with coefficients that periodically depend on time. For some values of the vertical component parameters of the seismic action, namely the frequency and amplitude, the solutions of these equations are infinitely increasing functions, i.e. at these values of the indicated parameters, a parametric resonance arises. These values form regions in the parameter plane called regions of dynamic instability. Next, these regions are being constructed. A concrete example is considered.

scholarly journals The dynamics of the centreing mechanism of piercing mill mandrel of the pipe-rolling plant

2020 ◽  
Vol 7 (1) ◽  
pp. 51-63
Author(s):  
S.R. Rakhmanov ◽  
◽  
Yu.G. Gulyaev ◽  
S.V. Zdanevich ◽  
◽  
...  
Keyword(s):  
Mechanical System ◽  
Dynamic Model ◽  
Thickness Measurement ◽  
Piercing Mill ◽  
Pipe Rolling ◽  
Starting Point ◽  
Rod System ◽  
Rolling Plant ◽  
Steel 20 ◽  
Mill Mandrel

The paper presents the results of the vibrodiagnostics of a centering machine mechanism for holding piercing mill mandrel N1 of the pipe-rolling plant (PRP) 350. In the paper, it is established that vibration acceleration of a bearing roller lever of the centering machine mechanism for holding piercing mill mandrel during milling of an Æ282х50 mm shell, steel 20 reaches 5…12 m/s2, and of the upper roller’s vibration frequency is 33.3 Hz. The paper presents the results of the thickness measuring of the Æ282х50 shell, steel 20 after using the piercing mill N1 350. The results shows the distinctive influence of the dynamics of the milling holding mechanism rod. The system is put forth for calculating the energy-power parameters during the realization of the technical process for making shells of the required specifications in a piercing mill. The paper establishes the value of the milling axial resistance to the flow of the milled metal (taking the calibration values into account). The paper presents a refined system for making a dynamic model for the piercing bill milling holding mechanism rod with the milling calibration parameters taken fully included. A differential equation for the milling rod movement is made, specifically for the dynamic model of the PRP piercing mill mechanical system. The dynamic values of the mechanical system are refined, which is used as a starting point for solving the tasks dealing with the analysis of the PRP piercing mill milling rod’s vibroactivity state. In order to decrease rod vibroactivity levels, the paper recommends choosing rational milling calibration and to set the shell milling modes using mechanical system dynamics modelling during the corresponding stages of the design of technological processes. The paper pro-poses a scheme for modernization of the PRP 350 piercing bill exit side by switching the centering machine rod system holding bridges gear to proportional hydraulics. Keywords: piercing mill, vibration diagnostics, thickness measurement, piercing, sleeve; difference in wall thickness, energy-power parameters, calibration, mandrel, vibroactivity, dynamics, mandrel retention mechanism.

Study of the dynamics of ТПА 350 automatic mill working stand elements

2020 ◽  
Vol 76 (8) ◽  
pp. 830-840
Author(s):  
S. R. Rakhmanov ◽  
V. V. Povorotnii
Keyword(s):  
Mechanical System ◽  
Dynamic Model ◽  
Maximum Amplitude ◽  
Calculation Scheme ◽  
Dynamic Loads ◽  
Forced Oscillations ◽  
Mass Model ◽  
Automatic Mill ◽  
Hollow Billet ◽  
Oscillation Movement

To form a necessary geometry of a hollow billet to be rolled at a pipe rolling line, stable dynamics of the base equipment of the automatic mill working stand has a practical meaning. Among the forces, acting on its parts and elements, significant by value short-time dynamic loads are the least studied phenomena. These dynamic loads arise during transient interaction of the hollow billet, rollers, mandrel and other mill parts at the forced grip of the hollow billet. Basing of the calculation scheme and dynamic model of the mechanical system of the ТПА 350 automatic mill working stand was accomplished. A mathematical model of dynamics of the system “hollow billet (pipe) – working stand” within accepted calculation scheme and dynamic model of the mechanical system elaborated. Influence of technological load of the rolled hollow billet variation in time was accounted, as well as variation of the mechanical system mass, and rigidity of the ТПА 350 automatic mill working stand. Differential equations of oscillation movement for four-mass model of forked sub-systems of the automatic mill working stand were made up, results of their digital calculation quoted. Dynamic displacement of the stand elements in the inter-roller gap obtained, which enabled to estimate the results of amplitude and frequency characteristics of the branches of the mill rollers setting. It was defined by calculation, that the maximum amplitude of the forced oscillations of elements of the ТПА 350 automatic mill working stand within the inter-roller gap does not exceed 2 mm. It is much higher than the accepted value of adjusting parameters of the deformation center of the ТПА 350 automatic mill. A scheme of comprehensive modernization of the rollers setting in the ТПА 350 automatic mill working stand was proposed. It was shown, that increase of rigidity of rollers setting in the ТПА 350 automatic mill working stand enables to stabilize the amplitude of forced oscillations of the working stand elements within the inter-rollers gap and considerably decrease the induced nonuniform hollow billet wall thickness and increase quality of the rolled pipes at ТПА 350.

scholarly journals The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 799
Author(s):  
Xiangli Pei ◽  
Ying Tian ◽  
Minglu Zhang ◽  
Ruizhuo Shi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Model ◽  
Control Method ◽  
System Modeling ◽  
Working Environment ◽  
Partial Differential ◽  
External Interference ◽  
Differential Control ◽  
Differential Control Method

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.

High-frequency vibration energy harvesting from repeated impulsive forcing utilizing intentional dynamic instability caused by strong nonlinearity

2016 ◽  
Vol 28 (4) ◽  
pp. 468-487 ◽  
Author(s):  
Kevin Remick ◽  
D Dane Quinn ◽  
D Michael McFarland ◽  
Lawrence Bergman ◽  
Alexander Vakakis
Keyword(s):  
Energy Harvesting ◽  
Mechanical System ◽  
High Frequency ◽  
Large Amplitude ◽  
Electromechanical Coupling ◽  
Dynamic Instability ◽  
Vibration Energy ◽  
Primary System ◽  
Vibration Energy Harvesting ◽  
Strongly Nonlinear

The work in this study explores the excitation of high-frequency dynamic instabilities to enhance the performance of a strongly nonlinear vibration-based energy harvesting system subject to repeated impulsive excitations. These high-fraequency instabilities arise from transient resonance captures (TRCs) in the damped dynamics of the system, leading to large-amplitude oscillations in the mechanical system. Under proper forcing conditions, these high-frequency instabilities can be sustained. The primary system is composed of a grounded, weakly damped linear oscillator, which is directly subjected to impulsive forcing. A light-weight, damped nonlinear oscillator (nonlinear energy sink, NES) is coupled to the primary system using electromechanical coupling elements and strongly nonlinear stiffness elements. The essential (nonlinearizable) stiffness nonlinearity arises from geometric and kinematic effects resulting from the traverse deflection of a piano wire coupling the two oscillators. The electromechanical coupling is composed of a neodymium magnet and inductance coil, which harvests the energy in the mechanical system and transfers it to the electrical system which, in this present case, is composed of a simple resistive element. The energy dissipated in the circuit is inferred as a measure of energy harvesting capability. The large-amplitude TRCs result in strong, nearly irreversible energy transfer from the primary system to the NES, where the harvesting elements work to convert the mechanical energy to electrical energy. The primary goal of this work is to numerically and experimentally demonstrate the efficacy of inducing sustained high-frequency dynamic instability in a system of mechanical oscillators to achieve enhanced vibration energy harvesting performance. This work is a continuation of a companion paper (Remick K, Quinn D, McFarland D, et al. (2015) Journal of Sound and Vibration Final Publication) where vibration energy harvesting of the same system subject to single impulsive excitation is studied.

Mechanical Modeling and Design for Reduction of Parkinsonian Hand Tremor

2010 ◽  
Author(s):  
Timothy A. Doughty ◽  
Nicholas Bankus
Keyword(s):  
Differential Equation ◽  
Mechanical System ◽  
Model Identification ◽  
Equation Model ◽  
Vibration Absorber ◽  
Differential Equation Model ◽  
Hand Tremor ◽  
Test Fixture ◽  
Parkinsonian Tremor ◽  
Active Research

Most of the active research in reducing Parkinsonian tremor involves invasive surgeries or medical treatment. In this paper hand tremors associated with Parkinson’s Disease (PD) are studied and passive vibration control methods are developed and tested. Patients with PD are surveyed regarding difficulties with hand tremor during the act of eating. The result leads to design criteria for an enhanced eating utensil and the establishment of meaningful testing methods for measuring hand tremor. Tremor data collected from several PD patients provides insight into the nature of the motion and allows for the development of test fixture and prototypes. This experimental data is coupled with linear model identification testing for the free response of a “healthy” hand undergoing the same motions. The resulting differential equation model, where the system input is realized as actuation through the biomechanics of the forearm and wrist, is used in the design of an eating utensil for vibration reduction. With self-excitation and the existence of harmonics, the tremor data is also used to develop a nonlinear differential equation model, where the complete neurological/mechanical system is realized with an equivalent mechanical system. This nonlinear model is shown to mimic the tremor data and is used to enhance the development of the vibration absorber. A prototype of the vibration absorber is built, validated on the test fixture, and tremor reduction data is collected again with PD patients.

Mathematical Modeling of Process Moving Cargo by Overhead Crane

2014 ◽  
Vol 701-702 ◽  
pp. 715-720 ◽  
Author(s):  
Vitaly Shcherbakov ◽  
Mikhail Korytov ◽  
Roman Sukharev ◽  
Elena Volf
Keyword(s):  
Mathematical Modeling ◽  
Mechanical System ◽  
Second Generation ◽  
Block Diagram ◽  
Design Stage ◽  
Bridge Crane ◽  
Overhead Crane ◽  
Operating Modes ◽  
Design Scheme ◽  
Simulink Model

According to the proposed design scheme of the overhead crane, with the use of blocks package SimMechanics Second Generation of MATLAB, a conceptual block diagram of connections was developed, according to which the was created Simulink-model of the mechanical system of the bridge crane with PID regulator. Simulink-model allows us to study the operating modes of the overhead crane on the its design stage.

scholarly journals Drive System Dynamics Compensator for a Mechanical System Emulator

2015 ◽  
Vol 62 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Chengwei Gan ◽  
Rebecca Todd ◽  
Judith M. Apsley
Keyword(s):  
System Dynamics ◽  
Mechanical System ◽  
Drive System
Sign in / Sign up

Export Citation Format

Share Document