Torsional Vibration Method Research Articles

Nonlinear dynamic characteristics analysis method of planetary gear train torsional vibration considering meshing oil film force

Planetary gear train is an important part of automatic transmission. The oil film between teeth is one of the key factors affecting the torsional vibration of planetary gear train. Selecting the appropriate oil film stiffness is of great significance for analyzing the nonlinear dynamic characteristics of planetary gear train. A method for analyzing the nonlinear dynamic characteristics of planetary gear system torsional vibration considering the oil film force between teeth is proposed in this paper. A 3-DOF torsional vibration model of planetary gear train considering oil film is established. In this model, the oil film between teeth is equivalent to a time-varying nonlinear spring-damper element, and nonlinear factors such as backlash and meshing error are also considered. The effects of meshing oil film thickness on oil film stiffness and damping are analyzed, and the torsional vibration characteristics of planetary gear train under different meshing stiffness, meshing damping ratio, and rotational speed are analyzed based on bifurcation diagrams. The results show that in one meshing cycle, the meshing oil film thickness first becomes larger and then becomes smaller. When the meshing oil film thickness increases, the meshing oil film stiffness and the equivalent meshing oil film damping become smaller. The torsional vibration of planetary gear train can be effectively reduced by increasing meshing stiffness, damping ratio, rotational speed within a certain range. This method provides technical support for reducing torsional vibration of planetary gear train and realizing stable transmission of planetary gear train.

Testing of wood shear modulus based on cantilevered square plate torsional vibration method

ABSTRACT The application of the energy method has proposed a dynamic testing method for the shear modulus in two mutually perpendicular directions on the principal surface of wood using a cantilevered square plate torsional vibration method. In the study, this method was applied to measure the shear modulus of larch wood in the LT and TL directions, as well as the longitudinal and transverse shear modulus of Laminated Veneer Lumber (LVL) sheets. The validity of the results was confirmed through experimental verification using the asymmetric four-point bending beam method, the free plate torsional vibration method, and the free square plate torsional mode method. Simulation calculations of the principal shear modulus for six species of trees with width-to-thickness ratios ranging from 10 to 25 were also conducted using this method. The conclusions drawn suggest that a width-to-thickness ratio of 15 for the cantilevered square plate provides sufficient accuracy for testing the principal shear modulus of wood. Furthermore, the difference in shear modulus between two mutually perpendicular directions on the principal surface of wood is dependent on the width-to-thickness ratio of the cantilevered square plate, indicating that this method outperforms other dynamic methods for testing wood shear modulus.

Measurement and Analysis of the Vibration Responses of Piano Soundboards with Different Structures.

The effect of structure on the vibration response was explored for four piano soundboards with different but commonly adopted structures. The vibration response was obtained using the free-vibration method, and the values of the dynamic modulus of elasticity and dynamic shear modulus obtained using the free-vibration frequency method (EF and GF) were compared with the dynamic modulus of elasticity obtained using the Euler beam method (EE) and dynamic shear modulus obtained using the free-plate torsional vibration method (GT), respectively. It was found that the soundboards with different structures had different vibration modes and that excitation at different locations highlighted different vibration modes. For all the soundboards analyzed, the EE and GT were higher than EF and GF by 2.2% and 24.3%, respectively. However, the trends of the results of these methods were the same. The four piano soundboards with different structures possessed varying dynamic moduli of elasticity and dynamic shear moduli. These rules are consistent with the grain directions of the soundboards and the anisotropy of the wood (the direction of the units of the soundboards). The results show that the vibration mode of the piano soundboard is complex. The dynamic elastic modulus of the soundboard can be calculated using the Euler beam method. The results provide a reference for studies on the vibration response, material selection, production technology, and testing of piano soundboards.

Interlaminar shear modulus of cardboard obtained by torsional and flexural vibration tests

Abstract The interlaminar shear modulus of cardboards was measured using torsional vibration (TV) and flexural vibration (FV) methods. In the TV method, the sample widths were decreased during the tests, and the interlaminar and in-plane shear moduli were determined using the data obtained based on the different widths. By contrast, in the FV method, the resonance frequencies from the first to third FV modes were measured using samples of various lengths, and the interlaminar shear modulus and Young’s modulus in the length direction were calculated using Timoshenko’s vibration theory. In addition to the experiment, modal analyses based on the finite element (FE) method were performed, and the sample configurations used to accurately obtain the interlaminar shear modulus were experimentally and numerically investigated. The TV method did not allow the interlaminar shear modulus to be obtained appropriately because the vibration behavior often deviated from that theoretically derived by the TV equation. By contrast, the FV method allowed the interlaminar shear modulus to be obtained appropriately for a wide range of sample lengths.

Research progress on dynamic testing methods of wood shear modulus: A review

Wood is a non-homogeneous and orthotropic natural polymer material. It is important to test the wood shear modulus and elastic constants accurately and reliably using dynamic methods. Based on the introduction of the advantages of six common methods for dynamic testing of wood shear modulus, such as free plate torsional mode method, free bar torsional vibration method, and Timoshenko beam iterative method, issues associated with the applicability and accuracy of these methods are also pointed out. Recent methods, such as the free square plate torsional mode method and the square plate static torsional strain method, that were developed to dynamically test the shear modulus of wood and wood composite materials, are presented as effective ways to tackle these issues. These new approaches are expected to provide beneficial technical support for using small specimens, overcoming the size effect of specimens, simplifying the testing procedures, improving the test accuracy, and expanding the application range in the dynamic testing of wood shear modulus. These approaches have practical significance in promoting the industrialization and development of structural engineering, furniture and interior decoration, transportation, military, and musical instrument industries.

Identification of Defective Joints in Beams via Torsional Vibration

The determination of the shear dynamic modulus in wood product panels is of greater importance than its determination in wood beams. Yet with regards to the effect of defects on the obtained values of shear modulus, this factor is used to detect the defects and the degree of the defects. In this study, the effect of gluing defects in two joint shapes (scarf (45°) and finger joints (10 mm length and 3 mm pitch) were evaluated non-destructively using the torsional vibration method. Rectangular wood specimens with dimensions of 20 mm × 40 mm × 360 mm (R × T × L) were prepared from clear eastern beech. The joints were located at similar positions in the middle of the beams. The results showed that creating a healthy joint did not significantly change the values obtained for the shear modulus in either of the joint shapes. However, reducing the adhesion level in both types of joints caused a significant reduction in the shear modulus values. The results show that the changes in the dynamic shear modulus values in both joint types, as a result of changes in the glue coverage rating (fully, medium and low-glued joints) allows the detection of the defects as well as the degree of the defects.

Model of a Drive System for Low-Floor Trams with a Four-Linkage Coupling

The article describes the structure and principles of operation of a drive system used in some low-floor trams. The system consists of electric motors, gear transmissions as well as hollow shaft s and four-linkage couplings causing the wheels to move. During the study, a dynamic model was built and the parameters needed to carry out a simulation were determined. NGT6 low-floor tram wagons operated by MPK S.A. Cracow were used as examples of existing vehicles. Due to the lack of available data, part of the work was devoted to determining mass moments of inertia of drive system components using an experimental method of torsional vibrations of a string. In subsequent chapters, a mathematical model was developed and a tram start-up simulation was performed based on specific parameters of the individual system components. Some of the results were presented in the form of graphs. Keywords: tram riding simulation, mathematical model of dynamics, start-up, mass moments of inertia, method of torsional vibration of string

VISCOSITY OF CuPb, CuPbSn, CuPbSnGa AND CuPbSnGaBi MELTS OF EQUIATOMIC COMPOSITIONS

We investigated the viscosity of CuPb, CuPbSn, CuPbSnGa and CuPbSnGaBi melts of equiatomic compositions by the method of damped torsion vibrations of a crucible. We saw the melts of equiatomic composition as the melts high-entropy. All the investigated melts demonstrated the different temperature dependences of viscosity for heating and cooling. There is an anomalous reduction in viscosity resulted when the melt is heated to a specific temperature. The anomalous behaviour for viscosity we interpreted in terms of melt structure. This structural changes in the melt resulted when the melt is heated to a specific temperature. The microstructure of CuPbSnGaBi ingot of equiatomic composition we investigated using optical microscopy and measurement of microhardness. Collations data of the microstructures with of the microhardness gave three structural components: CuGa2 dendrites, (Sn) + (Bi) + Bi3Pb7 ternary eutectic and rounded Pb inclusions having dimensions of 5 m.

Excitation method and electromechanical coupling dynamic model of a novel torsional piezoelectric actuator

Torsional piezoelectric actuators have been widely applied in many fields due to their specific vibration mode. However, the conventional torsional vibration piezoelectric actuators require circumferentially polarized piezoelectric ceramics or special structural designs, increasing manufacturing difficulty and processing costs, and seriously limiting their applications. In order to solve these problems, a novel excitation method of torsional vibration is proposed in this study through the arrangement of the regular piezoelectric ceramic plates polarized along their thickness direction, and then two surface-bonded type torsional piezoelectric actuators are constructed to stimulate the odd and even order torsional vibration modes, respectively. A novel transfer matrix model of describing the torsional vibration, which involves in the mechanical and electrical properties, is created first for the piezoelectric composite beam element. Then a general electromechanical coupling dynamic model is developed to reveal dynamic behaviors of the proposed surface-bonded type torsional piezoelectric actuators. In addition, the finite element simulation and experimental investigations are carried out to confirm the validation of the proposed excitation method of torsional vibration and to verify the correctness of the developed electromechanical coupling dynamic model. The comparisons showed that the results calculated by the developed theoretical model, simulated by the finite element method, and tested by the experiments matched well, indicating that the developed electromechanical coupling dynamic model is correctness and the excitation method of torsional vibration is effective. Finally, the output characteristics of the two proposed actuator prototypes are measured, further confirming the feasibility of the proposed torsional vibration excitation method.

Study on curing kinetics and behaviours of PGN adhesives.

The curing kinetics between PGN and N100 were studied by Fourier transform infrared spectroscopy and dynamic torsional vibration method. The results showed that the entire curing process of adhesives was divided into three stages. Infrared spectroscopy can only monitor the first and second stages, while dynamic torsional vibration method monitors the second and third stages. Combining the two analysis methods allows the complete monitoring of the entire curing process in this system. Besides, differential scanning calorimeter is not suitable for studying this process.

Determination the yaw moment of inertia of an SUV in laboratory conditions

The vehicle oscillates in different planes relative to the three axes while driving. Especially important are the turns of the vehicle by dint of steered wheels. During such highspeed turns, the vehicle is subjected to additional charges of various systems, including the control system. Therefore, in the calculations of the control system of the vehicle, it is necessary to take into account the inertial mass of the vehicle. In general, the inertial characteristics of some solid body during its rotation are determined by the moments of inertia of this body. The moment of inertia of a solid body concerning the axis of rotation is simply the mass times the square of the perpendicular distance to the rotation axis. To test the results obtained by means of the analytical method, it is necessary to determine the moment of inertia of a vehicle in an experimental way. A convenient method of measuring the moment of inertia of a vehicle can be the method of torsional vibrations. The moment of inertia of a vehicle was determined using special equipment, which was constructed in the laboratory of the Department of Motor Vehicles of the National Transport University.

Physicochemical characteristics of melts of corrosion resistant nitrogen-alloyed steels

Physicochemical characteristics of the nitrogen-alloyed steel melt of the 04Kh20N6G11M2AFB grade (nitrogen content 0.47–0.49%) are investigated by using the torsional vibration method of a crucible with metal in the atmosphere, which provides a stable nitrogen content during the experiment (80% nitrogen and 20% helium). Using the method sensitivity to the aggregate state of the tested substance, at a heating rate of 0.0033–0.0050 K/s, the liquidus temperatures are experimentally determined for the 04Kh20N6G11M2AFB steel (1660–1666 K) and low nitrogen steel ([N] = 0.063%) with the identical content of other elements (1685–1690 K). These results make it possible to recommend the value of the coefficient –60 K/% [N] for the calculated assessment of nitrogen influence on the liquidus temperature of complex and high alloy steels. The viscosity of the 04Kh20N6G11M2AFB steel melt is relatively high ((11.5 ± 0.7) ×10–7 m2/s) in comparison with the traditional austenitic steels ((8.2 ± 0.2) × 10–7 m2/s) with a relatively small partial effect of nitrogen. A significant nonequilibrium of the structural state of the 04Kh20N6G11M2AFB steel melt is revealed by the high-temperature viscometry methods. The comparative analysis of polytherms and kinematic viscosity isotherms of the 04Kh20N6G11M2AFB steel melt and its low nitrogen ([N] = 0.063%) analogue makes it possible to conclude that the nitrogen presence in concentrations close to saturation plays a decisive role in the melt nonequilibrium level and low relaxation rate. This is confirmed by the results of special experiments on saturation with nitrogen of low nitrogen steel, in which a sharp increase in nonequilibrium of the melt structural state is recorded when nitrogen concentration in metal reaches the limiting values (0.45–0.50%). There is a potential possibility to increase and stabilize the operational properties of corrosion resistant nitrogen-alloyed steels due to reducing the melt’s structural state nonequilibrium by excluding the excess of limiting values of nitrogen concentrations for the chemical composition considered.

Management of the dynamic properties of a base modified by deep soil mixing technology

Conversion of building properties is performed primarily to reduce the compressibility of the base and increase strength. However, in addition to changing the static properties of soils, it is necessary to take into account changes in dynamic properties, such as dynamic shear modulus, damping coefficient, velocity of elastic shear and longitudinal waves. Thus, it is possible to control the dynamic properties of the base by converting the construction properties of soils. In this paper, we consider the change in the velocity of shear waves in a base transformed by the technology of deep soil mixing (DSM). In the work, the influence of additional vertical stresses on the dynamic properties of the bases transformed using deep soil mixing technology was evaluated. As a parameter that allowed us to evaluate the dynamic properties, the propagation velocity of elastic shear waves was chosen. Shear wave velocity was estimated based on the results of triaxial tests using the method of low-amplitude torsional vibrations in a resonant column. The research results showed that at small values of axial strains, there is no significant increase in the velocity of shear waves, an increase in the speed of shear waves by two times with an increase in stress by 0.6 MPa.

Studies of the shear wave velocity in soil cement under the anisotropic stress state

Introduction. Deep soil mixing, that alters construction properties of foundations, allows to construct buildings and structures on the sites that have loose soils. As a rule, adverse geotechnical conditions are accompanied by dynamic forces that affect designed buildings and structures. The objective of these studies is to predict changes in mechanical properties of soils that follow the alteration of structural properties of a foundation. Soil cement is the focus of this study. Materials and methods. The findings of special laboratory tests of soil cement samples using the method of low amplitude torsional vibrations inside a resonant column in the anisotropic triaxial compression mode allowed to assess the effect of the supplementary vertical load on the velocity of shear elastic wave propagation. The co-authors present a description of the research method and provide an overview of the equipment used to conduct special laboratory tests. Tests were performed on undisturbed soil cement samples that had a natural water content. The anisotropic stress state of soil cement samples exposed to triaxial tests in the resonant column was caused by special behaviour features of the foundation. Results. In this study, laboratory tests had two stages. At the first stage, the effect of the vertical stress on the velocity of shear wave propagation was assessed. Correlation dependences between the shear wave velocity and the ratio of vertical and lateral stresses were obtained. At the second stage, shear wave propagation velocity values were identified at various combinations of lateral σ3 and vertical σ1 stresses. The results of the second stage are designated for the assessment of the effect of the anisotropic stress state and the projection of shear wave velocities at the stress levels anticipated on the site that will accommodate designed heavy structures. Conclusions. The findings allow to assess the effect of lateral and vertical stresses on changes of shear wave velocities in the triaxial compression mode. It was identified that at equal values of lateral stresses σ3, a 7-fold vertical stress σ1 increase leads to a 15 % increase in the shear wave velocity in soil cement Vs. At the same time, an increase in the ratio of vertical to lateral stresses σ1/σ3 by a factor of 15 causes an 11 % increase in the shear wave velocity. It is noted that the smaller the initial value of lateral stress σ3, the higher the rise in the shear wave velocity Vs in the course of testing. Correlation dependencies, presented in this study, can be used to assess the effect of the anisotropic state as the first approximation (for preliminary calculations) in the design of heavy structures on soil cement foundations.

The Physicochemical Characteristic Study of Melts of Corrosion Resistant Nitrogen-Alloyed Steels

Physicochemical characteristics of the nitrogen-alloyed steel melt of the 04Kh20N6G11M2AFB grade (nitrogen content 0.47–0.49%) are investigated by using the torsional vibration method of a crucible with metal in the atmosphere, which provides a stable nitrogen content during the experiment (80% nitrogen and 20% helium). Using the method sensitivity to the aggregate state of the tested substance, at a heating rate of 0.0033–0.0050 K/s, the liquidus temperatures are experimentally determined for the 04Kh20N6G11M2AFB steel (1660–1666 K) and low nitrogen steel ([N] = 0.063%) with the identical content of other elements (1685–1690 K). These results make it possible to recommend the value of the coefficient –60 K/% [N] for the calculated assessment of nitrogen influence on the liquidus temperature of complex and high alloy steels. The viscosity of the 04Kh20N6G11M2AFB steel melt is relatively high ((11.5 ± 0.7) ×10–7 m2/s) in comparison with the traditional austenitic steels ((8.2 ± 0.2) × 10–7 m2/s) with a relatively small partial effect of nitrogen. A significant nonequilibrium of the structural state of the 04Kh20N6G11M2AFB steel melt is revealed by the high-temperature viscometry methods. The comparative analysis of polytherms and kinematic viscosity isotherms of the 04Kh20N6G11M2AFB steel melt and its low nitrogen ([N] = 0.063%) analogue makes it possible to conclude that the nitrogen presence in concentrations close to saturation plays a decisive role in the melt nonequilibrium level and low relaxation rate. This is confirmed by the results of special experiments on saturation with nitrogen of low nitrogen steel, in which a sharp increase in nonequilibrium of the melt structural state is recorded when nitrogen concentration in metal reaches the limiting values (0.45–0.50%). There is a potential possibility to increase and stabilize the operational properties of corrosion resistant nitrogen-alloyed steels due to reducing the melt’s structural state nonequilibrium by excluding the excess of limiting values of nitrogen concentrations for the chemical composition considered.

Dynamic properties of steel slag improved with sand–tyre shreds admixture

To achieve recycled use of waste steel slag and waste tyres, it was proposed to incorporate waste tyre particles into waste steel slag and mix with sand to form a new geomaterial. Considering the effects of confining pressure, incorporation ratios of tyre particles and in corporation ratios of sand, the dynamic shear modulus and damping ratio of the new geomaterial were studied by a torsional shear vibration method based on resonance column tests. The specific control density of steel slag combined with different mixing ratios of tyre particles and sand were determined according to the relative density. The relationship between the dynamic shear modulus and the shear strain of the new geomaterial suited the hyperbolic model of Davidenkov. The maximum dynamic shear moduli of the new geomaterial with the tyre particle mixing ratio of 5% reached 166 MPa at the confining pressure of 200 kPa and were close to those of Fujian standard sand. The maximum dynamic shear modulus of the new geomaterial with the tyre particle mixing ratio of 15% was 103 MPa at the confining pressure of 200 kPa and was larger than those of Nanjing fine sand. The minimum damping ratio of the new geomaterial was in the range of 0·21–1·95% at the confining pressure of 200 kPa and was larger than that of the pure steel slag with 0·15–1·2%. These findings showed that the new geomaterial could be applied instead of sand.

A Study on the Modeling and Simulation Method of Torsional Vibration Considering Dynamic Properties of Rubber Parts for Engine Crankshaft System with Rubber Damper Pulley

A Study on the Modeling and Simulation Method of Torsional Vibration Considering Dynamic Properties of Rubber Parts for Engine Crankshaft System with Rubber Damper Pulley

A novel variable structure PID fuzzy controller for torsional vibration in mechanical transmission system

Mechanical transmission systems are susceptible to vibration for torsional moment in work, which causes flutter and buffeting during mechanical transmission, affecting the precision of the mechanical transmission control and resulting in steady-state error. Therefore, an optimal control method of torsional vibration in mechanical transmission system based on variable structure PID fuzzy control is proposed. With this method, a constraint parametric model for torsional vibration in mechanical transmission system is constructed. The simulation experiment results show that the proposed method can control the torsional vibration in the mechanical transmission system steadily with relative strong adaptive tracking compensation ability of torsional moment and other parameters, which indicates that the method improves the robustness of mechanical transmission with good buffeting elimination and suppression performance during mechanical transmission.

The influence of stress state, density and moisture on the dynamic properties of soil cement samples created by the method of deep soil mixing

The transformation of the properties of the bases by the method of deep soil mixing allows the construction of buildings and structures on sites with soft soils. As a rule, adverse geological conditions are accompanied by the presence of dynamic effects on the designed buildings. The objective of this research is to forecast changes in the mechanical properties of the base under dynamic loads. The object of study is the propagation velocity of elastic shear waves, since these parameters significantly affect the calculations of deformations and stability of earthquake-resistant industrial and civil buildings and structures, as well as objects of energy and transport construction. The paper contains a review of similar studies, on the basis of which the conclusions obtained during the experiments are further generalized. Based on the analysis of the results of laboratory tests performed by the authors of this work, by the method of low-amplitude torsion vibrations in a resonant column in the anisotropic triaxial compression mode, the influence of the density of soil cement samples, humidity, and additional load on the propagation velocity of elastic transverse waves is estimated. The paper provides a description of the essence of the research method, a review of the equipment on which special laboratory tests were performed. The tests were carried out on samples of unbroken soil cement taken from the base of a nuclear power plant (NPP) under construction. Dried samples of soil cement were investigated, and tests were carried out at full water saturation and at a given humidity. The anisotropic stress state of soil cement samples during triaxial tests in a resonance column was due to the features of the base of the designed NPP. Studies have shown that the most significant factor affecting the shear wave velocity is the additional vertical load. It is noted that with increasing density, the velocity of the shear waves decreases. Humidity is directly related to the density of soil cement and the amount of water in the pores, so the assessment of its effect on the dynamic properties of soil cement is similar to the effect of changes in density.

Adaptive vibration absorbing method of torsional vibrations for processing equipment

This article describes issues relating to monitoring vibrations affecting the processing equipment. Especially, the problem of negative influence from the increased vibration background in well drilling, where the issue is the most acute, is being described. The urgency of creating methods to monitor vibration condition, due to which it becomes possible to design reliable and efficient structures with the required characteristics and purpose, is shown. Particular attention is paid to passive methods for monitoring torsional vibrations of pipe columns. In this case, the developed method for monitoring the vibration condition of torsional vibrations is presented, and its effectiveness is shown. In addition, a new device for monitoring torsional vibrations to the developed method, which is distinguished by its simplicity as well as high potential of reliability and efficiency, is shown.