Dynamic investigation of a spatial multi-body mechanism considering joint clearance and friction based on coordinate partitioning method

The dynamic response of the model, which is the series connection of a planar four-bar mechanism and a spatial RSSR mechanism, is analyzed considering revolute joint clearance and friction. A non-holonomic constraint equation is proposed to solve the Euler angles. The dynamic equations are established by combining the Lagrange equation with the modified contact model and the LuGre friction model. A dynamic solution program based on the coordinate partitioning method is designed to solve the dynamic equations. The paper verifies the correctness and applicability of the solution program by comparing the numerical calculation results with Adams simulation. Compared with the results of eccentricity, it is found that the maximum penetration is very sensitive to the change of the slider speed rather than the clearance. The equivalent damping coefficient proposed by authors not only represents whether a collision occurs, but reflects the hysteresis caused by damping. The macroscopic manifestation of the up and down oscillation of eccentricity is the swing of the contact point. Besides, the system quickly changes from the collision into the stable state due to considering friction, and the peak value of each collision reduces greatly. Therefore, when the clearance is unavoidable, the clearance joint should be coated with a material with a large friction coefficient and not easy to wear.

Fabrication and characterization of highly controllable magnetorheological material in compression mode

This article is focused on the development and characterization of highly controllable magnetorheological materials for stiffness and damping control in semi-active control applications. Two types of magnetorheological materials are developed in-house: magnetorheological elastomer with soft base elastomer, and magnetorheological fluid encapsulated in regular elastomer, namely magnetorheological fluid-elastomer. In both cases of magnetorheological elastomers and magnetorheological fluid-elastomers, the samples are evaluated using in-house-developed shear and compression test rigs, which are equipped with electromagnets and Hall effect sensors for measuring the magnetic field. These features provide the capability to precisely control a wide range of magnetic fields during the experiments. In the case of magnetorheological elastomers, the experimental results of the in-house magnetorheological elastomers are compared with commercially available counterparts made of hard base elastomer. It is shown that the controllability of the material, that is, the relative magnetorheological effect, is significantly improved in the case of magnetorheological elastomer with soft base elastomer. In addition to various magnetic fields, the samples are subjected to a range of loading amplitudes and frequencies. A general trend is observed where the frequency and strain amplitude cause an opposite effect on both the shear and compressive moduli: the increase in frequency gives rise to a higher value of modulus whereas the increase in amplitude reduces the modulus. Furthermore, the effect of bonding on the performance of the magnetorheological elastomers in compression mode is evaluated and the results indicate a significant increase in the modulus and decrease in the loss factor. In all the cases, however, the change of loss factor does not exhibit a predictable trend as a function of magnetic fields. In order to investigate a magnetorheological-based solution for controlling the damping of a semi-active system, magnetorheological fluid-elastomer samples are made in-house. These samples are fabricated using three different iron concentrations, and are tested in compression (squeeze) mode. The results of these experiments confirm that the equivalent damping coefficient of the material rises with the increase in magnetic field, and this effect becomes stronger as the iron concentration of magnetorheological fluids increases. It is also demonstrated that the magnetorheological effect is highly dependent on the loading frequency and amplitude, where the equivalent damping coefficient decreases with the increase in loading frequency and amplitude. In all the aforementioned cases, the stiffness of magnetorheological fluid-elastomers exhibits minor changes, which offers the in-house-developed magnetorheological fluid-elastomers as a damping only control option, a development that is different from the magnetorheological fluid-elastomers reported in the literature.

A new type of damper combining eddy current damping with rack and gear

A new type of damper combining eddy current damping with rack and gear, which can simultaneously export damping and inertial forces, is proposed. Eddy current damping with rack and gear is supposed to be installed between the building superstructure and foundation to mitigate the seismic response of the building. First, the concept of eddy current damping with rack and gear is introduced in detail and its apparent mass and equivalent damping coefficient are both theoretically investigated. Second, a prototype of eddy current damping with rack and gear is manufactured, and a series of tests on the prototype are carried out to verify its structural parameters. The experimental and theoretical results of the apparent mass of the prototype agree well with each other. The experimental result of the equivalent damping coefficient of the prototype is slightly lower than the numerical results obtained from COMSOL Multiphysics and its maximum relative differences are 11.3% and 13.6% for α = 0° and 45°, respectively. Third, detailed parametric studies on the damping force, including the effects of the thickness of the conductor plate, air gap, and number and location of permanent magnets, are conducted. The results show that the damping force keeps a linear relationship with velocity if it is lower than 0.15 m/s, and with the increase of the velocity, a strong nonlinear relationship between the damping force and the velocity is observed. The available maximum damping force can be increased by decreasing the thickness of the conductor plate and the air gap, increasing the number of permanent magnets. There is an optimal location about the permanent magnets for the available maximum damping force. In addition, the hysteretic curves of the eddy current damping with rack and gear obtained from the test indicate that the ability of energy dissipation is considerable.

Research on the Vertical Vibration Characteristics of Hydraulic Screw Down System of Rolling Mill under Nonlinear Friction

The rolling mill with hydraulic system is widely used in the production of strip steel. For the problem of vertical vibration of the rolling mill, the effects of different equivalent damping coefficient, leakage coefficient, and proportional coefficient of the controller on the hydraulic screw down system of the rolling mill are studied, respectively. First, a vertical vibration model of a hydraulic screw down system was established, considering the nonlinear friction and parameter uncertainty of the press cylinder. Second, the correlation between different equivalent damping coefficient, internal leakage coefficient, proportional coefficient, vertical vibration was analyzed. The simulation results show that, in the closed-loop state, when Proportional-Integral-Derivative (PID) controller parameters are fixed, due to the change of the equivalent damping coefficient and internal leakage coefficient, the system will have parameter uncertainty, which may lead to the failure of the PID controller and the vertical vibration of the system. This study has theoretical and practical significance for analyzing the mechanism of vertical vibration of the rolling mill.

Study on Equivalent Viscous Damping Coefficient of Sucker Rod Based on the Principle of Equal Friction Loss

Equivalent viscous damping coefficient is an important parameter of wave equation for sucker rod string. In this paper, based on the principle of equal friction loss, when the viscous energy consumption and the local damping energy consumption are taken into account, effects of equivalent viscous damping coefficients are obtained. Through deducing energy consumption equation of oil and energy consumption equation of the coupling, theoretical formula for equivalent damping coefficient of sucker rods is received. Results show that the smaller the K is (K is the ratio of sectional area of tubing to sucker rod), the larger the proportion of damping coefficient caused by viscous energy consumption in the equivalent damping coefficient of sucker rod system is. When K< 0.095, the proportion of damping coefficient caused by viscous energy consumption is more than 90%. Reducing the sudden change of cross-section area at sucker rod coupling has remarkable effect on reducing damping force of the sucker rod system. The research provides a theoretical basis for the application and design of sucker rod and tubing.

Damping performance analysis of magnetorheological damper with serial-type flow channels

In order to obtain a larger damping force with the limited axial size of the vehicle suspension system, a new magnetorheological damper with serial-type flow channels was developed. The piston head was equipped with two piston end covers, three piston non-magnetic sleeves, and four piston magnetic sleeves, which were sequentially combined into three serial-type flow channels to form three groups of effective damping gaps. The structure and principle of the proposed magnetorheological damper were described in detail, and the model for calculating damping force was deduced too. Simulation and analysis for the proposed magnetorheological damper was implemented using electromagnetic field simulation software. The damping performance was tested and analyzed on the test rig under different applied current, amplitude, and frequency excitation. The experimental results show that the damping force is 6838 N under the load excitation with frequency of 1 Hz, amplitude of 7.5 mm, and current of 1.5 A, which is 1.6 times than the expected damping force. The equivalent damping coefficient is attained to 290 kN/s m−1, which shows that the developed magnetorheological damper has high vibration control ability and good mechanical properties.

Kinetodynamic Model and Simplified Model of X-Type Seat System with an Integrated Spring Damper

A simplified analytical model with transformation coefficients of X-type seat system with an integrated spring damper for control strategies development is proposed on the basis of a kinetodynamic model. Firstly, based on a commercial seat of trucks, the relationship between the suspension support force and the spring force was created by using virtual work principle. The analytical formulae of the equivalent stiffness Ke and the stiffness transformation coefficient ρk were deduced. Based on the principle of conservation of energy, the analytical formulae of the equivalent damping coefficient Ce and the damping transformation coefficient ρc were deduced. Then, the motion equation of the simplified model was created. Secondly, the nonlinear dynamic equation of a complex seat model including the kinematic characteristics was established. Thirdly, the road test was conducted using a heavy truck to collect the seat vibration signals. Finally, the simplified model was validated by the tested data and compared with the complex model. The results show that the accuracy of the simplified model is acceptable. Moreover, the influence laws of kinematic parameters on ρk and ρc were revealed. The proposed simplified model provides an accurate and efficient tool for designing controllable seat suspension system that minimizes a necessary tuning process.

Study on Dynamic Characteristics of Aerostatic Bearing with Elastic Equalizing Pressure Groove

Microvibration has an important influence on the dynamic performance of aerostatic bearings. Dynamic stiffness and equivalent damping coefficient are the main indexes to evaluate the dynamic characteristics of the aerostatic bearing. In order to study the dynamic characteristics of a new type of aerostatic bearing with the elastic equalizing pressure groove (EEPG), the dynamic characteristics of the new type of bearing are studied by theoretical calculation and experiment. First, the dynamic gas-solid coupling control equation is established. Then, the steady term and the perturbation term are decomposed by the perturbation method. By solving the coupling model, the dynamic characteristics of the bearing are calculated and analyzed. The calculation results show that the perturbation frequency has a significant effect on the dynamic stiffness and equivalent damping coefficient of the aerostatic bearing with EEPG. The dynamic stiffness increases with the increase of frequency, and the equivalent damping coefficient decreases with the increase of frequency. The experimental results are basically the same with the theoretical results, which effectively verify the correctness of the theoretical analysis.

Determining the level of damping vibration in bridges and footbridges

While designing slim and slender structures such as cable-stayed, suspended and arch bridges and footbridges, data on the dynamic behavior of structure are required. One of the main quantities, included in the calculations, is the damping parameter of vibration of the structure whose corresponding value has a direct impact on the proper behavior of the facility. One of currently applied approaches in the case of complex constructions, is the use of methods defining the equivalent damping coefficient which refers to the given form of natural vibrations. Among these methods, the collocation method and energy method can be distinguished. The collocation method refers to the existing facilities and requires performing measurements of vibration and spectral processing of time course of vibrations. The energy method requires the creation of FEM model of construction and it estimates the kinetic energy of the vibrating system. The above- mentioned methods are used in the calculations of the damping level of vibration of two structures, i.e.: arch John Paul II Bridge in Pulawy and a footbridge located in Lublin.