Nonlinear Dynamics Analysis of Multifactor Low Speed Heavy Load Gear System with Temperature Effect Considered

Low-speed and heavy-duty gears will generate a lot of heat during meshing transmission, which will cause thermal deformation of the gears and affect the transmission performance of the gear system. It is of great significance to explore the influence of temperature effects on the nonlinear dynamics of the gear system. Taking the spur gear system as the research object, considering the nonlinear factors such as time-varying meshing stiffness, tooth backlash and comprehensive error, and introducing the influence of temperature change, the nonlinear dynamic model of the gear system is established, using 4~5th order Runge -Kutta algorithm performs simulation calculation on the model, combined with bifurcation diagram, maximum Lyapunov exponent diagram, phase diagram and Poincare section diagram, etc., to analyze the influence of temperature changes and time-varying stiffness coefficients on the motion characteristics of the gear system. The results show that the influence of temperature change on the gear system is related to the value of the time-varying stiffness coefficient. The larger the value, the more obvious the influence of temperature change; the system will show different dynamic response with the change of the time-varying stiffness coefficient, including four states of single-period motion, multiple-period motion, bifurcation and chaotic motion. The relevant conclusions can provide references for the design of gear systems under special working conditions.

Pullback Attractors for Nonautonomous Degenerate Kirchhoff Equations with Strong Damping

In this paper, we obtain the existence of pullback attractors for nonautonomous Kirchhoff equations with strong damping, which covers the case of possible generation of the stiffness coefficient. For this purpose, a necessary method via “the measure of noncompactness” is established.

Frequency Response Function and Design Parameter Effects of Hydro-Pneumatic Tensioner for Top-Tensioned Riser

The top-tensioned riser is an important equipment in offshore oil and gas development. The hydro-pneumatic tensioner is an essential device to ensure the safety of the top-tensioned riser. To investigate the dynamic performance of the marine platform hydro-pneumatic tensioner, this paper proposed a first-order Taylor approximation method and created the frequency response function of the hydro-pneumatic tensioner. According to the frequency response function, the hydro-pneumatic tensioner is a first-order spring-mass system. With the given parameters, the system stiffness coefficient is 66.1 kN/m, the natural annular frequency is 20.99 rad/s and the damping ratio is 2.23 × 10−4. The effects of the high-pressure accumulator, low-pressure accumulator, hydraulic cylinder and pipeline design parameters on the stiffness coefficient, natural annular frequency and damping ratio are analyzed. The stiffness coefficient can be increased by (1) increasing the high-pressure accumulator pressure and reducing the high-pressure accumulator volume; (2) increasing the pressure of the low-pressure accumulator and reducing the low-pressure accumulator volume; (3) increasing the piston diameter; and vice versa. The natural annular frequency can be increased by: (1) increasing the high-pressure accumulator pressure and reducing the high-pressure accumulator volume; (2) increasing the pressure of the low-pressure accumulator and reducing the low-pressure accumulator volume; (3) increasing the piston diameter; and vice versa. The damping ratio can be increased by increasing the pipeline length and reducing the pipeline inner diameter.

Stability and Modal Conversion Phenomenon of Pipe-in-Pipe Structures with Arbitrary Boundary Conditions by Means of Green’s Functions

In this paper, a closed-form frequency equation of the pipe-in-pipe (PIP) structure with arbitrary boundaries is obtained. The frequency equation is derived from Green’s function of the transverse forced vibration of the PIP structure and takes into account the effects of internal two-phase flow and axial pressure. The reliability of the method in this paper is proved by comparison with the published literature. In the numerical discussion part, the PIP structures with clamped-clamped, clamped-free, and elastic boundary conditions are used as examples to discuss. The effects of equivalent stiffness coefficient, internal flow velocity, and gas volume fraction on the stability of PIP structure are studied. The results show that the stability of the PIP structure is better than that of the single-pipe structure, and the greater the equivalent stiffness coefficient of the elastic layer, the higher the critical flow velocity of the structure. In addition, a modal conversion phenomenon existing in the PIP structure is discovered. There are different forms of modal conversion for different boundary conditions, and the modal conversion makes the order of instability of the PIP structure different from that of a single-pipe. The conclusion of this paper has positive significance for the dynamic research of PIP structure.

About the weight and size parameters of electromagnetic stiffness correctors

A significant reduction in the levels of general ship vibrations can be achieved by using vibration isolators with a “floating” section of zero stiffness in vibration protection suspensions. In such devices, in parallel to the main elastic element, the so-called stiffness corrector (compensator) is switched on - a device with a negative coefficient of static stiffness, equipped with a restructuring system that ensures the retention of the corrector elements when the relative position of the vibrating and protected objects, caused by a change in static forces acting on these objects. One of the variants of the corrector is an electromagnetic stiffness corrector, in which the power characteristic with a negative stiffness coefficient is provided by two electromagnets with a common armature turned on in opposite directions. The disadvantage of such correctors is the dependence of their overall dimensions on the value of the permissible relative displacement of the vibrating and protected objects. The article deduced mathematical expressions that approximately determine the dependence of the overall dimensions of the stiffness corrector electromagnets on the value of the calculated relative displacement of the vibrating and protected objects, the possible field of application of vibration isolators Xwith electromagnetic stiffness correctors is determined.

Experimental and numerical study on the screw connection strength of bamboo-oriented strand board compared with wood-oriented strand board

The utilization of resourceful bamboo can alleviate the wood shortage problem. Bamboo-oriented strand board (BOSB) with the highest utilization of bamboo ratio and excellent mechanical properties was considered as a good engineering and furniture material. The strength of joints affects the safety of BOSB structure. This study aims to investigate the effect of screw spacing on the tensile and compressive stiffness and strength of corner joints from BOSB by experimental method combined with finite element method (FEM) compared with wood-oriented strand board (WOSB). The results showed that (1) the strength and stiffness of the corner joint was significantly affected by the screw spacing, and it affected the compressive strength and stiffness of WOSB more significantly; (2) the bending moment and stiffness coefficient of BOSB compressed joint decreased with the increase of spacing, while that of tensile joint increased first and then decreased, and it reached the maximum value, when the spacing was 48 mm; (3) compared with WOSB joint, BOSB joint had higher strength and stiffness, and the failure of the joint was due to the yielding of self-drilling screws. This was also verified by numerical analysis results; (4) the bending moment of BOSB joints was about 2.5 times that of WOSB joints, while the difference between stiffness coefficient was small; (5) the elastic deformations resulted from experimental tests and FEM are similar. It was shown that when the screw spacing is 48 mm, the Von Mises stresses on the BOSB joint were smaller, and the bending strength and stiffness were larger, which was the most suitable screw spacing.

Research on boundary slip of hydrostatic lead screw under different driving modes

The flow state of oil film in the hydrostatic lead screw directly affects the transmission performance of the screw pair. The static and dynamic characteristics of a new type of double driven hydrostatic screw-nut pair (DDHSNP) are studied under different motion modes. The boundary condition of navier slip model is introduced into the lubricating mathematical model of DDHSNP, and the influences of boundary slip on the axial bearing capacity, axial stiffness and damping coefficient in micro scale are researched by finite difference method. The results show that when the motor runs at high speed (the rotating speed range of the screw and nut driven motor is 1000–9000 rpm), the existence of boundary slip leads to a improvement of the axial bearing capacity and stiffness coefficient of DDHSNP in the case of single-drive operation and dual-drive differential feed (the range of rotation difference is 10–100 rpm), which is more obvious under the single-drive mode. The increase rate of stiffness coefficient induced by boundary slip is much larger than that of bearing capacity. In addition, the boundary slip has little effect on the damping coefficient of DDHSNP in either single drive operation or dual drive differential operation.

Wood-based boards mechanical properties and their effects on the cutting process during shredding

In order to design effective shredding machines dedicated to shredding wood-based waste, information about the mechanical properties of materials subjected to shredding is necessary. A number of mechanical properties of particleboard, oriented strand boards, and medium-density fibreboards in the aspect of shredding process have been experimentally determined in the article. The influence of material type, blade geometries, and cutting depth on cutting force and elasticity coefficient were analysed. Blade geometries reflect different phases of rotation of the cylindrical wood chipper’s knife. It has been shown that a knife with the most favourable geometry is characterized by the lowest values of the stiffness coefficient for each of the materials. This is the geometry of the cylindrical wood chipper’s knife exactly halfway into the cutting process. By contrast, the least favourable geometry is characterized by a knife corresponding to the beginning of the cutting process. Among the tested materials, the medium density board requires the most energy to change its structure, and the laminated particleboard requires the least. The presented results can be a set of input data necessary to model the work required to implement the cutting process, but also enable validation of existing cutting models.

Multi-parametric Dynamic Analysis of a Rolling Bearings System

A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

Modeling and Analysis for the Transmission Characteristics of a Proposed Dual-Drive Hydrostatic Lead-Screw System

This paper proposes a novel dual-drive hydrostatic lead-screw system (DDHLS). The design enables a lower feed speed and a better transmission performance than the conventional hydrostatic lead screw (HLS). Considering the nut-misalignment, the lubricating mathematical model of the DDHLS is established based on the perturbation method and solved by the finite difference method. The influences of the nut-radial-displacement, the nut-tilt, and the dual-drivable design on the transmission performance of the DDHLS are researched. The results show the nut-misalignment can regularly reduce or increase the axial load capacity, the axial stiffness coefficient, and the axial damping coefficient. Significantly, the dual-drivable design can improve the axial load capacity and the axial stiffness coefficient while hardly affects the axial damping coefficient.