Contact Model of Revolute Joint with Clearance Based on Fractal Theory

The contact sti ness of a mechanical bonding surface is an important parameter in determining the normal and radial contact force. To improve the calculation accuracy of the contact force model, the surface roughness of the bonding surface and the energy loss that necessarily occurs during the impact process should be considered com?prehensively. To study the normal contact force of a revolute joint with clearance more accurately in the case of dry friction, a nonlinear sti ness coe cient model considering the surface roughness was established based on fractal theory, which considers the elastic, elastic?plastic, and plastic deformations of the asperities of the contact surface during the contact process. On this basis, a modified nonlinear spring damping model was established based on the Lankarani–Nikravesh contact force model. The laws influencing the surface roughness, recovery coe cient, initial velocity, and clearance size on the impact force were revealed, and were compared with the Lankarani–Nikravesh model and a hybrid model using MATLAB. The maximum impact force was obtained using a modified contact force model under di erent initial velocities, di erent clearances, and di erent degrees of surface roughness, and the calculated results were then compared with the experiment results. This study indicates that the modified model can be used more widely than other models, and is suitable for both large and small clearances. In particular, the modified model is more accurate when calculating the contact force of a revolute joint with a small clearance.     

Bifurcation and chaos analysis of nonlinear rotor system with axial-grooved gas-lubricated journal bearing support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.     

航空发动机高速滚珠轴承振动特性研究（英文）

Ball bearing is widely used as rotor supporting.It is a non-negligible source of vibration in aero-engines.The vibration characteristics of the highspeed ball bearing are studied in this paper.Bearing kinematics theory is applied to discuss the basic characteristics of ball bearings.The vibration factors caused by ball bearings are analyzed,and then the vibration model of ball bearings is set up.The effect of the unbalance,the ball passage vibration,the radial clearance and the surface waviness ...     

ACCURACY ANALYSIS FOR PLANAR LINKAGE WITH MULTIPLE CLEARANCES AT TURNING PAIRS

Clearance at turning pair has a strong impact on the kinetic accuracy of linkage, but there is short of a generic model to analyze it so far. Clearance error, input error, and manufacturing tolerance of links are taken into consideration as the random variables synthetically. The kinematics and dynamics accuracy analysis models for planar linkages with multiple clearances at joints are built up as well. At last a typical planar linkage is selected for nurnerical illustration. These models stated in matrix resolve the relativity of output parameter errors of mechanism and therefore are of vital significance for the reliability analysis and synthesis of mechanism with clearances.     

Nonlinear vibration induced by the water-film whirl and whip in a sliding bearing rotor system

Many industrial applications and experiments have shown that sliding bearings often experience fluid film whip due to nonlinear fluid film forces which can cause rotor-stator rub-impact failures. The oil-film whips have attracted many studies while the water-film whips in the water lubricated sliding bearing have been little researched with the mechanism still an open problem. The dynamic fluid film forces in a water sliding bearing are investigated numerically with rotational, whirling and squeezing motions of the journal using a nonlinear model to identify the relationships between the three motions. Rotor speed-up and slow-down experiments are then conducted with the rotor system supported by a water lubricated sliding bearing to induce the water-film whirl/whip and verify the relationship. The experimental results show that the vibrations of the journal alternated between increasing and decreasing rather than continuously increasing as the rotational speed increased to twice the first critical speed, which can be explained well by the nonlinear model. The radial growth rate of the whirl motion greatly affects the whirl frequency of the journal and is responsible for the frequency lock in the water-film whip. Further analysis shows that increasing the lubricating water flow rate changes the water-film whirl/whip characteristics, reduces the first critical speed, advances the time when significant water-film whirling motion occurs, and also increases the vibration amplitude at the bearing center which may lead to the rotor-stator rub-impact. The study gives the insight into the water-film whirl and whip in the water lubricated sliding bearing.     

PRINCIPLES AND PARAMETER DESIGN FOR AC-DC THREE-DEGREE FREEDOM HYBRID MAGNETIC BEARINGS

To simplify the mechanical structure, decrease the overall system size of the 3-degree freedom axial-radial magnetic bearings and reduce the manufacturing costs as well as operating costs, an innovated AC-DC 3-degree freedom hybrid magnetic bearing is proposed, which is driven by a DC amplifier in axial direction and a 3-phase power converter in radial directions respectively, and the axial and radial bias magnetic fluxes are provided with a common radial polarized permanent magnet ring. The principle producing magnetic suspension forces is introduced. By using equivalent magnetic circuit method, the calculation formulas of magnetic suspension forces and the mathematics models of the system are deduced. Nonlinearities of suspension forces and cross coupling between different degree freedoms are studied further by calculating the suspension forces at different displacements and control currents to validate the feasibility of the mathematics model. Then based on the mathematics models of the bearing, a control method of this novel bearing is designed. Lastly, the methods on parameter design and calculations of the bearing are presented, and an applicable prototype is simulated to analyze the magnetic path by using finite element analysis. The theory analysis and simulation results have shown that this magnetic bearing incorporates the merits of 3-phase AC drive, permanent magnet flux biased and axial-radial combined control, and reduces overall system size and has higher efficiency and lower cost. This innovated magnetic bearing has a wide application in super-speed and super-precision numerical control machine tools, bearingless motors, high-speed flywheels, satellites, etc.     

Measurements of Non-reacting and Reacting Flow Fields of a Liquid Swirl Flame Burner

The understanding of the liquid fuel spray and flow field characteristics inside a combustor is crucial for designing a fuel efficient and low emission device.Characterisation of the flow field of a model gas turbine liquid swirl burner is performed by using a2-D particle imaging velocimetry(PIV)system.The flow field pattern of an axial flow burner with a fixed swirl intensity is compared under confined and unconfined conditions,i.e.,with and without the combustor wall.The effect of temperature on the main swirling air flow is investigated under open and non-reacting conditions.The result shows that axial and radial velocities increase as a result of decreased flow density and increased flow volume.The flow field of the main swirling flow with liquid fuel spray injection is compared to non-spray swirling flow.Introduction of liquid fuel spray changes the swirl air flow field at the burner outlet,where the radial velocity components increase for both open and confined environment.Under reacting condition,the enclosure generates a corner recirculation zone that intensifies the strength of radial velocity.The reverse flow and corner recirculation zone assists in stabilizing the flame by preheating the reactants.The flow field data can be used as validation target for swirl combustion modelling.     

Reciprocal screw theory based singularity analysis of a novel 3-DOF parallel manipulator

Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.     

Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms

Common compliant joints generally have limited range of motion, reduced fatigue life and high stress concentration. To overcome these shortcomings, periodically corrugated cantilever beam is applied to design compliant joints. Basic corrugated beam unit is modeled by using pseudo-rigid-body method. The trajectory and deformation behavior of periodically corrugated cantilever beam are estimated by the transformation of coordinate and superposition of the deformation of corrugated beam units. Finite element analysis（FEA） is carried out on corrugated cantilever beam to estimate the accuracy of the pseudo-rigid-body model. Results show that the kinetostatic behaviors obtained by this method, which has a relative error less than 6%, has good applicability and corrugated cantilever beam has the characteristics of a large range of motion and high mechanical strength. The corrugated cantilever beam is then applied to design a flexible rotational joint to obtain a larger angle output. The paper proposes a pseudo-rigid-body model for corrugated cantilever beam and designed a flexible rotational joint with large angle output.