Optimal design of a six-axis vibration isolator via Stewart platform by using homogeneous Jacobian matrix formulation based on dual quaternions

A six-axis vibration isolation system is essential to high-precision space systems for attenuating vibrations on precise instruments. The kinematic optimal design is researched for the space six-axis vibration isolator via Stewart mechanism. Jacobian matrix is the basis of the kinematic performance index. However, the conventional Jacobian matrix is not usually dimensionally homogeneous due to the inhomogeneous physical units, caused by the different mathematical representations of the rotation and translation. In this paper, we propose a dual quaternion approach to derive the dimensionally homogeneous Jacobian matrix of a general six-axis parallel mechanism. Two quaternions are used to parameterize the rotation and translation of the platform. The dimensionally scaling factor for the generalized Jacobian matrix is defined as the ratio of the norms of the two quaternions. The dimensionally homogenous Jacobian matrix is then obtained and applied to the optimal design of the six-axis vibration isolator. The performance index of isotropy is considered to make the isolator minimum kinematic coupling in its working configuration.     

Chute design of mackerel automatic grader using multibody dynamics

An automatic mackerel grader is a machine that automatically sorts mackerel according to size. The chute spreads the mackerel to allow the latter to enter each roller evenly. Sorting is simulated to confirm that the multibody dynamics model of the automatic grader correctly sorts the mackerel. This process is completed according to the shape of the chute to confirm the effect on performance. A new shape of the chute and the application are proposed and evaluated by a comparison with conventional chute shapes. RecurDyn, a multi-body dynamics program, is used for the sorting simulation. The contact parameters are defined by Hertzian contact theory using the material information of mackerel and C/S steel. A rigid-body mackerel model is used to express the behavior of mackerel. Sorting is simulated for each shape. The sorting accuracy and error of the new shape are compared with those of two existing shapes. The new shape shows a 0.29 mm sorting error and better sorting accuracy than the existing shapes.     

Rolling element bearings absolute life prediction using modal analysis

In this paper, the authors introduce an experimental procedure for predicting the fatigue life of each individual rolling element bearing separately using vibration modal analysis. The experimental procedure was developed based on a statistical analysis. A statistical analysis was performed to find an empirical model that correlates the dynamic load capacity of rolling bearings to their dynamic characteristics (Natural frequencies and damping). These dynamic characteristics are obtained from the frequency response function of each individual bearing that results from vibration modal analysis. A modified formula to the already known Lundberg-Palmgren life formula is proposed for rolling element bearings. Given the modified formula, one can predict the fatigue life of each individual rolling element bearing based on its dynamic characteristics. The paper compares the results from the modified formula with those from Lundberg-Palmgren formula. The modified formula provides an accurate prediction for the fatigue life of each individual bearing based on its dynamic characteristics. The experimental validation of the modified formula is considered for future work. Therefore, it can be used in various applications of rolling element bearings in machinery systems.     

Accurate measurement of residual stresses of 2219-T87 aluminum alloy friction stir welding joints based on properties of joints

In order to avoid the deviation caused by calculating the residual stresses of welding joints with the release coefficients of the same parent metal, a new method has been proposed based on the properties of weld joints. Since the mechanical property of 2195-F Al alloy is close to that of 2219-T87 Al alloy Friction stir welding (FSW) joint, 2195-F Al alloy is selected as the substitute material of 2219-T87 Al alloy FSW joint in the calibration test. Release coefficients of 2195-F Al alloy and proper correction coefficient are used to calculate the residual stresses of 2219-T87 Al alloy FSW joints. Compared to the results calculated with release coefficients of its parent metal, it has been proved that the proposed correction method is more precise in residual stresses measurement of weld joints. The mathematical analysis and the results of verification tests have shown that this new method is reliable, and it will provide guidance in academic research and engineering application of the spherical indentation strain-gauge method.     

Numerical investigation on radial impeller induced vortex rope in draft tube under partial load conditions

The vortex rope phenomena appearing in a draft tube under partial load operations were investigated. The efforts were carried out by using a homogeneous equilibrium vapor-liquid two-phase model and a blending SST turbulence model, and the former takes account of the weak compressibility of mixed media. The vortex rope phenomena were induced by the radial impeller and three kinds of flow regimes were illustrated. Vortex rope was visible at some conditions and it displayed various patterns, while no obvious vortex rope was found under some conditions. It was found that the plant cavitation number determines that whether the vortex rope was visible or invisible. An interesting profile was that a secondary vortex filament ring entwining the vortex rope appeared clearly near the design condition. Both flow structures and pressure characteristics were studied to depict the vortex mechanism and the characteristics of the η-σ curves. Further analysis found that the shedding frequency of the vortex ring is similar with that of the precession movement.     

Generalized model of vibro-isolation systems with seated human body for single-axis transmission of vibration

A generalized model of vibration isolation systems with a human body in a seated position is developed. The system dynamics is modeled for a single-axis transmission of vibration, that is, longitudinal x, lateral y and vertical z, to limit whole-body vibration exposure. The developed model can be successfully employed to describe the propagation of vibration waves from the source to a vibrating object. The proposed mathematical model can be widely used to protect a human body against vibration.     

Estimation of ambient temperature impact on vertical dynamic behaviour of passenger rail vehicle with damaged wheels

Maintenance and repair specialists of rolling stock face the problem related to accurate and reliable assessment of the vibrations of the car body of passenger rail vehicle, caused by wheel damage, and its impact on passengers. Another important aspect is to deter-mine the permissible speed at which the passenger car with wheel damage could move to the nearest station or depot without badly damaging the rails. The purpose of this research is to examine the dynamic processes of the interaction of the passenger car chassis with the railway track using a newly developed mathematical models called the “Passenger Car - Track” system. During the simulation, the dynamic characteristics of the track, bogies and car body in different season temperature were estimated. The validation of theoretical results was obtained based on the field tests of the test train as well as the results of measurements of changes in track stiffness temperatures. Finally, conclusions and suggestions are presented.     

Compound fault diagnosis of bearings using improved fast spectral kurtosis with VMD

The fast spectrum kurtosis (FSK) algorithm can adaptively identify resonance bands of a signal, and fault characteristics can be extracted by analyzing the selected frequency bands. However, in practical applications, the bearing failure may be composed of various faults (inner ring/outer ring/rolling element) and the faults may be located in different resonant bands. Due to the interference between different fault components and noise, the weak components may be submerged when FSK is used to deal with compound fault signals. To improve the accuracy of an FSK processing compound fault located in different resonance bands, an improved FSK method combined with the variational mode decomposition (VMD) is proposed. First, the parameters (number of components K / penalty factor α ) in the VMD decomposition are selected, and the original compound fault signal is preprocessed by VMD decomposition, so that the original signal is decomposed into K variational intrinsic mode function (VIMF) components. The resonance center bands of these signals are different from each other, so the different fault information is located in different VIMF. Finally, each VIMF component is calculated by FSK. Through the simulated and experimental analysis, the method can accurately identify the resonance bands, and identify the weak fault characteristics of compound bearing fault.     

Optimization of excitation frequency and guided wave mode in acoustic wavenumber spectroscopy for shallow wall-thinning defect detection

In plate-like structures, wall-thinning defects resulting from corrosion may not be accompanied by any indication of damage on the surface. Thus, inspections are required to ensure that wall-thinning defects are within allowable limits. However, conventional ultrasonic techniques require physical contact to the structure. Alternatively, acoustic wavenumber spectroscopy (AWS) may be used for detecting, locating, and characterizing defects. This paper describes the performance of AWS in the estimation of a wall-thinning defect size in thinplate structures using finite element analysis (FEA). Through a series of FEAs, the structure’s steady-state response to a single-tone ultrasonic excitation is simulated, and the wall-thinning defect-size effect on the wavenumber-estimation accuracy is investigated. In general, the A0 guided wave mode is widely used to visualize defects because of the nature of the wave speed variation in relation to the plate thickness. However, it is not appropriate for the detection of relatively shallow wall-thinning defects, because the rate of change in wave speed with the thickness decreases with increasing plate thickness. To overcome this limitation, we propose a method to optimize excitation frequency and effective guided wave mode instead of utilizing the A0 mode. The results can be used to determine the size of shallow wall-thinning defects in plate-like structures.     

Reducing undesirable vibrations of planar linkage mechanism with joint clearance

An optimization design method is presented to reduce the undesirable vibrations caused by clearance for planar linkage mechanism. A clearance joint is defined and considered a contact/impact force constraint. Contact and impact force models for the clearance joint are established using a normal contact force model based on Hertz model with energy loss and a tangential friction model based on modified Coulomb model with dynamic friction coefficient, respectively. In view of the clearance joint, dynamic equations and optimization method for a planar four-bar mechanism are then presented as an application example. The optimization aims to minimize the maximum absolute acceleration peaks of the mechanism by determining the link lengths of the planar linkage mechanism. Finally, the optimization design is solved by a generalized reduced gradient algorithm. Results show evident decrease in vibration peaks of the mechanism and obvious reduction in the contact forces in the clearance joint, which contribute to a good performance of planar linkage mechanism systems.