Temperature Field in Laser Line Scanning Thermography: Analytical Calculation and Experiment

The temperature field in laser line scanning thermography is investigated comprehensively in this work,including analytical calculation and experiment.Firstly,the principle of laser line scanning thermography is analyzed.On this basis,a physical laser line scanning model is proposed.Afterwards,based on Fourier transform(FT)and segregation variablemethod(SVM),the heat conduction differential equation in laser line scanning thermography is derived in detail.The temperature field of the composite-based coatings model with defects is simulated numerically.The results show that the laser line scanning thermography can effectively detect the defects in the model.The correctness of the analytical calculation is verified by comparing the surface temperature distribution obtained by analytical calculation and numerical simulation.Additionally,an experiment is carried out and the changeable surface temperature obtained by analytical calculation is compared with the experimental results.It shows that the error of maximum temperature obtained by analytical calculation and by experiment is 8%with high accuracy,which proves the correctness of analytical calculation and enriches the theoretical foundation of laser line scanning thermography.

Analytical Calculation of the Energy in a Permanent Magnet

The energy in permanent magnet is not a trivial problem because it exist two types of energy: the field energy and the demagnetizing energy. For parallelepiped shape, the magnet energy has been calculated by fully analytical expressions in 3D. The result has been obtained after four successive integrations of Arctangent and Logarithm functions. The analytically calculated energy corresponds to the demagnetization energy in the magnet. The analytical results have been compared with different terms of energy obtained by computation.

Analytical Calculation Method of Reliability Sensitivity Indexes for Distribution Systems Based on Fault Incidence Matrix

An analytical calculation method for the reliability sensitivity indexes of distribution systems is proposed to explicitly quantify the impact of various influence factors on system reliability.Firstly,the analytical calculation formulas for the reliability indexes of distribution systems are derived based on the fault incidence matrix(FIM).Secondly,the factors that affect system reliability are divided into two categories:quantifiable parameter factors and non-quantifiable network structure factors.The sensitivity indexes for the quantifiable parameter factors are derived using the direct partial derivation of the reliability calculation formulas.The sensitivity indexes for the nonquantifiable network structure factors are derived using the transformation of FIMs.Finally,the accuracy and efficiency of the proposed sensitivity calculation method are verified by applying them to an IEEE 6-bus RBTS system.This paper sums up the factors that influence system reliability in detail and gives the explicit analytical calculation method for the sensitivity of each factor.Repetitive calculation of the reliability index can be avoided during the sensitivity analysis.The bottleneck that affects the reliability level of distribution systems can be identified efficiently,and valuable information and guidance can be provided to enhance the reliability of distribution systems.

Analytical calculation method and simulation of deformation and stress of Z-type guide arm for interconnected air suspensions

To design and check the strength of the Z-type guide arm of interconnected air suspensions for semi-trailers rapidly and effectively,this paper proposes the analytical calculation methods of its deformation and stress.First,based on the guide arm structure,it is marked as two parts by its mountpoint on the axle as the boundary.The part containing the eye was marked as Arm-1.The other part was marked as Arm-2.Then the analytical formulas of their stiffness and stress were derived,respectively.With a case study,the deformation and the stress were computed and simulated.The results show that the values computed are close to those simulated.The relative deviations are not more than 5.0%.The results show that the analytical formulas are acceptable.Moreover,it can be seen that for the superimposed Arm-1,when the other structural parameters are fixed,the position of the maximum stress is affected by the thickness ratio of the end thickness to the root thickness for each piece.Finally,a stiffness test was performed on the Z-type guide arm.The results show that the computed stiffness values are closed to those tested and the relative deviations are not more than 3.5%.This further verified the validity of the established model and methods.

Behaviour and Analysis of Horizontally Curved Steel Box-Girder Bridges

Various theories and analytical formulations were implemented and exploited in the 1980s and 1990s for the design of bridge beams or decks curved in the horizontal plane and subjected to out-of-plane loads. Nowadays, the Finite Element Method (FEM) is a valid tool for the analysis of structures with complex geometries and, therefore, the development of sophisticated analytical formulations is not needed anymore. However, they are still useful for the validation of FE models. This paper presents the case study of an existing viaduct built in North Italy, aiming to compare analytical approaches and numerical modelling. The bridge is characterized by an axis curved in two directions and a rectilinear segment. The global analysis of the viaduct is carried out with special attention to the attributes that cause torque action and bending moment. The theoretical developments focus on a deeper understanding of the torsional response under different constraint and loading conditions and aspire to raise awareness of the mutual interaction of flexural and torsional behaviour, that are always present in these complex curved systems. The examination of the case study is also obtained by comparing the response of isostatic and hyperstatic curvilinear steel box-girders.

EMF Waveform Optimization using the Permanent Magnet Volume-Integration Method

The emf expression can be derived with the PM volume-integration method,allowing easier optimization and prediction of the emf harmonic content.An analytical expression is developed for predicting the electromotive force(emf)waveforms and flux linkage resulting from the motion of permanent magnets(PM)in the case of two cylinders,where the outer cylinder carries a surface-mounted winding and the inner cylinder carries the PMs.The expressions are based on the PM Volume-Integration Method,which uses a volume integral calculated over the magnet volume,rather than the usual surface integral over the coil surface.The specific case of surface-mounted arc PM with radial magnetization is analyzed.An outer cylinder with infinitely thin winding distribution on its inner surface is considered.The chording factor,slot factor and spread factor are included in the analytical expression.The emf waveform and related harmonics are predicted analytically and validated by comparing with a finite element analysis and with experiment.

Analytical modeling and simulation on lateral mechanical characteristics of high-speed train traction motor hanging leaf spring

In this paper,using the theoretical analysis method,according to the actual structure of the hanging leaf spring of the traction motor mounted on the frame,the lateral force model of the hanging leaf spring of the traction motor was established.Then,through theoretical deduction,the deformation analytical calculation formula and the stress analytical calculation formula of the hanging leaf spring were established.The correctness of the leaf spring’s lateral force model was established and its deformation and stress analytical formulae were verified using ANSYS finite element analysis software.Based on this,according to the deformation analytical formula and the stress analytical formula of the leaf spring established,the influence of the main structural parameters on the mechanical characteristics of the leaf spring was discussed,and the reliability of the analytical analysis method of the lateral mechanical characteristics of the traction motor hanging leaf spring was verified by the loading–unloading test.The results show that the deformation and the load of the leaf spring change linearly.The changes of leaf spring’s stress at different positions can be considered as being composed of three sections:a linear change section in the root,a nonlinear change section in the middle,and a nonlinear change section in the end.In the structural parameters,the end thickness h2 has the greatest influence on the stiffness and the stress of the leaf spring,and the maximum thickness of the leaf spring eye h1 has the least influence on the stiffness and the stress of the leaf spring.The influence degree of other parameters on the stiffness of the leaf spring is h_(3),L_(1),L_(3),L_(2) in order,and the influence degree on the stress of the leaf spring is h_(3),L_(1),L_(2),L_(3) in order.In addition,when the root thickness h_(3) is greater than a certain value,the maximum stress point of the leaf spring appears at the end position L_(2).This study can provide a useful reference for the intelligent forward design and the rapid analysis of the mechanical characteristics of high-speed train traction motor hanging leaf spring.