Mechanism of principal stress rotation and deformation failure behavior induced by excavation in roadways

The failure modes of rock after roadway excavation are diverse and complex.A comprehensive investigation of the internal stress field and the rotation behavior of the stress axis in roadways is essential for elucidating the mechanism of roadway failure.This study aimed to examine the spatial relationship between roadways and stress fields.The law of stress axis rotation under three-dimensional(3D)stress has been extensively studied.A stress model of roadways in the spatial stress field was established,and the far-field stress state at different spatial positions of the roadways was analyzed.A mechanical model of roadways under a 3D stress state was established using far-field stress solutions as boundary conditions.The distribution of principal stressesσ1,σ2 andσ3 around the roadways and the variation of the stress principal axis were solved.It was found that the stability boundary of the stress principal axis exhibits hysteresis when compared with that of the principal stress magnitudes.A numerical analysis model for spatial roadways was established to validate the distribution of principal stress and the mechanism of principal axis rotation.Research has demonstrated that the stress axis undergoes varying degrees of spatial rotation in different orientations and radial depths.Based on the distribution of principal stress and the rotation law of the stress principal axis,the entire evolution mechanism of the two stress adjustments to form the final failure form after roadway excavation has been revealed.The on-site detection results also corroborate the findings presented in this paper.The results provide a basis for the analysis of the failure mechanism under a 3D stress state.

Improved Units of Measure in Rotational Mechanics

The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.

Type Synthesis and Characteristic Analysis of a Family of 2-DOF Rotational Decoupled Parallel Mechanisms

It is widely used for the rotational parallel mechanism in the field of spatial orientation. While owing to the existence of coupling, the forward kinematic solution and the control of the general rotational parallel mechanism are especially difficult. If decoupling can be realized, the kinematic analysis of the mechanism will be very simple. Presently, the research of the parallel mechanism is focused on the inverse solution and structure optimization, and there is a lack of rotation decoupled parallel mechanisms （DPMs）. So this paper proposes a family of 2 degree of freedom （DOF） rotational DPMs based on the four-bar linkage mechanism, and performs a characteristic analysis. This family of DPMs is composed of a moving platform, a fixed base and three limbs. Taking U_RRU SPU DPM as an example, the motion feature of this DPM is analyzed with the constraint screw method, and its mobility is calculated by using the Modified Kutzbach-Grtibler criterion. The inverse and forward displacement problems of the proposed parallel mechanism are solved. The decoupled feature of the proposed parallel mechanism is validated by the deduction of the expression of the Jaeobian matrix. Three kinds of singularity conditions of this DPM are discussed, and the atlases of the output parameter concerning different geometric parameters are plotted with the theory of the physical model of the solution space. The proposition and characteristic analysis of the novel rotational DPMs in this paper should be useful for further research and application of the parallel mechanisms.

New Family of 3-DOF UP-Equivalent Parallel Mechanisms with High Rotational Capability

Parallel mechanisms(PMs) having the same motion characteristic with a UP kinematic chain(U denotes a universal joint, and P denotes a prismatic joint) are called UP-equivalent PMs. They can be used in many applications, such as machining and milling. However, the existing UP-equivalent PMs suffer from the disadvantages of strict assembly requirements and limited rotational capability. Type synthesis of UP-equivalent PMs with high rotational capability is presented.The special 2 R1 T motion is briefly discussed and the fact that the parallel module of the Exechon robot is not a UP-equivalent PM is disclosed. Using the Lie group theory, the kinematic bonds of limb chains and their mechanical generators are presented. Structural conditions for constructing such UP-equivalent PMs are proposed,which results in numerous new architectures of UP-equivalent PMs. The high rotational capability of the synthesized mechanisms is illustrated by an example. The advantages of no strict assembly requirements and high rotational capability of the newly developed PMs will facilitate their applications in the manufacturing industry.

Type Synthesis of Two-Degrees-of-Freedom Rotational Parallel Mechanism with Two Continuous Rotational Axes

The two-rotational-degrees-of-freedom（2R） parallel mechanism（PM） with two continuous rotational axes（CRAs） has a simple kinematic model.It is therefore easy to implement trajectory planning,parameter calibration,and motion control,which allows for a variety of application prospects.However,no systematic analysis on structural constraints of the 2R-PM with two CRAs has been performed,and there are only a few types of 2R-PM with two CRAs.Thus,a theory regarding the type synthesis of the 2R-PM with two CRAs is systematically established.First,combining the theories of reciprocal screw and space geometry,the spatial arrangement relationships of the constraint forces applied to the moving platform by the branches are explored,which give the 2R-PM two CRAs.The different distributions of the constraint forces in each branch are also studied.On the basis of the obtained structural constraints of branches,and considering the geometric relationships of constraint forces in each branch,the appropriate kinematic chains are constructed.Through the reasonable configuration of branch kinematic chains corresponding to every structural constraint,a series of new 2R-PMs with two CRAs are finally obtained.

Structural Synthesis of Parallel Mechanisms with High Rotational Capability

Most parallel mechanisms(PMs) encountered today have a common disadvantage, i.e., their low rotational capability.In order to develop PMs with high rotational capability, a family of novel manipulators with one or two dimensional rotations is proposed. The planar one-rotational one-translational(1 R1 T) and one-rotational two-translational(1 R2 T)PMs evolved from the crank-and-rocker mechanism(CRM) are presented by means of Lie group theory. A spatial 2 R1 T PM and a 2 R parallel moving platform with bifurcated large-angle rotations are proposed by orthogonal combination of the RRRR limbs. According to the product principle of the displacement group theory, a hybrid 2 R3 T mechanism in possession of bifurcated motion is obtained by connecting the 2 R parallel moving platform with a parallel part, which is constructed by four 3 T1 R kinematic chains. The presented manipulators possess high rotational capability. The proposed research enriches the family of spatial mechanisms and the construction method provides an instruction to design more complex mechanisms.

A Novel Method for Type Synthesis of Parallel Mechanism Without Parasitic Motion Based on 2R1T Parallel Mechanism with Rotational Bifurcation

The parasitic motion has been widely recognized as the major drawback of the parallel mechanism.Therefore a class of 2R1T PMs(parallel mechanism)without parasitic motion has been synthesized.However,these PMs can only rotate around two axes in sequential order.It decreases the performance of the balancing adjustment of the end-efector.In this paper,a family of 2R1T PMs without parasitic motion was reconstructed by using a novel method based on the remarkable properties of rotational bifurcation mechanisms,which can rotate in sequential order.Furthermore,some PMs rotating around two continuous axes in an arbitrary order are established by adding single joints.Taking the practicability of these structures into consideration,the workspace of 3-PRPS PM was analyzed as an example.Moreover,this study explores the practical application of the PMs without parasitic motion in developing balance mechanisms in rough-terrain fre-fghting robots.During the climbing process,the tank is adjusted to be parallel to the horizontal plane in real-time.It is proved that this kind of structure realizes continuous rotation around two rotation axes on the premise of no parasitic motion.

Expert Diagnosing System for a Rotation Mechanism Based on a Neural Network

By combining the artificial neural network with the rule reasoning expert system, an expert diagnosing system for a rotation mechanism was established. This expert system takes advantage of both a neural network and a rule reasoning expert system; it can also make use of all kinds of knowledge in the repository to diagnose the fault with the positive and negative mixing reasoning mode. The binary system was adopted to denote all kinds of fault in a rotation mechanism. The neural networks were trained with a random parallel algorithm (Alopex). The expert system overcomes the self learning difficulty of the rule reasoning expert system and the shortcoming of poor system control of the neural network. The expert system developed in this paper has powerful diagnosing ability.

Effect of tool rotational speed on the particle distribution in friction stir welding of AA6092/17.5 SiCp-T6 composite plates and its consequences on the mechanical property of the joint

This study investigates the effect of tool rotational speed(TRS)on particle distribution in nugget zone(NZ)through quantitative approach and its consequences on the mechanical property of friction stir welded joints of AA6092/17.5 SiCp-T6 composite.6 mm thick plates are welded at a constant tool tilt angle of 2°and tool traverse speed of 1 mm/s by varying the TRS at 1000 rpm,1500 rpm and 2000 rpm with a taper pin profiled tool.Microstructure analysis shows large quantity of uniformly shaped smaller size SiC particle with lower average particle area which are homogeneously distributed in the NZ.The fragmentation of bigger size particles has been observed because of abrading action of the hard tool and resulting shearing effect and severe stress generation due to the rotation of tool.The particles occupy maximum area in the matrix compared to that of the base material(BM)due to the redistribution of broken particles as an effect of TRS.The migration of particles towards the TMAZ-NZ transition zone has been also encountered at higher TRS(2000 rpm).The microhardness analysis depicts variation in average hardness from top to bottom of the NZ,minimum for 1500 rpm and maximum for 2000 rpm.The impact strength at 1000 rpm and 1500 rpm remains close to that of BM(21.6 J)while 2000 rpm shows the accountable reduction.The maximum joint efficiency has been achieved at 1500 rpm(84%)and minimum at 1000 rpm(68%)under tensile loading.Fractographic analysis shows mixed mode of failure for BM,1000 rpm and 1500 rpm,whereas 2000 rpm shows the brittle mode of failure.

Rock strength weakening subject to principal stress rotation:Experimental and numerical investigations

During the construction and operation of gas storage reservoirs,changes in the principal stress direction can induce fracture propagation under conditions of lower differential stress,potentially leading to failure in the surrounding rock.However,the weakening of strength due to pure stress rotation has not yet been investigated.Based on fracture mechanics,an enhanced Mohr-Coulomb strength criterion considering stress rotation is proposed and verified with experimental and numerical simulations.The micro-damage state and the evolution of the rock under the pure stress-rotation condition are analyzed.The findings indicate that differential stress exceeding the crack initiation stress is a prerequisite for stress rotation to promote the development of rock damage.As the differential stress increases,stress rotation is more likely to induce rock damage,leading to a transition from brittle to plastic failure,characterized by wider fractures and a more complex fracture network.Overall,a negative exponential relationship exists between the stress rotation angle required for rock failure and the differential stress.The feasibility of applying the enhanced criterion to practical engineering is discussed using monitoring data obtained from a mine-by tunnel.This study introduces new concepts for understanding the damage evolution of the surrounding rock under complex stress paths and offers a new theoretical basis for predicting the damage of gas storage reservoirs.

Mei Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.

Instability Mechanism of a Rotating Disc Subjected to Various Transverse Interactive Forces

In the past three decades, numerous papers have bee n publishedon the dynamics of rotating discs. most of them have focused on the ma thematical modeling and solution for a specific interactive force, such as a n elastic force produced by a stationary spring or a damping force from a statio nary viscous damper. Few of them have looked into the instability mechanisms. This study has established a generalized approach to investigate the instability mechanisms that are involved in the interaction between a rotating and an arbit rary interactive force. An energy flux equation has been developed, which leads to the following conclusions: (1) The possibility of the occurrence of instability due to any interactive forc es may be identified based on the energy flux analysis, even without solving equ ations. (2) Instabilities will occur if the interactive forces are in phase with the vel ocity measured at the interactive point from the coordinates rotating with the d isc. (3) Instability cannot occur when a rotating disc is subjected to a stationary c onstant lateral force, but a stationary harmonic lateral force, a moving constan t lateral force or a moving harmonic lateral force may cause instability. (4) Conservative forces may only cause coupling instability associated with two modes, and non-conservative forces usually cause terminal instability where onl y one mode is involved.

THE THEORY OF RELATIVISTIC ANALYTICAL MECHANICS OF THE ROTATIONAL SYSTEMS

The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics' of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems [GRAPHICS] and the generalized acceleration energy function [GRAPHICS] are constructed, and furthermore, the Hamilton principle and three kinds of D'Alembert principles are given. For the systems with holonomic constraints, the relativistic Lagrange equation, Nielsen equation, Appell equation and Hamilton canonical equation of the rotational systems are constructed; For the systems with nonholonomic constraints, the relativistic Routh equation, Chaplygin equation, Nielsen equation and Appell equation of the rotational systems are constructed; the relativistic Noether conservation law of the rotational systems are given too.

Multi-Barycenter Mechanics, N-Body Problem and Rotation of Galaxies and Stars

In the present paper, the establishment of a systematic multi-barycenter mechanics is based on the multi-particle mechanics. The new theory perfects the basic theoretical system of classical mechanics, which finds the law of mutual interaction between particle groups, reveals the limitations of Newton’s third law, discovers the principle of the intrinsic relationship between gravity and tidal force, reasonably interprets the origin and change laws for the rotation angular momentum of galaxies and stars and so on. By applying new theory, the multi-body problem can be transformed into a special two-body problem and for which an approximate solution method is proposed, the motion law of each particle can be roughly obtained.

Influence of multipass high rotating speed friction stir processing on microstructure evolution,corrosion behavior and mechanical properties of stirred zone on AZ31 alloy

The influence of multipass high rotating speed friction stir processing(FSP)on the microstructure evolution,corrosion behavior,and tensile properties of the stirred zone(SZ)was investigated by EBSD,TEM,SEM,electrochemical workstation and electronic universal testing machine.The mean grain size of the SZ is significantly refined,and it increases with the increase of the processing pass.In addition to an obvious increase in the number,the distribution ofβ-Al12Mg17 precipitates also becomes more uniform and dispersed with increasing the processing pass.Compared with the as-received AZ31 alloy,the tensile properties of the SZ are hardly improved,but the corrosion resistances are significantly enhanced.The corrosion potential of the SZ prepared by 4-pass FSP is increased from−1.56 V for the unprocessed AZ31 alloy to−1.19 V,while the corrosion current is decreased from 1.55×10^−4 to 5.47×10^−5 A.

Design of a Mobile Mechanism for Missing Miner Search Robots in Underground Mines

A mobile mechanism with four tracked-units for a missing miner search robot (MMSR) is presented, with a design based on the terrain features and atrocious environment of an underground mine. Its structure and working prin- ciple is discussed. The four tracked-units are controlled independently and driven cooperatively. By means of two DC motors being controlled respectively, one tracked-unit can accomplish two types of driving mode: tracked travel and in- tegral unit legged rotation (IULR), forming a track-legged compound function mechanism. Its capabilities of surmount- ing obstacles and its toppling stability in underground mines have also been analyzed. The results show that the mobile mechanism can directly surmount an obstacle of the height less than the length of one tracked-unit and get across a raceway with a span less than the length of one tracked-unit by using tracked travel and IULR. Its unstable slope angle is 51.3°. Toppling stability is determined by its structural size, moving direction and slope angle. IULR of four tracked-units can adjust the robot’s posture and then enhance toppling stability or assist in surmounting obstacles. Its track-legged compound function mechanism makes it suitable for working in underground mines.

Optimum traveling and rotation speeds in friction stir welding for dissimilar Al alloys

Aluminum alloys are subjected to large deformation and decreased strength due to the high expansion modulus caused by heat effects during friction stir welding （FSW）.The optimum conditions for friction stir welding of 5052-O and 6061-T6 Al alloys were determined.The optimum traveling and rotation speeds were identified to be 61mm/min and 1600r/min using various mechanical characteristic evaluation methods.

Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion.To provide an accurate prediction for the theoretical solution of the critical face pressure,this study adopts the piecewise linear method(PLM)to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule.The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem;it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables(m is the number of segments).Meanwhile,two classic linearized measures,the generalized tangential technique(GTT)and equivalent Mohr-Coulomb parameters method(EMM),are incorporated into the analysis for comparison.Surprisingly,the parametric study indicates a significant improvement in support pressure by up to 13%compared with the GTT,and as expected,the stability of the tunnel face is greatly influenced by the rock strength parameters.The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state.Although the limit analysis is incapable of calculating the true stress distribution in rock masses,a rough approximation of the stress vector on the rupture surface is permitted.In the end,sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.

Motion Characteristics Analysis of a Novel Spherical Two-degree-of-freedom Parallel Mechanism

Current research on spherical parallel mechanisms(SPMs)mainly focus on surgical robots,exoskeleton robots,entertainment equipment,and other fields.However,compared with the SPM,the structure types and research contents of the SPM are not abundant enough.In this paper,a novel two-degree-of-freedom(2DOF)SPM with symmetrical structure is proposed and analyzed.First,the models of forward kinematics and inverse kinematics are established based on D-H parameters,and the Jacobian matrix of the mechanism is obtained and verified.Second,the workspace of the mechanism is obtained according to inverse kinematics and link interference conditions.Next,rotational characteristics analysis shows that the end effector can achieve continuous rotation about an axis located in the mid-plane and passing through the rotation center of the mechanism.Moreover,the rotational characteristics of the mechanism are proved,and motion planning is carried out.A numerical example is given to verify the kinematics analysis and motion planning.Finally,some variant mechanisms can be synthesized.This work lays the foundation for the motion control and practical application of this 2DOF SPM.

Effect of reverse dual rotation process on properties of friction stir welding of AA7075 to AISI304

The friction stir lap welding of AISI304 stainless steel to AA7075 aluminium alloy was investigated using the conventional friction stir welding (C-FSW) and the reverse dual rotation friction stir welding (DR-FSW) processes. In order to reduce the heat input, a dual rotation tool with a lower shoulder rotating speed was used. The results showed that both processes provide welds with excellent appearance and free of internal defects. The use of the DR-FSW process with the tool shoulder rotating reversely at low speed results in larger grain refinement in the nugget and less change in the microstructure of the aluminium alloy than using the C-FSW. The use of DR-FSW process at low speed of rotation allows to reduce the amount of intermetallic compounds in the welding interface, but does not prevent their formation. Although DR-FSW welding exhibits tensile strength superior to that achieved with the conventional process (C-FSW), both exhibit brittle behaviour with fracture at the weld interface.