Improved Quality Prediction Model for Multistage Machining Process Based on Geometric Constraint Equation

Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.

Connecting Conditions and Constraint Equations in Applied Science

To solve the optimal solution of some issues in applied science, studying of connecting conditions, constraint conditions and constraint equations is made. This paper cites an example in point in vibration mechanics and seeks the connecting conditions and constraint equations of high speed compound rotating system. This paper points out that the selection of the boundary conditions or connection conditions can effect on the optimal solution of the issue as soon as the object function is determined.

THE SOLUTION FOR THE GENERALIZED RICCATIALGEBRAIC EQUATIONS OF LINEAR EQUALITY CONSTRAINT SYSTEM

Based on the dynamic equation, the performance functional and the system constraint equation of time-invariant discrete LQ control problem, the generalized Riccati equations of linear equality constraint system are obtained according to the minimum principle, then a deep discussion about the above equations is given, and finally numerical example is shown in this paper.

Solving single-frequency phase ambiguity using parameter weights fitting and constrained equation ambiguity resolution methods

Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.

The Double Self—Dual Gravity with Cosmological Term and Constraints Under the Double Constant Conformal Transformation

The double constraint equations in the self-dual gravitational theory containing the cosmological term are derived in gravity. Furthermore, in order to deeply study the Lorentzian and Euclidean reality conditions for this theory, the relations between constraints are discussed by introducing the double constant conformal transformation and the double complex function method.

THE INTEGRATION METHODS OF VACCO DYNAMICS EQUATION OFNONLINEAR NONHOLONOMIC SYSTEM

This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.

Application of 1D/3D finite elements coupling for structural nonlinear analysis

An element coupling model (ECM) method was proposed to simulate the global behavior and local damage of a structure.In order to reflect the local damage and improve the computational efficiency,three-dimensional (3D) solid elements and one-dimensional (1D) beam element were coupled by the multi-point constraint equations.A reduced scale 1?8 model test was simulated by the ECM and a full three dimensional model (3DM) contrastively.The results show that the global behavior and local damages of ECM agree well with the test and 3DM.It is indicated that the proposed method can be used in the structural nonlinear analysis accurately and efficiently.

A novel finite element model for single-layered wire strand

A new finite element model for single-layered strand was investigated for accurate and efficient mechanical behavior analysis.Mathematical model was created by sectional path-nodes sweeping and dynamic node-beam mapping.Geometric relations between nodes in center core wire and helical wires were deduced in tension and bending incorporating material elasticity theory and deformation geometrical compatibility.Based on Timoshenko beam theory,strand of a pitch length was modeled with specific material,geometric parameters and synthesized constraint equations defined in ANSYS software,and predetermined load cases were performed.The obtained results show that discrepancies between suggested method and Costello theory do not exceed 1.51% in tension and 6.21% in bending,which verifies the correctness and accuracy of the suggested finite element model in predicting mechanical behavior of single-layered wire strand.

Design and Structural Analysis of Flexible Wearable Chair Using Finite Element Method

The flexible wearable chair is like a light weight mobile exoskeleton that allows people to sit any-where in any working position. The traditional chair is difficult to move to different working locations due to its large size, heavy weight (~5 - 7 kg) and rigid structure and thus, they are inappropriate for workplaces where enough space is not available. Flexible wearable chair has a gross weight of 3 kg as it utilizes light-weight aluminium alloy members. Unlike the traditional chair, it consists of kinematic pairs which enable taking halts between continuous movements at any working position and thus, it is capable of reducing the risk of the physical musculoskeletal disorder substantially among workers. The objective of this paper is to focus on the mechanical design and finite element analysis (FEA) of the mechanism using ANSYS® software. In the present work, all the parts of the mechanism are designed under static load condition. The results of the analysis indicate that flexible wearable chair satisfies equilibrium and stability criterion and is capable of reducing fatigue during working in an assembly line/factory.

Healing Temperature of Hybrid Structures Based on Genetic Algorithm

The healing temperature of suspen-dome with stacked arches(SDSA)and arch-supported single-layer lattice shell structures was investigated based on the genetic algorithm. The temperature field of arch under solar radiation was derived by FLUENT to investigate the influence of solar radiation on the determination of the healing temperature. Moreover, a multi-scale model was established to apply the complex temperature field under solar radiation. The change in the mechanical response of these two kinds of structures with the healing temperature was discussed. It can be concluded that solar radiation has great influence on the healing temperature, and the genetic algorithm can be effectively used in the optimization of the healing temperature for hybrid structures.

TIME PRECISE INTEGRATION METHOD FOR CONSTRAINED NONLINEAR CONTROL SYSTEM

For the constrained nonlinear optimal control problem, by taking the first term of Taylor series, the dynamic equation is linearized. Thus by, introducing into the dual variable (Lagrange multiplier vector), the dynamic equation can be transformed into Hamilton system from Lagrange system on the basis of the original variable. Under the whole state, the problem discussed can be described from a new view, and the equation can be precisely solved by, the time precise integration method established in linear dynamic system. A numerical example shows the effectiveness of the method.

Quasi-static Deployment Simulation for Deployable Space Truss Structures

A new method was proposed for quasi-static deployment analysis of deployable space truss structures. The structure is assumed a rigid assembly, whose constraints are classified as three categories:rigid member constraint, joint-attached kinematic constraint and boundary constraint. And their geometric constraint equations and derivative matrices are formulated. The basis of the null space and M-P inverse of the geometric constraint matrix are employed to determine the solution for quasi-static deployment analysis. The influence introduced by higher terms of constraints is evaluated subsequently. The numerical tests show that the new method is efficient.

STABLE PROGRAMMED MANIFOLD SOLVER FOR VIRTUAL PROTOTYPING MOTION SIMULATION

Based on constructing programmed constraint and constraint perturbation equation, a kinematics and dynamics numerical simulation model is established for virtual mechanism, in which the difference scheme guarantee precision in simulation procedure and its mtmerical solutions satisfy programmed manifold stability. A crank-piston mechanism in a car engine, a steering mechanism and a suspension mechanism are simulated in a virtual environment, then comparing the simulation results with those obtained in ADAMS under the same circumstances proved the solver valid.

Dynamics of a spacecraft with large flexible appendage constrained by multi-strut passive damper

This paper is concerned with the dynamics of a spacecraft with multi-strut passive damper for large flexible appendage.The damper platform is connected to the spacecraft by a spheric hinge,multiple damping struts and a rigid strut.The damping struts provide damping forces while the rigid strut produces a motion constraint of the multibody system.The exact nonlinear dynamical equations in reducedorder form are firstly derived by using Kane＇s equation in matrix form.Based on the assumptions of small velocity and small displacement,the nonlinear equations are reduced to a set of linear second-order differential equations in terms of independent generalized displacements with constant stiffness matrix and damping matrix related to the damping strut parameters.Numerical simulation results demonstrate the damping effectiveness of the damper for both the motion of the spacecraft and the vibration of the flexible appendage,and verify the accuracy of the linear equations against the exact nonlinear ones.

Springback equation of small curvature plane bending

A new analytical method for springback of small curvature plane bending is addressed with unloading rule of classical elastic-plastic theory and principle of strain superposition.We start from strain analysis of plane bending which has initial curvature,and the theoretic derivation is on the widely applicable basic hypotheses.The results are unified to geometry constraint equations and springback equation of plane bending,which can be evolved to straight beam plane bending and pure bending.The expanding and setting round process is one of the situations of plane bending,which is a bend-stretching process of plane curved beam.In the present study,springback equation of plane bending is used to analyze the expanding and setting round process,and the results agree with the experimental data.With a reasonable prediction accuracy,this new analytical method for springback of plane bending can meet the needs of applications in engineering.

Solving Topological and Geometrical Constraints in Bridge Feature Model

The capacity that computer can solve more complex design problem was gradually increased. Bridge designs need a breakthrough in the current development limitations, and then become more intelligent and integrated. This paper proposes a new parametric and feature-based computer aided design (CAD) models which can represent families of bridge objects, includes knowledge representation, three-dimensional geometric topology relationships. The realization of a family member is found by solving first the geometric constraints, and then the topological constraints. From the geometric solution, constraint equations are constructed. Topology solution is developed by feature dependencies graph between bridge objects. Finally, feature parameters are proposed to drive bridge design with feature parameters. Results from our implementation show that the method can help to facilitate bridge design.

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.

A Symmetric Inertial Alternating Direction Method of Multipliers for Elliptic Equation Constrained Optimization Problem

A new algorithm,called symmetric inertial alternating direction method of multipliers(SIADMM),is designed for separable convex optimization problems with linear constraints in this paper.The convergence rate of the SIADMM is proved to be O(1/√k).Two kinds of elliptic equation constrained optimization problems,the un-constrained cases as well as the box-constrained cases of the distributed control and the Robin boundary control,are analyzed theoretically and solved numerically.First,the existence and uniqueness of the solutions to these problems are proved.Second,these continuous optimization problems are transformed into discrete optimization problems by thefinite element method,and then the discrete optimization problems are solved by the proposed SIADMM.Numerical experiments with different problems are investigated to demonstrate the efficiency of the SIADMM.And the numerical per-formance of the SIADMM is better than the performance of the ADMM.Moreover,the numerical results show that the convergence rate of the SIADMM tends to be faster than O(1/√k)in calculation process.

Trajectory-tracking controller for vehicles on inclined road based onUdwadia–Kalaba equation

Vehicle lateral control is an important subtask of vehicle autonomous driving.There are many external disturbances that will affect the lateral control accuracy of the vehicle,and the inclination of the road is one of the most important ones.The inclined road will lead to additional lateral forces on the vehicle and will also change the magnitude of support force on the vehicle.The change of lateral force and support force will ultimately affect the trajectory tracking performance of the vehicle.Most of the current trajectory tracking methods only consider the trajectory tracking problem on the plane.If the influence of the road surface is considered in the design of the vehicle's trajectory tracking controller,the dynamic response and the tracking accuracy of the vehicle can be improved.This paper proposes a method based on Udwadia–Kalaba equation to calculate the normal and lateral force on a vehicle tracking a desired trajectory on an inclined road.Further,a trajectory tracking controller that considers the road inclination is designed.Finally,the simulation of trajectory tracking performance with an inclination angle is carried out to verify the effectiveness of the proposed controller.

Influence of shock attenuation on tailored operation in free piston shock tunnels

The free piston shock tunnel is a type of shock tunnel with high performance. For this type of tunnel, the influence mechanism of shock wave attenuation on tailored operation is explored by numerical simulation and theoretical analysis. By introducing the normalized velocity, the simple constraint equation for shock wave under the tailored operation is deduced. Moreover, the real gas effect is also taken into account in this equation. Based on the equation, the tailored operation of shock tunnels can be predicted with very few calculations. The present study shows that the change rate of the thermodynamic state of the gas behind the shock wave is inconsistent with the attenuation rate of the shock wave, which is the fundamental reason why the wind tunnel achieves tailored operation at a lower Mach number of shock waves. This lower Mach number of shock waves differs from the corresponding ideal value by a factor, which is about the square root of shock attenuation rate.