Randy J. Gu

Thermal analysis of the grinding process

A two-dimensional mathematical model for the thermal aspects of a grinding process is presented. The model includes heat conduction in the grinding wheel, workpiece, and coolant. The heat generation through friction, heat loss to the environment as well as debris, and the interaction among the three components are described in detail. A finite-element algorithm is implemented to solve the nonlinear problem. Numerical results, such as temperatures in the grinding wheel and workpiece, are presented.

A New Method for Estimating Nonproportional Notch-Root Stresses and Strains

This paper presents a generalized two-step endochronic approach for estimating notch stresses and strains based on elastic stress solutions. In the first stress-controlled step, notch root strains are calculated from elastic stresses using a conventional uniaxial method, such as Glinka`s energy density method and Neuber`s rule. In the second strain-controlled step notch root stresses corresponding to the estimated local strains are calculated from the given material properties. Both stress-controlled and strain-controlled algorithms based on endochronic plasticity theory are presented herein. The proposed method is used to calculate multiaxial strains under monotonic and nonproportional loads. Various geometric constraints (plane stress, plane strain, and intermediate level) are also examined. The results are compared with experimental measurements by other researchers and with predictions from other models.

Thermal and wear analysis of an elastic beam in sliding contact

The heat conduction and wear of a cantilever beam in contact with a moving object at the free end is studied. The problem is formulated as a system of coupled nonlinear differential equations. A finite element algorithm, which incorporates an implicit time integration scheme, is developed to solve the problem. Numerical results are presented and discussed.

Effect of Internal Cooling on Tool-Chip Interface Temperature in Orthogonal Cutting

A numerical method to study the effect of internal heat sink variables on the tool-chip interface temperature in orthogonal cutting was presented. The analytical method is based on two main assumptions that the chip can be treated as a semi-infinite body with a moving heat source at the tool-chip interface and the tool can be treated as a semi-infinite body with a stationary heat source at the tool-chip interface and a uniform plane heat sink inside the semi-infinite body. An approach using the point heat partition coefficient is employed to obtain the tool-chip interface temperature distribution. The temperature distributions along the tool-chip interface with different heat sink intensities, heat sink distances from the tool-chip interface, and heat sink areas were presented. The effects of the heat sink intensity, heat sink distance from the tool-chip interface, and heat sink area on the tool-chip interface temperature were investigated. It was found that the internal cooling with a heat sink in the cutting tool could greatly affect the tool-chip interface temperature. Presented at the STLE Annual Meeting in Toronto, Ontario, Canada May 17-20, 2004 Review led by Jane Wang

Calculations of Strains and Internal Displacement Fields Using Computerized Tomography

A novel treatment of computerized tomography is developed to calculate strains and displacements at internal nodes from known boundary displacements. The formulation is blended with finite element numerical scheme. Numerical simulations are performed to verify accuracy of this new technique using several plane problems whose solutions exist in closed form. Excellent agreement shows the potential of developing the tomographic technique into a hybrid numerical-experimental method for solving mechanics problems.

Use of penalty variable in finite element analysis of contacting objects

In this paper, we investigate the solution to a subset of contact problems where the finite element systems are positive semidefinite resulting from insufficient supports to the objects at the onset of the analysis. A finite element algorithm, which incorporates a penalty variable defined as a function of the constraint condition, is developed to solve these kinds of contact problems. The solution algorithm employs an iterative technique to calculate the deformation of the object while enforcing compatibility through a modified penalty function. The new method is applied to example problems having the above characteristics. The method accurately predicts the contact zones and deformed configurations of the objects.

A finite element-based methodology for inverse problem of determining contact forces using measured displacements

The identification of contact forces applied on a solid body or structure is a special case of a general class of inverse problems. This problem is very complicated, especially when there is insufficient boundary information in the region where the contact forces need to be identified. In this article, the unknown loads or contact forces are identified by minimizing the criterion function derived as the sum of squares of the differences between measurements and numerical results of the finite element method. A detailed description of the formulation, analysis and solution of the inverse problems are given. The Tikhonov–Phillips regularization technique is employed to reduce the noise in the measurements. Three examples are chosen to demonstrate the accuracy of the numerical algorithm.

Moving finite element analysis for two-dimensional frictionless contact problems

Abstract A moving finite element analysis is presented to tackle two-dimensional elastic contact problems with absence of slipping and friction between the contact bodies. In addition to the governing equation, the interface equation is also extracted by application of the principle of minimum potential energy. The interface equation may be used to determine the unknown location of the marginal node separating the non-contact and contact regions. After the described transformation is introduced, nodal points in the finite element mesh are fixed in the transformed plane, although they are in fact traveling within the undeformed geometry in the physical plane. The incremental and uncoupled moving finite element scheme is also presented. Several examples are used to demonstrate the accuracy of the numerical scheme.

The strain-controlled creep damage law and its application to the rupture analysis of thick-walled tubes

Abstract A simplified uniaxial strain-controlled creep damage law is deduced with the use of experimental observation from a more complex strain-dependent law. This postulated creep damage law correlates the creep damage, which is interpreted as the density variation in the material, directly with the accumulated creep strain. Continuum mechanical creep rupture analyses are carried out in detail for a plane strain tube problem with temperature gradients present. As rupture propagates from an initial point or surface, a rather complex non-linear moving (free) boundary problem is encountered. A numerical technique is developed to solve the governing differential equations, and the computed results are presented and discussed in detail.

Moving finite element analysis for the identification of elastic beams

Abstract A numerical technique called moving finite element analysis is developed to tackle the indentation of elastic beams whose closed-form solutions exist. The governing equation with Lagrange multipliers embedded, derived from the variational principles, is now subjected to the constraint equations and the interface equation. In practice, the constraint equations are used to match both the deflection and the slope of the beam within the contact region with the geometric description of the indentor, while the interface equation is utilized to calculate the incremental movement of the marginal node in one load step. The numerical results calculated from the proposed algorithm incorporated with incremental and iterative procedures are displayed and compared against the closed-form solutions obtained from elementary beam theory. A discussion on the inclusion of shear effects is also presented.