Tong Gao

Numerical Prediction of Static Form Errors in Peripheral Milling of Thin-Walled Workpieces With Irregular Meshes

The finite element formulation is studied in this paper to predict static form errors in the peripheral milling of complex thin-walled workpieces. Key issues such as cutter modeling, finite element discretization of cutting forces, tool-workpiece coupling and variation of the workpiece s rigidity in milling are investigated. To be able to predict static form errors on the machined surface of complex form, considerable improvements are made on the proper modeling of the material removal in milling and the iterative calculations of tool-workpiece deflections. A general simulation approach is developed based on 3D irregular finite element meshes. By using illustrative examples, rigid and flexible models are compared with existing ones to show the validity of the approach.

Numerical Simulation of Machined Surface Topography and Roughness in Milling Process

Machined surface topography is very critical since it directly affects the surface quality, especially the surface roughness. Based on the trajectory equations of the cutting edge relative to the workpiece, a new method is developed for the prediction of machined surface topography. This method has the advantage of simplicity and is a mesh-independent direct computing method over the traditional interpolation scheme. It is unnecessary to discretize the cutting edge or to mesh the workpiece. The topography value of any point on the machined surface can be calculated directly, and the spindle runout can be taken into account. The simulation of machined surface topography is successfully carried out for both end and ball-end milling processes. In the end milling process, a fast convergence of solving the trajectory equation system by the Newton-Raphson method can be ensured for topography simulation at any node on the machined surface thanks to the appropriate choice of the starting point. In the ball-end milling process, this general algorithm is applicable to any machined surface. Finally, the validity of the method is demonstrated by several simulation examples. Simulation results are compared to experimental ones, and a good agreement is obtained.

A New Algorithm for the Numerical Simulation of Machined Surface Topography in Multiaxis Ball-End Milling

In milling process, surface topography is a significant factor that affects directly the surface integrity and constitutes a supplement to the form error associated with the workpiece deformation. Based on the tool machining paths and the trajectory equation of the cutting edge relative to the workpiece, a new and general iterative algorithm is developed here for the numerical simulation of the machined surface topography in multiaxis ball-end milling. The influences of machining parameters such as the milling modes, cutter runout, cutter inclination direction, and inclination angle upon the topography and surface roughness values are studied in detail. Compared with existing methods, the basic advantages and novelties of the proposed method can be resumed below. First, it is unnecessary to discretize the cutting edge and tool feed motion and rotation motion. Second, influences of cutting modes and cutter inclinations are studied systematically and explicitly for the first time. The generality of the algorithm makes it possible to calculate the pointwise topography value on any sculptured surface of the workpiece. Besides, the proposed method is proved to be more efficient in saving computing time than the time step method that is commonly used. Finally, some examples are presented and simulation results are compared with experimental ones.

Thermo-Elastic Problems

Thermo-elastic topology optimization is complicated because it belongs to a kind of design-dependent problem with the thermal stress load changing along with the spatial distribution of solid material phases. Generally, the aim is to achieve one such design that produces a optimized structure that is stiff enough to support the mechanical load and compliant enough in proper areas to release the thermal stress.

Low-Density Areas in Topology Optimization

Localized mode often appears in topology optimization for maximizing the natural frequencies or buckling loads. It means that the vibration or buckling takes place only in the low-density areas related to void elements that should not physically have a mechanical effect. Consequently, structural responses and sensitivities are incorrectly calculated which misleads the optimization process. This phenomenon is actually recognized as a type of numerical singularity due to the improperly defined material properties for the void elements, especially when the popular SIMP model is directly used.

Potential Applications of Topology Optimization

In most existing work on engineering structural designs, typical conceptual designs were obtained from the best load carrying path generated by a global strain energy-based topology optimization design. Further detailed shape and sizing optimization designs were subsequently carried out to improve local performances such as strength and stability, etc. However, in many cases, it is crucial to restrain the warping deformations and maintain the coordinated displacements during the procedures of structural design, manufacturing, assembling and service. The design specification is to obtain better deformation behaviors of the elastic bodies, which is more than a global strain energy design. For example, structures on the aircraft front fuselage, will be designed properly not only for strength and stiffness performance, but also to ensure a coordinate deformation of the windshield to avoid cracking. Similar design requirements can be found for the supporting structures of the large numbers of openings and components on the aircraft.

Standard Material Layout Design

In most engineering applications, topology optimization has been recognized as an effective approach for conceptual design. Topology optimization results were considered as a design of the most effective load carrying path, while the structural details in the design domain, such as structural chamfers and fillets, stiffeners, joints and cross-sections, were designed in the following shape and sizing optimization procedure.

Optimization with Constraints on Multifastener Joint Loads

In an assembled aircraft structure, bolts or rivets are widely used as multifastener joints. They are sometimes the weakest component of a structure due to the high intensity of joint load. Earlier studies were focused on developing analytical and numerical methods for stress and failure predictions of multifastener joints. Typical models concerned panels joined by single or multiple joints, in which joint loads as well as stress distributions around pin holes, etc., are mostly analyzed. Poon and Xiong and Oh et al . considered the optimization of fastener joint locations, ply angles and stacking sequences of laminates, fastener diameters and edge distances, etc., to avoid the failure of fasteners. Bianchi et al . developed an optimization procedure maximizing the load-carrying capability of the joint system to balance the number and size of bolts. Ekh and Schon evaluated the effects of different parameters on the load distribution, such as the mismatch of member plates, length of the overlap region and the fastener’s stiffness. Optimization was then carried out to minimize the bearing stress. In the work of Oinonen et al . a “weakest link” method was proposed to optimize the layout of fasteners for the bracket-to-beam joints. The design objective was to ameliorate Von-Mises equivalent strain as well as shear loads in the joints.

Integrated Layout and Topology Optimization

A multicomponent system is a structural system consisting of a certain number of components of specific form, a container and the supporting structure that interconnects the components and the container for its integrity. Most structural systems in mechanical and aerospace engineering can be considered as a kind of multicomponent system. Compactness, structural efficiency, static and dynamic responses have to be optimized for the functionality and mechanical performance. On the one hand, the given components are assembled in the limited space of the container to satisfy various functional constraints, which are a packing optimization or a layout optimization. On the other hand, proper supporting structures have to be identified to satisfy the mechanical performances of the system, which is a typical topology optimization. In this work, the integrated layout and topology optimization are discussed for the maximum rigidity design where the spatial placement of components and the configuration of the supporting structure have to be optimized simultaneously.