Tool Contact Maps by Rectangular Grid Decomposition

Author(s):  
Eyyup Aras

This paper is intended to contribute to ongoing research [1–3] in geometric modeling of the virtual machining. In geometric modeling the tool paths are verified by performing the machining simulations and also the cutter workpiece engagements (CWEs) are extracted. CWE geometry is a key input to force calculations and feed rate scheduling in milling operations. Finding these engagements is challenging due to the complicated and changing intersection geometry between the cutter and the in-process workpiece. This paper presents a discrete model based methodology for extracting CWEs generated during a multi axis machining of free form surfaces using a range of different types of milling tools. In this method the in-process workpiece is represented by a set of z-axis aligned rectangular grids. Each grid is made up of four planes, with their normals aligned with respect to the x and y-axis of the Cartesian coordinate system. In developing the methodology the parametric representations of the automatically programmed tool (APT)-type milling cutters are used. The milling tool surfaces are decomposed into circles. During the material removal process only some portions of those circles which are called the engagement arcs may contact the in-process workpiece. To find the geometric limits of those arcs the concept of the feasible contact surface is utilized. The CWE extraction simulation is performed through intersecting those arcs with the planes of each rectangular grid. Thus the intersection calculations reduce to circle/plane intersections which can be performed analytically for the geometry found on milling cutters. To be used in the force model, the CWE boundaries are mapped from Euclidean 3D space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry. Then using a sort algorithm the neighboring engagements in the same arc level are combined.

Author(s):  
Eyyup Aras ◽  
Derek Yip-Hoi

This paper presents a Solid modeling methodology for finding Cutter Workpiece Engagements (CWEs) generated during 3+2 -axis machining (spindle can tilt) of free – form surfaces using a range of different types of cutting tools and tool paths. Swept volumes of the cutters are generated utilizing the envelope theory. For the CWE extractions the removal volumes of the cutter constituent surfaces are used. For this purpose the cutter surfaces are decomposed with respect to the tool feed direction and then they intersected with their removal volumes for obtaining the boundary curves of the closed CWE area. The CWE boundary curves are mapped from Euclidean space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry. The reported method has been implemented using a commercial geometric modeler (ACIS) which is selected to be the kernel around which the geometric simulator is built. The described geometric methodology is being developed as part of a Virtual Milling methodology that combines the geometric modeling aspects of milling material removal with the modeling of the process.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.


2012 ◽  
Vol 201-202 ◽  
pp. 473-476
Author(s):  
Chong Yang Yuan ◽  
Di Zheng ◽  
Jian Ming Zhan ◽  
Li Yong Hu

In order to meet the needs for the precise polishing of free-form surfaces, a new compliant polishing tool system was designed based on a magnetorheological torque servo (MRT), and integrated into a CNC milling machine. Through analysis, it was pointed out that the key factor affecting the polishing quality of this system is the stability of the system. By means of the 3D geometric modeling software ProE, the finite element analysis software ANSYS, and the dynamic simulation software ADAMS, the rigid-flexible mixed model of the system was established and the stability of the polishing pressure and tool position was numerically analyzed.


2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Zhaozhao Lei ◽  
Xiaojun Lin ◽  
Gang Wu ◽  
Luzhou Sun

In order to improve the machining quality and efficiency and optimize NC machining programming, based on the existing cutting force models for ball-end, a cutting force prediction model of free-form surface for ball-end was established. By analyzing the force of the system during the cutting process, we obtained the expression equation of the instantaneous undeformed chip thickness during the milling process and then determined the rule of the influence of the lead angle and the tilt angle on the instantaneous undeformed chip thickness. It was judged whether the cutter edge microelement is involved in cutting, and the algorithm flow chart is given. After that, the cutting force prediction model of free-form surface for ball-end and pseudocodes for cutting force prediction were given. MATLAB was used to simulate the prediction force model. Finally, through the comparative analysis experiment of the measured cutting force and the simulated cutting force, the experimental results are basically consistent with the theoretical prediction results, which proves that the model established in this paper can accurately predict the change of the cutting force of the ball-end cutter in the process of milling free-form surface, and the error of the cutting force prediction model established in this paper is reduced by 15% compared with the traditional cutting force prediction model.


Author(s):  
Kumar Sambhav ◽  
Puneet Tandon ◽  
Sanjay G. Dhande

The presented work models the geometry of Single Point Cutting Tools (SPCTs) with generic profile. Presently few standard shapes of SPCTs defined in terms of projective geometry are being employed while there is a need to design free-form tools to efficiently machine free-form surfaces with few passes and chosen range of cutting angles. To be able to produce SPCT face and flanks with generic shapes through grinding, a comprehensive geometric model of the tool in terms of the varying grinding angles and the ground depths is required which helps design the tool with arbitrarily chosen tool angles. The surface modeling begins with the creation of a tool blank model followed by transformation of unbounded planes to get the cutting tool surfaces. The intersection of these surfaces with the blank gives the complete model of the tool. Having created the geometric model in two generations of generalization, the paper presents the methodology to obtain the conventional tool angles from the generic model. An illustration of the model has been provided showing variation of tool angles along the cutting edge with changing grinding parameters. When the geometric model is not to be related to the grinding parameters, the SPCT can be modeled as a composite NURBS surface which has been presented towards the end of the work.


1999 ◽  
Author(s):  
T. S. Lee ◽  
R. Farahati ◽  
Y. J. Lin

Abstract A comprehensive, 3D mathematical model of desired/optimal cutting force for end milling of free-form surfaces is proposed in this paper. The closed-form predictive model is developed based on a perceptive cutting approach resulting in a cutting force model having a comprehensive set of essential cutting parameters. In particular, the normal rake angle usually missing in most existing models of the same sort is included in the developed model. The model also enables quantitative analyses of the effect of any parameters on the cutting performance of the tool, providing a guideline to improving the tool performance. Since the axial depth of cut varies with time when milling sculptured surface parts, an innovative axial depth of cut estimation scheme is proposed for the generation of 3-D cutting forces. This estimation scheme improves the practicality of most existing predictive cutting force model for milling in which the major attention has been focused on planar milling surface generation. In addition, the proposed model takes the rake surface on the flute of mills as an osculating plane to yield 3-D cutting force expressions with only two steps. This approach greatly reduces the time-consuming mathematical work normally required for obtaining the cutting force expressions. A series of milling simulations for machining free-form parts under scenario cutting conditions have been performed to verify the effectiveness of the proposed cutting force model. The simulation results demonstrate accurate estimating capability of the proposed method for the axial depth of cut estimation. The cutting force responses from the simulation exhibit the same trends as what can be obtained using the empirical mechanic’s model referenced in the literature. Finally, through the simulation results it is also learned that designing a tool with a combination of different helix angles having cutting force signatures similar to that of the single helix angle counterparts is particularly advantageous.


2013 ◽  
Vol 589-590 ◽  
pp. 438-443
Author(s):  
Hui Xian Chen ◽  
Gong Chu ◽  
Meng Pei Wu ◽  
Hui Jun Yang

Because of the influence of tool geometry, when the fine slotting cutter is cutting, the cutting condition at every point of the type line cutting edge varies, which will lead to uneven loading on the whole cutting edge. Finally, partial earlier failure of the cutter would be initiated. To solve this problem, this paper presented a cutting simulation of the slotting cutter with zero rake angle, which could draw the variation law of cutting force at different locations on the type line. On the basis of micro-elemental milling force model, this paper established mathematical models of different sections along the turning axis of cutting tool, in which the relief angle changed to adapt to the variation of cutting force. The variation law of relief angle could be found by utilizing liner regression analysis. Then the 3D model of tool could be reconstructed. According to cutting experiment analysis of the reconstructed model, the distribution of cutting force at every point of the cutting edge tended to be reasonable, and the rationality of the optimal model was proved. This will offer a new idea to improve the level of slotting cutter design as well as a reference of complex forming cutter design that was completed by using the modern design method.


2012 ◽  
Vol 498 ◽  
pp. 121-126
Author(s):  
M. Arsuaga ◽  
Luis Norberto López de Lacalle ◽  
R. Lobato ◽  
G. Urbikain ◽  
F. Campa

Boring operations of deep holes with a slender boring bar are often hindered by the precision because of their low static stiffness and high deformations. Because of that, it is not possible to remove much larger depths of cuts than the nose radius of the tool, unlike the case of turning and face milling operations, and consequently, the relationship between the cutting force distribution, tool geometry, feed rate and depth of cut becomes non-linear and complex. This problem gets worse when working with a rotating boring head where apart from the cutting forces and the variation of the inclination angle because of shape boring, the bar and head are affected by de centrifugal forces. The centrifugal forces, and therefore the centrifugal deflection, will vary as a function of the rotating speed, boring bar mass distribution and variable radial position of the bar in shape boring. Taking in to account all this effects, a load and deformation model was created. This model has been experimentally validated to use as a corrector factor of the radial position of the U axis in the boring head.


Author(s):  
Mohammed M. Shalaby ◽  
Ashraf O. Nassef ◽  
Sayed M. Metwalli

Abstract The design and manufacture of free-form surfaces increased in industrial applications, especially for the re-manufacture of spare parts, or in the die and mold industry. Reverse engineering has become the status quo technique in reproducing parts whose original designs are no longer existing or for parts, which assume slightly different shapes after manufacturing as in the case of die and mold industry. Laser scanners have been used extensively in sampling points from parts surfaces. The sampled points are then fitted with a free-form surface using one of the geometric modeling techniques such as Bezier or B-Spline surfaces. Since Non-Uniform Rational B-Splines (NURBS) is the most general form of geometric modeling techniques, this paper presents the possible formulations of the fitting problem optimization and presents some guidelines of the choice of the independent NURBS parameters, once the control points are evaluated using least squares fitting. The work shows that the use of NURBS weights can provide better improvements for the significant reduction of the fitting error, rather than the widely used knot values. In addition the work shows that parts with semi planar surfaces do not need further refinement using non-linear optimization methods.


2006 ◽  
Vol 532-533 ◽  
pp. 877-880
Author(s):  
Yun Yong Cheng ◽  
Kun Pu ◽  
Yuan Peng Liu ◽  
Xin Bo Zhao

Turbine blade is one of the critical parts of the aero engine and usually has complex structures. The main purpose of this paper is to present a virtual cutting based method for aero engine turbine blade reverse modeling from its cone beam computed tomography (CBCT) images. Based on the turbine blade CBCT images, an improved Marching Cube algorithm was used to construct a 3D mesh model of the turbine blade. Then, cutting tools of parallel planes, concentric cylinders, concentric cones or revolved free form surfaces were used to cut the turbine blade mesh model to get the profile curves. After the profile curves were constructed by curve fitting and joining, the lofting geometric modeling technique was used to generate the turbine blade airfoil surface working in parallel flow, cylindrical flow, conical flow and revolved free form flow respectively. A set of computer simulating turbine blade CBCT images (512×512×512) was used to test the presented method and the testing results showed that the method was feasible and convenient.


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