Cutting plane methods for general integer programming

Integer programming (IP) problems are difficult to solve due to the integer restrictions imposed on them. A technique for solving these problems is the cutting plane method. In this method, linear constraints are added to the associated linear programming (LP) problem until an integer optimal solution is found. These constraints cut off part of the LP solution space but do not eliminate any feasible integer solution. In this report algorithms for solving IP due to Gomory and to Dantzig are presented. Two other cutting plane approaches and two extensions to Gomory's algorithm are also discussed. Although these methods are mathematically elegant they are known to have slow convergence and an explosive storage requirement. As a result cutting planes are generally not computationally successful

Reliability assessment of cutting tool life based on surrogate approximation methods

A novel reliability estimation approach to the cutting tools based on advanced approximation methods is proposed. Methods such as the stochastic response surface and surrogate modeling are tested, starting from a few sample points obtained through fundamental experiments and extending them to models able to estimate the tool wear as a function of the key process parameters. Subsequently, different reliability analysis methods are employed such as Monte Carlo simulations and first- and second-order reliability methods. In the present study, these reliability analysis methods are assessed for estimating the reliability of cutting tools. The results show that the proposed method is an efficient method for assessing the reliability of the cutting tool based on the minimum number of experimental results. Experimental verification for the case of high-speed turning confirms the findings of the present study for cutting tools under flank wear

An Innovative Experimental Study of Corner Radius Effect on Cutting Forces

The cutting forces are often modelled using edge discretisation methodology. In finish turning, due to the smaller corner radii, the use of a local cutting force model identified from orthogonal cutting tests poses a significant challenge. In this paper, the local effect of the corner radius on the forces is investigated using a new experimental configuration: corner cutting tests involving the tool nose. The results are compared with inverse identifications based on cylindrical turning tests and elementary cutting tests on tubes. The results obtained from these methods consistently show the significant influence of the corner radius on the cutting forces

Effective Interventions for Treating Superficial Self Mutilators

Self-cutting is the most common form of self-mutilation in adolescents but there is insufficient knowledge as to which treatment methods to reduce self-mutilation are most effective. This exploration into the causes of self-cutting and the treatment interventions, such as Dialectical Behavior Therapy (DBT), compares adolescents who had DBT treatment with those who have used other treatment methods. Research findings indicate that the average age of adolescents in treatment was 15 years old and had been in treatment at least one time prior. Adolescents in DBT treatment showed signs in reducing/stopping self-cutting behavior along with improving communication skills with caregivers. Implications of this study show the need for further research to help educate professionals about the effective treatment for treating adolescent self-cutters

Machining stability and machine tool dynamics

Machining is a common manufacturing process in industry due to its high flexibility and ability to produce parts which excellent quality. The productivity and quality in machining operations can be limited by several process constraints one of which is the self-excited chatter vibrations. Under certain conditions, the process may become unstable yielding oscillations with high amplitudes which result in poor surface finish and damage to the cutting tool, part and the machine tool itself. Stability analysis of the dynamic cutting process can be used to determine chatter-free machining conditions with high material removal rate. Since chatter is a result of the dynamic interactions between the process and the structures both cutting and machine tool dynamics are important elements of the stability analysis. In this paper, methods developed for stability analysis of cutting processes and machine tool dynamics will be presented. Implications of these methods in the selection of process parameters and machine tool design will be also discussed with example applications

Methodics of use of engage movements in milling

S neustálým růstem metod navrhování a jejich přístupností je vždy nutné zvýšit efektivitu výrobních operací. Jedním z prostředků pro zvýšení účinnosti je optimalizace řezných sil, které jsou součástí obráběcího procesu. Zapojení pohybových metod do frézovacích procesů má významný vliv na výstup frézovací strategie. Cílem diplomové práce bylo zhodnotit, které z metod pohybu pohybu v frézovacích strategiích jsou vhodnější pro výběr, aby se určily způsoby, jak lze zlepšit provozní efektivitu metod pohybu pohybu. Během čelního frézování rovného povrchu obrobku byl proveden experimentální přístup k posouzení účinku těchto metod na řezné síly. Metody použité v této studii byly přímý vstup nástroje, horizontální oblouk, vertikální oblouk, lineární rampa, spirálový pohyb, spirálová interpolace a přímý pokles. Materiál obrobku byl hliník 7075-T6. Siemens NX CAM byl použit pro návrh frézovaného rozvržení a vytvoření frézovací strategie pro pohyby záběru. Všechny pokusy se prováděly na vertikálním 3osém CNC obráběcím centru MAS VMC 500 s ovladačem. Měření řezné síly (Fx, Fy a Fz) byla měřena za použití rotačního Kistler 4-komponentního dynamometru RCD typu 9132C. K analýze opotřebení nástroje byl použit optický mikroskop VHX 6000 s přesností s Keyence čočkami VH-ZST / RZ x20-200. Využití metod pohybu pohybu mělo významný vliv na řezné síly, výsledná síla při frézování byla nejvyšší ze všech testovaných metod. Lineární vstup do rampy ukázal závislost na úhlu rampy pro udržení malé hodnoty výsledné síly. Řezné síly v technikách oblouku byly menší než přímé vstupní řezné síly, i když byly použity stejné posuvy a rychlost. Ačkoli suché frézování hliníku 7075-T6 není účelné, lze u tohoto materiálu dosáhnout minimálních řezných sil bez ohledu na strategii zapojení řezného nástroje a obrobku s využitím optimálních řezných parametrů.With the constant growth of design methods and their accessibility, there is always a need to enhance the efficiency of manufacturing operations. One of the means to enhance efficiency is by optimizing the cutting forces involved in the machining process. Engage movement methods in milling processes have a significant influence on the output of a milling strategy. The thesis aimed to evaluate which of the engage movement methods in milling strategies are more suitable for selection in order to determine ways through which the operational effectiveness of the engage movement methods can be improved. An experimental approach to examine the effect of these methods on cutting forces was carried out during an end milling of a flat workpiece surface. The methods employed in this study were straight tool entry, horizontal arching, vertical arching, linear ramping, spiral movement, helical interpolation, and straight plunge. The workpiece material was 7075-T6 Aluminum. Siemens NX CAM was used for designing the milled layout and creating the milling strategy for the engage movements. All machining trials were carried out on a vertical 3-axis CNC Machining Center MAS VMC 500 with a controller. Cutting force measurements (Fx, Fy, and Fz) were measured using a Rotating Kistler 4-Component Dynamometer RCD type 9132C. The VHX 6000 Accuracy Optical Microscope with the Keyence Lenses VH-ZST/ RZ x20-200, were used to analyze the tool wear. The employment of engage movement methods had significant effects on the cutting forces, the resultant force in plunge milling was the highest among all tested methods. Linear ramping entry showed dependence on the ramp angle for maintaining a small value of resultant force. The cutting forces in the arcing techniques were smaller than the straight entry cutting forces, even when the same feed and speed were used. Although the dry milling of Aluminum 7075-T6 is not expedient, the minimal cutting forces can be achieved for this material regardless of the cutter-workpiece engagement strategy, using the optimal cutting parameters

Tool Life of PM-HSS Cutting Tools when Milling of Titanium Alloy

Machining of titanium alloys meets with poor life of a cutting tool. It is caused by a low thermal conductivity and by a high strength-to-weight ratio of the alloys. Various approaches for cost-effective and productive machining titanium alloys are still researched. One of methods can be using the cutters made of modern high-speed steel (HSS) as a product of a powder metallurgy (PM) process. These materials (PM-HSS) possess better and homogenous mechanical properties than conventional high-speed steel. The PM-HSS cutters equipped with any effective coating allow increase cutting speed to the level which is typical for uncoated cemented carbide, while price of the tool is lower. In the article several PM-HSS cutting tool materials were compared to conventional cobalt based HSS from the tool life point of view. It was proved that conventional high-speed steel offers very long tool life and high tool performance at speed of 30 m/min. However the regular tooth pitch significantly decreases tool life for this cutting tool material. The main benefit of PM-HSS cutters can be fully utilized when cutting speed about 50 m/min is applied. The cutters coated by effective thermal barrier showed longer tool life and higher performance of the cutting tools

Multi-scale simulation of the nano-metric cutting process

Molecular dynamics (MD) simulation and the finite element (FE) method are two popular numerical techniques for the simulation of machining processes. The two methods have their own strengths and limitations. MD simulation can cover the phenomena occurring at nano-metric scale but is limited by the computational cost and capacity, whilst the FE method is suitable for modelling meso- to macro-scale machining and for simulating macro-parameters, such as the temperature in a cutting zone, the stress/strain distribution and cutting forces, etc. With the successful application of multi-scale simulations in many research fields, the application of simulation to the machining processes is emerging, particularly in relation to machined surface generation and integrity formation, i.e. the machined surface roughness, residual stress, micro-hardness, microstructure and fatigue. Based on the quasi-continuum (QC) method, the multi-scale simulation of nano-metric cutting has been proposed. Cutting simulations are performed on single-crystal aluminium to investigate the chip formation, generation and propagation of the material dislocation during the cutting process. In addition, the effect of the tool rake angle on the cutting force and internal stress under the workpiece surface is investigated: The cutting force and internal stress in the workpiece material decrease with the increase of the rake angle. Finally, to ease multi-scale modelling and its simulation steps and to increase their speed, a computationally efficient MATLAB-based programme has been developed, which facilitates the geometrical modelling of cutting, the simulation conditions, the implementation of simulation and the analysis of results within a unified integrated virtual-simulation environment