Constrained Cutting Rate-Tool Life Characteristic Curve, Part 2: Convex Programs

1998 ◽  
Vol 120 (1) ◽  
pp. 160-165 ◽  
Author(s):  
C. L. Hough ◽  
Y. Chang
Keyword(s):  
Sensitivity Analysis ◽  
Tool Life ◽  
Simplex Method ◽  
End Milling ◽  
Characteristic Curve ◽  
Convex Programs ◽  
Machining Economics ◽  
Cutting Rate ◽  
Primal Dual ◽  
Simplex Tableau

Based on the concept in Part 1, Theory and General Case, algorithms to determine the constrained R-T characteristic curve are established for convex constrained machining economics problems. The first algorithm is for posynomial problems with the linear-logarithmic tool life equation. The R-T curve may be determined by applying the simplex method to the log-dual problems. Sensitivity analysis of the optimal simplex tableau enables obtaining the loci of optima easily. The second algorithm is for the quadratic posylognomial problems with quadratic-logarithmic tool life equation using the property of primal-dual feasibility. End milling examples constructed in Part 1 illustrate the algorithm comparing to the exhaustive method.

Constrained Cutting Rate-Tool Life Characteristic Curve, Part 1: Theory and General Case

1998 ◽  
Vol 120 (1) ◽  
pp. 156-159 ◽  
Author(s):  
C. L. Hough ◽  
Y. Chang
Keyword(s):  
Tool Life ◽  
Characteristic Curve ◽  
Sufficient Conditions ◽  
Global Optimum ◽  
Optimal Parameters ◽  
Constraint Equations ◽  
Machining Economics ◽  
Life Model ◽  
Cutting Rate ◽  
Necessary And Sufficient

The concept of a cutting rate-tool life (R-T) characteristic curve is extended to the general machining economics problem (MEP) with a quadratic-logarithmic tool life and constraint equations. The R-T characteristic curve presents the general loci of optima, which is useful in selecting optimal parameters for multiple machining conditions. The necessary and sufficient conditions for the global optimum of the unconstrained MEP are presented. These conditions are equivalently applied to the concept of the constrained R-T characteristic curve. In terms of quadratic geometric programming the objective function and constraints of the general MEP are called as quadratic posylognomials (QPL). The QPL problems are classified as convex and nonconvex and the convexity is determined by the second order terms of the tool life model. Nonlinear programming and an exhaustive method are demonstrated to determine the R-T characteristic curve for three cases of posynomial, convex QPL, and non-convex QPL problems.

scholarly journals OPTIMASI KAPASITAS PRODUKSI UKM DENGAN GOAL PROGRAMMING

2020 ◽  
Vol 5 (2) ◽  
pp. 146
Author(s):  
Welly Sugianto
Keyword(s):  
Sensitivity Analysis ◽  
Goal Programming ◽  
Simplex Method ◽  
Target Problem ◽  
Optimal Value ◽  
The Matrix ◽  
Primal Dual ◽  
Medium Enterprise ◽  
Calculation Analysis

UKM Jovelyn is a small medium enterprise (SME) that engaged in the field of bakery production. Until now, they produce cakes and cookies. They sell products throughout the Batam area which includes (Tiban market, aviari market, mitra market and puja bahari market), shops, school canteens and so on. The SME targets several things such as profit per month, number of hours worked, number of overtime hours, machine utilities, labor utilities and so forth. Until now, the SME has not been able to reach  the targets because the UKM has not determined the production amount based on the appropriate calculation. The number of products made is determined only on an intuitive basis. Determination of the amount of production cannot be determined by the usual simplex method because the objective function in the usual simplex method contains a target. Problem solving is done by using goal programming. The results of the calculation analysis show that to achieve the optimal value, the SME must produce coconut root cookies, butter cookies, nastar cookies, snow princess cookies and peanut cookies respectively 11.89 kg, 22.43 kg, 24.96 kg , 1.97kg and 0 kg. Sensitivity analysis is carried out after there are changes in conditions that result in changes in the linear program matrix, so the number of products that must be made also changes which include coconut root cookies as much as 12.8 kg, as much as 16.91 kg of butter cookies, nastar cookies as much as 25.7 and the last is 3.39 kg of nut cookies which in the initial calculation, nut cookies were not produced. The sensitivity analysis is not done by recalculation but rather by modifying the matrix and completing iteration with primal dual.

Cutting Rate-Tool Life Characteristic Functions for Material Removal Processes—Part 1: Theory

1976 ◽  
Vol 98 (2) ◽  
pp. 481-486 ◽  
Author(s):  
M. Y. Friedman ◽  
V. A. Tipnis
Keyword(s):  
Tool Life ◽  
Material Removal ◽  
Characteristic Curve ◽  
Geometric Interpretation ◽  
Characteristic Functions ◽  
Economic Optimization ◽  
Profit Rate ◽  
Comprehensive Development ◽  
Cutting Rate ◽  
Removal Processes

The existence of cutting rate-tool life (R-T) characteristic functions for material removal operations is introduced in this paper. This new concept enables a comprehensive development of a theory for economic optimization encompassing commonly used criteria of cost, production rate, and profit rate in machining when more than one cutting variable is involved. The theory provides conditions for the existence of economic optima, all of which must lie on the R-T characteristic curve for a given operation. The analysis of the theory is carried out for one and two independent cutting variables. For these two cases, it is proven that the locus of the tangent points of constant cutting rate and constant tool life curves describes the R-T characteristic curve, and also that the tool life is maximum along a given constant cutting rate curve at the point of tangency and vice versa. This geometric interpretation provides useful application of the concept as shown in Part 2.

Investigation on the Tool Wear Model and Equivalent Tool Life in End Milling Titanium Alloy Ti6Al4V

2018 ◽  
Author(s):  
Kai Guo ◽  
Bin Yang ◽  
Jie Sun ◽  
Vinothkumar Sivalingam
Keyword(s):  
Tool Wear ◽  
Titanium Alloys ◽  
Tool Life ◽  
End Milling ◽  
Cutting Speed ◽  
Carbide Tool ◽  
Wear Model ◽  
Wear Process ◽  
Coated Carbide Tool ◽  
Coated Carbide

Titanium alloys are widely utilized in aerospace thanks to their excellent combination of high-specific strength, fracture, corrosion resistance characteristics, etc. However, titanium alloys are difficult-to-machine materials. Tool wear is thus of great importance to understand and quantitatively predict tool life. In this study, the wear of coated carbide tool in milling Ti-6Al-4V alloy was assessed by characterization of the worn tool cutting edge. Furthermore, a tool wear model for end milling cutter is established with considering the joint effect of cutting speed and feed rate for characterizing tool wear process and predicting tool wear. Based on the proposed tool wear model equivalent tool life is put forward to evaluate cutting tool life under different cutting conditions. The modelling process of tool wear is given and discussed according to the specific conditions. Experimental work and validation are performed for coated carbide tool milling Ti-6Al-4V alloy.

Tool life model for end milling steel (190 BHN)

1997 ◽  
Vol 68 (1) ◽  
pp. 50-59 ◽  
Author(s):  
M. Alauddin ◽  
M.A. El Baradie
Keyword(s):  
Tool Life ◽  
End Milling ◽  
Life Model
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