Sufficient Conditions for Cutting Rate–Tool Life Characteristic Functions for Metal Removal Processes

1986 ◽  
Vol 108 (3) ◽  
pp. 235-237 ◽  
Author(s):  
C. L. Hough
Keyword(s):  
Tool Life ◽  
Metal Removal ◽  
Sufficient Conditions ◽  
Characteristic Functions ◽  
Cutting Rate ◽  
Removal Processes

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.

Cutting Rate-Tool Life Characteristic Functions for Material Removal Processes—Part 2: Verification and Applications

1976 ◽  
Vol 98 (2) ◽  
pp. 487-495 ◽  
Author(s):  
V. A. Tipnis ◽  
M. Y. Friedman
Keyword(s):  
Tool Life ◽  
Material Removal ◽  
The Other ◽  
Characteristic Functions ◽  
Designed Experiments ◽  
Cutting Rate ◽  
Removal Processes ◽  
T Domain ◽  
Economic Selection ◽  
Selection Of

The experimental verification, interpretations, and applications of the concept of cutting rate-tool life (R-T) characteristic functions are presented in this paper. Two statistically designed experiments, one on sawing and the other on milling, verifying the concept are described. The analytical and geometrical interpretations of the concept, including the existence of optima in the R-T domain, are presented. The applications discussed include economic selection of machining conditions, economic tool life determinations, comparison of machining response, objective function for adaptive control, and maximization of material removal at a desired level of surface integrity. The concept can be applied to other machining responses of conventional as well as nontraditional material removal processes.

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.

Highlights of the DARPA Advanced Machining Research Program

1985 ◽  
Vol 107 (4) ◽  
pp. 325-335 ◽  
Author(s):  
R. Komanduri ◽  
D. G. Flom ◽  
M. Lee
Keyword(s):  
Thermal Properties ◽  
Tool Wear ◽  
Titanium Alloys ◽  
Tool Life ◽  
Research Program ◽  
High Speed ◽  
Metal Removal ◽  
High Speed Machining ◽  
Advanced Machining ◽  
Nickel Base

Results of a four-year Advanced Machining Research Program (AMRP) to provide a science base for faster metal removal through high-speed machining (HSM), high-throughput machining (HTM) and laser-assisted machining (LAM) are presented. Emphasis was placed on turning and milling of aluminum-, nickel-base-, titanium-, and ferrous alloys. Experimental cutting speeds ranged from 0.0013 smm (0.004 sfpm) to 24,500 smm (80,000 sfpm). Chip formation in HSM is found to be associated with the formation of either a continuous, ribbon-like chip or a segmental (or shear-localized) chip. The former is favored by good thermal properties, low hardness, and fcc/bcc crystal structures, e.g., aluminum alloys and soft carbon steels, while the latter is favored by poor thermal properties, hcp structure, and high hardness, e.g., titanium alloys, nickel base superalloys, and hardened alloy steels. Mathematical models were developed to describe the primary features of chip formation in HSM. At ultra-high speed machining (UHSM) speeds, chip type does not change with speed nor does tool wear. However, at even moderately high speeds, tool wear is still the limiting factor when machining titanium alloys, superalloys, and special steels. Tool life and productivity can be increased significantly for special applications using two novel cutting tool concepts – ledge and rotary. With ledge inserts, titanium alloys can be machined (turning and face milling) five times faster than conventional, with long tool life (~ 30 min) and cost savings up to 78 percent. A stiffened rotary tool has yielded a tool life improvement of twenty times in turning Inconel 718 and about six times when machining titanium 6A1-4V. Significantly increased metal removal rates (up to 50 in.3/min on Inconel 718 and Ti 6A1-4V) have been achieved on a rigid, high-power precision lathe. Continuous wave CO2 LAM, though conceptually feasible, limits the opportunities to manufacture DOD components due to poor adsorption (~ 10 percent) together with high capital equipment and operating costs. Pulse LAM shows greater promise, especially if new laser source concepts such as face pump lasers are considered. Economic modeling has enabled assessment of HSM and LAM developments. Aluminum HSM has been demonstrated in a production environment and substantial payoffs are indicated in airframe applications.

Infinite block-structured transition matrices and their properties

1998 ◽  
Vol 30 (2) ◽  
pp. 365-384 ◽  
Author(s):  
Yiqiang Q. Zhao ◽  
Wei Li ◽  
W. John Braun
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Block Structure ◽  
Sufficient Conditions ◽  
Characteristic Functions ◽  
Scalar Case ◽  
Transition Matrices ◽  
Positive Recurrent ◽  
Infinite State ◽  
Block Structured

In this paper, we study Markov chains with infinite state block-structured transition matrices, whose states are partitioned into levels according to the block structure, and various associated measures. Roughly speaking, these measures involve first passage times or expected numbers of visits to certain levels without hitting other levels. They are very important and often play a key role in the study of a Markov chain. Necessary and/or sufficient conditions are obtained for a Markov chain to be positive recurrent, recurrent, or transient in terms of these measures. Results are obtained for general irreducible Markov chains as well as those with transition matrices possessing some block structure. We also discuss the decomposition or the factorization of the characteristic equations of these measures. In the scalar case, we locate the zeros of these characteristic functions and therefore use these zeros to characterize a Markov chain. Examples and various remarks are given to illustrate some of the results.

Determining the Tool Life of a Cemented Carbide Drill Using Optimized Process, Delivery System, and Drill Design Parameters in Deep Hole Drilling Using Environment Friendly Machining Method

2010 ◽  
Author(s):  
Muhammad I. Hussain ◽  
A. Filipovic ◽  
J. Dasch ◽  
D. Simon
Keyword(s):  
Tool Life ◽  
Metal Removal ◽  
Cemented Carbide ◽  
Design Parameters ◽  
Innovative Technology ◽  
Hole Drilling ◽  
Deep Hole ◽  
Deep Hole Drilling ◽  
High Production ◽  
Cemented Carbide Drills

Near dry machining or Minimum Quantity Lubrication (MQL) methodology appears to be a valid solution to meet environmental challenges of metal removal processes. However, in order to implement environmentally friendly machining into high production manufacturing environments, it is imperative to invent a robust solution for a wide variety of machined features. In previous work by the authors, capabilities of the MQL process, calibrated for machining extremely deep holes with length to diameter (L/D) ratio of up to 15, were proven. An optimal machining solution was developed using the Box and Behnken experimental design approach, and it was demonstrated that cemented carbide drills with proper cutting geometry and MQL settings can be used for deep hole drilling of aluminum. This work, focused on developing a production ready application, proved that MQL technology is also robust enough to achieve adequate tool life for high volume manufacturing requirements. It actually exhibited that such approach may even exceed tool life requirements currently enforced for conventional processes using gun drills or G-drills. In addition, machining time was significantly reduced with this innovative technology achieving productivity approximately 7 times higher than in traditional drilling operations. Considering these achievements, MQL has been demonstrated to be the drilling technology of future that will help reducing capital investments into production machinery and minimize landfill discharges of high production manufacturing facilities.

scholarly journals Perfect hypercomplex algebras: Semi-tensor product approach

2021 ◽  
Vol 1 (4) ◽  
pp. 177-187
Author(s):  
Daizhan Cheng ◽  
◽  
Zhengping Ji ◽  
Jun-e Feng ◽  
Shihua Fu ◽  
...  
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Characteristic Functions ◽  
Hypercomplex Numbers ◽  
3 Dimensional ◽  
Zero Sets ◽  
Higher Dimensional ◽  
Product Approach ◽  
Necessary And Sufficient

<abstract><p>The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebras (PHAs) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product (STP) of matrices are reviewed. The zero sets are defined for non-invertible hypercomplex numbers in a given PHA, and characteristic functions are proposed for calculating zero sets. Then PHA of various dimensions are considered. First, classification of $ 2 $-dimensional PHAs are investigated. Second, all the $ 3 $-dimensional PHAs are obtained and the corresponding zero sets are calculated. Finally, $ 4 $- and higher dimensional PHAs are also considered.</p></abstract>

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