Nand K. Jha

Geometric programming based robot control design

Abstract The optimal control of robot is obtained by geometric programming technique. The condesation approach of geometric program and Persevals theorem are the basis of mathematical modeling. The relationships of sampling time versus the optimum proportional gain ( K p ), the optimum integral gain ( K i ), and the optimum derivative gain ( K v ) are studied. The overall conclusion is that as the sampling time increases so the K p , K i and K v values decrease before becoming flat. The optimum control is dependent on the choice of constraints. The approach is illustrated through an example.

Optimal image correlation in experimental mechanics

The integration of optimization techniques for use in digital image correlation problems in experimental mechanics is discussed. Stereo sets of images of a speckle pattern on a loaded body are correlated using four types of optimization routines. The results obtained using the gradient-based first-order method and nongradient-based pattern search, simplex, and Powells methods compare extremely well with the original experimental results. The effectiveness and accuracy of these different optimal image processing techniques have also been analyzed and found suitable for this example

Integrated computer-aided optimal design and finite element analysis of a plain milling cutter

This paper presents the computer-aided integration of solid modelling, optimization, and finite element analysis. Interactive (three-dimensional) solid modelling is used in the development of relatively efficient and fast solutions to the many constraints and/or limitations encountered in the design process. The study also addresses the fatigue analysis using 3D finite element analysis on a workstation. Throughout the study, interactive 3D solid modelling is used in the development of a practical and economical design procedure. The research highlights the interactive and integrated nature of the design tasks. An optimal formulation of an automatic design algorithm is also carried out. The cost minimization objective function along with design constraints and behavior constraints are developed. The optimal design parameters thus obtained are tested for stresses at the tip of the tool and at the fillets. Interactive application of optimization, solid modelling, and finite element techniques produce the acceptable optimal design. The design methodology presented in this paper is general and generic in nature. This has been illustrated through an example of design of a plain milling cutter.

Optimizing the number of tools and cutting parameters in multi-tool turning for multiple objectives through geometric programming

Abstract Multiple tool turning is often considered an economic alternative to single tool turning but for its rational application, however, accurate process planning is essential. This paper investigates the automatic (computerized) process planning for a multiple tool turning operation. A unified or multiple objective function based on cost of production and rate of production has been developed. The unified objective function is optimized, subject to constraints, such as component characteristics, machine power available, cutting speed, feed, and depth of cut rate. In all, 14 constraints are applied to the multiple objective function. During analysis, however, it was discovered that the integrality requirement on the number of tools, poses a great problem. Due to this constraint, the optimization problem became one of the ‘nonlinear mixed integer programming’ class. Nonlinear programming, coupled with integer programming, is always a complex problem and was tackled by suitably modifying the geometric programming technique. The mathematical model developed was further modified to include discrete steps of speed and feed on the machine. It was found that in discrete cases, the number of passes required for completing the job was more than in the continuous case. The approach has been demonstrated through an example.

Probabilistic cost estimation in advance of production in a computerized manufacturing system through stochastic geometric programming

A mathematical model for stochastic cost optimization has been developed. The model contains cost terms such as inventory cost, penalty cost for due date violation, and the machining cost. The probable range of cost has been estimated by a stochastic geometric program. If an exact solution is desired, a two stage stochastic geometric program has to be solved. This is mathematically tedious and requires great computational effort. However, managers are often concerned with a policy decision which can be based on the probable lower and upper bounds on the cost function. The probability level on the lower bound of cost has been calculated through the theory of error propagation. This approach is explained through an example.

Stochastic mathematical modelling and manufacturing cost estimation in uncertain industrial environment

In the present day high-tech uncertain industrial environment, there is often a need for determining expected cost per piece or per batch in advance of production. A mathematical model for stochastic cost optimization has been developed. If an exact solution is desired, a two stage stochastic geometric program has to be solved. This is tedious and requires great computational effort. However, managers are often concerned with a policy decision which can be based on the probable lower and upper bound on the stochastic cost function. This paper deals with estimating the probable cost range and also calculating the exact expected cost. The probability level on the lower bound of cost has been calculated through the theory of error propagation. A decomposition algorithm has been used to find the exact expected cost under a set of real-world constraints. The whole approach has been explained through an example

Unified theory of automation in process planning utilizing multiobjectives under real world constraints

Abstract This paper investigates the unified theory of automation in process planning of the milling operation. The unified function has been developed based on the cost and rate of production. The unified objective function thus developed is supposed to act as a true arbiter of individual objective functions. The unified objective function is optimized under a large number of real-world constraints. Because of the discrete nature of machine settings the feed and speed are discretized, and integrality constraints are imposed on the feed and speed. Because of these constraints the process planning automation of the milling operation becomes a nonlinear mixed integer programming (NLMIP) problem. The approach has been illustrated with an example. The results obtained show relevance to real-world practice.

Computer-aided optimal turning of stepped shaft

Abstract An analysis for the turning of stepped shaft is performed to select optimally the multi-pass cutting variables by applying the geometric programming concept. A system is developed for the turning of stepped shaft. Several possible manufacturing-system constraints are considered to make the problem realistic. From a practical stand-point, every restriction adds at least one degree of difficulty to the analysis. An example of a stepped shaft with eleven surfaces, of which one is tapered, is considered. The program is run on a VAX-8350.

Computer-aided formulation and optimal control of an integrated production system for competitive products

Abstract An integrated production, inventory and advertising system has been formulated based on control engineering principles. In this system, the customers demand is satisfied from stock, which in turn is replenished from production facilities. But sales reflect the advertising effort, present as well as past. The past effort has been considered as a delay with an assumed delay period. The problem is formulated as a state and observation model. Out of this an augmented model of state and parameters is formed. The parameters describing the model are estimated from MAP discrete filter algorithm. It is shown that sales of product 1 or product 2 at (k + l)th period is effected by sales and advertising of product 1 or product 2 at the kth period, and also by sales and advertising of product 2 or product 1 at (k-θ)th period, where 6 is the delay.

A set-theoretic automatic selection of cutting tools in manufacturing system

Abstract The selection of the optimum number and right type of cutting tools in manufacturing systems is very important. Set theory has been used for such decision making in this paper. From the known work load and known characteristics of the cutting tool, set-theory analysis leads to the identification of constraints bearing upon the selection of cutting tools. A linear programming formulation then helps in the selection of the optimum number and type of cutting tools. In this paper, this approach has been illustrated by selecting cutting tools for an aircraft-engine parts manufacturing system.