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Linear Interpolation Motion (in G-Coding)

( OLD )
In linear interpolation, the tool moves in a straight line from start to end along two or three axes. Theoretically, all types of profiles can be produced by this method by making the increments between the points small. However, a large amount of data has to be processed in order to do so.
(Kalpakjian S., Schmid S.R., Manufacturing engineering and technology, Ed. 5th, p.1158)

( NEW / BETTER )

Linear interpolation is closely related to the rapid positioning motion. While the rapid tool motion is meant to be used from one position of the work area to the anotjer position wiyhour cutting, the linear interpolation mode is designed for actual material removal, such as contouring, pocketing, face milling and many other cutting motions.

Linear interpolation is used in part programming to make a straight cutting motion from the start position of the cut to its end position. It always uses the shortest distance the cutting tool path can take.  The motion programmed in linear interpolation mode is always a straight line, connecting the contour  start and end points.

In this mode, the cutter moves from one position to another by the shortest distance between the end points. This is a very important programming feature, used mainly in contouring and profiling. Any angular motion ( such as chamfers, bevels, anglers, lapers, etc. ) must be programmed in this mode to be accurate. Three types of motion can be generated in linear interpolation mode :

·         Horizontal Motion

·         Vertical Motion

·         Angular Motion

The term interpolation motion means that the control system is capable to calculate the thousands of intermadiate coordinate points between the start point and end point of the cut. The result of the calculation is the shortest path between the two points. All calculations are automatic – the control system constantly coordinates and adjusts the feedrate for all cutting axess , normally two or three.

( CNC programming handbook: a comprehensive guide to practical CNC programming, p.159 )

Proportional–Integral–Derivative Controller (PID controller) 

( OLD )

Many mechanical systems are controlled by proportional-integral-derivative (PID) controllers. There are many permutations of such controllers which use only certain portions of the PID controllers or use variations of this kind of controller. In this section we consider this very common type of controller.

Proportional Control
Proportional control results in action that is linear with the error (recall the error definition in ) The proportional term, Kp • e, has the greatest effect when the process value is far from the desired setpoint. However, very large values of Kp will tend to force the system into oscillatory response. The proportional gain effect of the controller goes to zero as the process approaches set point. Purely proportional control should therefore only be used when
• The time constant of the process is small and hence a large controller gain can be used;
• The process load changes are relatively small so that the steady-state offset is limited;
• The steady-state offset is within an acceptable range.
Integral Control
Integral control makes a process adjustment based on the cumulative error, not its current value. The integral term Ki is the reciprocal of the reset time, Tr, of the system. The reset time is the duration of each error-summing cycle. Integral control can cancel any steady-state offsets that would occur when using purely proportional control. This is sometimes called reset control.
Derivative Control
Derivative control makes a process adjustment based on the current rate of change of the process control error. Derivative control is typically used in cases where there is a large time lag between the controlled device and the sensor used for the feedback. This term has the overall effect of preventing the actuator signal from going too far in one direction or another, and can be used to limit excessive overshoot.
(Mechanical Engineering Handbook, Ed. Frank Kreith, Boca Raton: CRC Press LLC, 1999, sec.6, p29-30)

( NEW / BETTER )

Despite numerous advancements in process control methodologies, Proportional–Integral–Derivative (PID) control is still the most efficient and widely used feedback control strategy.

This is due to its simplicity and satisfactory control performance. PID controller was introduced in 1910 and its use and popularity had grown particularly after the Ziegler–Nichols empirical tuning rules in 1942 and  The development in artificial intelligence and digital technology have resulted in many intelligent control schemes such as fuzzy logic control, neural network control and adaptive control But no other technique could replace PID algorithm and more than 90% of industrial controllers are still based on PID control The wide use of PID control has sustained research on finding the key methodology for PID tuning to obtain best possible performance out of the PID control.

The optimally combined three terms functioning of PID controller can provide treatment for both the transient and steady state responses. In fact, optimal control performance can only be achieved after identifying the finest set of three gains, that is, proportional gain (Kp), integral gain (Ki) and derivative gain (Kd). Many approaches have been reported in literature for tuning parameters of PID controller. The conventional PID tuning techniques include Z–N, Cohen Coon, and relay feedback methods . The modern techniques are based on artificial intelligence techniques such as neural network, fuzzy logic and evolutionary computation; these are the most recent techniques.

Recently, many attempts have been made by several researchers to tune the PID controller parameters using various EAs, such as genetic algorithm (GA), covariance matrix adaptation evolution strategy (CMAES), particle swarm optimization (PSO), differential evolution (DE), tribes algorithm (TA), ant colony optimization (ACO), and discrete binary particle swarm optimization for both the single and multi-variable processes.

AI-based evolutionary computational techniques can determine the most optimal sets of controller gains based on a given objective function in an iterative manner from thousands of possible alternate solutions that best fit the designer’s requirements. But the performance of different methods may significantly vary in different applications. In  comparative performance analysis of various EAs such as real coded genetic algorithm (RGA) with SBX crossover, differential evolution (DE), modified particle swarm optimization (MPSO) and covariance matrix adaptation evolution strategy (CMAES) was done and better performance of CMAES and MPSO in comparison to BLT, RGA with SBX and multi-crossover approaches, was reported in the paper. The MPSO algorithm is a variant of real coded particle swarm optimization algorithm.

( Expert Systems with Applications, volume 39, issue 4,  March 2012,  pages 4390-4401 )

NURBS (Term)

(OLD)

Deformable objects have been considered as important to virtual reality applications, as they

may model clothing, facial expression, human and animal characters. In particular,Non-Uniform

Rational B-Splines (NURBS) [4, 16] are often employed to represent such objects as they can be

used to produce a variety of shapes simply by manipulating their control points and weights.

However, NURBS surfaces are seldom used in interactive applications that demand realtime

rendering performance because of their high rendering cost. There have been a lot of work carried

out to address this problem. Most of the methods developed are based on tessellation

[1, 6, 8, 9, 10, 17]. This tessellation process subdivides the NURBS surfaces into polygons so that

the hardware graphics accelerator, if present, may render the polygons in real-time. However,

this process is computationally very expensive. As a NURBS surface is deforming, this process

must be executed in each frame to reflect the change of the object shape. Since in many real-time

applications such as computer games, we may want to have many deformable objects in the

environment. Existing rendering methods would be difficult to render these objects in real-time.

(Incremental Rendering of Deformable Trimmed NURBS Surfaces, Gary K. L. Cheung, Rynson

W.H. Lau, Frederick W.B. L, pg. 48)

( NEW / BETTER )

During the past two decades, Non-Uniform Rational B-  Splines (NURBS) have gained popularity  for shape model-  ing and  geometric design and were  incorporated into sev-  eral  commercial modeling systems mainly because  they  have many attractive properties.

  NURBS  offer a uni-fied  mathematical formulation for representing  not only  free-form curves  and  surfaces, but  also  standard analytic  shapes such  as  conics, quadrics, and surfaces  of revolution.  Through the manipulation of control points, weights,  and/or  knots, users can design a  vast  variety of shapes us- ing NURBS. Despite NURBS’ power and potential, users  are faced with the tedium of non-intuitively manipulating a  large number of geometric variables. Moreover, a particular  shape can often be represented non-uniquely, with different  values of knots, control points, and weights.

T h e  “geometric redundancy” of NURBS tends to make shape refinement  a d  h o c  and ambiguous.  To  ameliorate  the  geometric  design with  NURBS,  A  wide array of  techniques for NURBS manipulation  have  been  developed.Typical design techniques  include interactive editing, (regular or scattered) data inter-  polation, shape approximation, cross-sectional design, op-  timization, etc.  Recently,  energy optimization techniques  have  been widely  studied  in  shape modeling  especially  shape fairing.  In a nutshell, energy-based algorithms offer  designers a feasible and powerful solution that can alleviate  the burden of interactively manipulating degrees of freedom  (DOFs) of  NURBS and a metric  to evaluate the  extent to  which the final shape satisfies certain design requirements.  Prior work on energy optimization only focuses on func-  tionals whose variables  are either control  points  o r   nonunity  weights of NURBS.

 The computation of functionals  with respect to the additional shape flexibility resulted from  the non-uniform knots is yet to be fully investigated.  Because the knot variation will generally violate the lo-  cal support property of NURBS, this makes.the direct eval-  uation of  the gradient with  respect  to  knots  non-intuitive  in  principle.  In  our modeling algorithms, the NURBS ge-  ometry  is  systematically  transformed into  a  set  of  equiv-  alent rational Bezier  patches. This idea offers a  new  parametrization  for  the  same NURBS shape,  in  which  NURBS knots no longer affect the domain boundary for a  specific  curve / surface  patch.  Hence, the  new formulation  imposes no difficulties for the gradient derivation with re-  spect to knots.  Consequently, the  geometric modeling potential of NURBS can be fully exploited in an intuitive and uniform fashion.

 (Automatic Knot Determination of NURBS for Interactive Geometric Design, Hui Xie and Hong Qin, p. 267 )

Design for Environment  (Method)

( NEW / BETTER )

A growing number of managers believe that addressing environmental impacts in product-design decisions has tangible advantages to firms.Yet many firms struggle to diffuse design-for-environment (DfE) practices across their product-development teams. Four leading electronics firms' attempts to adopt DfE suggest that the establishment of highly interconnected, internal information networks may be a robust diffusion strategy. 

Technically competent centers acting as clearinghouses of companywide information relevant to environmental design and coordinated with specialists on individual product-design teams seem to be an effective organizational structure for diffusing DfE.Internal information networks reduce the cost to designers of assessing environmental costs and benefits and thus lower the motivational barriers of product managers. Environmental design tools may be a component of successful DfE practice but do not seem to be sufficient in themselves. The complexity of environmental issues requires an approach that continually generates new information. Dense information networks allow pockets of expertise to form in response to ever-changing needs.

In the late 1980s, when companies began to eliminate chlorofluorocarbons (CFCs) in their production processes, many discovered that they didn't need CFCs in many cases and could use other less costly materials. Too late, companies discovered that they could have avoided the liability, remediation, and process-change costs associated with the use of CFSs if the designers of their products and processes had only thought ahead and incorporated environmental issues in their designs. To prevent such future costs, many companies began to talk about designing for the environment.

Design-for-environment (DfE) is the explicit consideration of environmental concerns during the design of products and processes [Lenox and Ehrenfeld 1997]. DfE is a natural extension to such quality initiatives as design for manufacturability and design for servicability.Managers see DfE as potentially creating more desirable products at lower cost by reducing disposal and regulatory costs, increasing the end-of-life value of products, reducing material use, and minimizing liabilities. Regulators and environmental advocacy groups see DfE as an opportunity to reduce the environmental impact of industrial activity through the self-interested pursuits of firms. For these reasons, researchers and practitioners believe DfE is a critical component of ecologically sustainable business practice.

Design choices have impacts on the natural environment that are often difficult to assess and depend on a number of factors. Even experts find it difficult to identify what aspects of design will reduce environmental costs or create beneficial opportunities. Plastic may be the right environmental decision in some cases and wrong elsewhere. Emissions of hazardous material may increase liability in some circumstances but not in others. Consumer demand for environmentally benign products has been notoriously difficult to access. In general, it is difficult to make broad rules for green design.

( An Assessment of Design-for-Environment Practices in Leading US Electronics Firms. By: Lenox, Michael, Interfaces, 00922102, May/Jun2000, Vol.30, Issue 3 )

Shaft-Basis System (for dimensioning and tolerancing) 

( OLD )

In the Shaft-Basis system, the different clearances or interferences are obtained by associating various holes with a single shaft, whose upper deviation is zero. In this system, the size of shaft is the basic size, while the clearance or interference is applied to the dimensions of the hole. The system is denoted by the symbol 'h'. The shaft-basis system is popular in industries using semi-finished or finished shafting, such as bright bars, as raw material.

Shaft-basis system

(a) Clearance Fit

(b) Transition Fit

(c) Interference Fit

(Design of machine elements, Bhandari, p.77)

( NEW / BETTER )

There are two ways of representing a system. One is the hole basis and the  other is the shaft basis. In the hole basis system the dimension of the hole is  considered to be the datum, whereas, in the shaft basis system dimension of the  shaft is considered to be the datum.  The holes are normally made by drilling, followed by reaming. Therefore, the dimension of a hole is fixed due to the nature  of the tool used. On the contrary, the dimension of a shaft is easily controllable  by standard manufacturing processes. For this reason, the hole basis system is  much more popular than the shaft basis system. Here, we shall discuss fit  system on hole basis. 

( Module 1, Fundamentals of machine design, Version 2 ME, IIT Kharagpur )