Vibration analysis of a printed circuit board

The reliability of the printed circuit board assembly under dynamic environments, such as those found onboard airplanes, ships and land vehicles is receiving more attention. This research analyses the dynamic characteristics of the printed circuit board (PCB) supported by edge retainers and plug-in connectors. By modelling the wedge retainer and connector as providing simply supported boundary condition with appropriate rotational spring stiffnesses along their respective edges with the aid of finite element codes, accurate natural frequencies for the board against experimental natural frequencies are obtained. For a PCB supported by two opposite wedge retainers and a plug-in connector and with its remaining edge free of any restraint, it is found that these real supports behave somewhere between the simply supported and clamped boundary conditions and provide a percentage fixity of 39.5% more than the classical simply supported case. By using an eigensensitivity method, the rotational stiffnesses representing the boundary supports of the PCB can be updated effectively and is capable of representing the dynamics of the PCB accurately. The result shows that the percentage error in the fundamental frequency of the PCB finite element model is substantially reduced from 22.3% to 1.3%. The procedure demonstrated the effectiveness of using only the vibration test frequencies as reference data when the mode shapes of the original untuned model are almost identical to the referenced modes/experimental data. When using only modal frequencies in model improvement, the analysis is very much simplified. Furthermore, the time taken to obtain the experimental data will be substantially reduced as the experimental mode shapes are not required.In addition, this thesis advocates a relatively simple method in determining the support locations for maximising the fundamental frequency of vibrating structures. The technique is simple and does not require any optimisation or sequential search algorithm in the analysis. The key to the procedure is to position the necessary supports at positions so as to eliminate the lower modes from the original configuration. This is accomplished by introducing point supports along the nodal lines of the highest possible mode from the original configuration, so that all the other lower modes are eliminated by the introduction of the new or extra supports to the structure. It also proposes inspecting the average driving point residues along the nodal lines of vibrating plates to find the optimal locations of the supports. Numerical examples are provided to demonstrate its validity. By applying to the PCB supported on its three sides by two wedge retainers and a connector, it is found that a single point constraint that would yield maximum fundamental frequency is located at the mid-point of the nodal line, namely, node 39. This point support has the effect of increasing the structure's fundamental frequency from 68.4 Hz to 146.9 Hz, or 115% higher.

Optimizing PCB assembly for family setup strategy

Purpose – The purpose of this paper is to investigate the optimization for a placement machine in printed circuit board (PCB) assembly when family setup strategy is adopted. Design/methodology/approach – A complete mathematical model is developed for the integrated problem to optimize feeder arrangement and component placement sequences so as to minimize the makespan for a set of PCB batches. Owing to the complexity of the problem, a specific genetic algorithm (GA) is proposed. Findings – The established model is able to find the minimal makespan for a set of PCB batches through determining the feeder arrangement and placement sequences. However, exact solutions to the problem are not practical due to the complexity. Experimental tests show that the proposed GA can solve the problem both effectively and efficiently. Research limitations/implications – When a placement machine is set up for production of a set of PCB batches, the feeder arrangement of the machine together with the component placement sequencing for each PCB type should be solved simultaneously so as to minimize the overall makespan. Practical implications – The paper investigates the optimization for PCB assembly with family setup strategy, which is adopted by many PCB manufacturers for reducing both setup costs and human errors. Originality/value – The paper investigates the feeder arrangement and placement sequencing problems when family setup strategy is adopted, which has not been studied in the literature.

PCB assembly line assignment:a genetic algorithm approach

Purpose – This paper sets out to study a production-planning problem for printed circuit board (PCB) assembly. A PCB assembly company may have a number of assembly lines for production of several product types in large volume. Design/methodology/approach – Pure integer linear programming models are formulated for assigning the product types to assembly lines, which is the line assignment problem, with the objective of minimizing the total production cost. In this approach, unrealistic assignment, which was suffered by previous researchers, is avoided by incorporating several constraints into the model. In this paper, a genetic algorithm is developed to solve the line assignment problem. Findings – The procedure of the genetic algorithm to the problem and a numerical example for illustrating the models are provided. It is also proved that the algorithm is effective and efficient in dealing with the problem. Originality/value – This paper studies the line assignment problem arising in a PCB manufacturing company in which the production volume is high.

Editorial

This special issue of the Journal of the Operational Research Society is dedicated to papers on the related subjects of knowledge management and intellectual capital. These subjects continue to generate considerable interest amongst both practitioners and academics. This issue demonstrates that operational researchers have many contributions to offer to the area, especially by bringing multi-disciplinary, integrated and holistic perspectives. The papers included are both theoretical as well as practical, and include a number of case studies showing how knowledge management has been implemented in practice that may assist other organisations in their search for a better means of managing what is now recognised as a core organisational activity. It has been accepted by a growing number of organisations that the precise handling of information and knowledge is a significant factor in facilitating their success but that there is a challenge in how to implement a strategy and processes for this handling. It is here, in the particular area of knowledge process handling that we can see the contributions of operational researchers most clearly as is illustrated in the papers included in this journal edition. The issue comprises nine papers, contributed by authors based in eight different countries on five continents. Lind and Seigerroth describe an approach that they call team-based reconstruction, intended to help articulate knowledge in a particular organisational. context. They illustrate the use of this approach with three case studies, two in manufacturing and one in public sector health care. Different ways of carrying out reconstruction are analysed, and the benefits of team-based reconstruction are established. Edwards and Kidd, and Connell, Powell and Klein both concentrate on knowledge transfer. Edwards and Kidd discuss the issues involved in transferring knowledge across frontières (borders) of various kinds, from those borders within organisations to those between countries. They present two examples, one in distribution and the other in manufacturing. They conclude that trust and culture both play an important part in facilitating such transfers, that IT should be kept in a supporting role in knowledge management projects, and that a staged approach to this IT support may be the most effective. Connell, Powell and Klein consider the oft-quoted distinction between explicit and tacit knowledge, and argue that such a distinction is sometimes unhelpful. They suggest that knowledge should rather be regarded as a holistic systemic property. The consequences of this for knowledge transfer are examined, with a particular emphasis on what this might mean for the practice of OR Their view of OR in the context of knowledge management very much echoes Lind and Seigerroth's focus on knowledge for human action. This is an interesting convergence of views given that, broadly speaking, one set of authors comes from within the OR community, and the other from outside it. Hafeez and Abdelmeguid present the nearest to a 'hard' OR contribution of the papers in this special issue. In their paper they construct and use system dynamics models to investigate alternative ways in which an organisation might close a knowledge gap or skills gap. The methods they use have the potential to be generalised to any other quantifiable aspects of intellectual capital. The contribution by Revilla, Sarkis and Modrego is also at the 'hard' end of the spectrum. They evaluate the performance of public–private research collaborations in Spain, using an approach based on data envelopment analysis. They found that larger organisations tended to perform relatively better than smaller ones, even though the approach used takes into account scale effects. Perhaps more interesting was that many factors that might have been thought relevant, such as the organisation's existing knowledge base or how widely applicable the results of the project would be, had no significant effect on the performance. It may be that how well the partnership between the collaborators works (not a factor it was possible to take into account in this study) is more important than most other factors. Mak and Ramaprasad introduce the concept of a knowledge supply network. This builds on existing ideas of supply chain management, but also integrates the design chain and the marketing chain, to address all the intellectual property connected with the network as a whole. The authors regard the knowledge supply network as the natural focus for considering knowledge management issues. They propose seven criteria for evaluating knowledge supply network architecture, and illustrate their argument with an example from the electronics industry—integrated circuit design and fabrication. In the paper by Hasan and Crawford, their interest lies in the holistic approach to knowledge management. They demonstrate their argument—that there is no simple IT solution for organisational knowledge management efforts—through two case study investigations. These case studies, in Australian universities, are investigated through cultural historical activity theory, which focuses the study on the activities that are carried out by people in support of their interpretations of their role, the opportunities available and the organisation's purpose. Human activities, it is argued, are mediated by the available tools, including IT and IS and in this particular context, KMS. It is this argument that places the available technology into the knowledge activity process and permits the future design of KMS to be improved through the lessons learnt by studying these knowledge activity systems in practice. Wijnhoven concentrates on knowledge management at the operational level of the organisation. He is concerned with studying the transformation of certain inputs to outputs—the operations function—and the consequent realisation of organisational goals via the management of these operations. He argues that the inputs and outputs of this process in the context of knowledge management are different types of knowledge and names the operation method the knowledge logistics. The method of transformation he calls learning. This theoretical paper discusses the operational management of four types of knowledge objects—explicit understanding; information; skills; and norms and values; and shows how through the proposed framework learning can transfer these objects to clients in a logistical process without a major transformation in content. Millie Kwan continues this theme with a paper about process-oriented knowledge management. In her case study she discusses an implementation of knowledge management where the knowledge is centred around an organisational process and the mission, rationale and objectives of the process define the scope of the project. In her case they are concerned with the effective use of real estate (property and buildings) within a Fortune 100 company. In order to manage the knowledge about this property and the process by which the best 'deal' for internal customers and the overall company was reached, a KMS was devised. She argues that process knowledge is a source of core competence and thus needs to be strategically managed. Finally, you may also wish to read a related paper originally submitted for this Special Issue, 'Customer knowledge management' by Garcia-Murillo and Annabi, which was published in the August 2002 issue of the Journal of the Operational Research Society, 53(8), 875–884.

Optimization of PCB component placements for the collect-and-place machines

This paper presents two hybrid genetic algorithms (HGAs) to optimize the component placement operation for the collect-and-place machines in printed circuit board (PCB) assembly. The component placement problem is to optimize (i) the assignment of components to a movable revolver head or assembly tour, (ii) the sequence of component placements on a stationary PCB in each tour, and (iii) the arrangement of component types to stationary feeders simultaneously. The objective of the problem is to minimize the total traveling time spent by the revolver head for assembling all components on the PCB. The major difference between the HGAs is that the initial solutions are generated randomly in HGA1. The Clarke and Wright saving method, the nearest neighbor heuristic, and the neighborhood frequency heuristic are incorporated into HGA2 for the initialization procedure. A computational study is carried out to compare the algorithms with different population sizes. It is proved that the performance of HGA2 is superior to HGA1 in terms of the total assembly time.

Optimal production planning for PCB assembly

It is indisputable that printed circuit boards (PCBs) play a vital role in our daily lives. With the ever-increasing applications of PCBs, one of the crucial ways to increase a PCB manufacturer’s competitiveness in terms of operation efficiency is to minimize the production time so that the products can be introduced to the market sooner. Optimal Production Planning for PCB Assembly is the first book to focus on the optimization of the PCB assembly lines’ efficiency. This is done by: • integrating the component sequencing and the feeder arrangement problems together for both the pick-and-place machine and the chip shooter machine; • constructing mathematical models and developing an efficient and effective heuristic solution approach for the integrated problems for both types of placement machines, the line assignment problem, and the component allocation problem; and • developing a prototype of the PCB assembly planning system. The techniques proposed in Optimal Production Planning for PCB Assembly will enable process planners in the electronics manufacturing industry to improve the assembly line’s efficiency in their companies. Graduate students in operations research can familiarise themselves with the techniques and the applications of mathematical modeling after reading this advanced introduction to optimal production planning for PCB assembly.

An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.

Integrated component scheduling models for chip shooter machines

This paper focuses on minimizing printed circuit board (PCB) assembly time for a chipshootermachine, which has a movable feeder carrier holding components, a movable X–Y table carrying a PCB, and a rotary turret with multiple assembly heads. The assembly time of the machine depends on two inter-related optimization problems: the component sequencing problem and the feeder arrangement problem. Nevertheless, they were often regarded as two individual problems and solved separately. This paper proposes two complete mathematical models for the integrated problem of the machine. The models are verified by two commercial packages. Finally, a hybrid genetic algorithm previously developed by the authors is presented to solve the model. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total assembly time.

A heuristic approach for component scheduling on a high-speed PCB assembly machine

The collect-and-place machine is one of the most widely used placement machines for assembling electronic components on the printed circuit boards (PCBs). Nevertheless, the number of researches concerning the optimisation of the machine performance is very few. This motivates us to study the component scheduling problem for this type of machine with the objective of minimising the total assembly time. The component scheduling problem is an integration of the component sequencing problem, that is, the sequencing of component placements; and the feeder arrangement problem, that is, the assignment of component types to feeders. To solve the component scheduling problem efficiently, a hybrid genetic algorithm is developed in this paper. A numerical example is used to compare the performance of the algorithm with different component grouping approaches and different population sizes.

Component scheduling for chip shooter machines: a hybrid genetic algorithm approach

A chip shooter machine for electronic component assembly has a movable feeder carrier, a movable X–Y table carrying a printed circuit board (PCB), and a rotary turret with multiple assembly heads. This paper presents a hybrid genetic algorithm (HGA) to optimize the sequence of component placements and the arrangement of component types to feeders simultaneously for a chip shooter machine, that is, the component scheduling problem. The objective of the problem is to minimize the total assembly time. The GA developed in the paper hybridizes different search heuristics including the nearest-neighbor heuristic, the 2-opt heuristic, and an iterated swap procedure, which is a new improved heuristic. Compared with the results obtained by other researchers, the performance of the HGA is superior in terms of the assembly time. Scope and purpose When assembling the surface mount components on a PCB, it is necessary to obtain the optimal sequence of component placements and the best arrangement of component types to feeders simultaneously in order to minimize the total assembly time. Since it is very difficult to obtain the optimality, a GA hybridized with several search heuristics is developed. The type of machines being studied is the chip shooter machine. This paper compares the algorithm with a simple GA. It shows that the performance of the algorithm is superior to that of the simple GA in terms of the total assembly time.

A genetic algorithm approach to optimising component placement and retrieval sequence for chip shooter machines

A chip shooter machine in printed circuit board (PCB) assembly has three movable mechanisms: an X-Y table carrying a PCB, a feeder carrier with several feeders holding components and a rotary turret with multiple assembly heads to pick up and place components. In order to get the minimal placement or assembly time for a PCB on the machine, all the components on the board should be placed in a perfect sequence, and the components should be set up on a right feeder, or feeders since two feeders can hold the same type of components, and additionally, the assembly head should retrieve or pick up a component from a right feeder. The entire problem is very complicated, and this paper presents a genetic algorithm approach to tackle it.

A genetic algorithm to optimise the component placement process in the PCB assembly

In printed circuit board (PCB) assembly, the efficiency of the component placement process is dependent on two interrelated issues: the sequence of component placement, that is, the component sequencing problem, and the assignment of component types to feeders of the placement machine, that is, the feeder arrangement problem. In cases where some components with the same type are assigned to more than one feeder, the component retrieval problem should also be considered. Due to their inseparable relationship, a hybrid genetic algorithm is adopted to solve these three problems simultaneously for a type of PCB placement machines called the sequential pick-and-place (PAP) machine in this paper. The objective is to minimise the total distance travelled by the placement head for assembling all components on a PCB. Besides, the algorithm is compared with the methods proposed by other researchers in order to examine its effectiveness and efficiency.

A hybrid genetic algorithm for sequencing PCB component placement

A chip shooter machine for electronic components assembly has a movable feeder carrier holding components, a movable X-Y table carrying a printed circuit board (PCB), and a rotary turret having multiple assembly heads. This paper presents a hybrid genetic algorithm to optimize the sequence of component placements for a chip shooter machine. The objective of the problem is to minimize the total traveling distance of the X-Y table or the board. The genetic algorithm developed in the paper hybridizes the nearest neighbor heuristic, and an iterated swap procedure, which is a new improved heuristic. We have compared the performance of the hybrid genetic algorithm with that of the approach proposed by other researchers and have demonstrated our algorithm is superior in terms of the distance traveled by the X-Y table or the board.

A hybrid genetic algorithm for component sequencing and feeder arrangement

This paper presents a hybrid genetic algorithm to optimize the sequence of component placements on a printed circuit board and the arrangement of component types to feeders simultaneously for a pick-and-place machine with multiple stationary feeders, a fixed board table and a movable placement head. The objective of the problem is to minimize the total travelling distance, or the travelling time, of the placement head. The genetic algorithm developed in the paper hybrisizes different search heuristics including the nearest neighbor heuristic, the 2-opt heuristic, and an iterated swap procedure, which is a new improving heuristic. Compared with the results obtained by other researchers, the performance of the hybrid genetic algorithm is superior to others in terms of the distance travelled by the placement head.

Simulation and control of a stepping motor

Open-loop operatlon of the stepping motor exploits the inherent advantages of the machine. For near optimum operation: in this mode, however, an accurate system model is required to facilitate controller design. Such a model must be comprehensive and take account of the non-linearities inherent in the system. The result is a complex formulation which can be made manageable with a computational aid. A digital simulation of a hybrid type stepping motor and its associated drive circuit is proposed. The simulation is based upon a block diagram model which includes reasonable approximations to the major non-linearities. The simulation is shown to yield accurate performance predictions. The determination of the transfer functions is based upon the consideration of the physical processes involved rather than upon direct input-outout measurements. The effects of eddy currents, saturation, hysteresis, drive circuit characteristics and non-linear torque displacement characteristics are considered and methods of determining transfer functions, which take account of these effects, are offered. The static torque displacement characteristic is considered in detail and a model is proposed which predicts static torque for any combination of phase currents and shaft position. Methods of predicting the characteristic directly from machine geometry are investigated. Drive circuit design for high efficiency operation is considered and a model of a bipolar, bilevel circuit is proposed. The transfers between stator voltage and stator current and between stator current and air gap flux are complicated by the effects of eddy currents, saturation and hysteresis. Frequency response methods, combined with average inductance measurements, are shown to yield reasonable transfer functions. The modelling procedure and subsequent digital simulation is concluded to be a powerful method of non-linear analysis.