Fixture Elements Research Articles

An investigation of the effectiveness of fixture layout optimization methods

Deriving the optimal layout of fixture elements is critical to minimizing the impact of fixture–workpiece deformation on machined feature error. Various optimization methods for solving this problem have been reported. Unfortunately no investigation has been executed to compare their relative performance. This paper presents the methodology and results of an extensive investigation into the relative effectiveness of the main elements of these competing methods. All methods were tested over a broad range of conditions. Performance measures that were tracked included solution quality, solution repeatability, and computation time. The results of this investigation show that the best overall performance is provided by optimization methods that use both the genetic algorithm and continuous interpolation for the distribution of boundary conditions.

An investigation into the use of spatial coordinates for the genetic algorithm based solution of the fixture layout optimization problem

The fixture layout optimization problem is highly modal. It has been shown that layout optimization methods that use the genetic algorithm (GA) are effective at finding high quality solutions. To date, such methods have used FEA node numbers to represent the locations of fixture elements. This paper presents a new GA based optimization method that uses spatial coordinates to represent the locations of fixture elements. This method integrates a number of important GA concepts such as real encoding, increased mutation, and sharing. Test results show that the new method provides higher quality solutions with substantially less numbers of generations than the old method. These results also show that the use of increased mutation and sharing significantly improves the performance of the new method.

Optimizing fixture layout in a point-set domain

This paper describes an approach to optimal design of a fixture layout with the minimum required number of elements, i.e., six locators and a clamp. The approach applies to parts with arbitrary 3D geometry and is restricted to be within a discrete domain of locations for placing the fixture elements of non-frictional contacts. The paper addresses two major issues: 1) to develop an efficient algorithm for fixture synthesis in the point set domain; and 2) to evaluate the acceptable fixture designs based on several performance criteria and to select the optimal fixture according to practical requirements. The performance objectives considered include the workpiece localization accuracy, and the norm and dispersion of the locator contact forces. An interchange algorithm with random initiation is developed. Also, the fixture performance characteristics are evaluated to understand their tradeoffs. The importance of the accurate localization and the contact force balance is discussed.

Improved Algorithm for Tolerance-Based Stiffness Optimization of Machining Fixtures

Current fixture design methods rely extensively on heuristics and lack a formal engineering approach to determine the necessary stiffness, dimensions, etc. This paper presents a model for stiffness optimization of machining fixtures based on the tolerance limit specified for the machined part surface. Specifically, the model allows systematic determination of the optimum fixture stiffness needed to keep the contribution of fixture deflection to the machined feature tolerance within a designer-specified level. Based on the stiffness optimization model presented here, the optimum dimensions of the fixture elements can also be determined. The model development relies on rigid body analysis methods, contact mechanics principles, and consideration of bulk elasticity of the fixture. The model is generic enough to be used for the design of dedicated or flexible fixtures consisting of mechanical elements. Two examples, one involving a pin-array type flexible fixture and another involving a dedicated fixture, are presented to illustrate the applicability of the model.

A model to predict minimum required clamp pre-loads in light of fixture–workpiece compliance

The determination of minimum required clamp pre-loads is an important process in the design of machining fixtures. This paper presents a linear, clamp pre-load (LCPL) model that can be applied to fixture–workpiece systems whose compliance is load invariant. The model considers the static deformation of the fixture–workpiece system in response to the clamping process and the machining process. Sources of compliance throughout a fixture–workpiece system are considered. The model computes the minimum required pre-loads necessary to prevent workpiece slip at the fixture–workpiece joints throughout the machining process. This paper also describes an experimental study that was used to characterize the accuracy of the LCPL model with regard to the application of a ramping external load to a fixture–workpiece system. Over the contact conditions tested, the LCPL model was observed to overestimate the minimum required clamp pre-loads by an average of 7%. This experimental study also revealed the sensitivity of the computed pre-loads to the relative compliance of the fixture elements as well as the coefficient of friction.

Iterative Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm

Fixture design is a critical step in machining. An important aspect of fixture design is the optimization of the fixture, the primary objective being the minimization of workpiece deflection by suitably varying the layout of fixture elements and the clamping forces. Previous methods for fixture design optimization have treated fixture layout and clamping force optimization independently and/or used nonlinear programming methods that yield sub-optimal solutions. This paper deals with application of the genetic algorithm (GA) for fixture layout and clamping force optimization for a compliant workpiece. An iterative algorithm that minimizes the workpiece elastic deformation for the entire cutting process by alternatively varying the fixture layout and clamping force is proposed. It is shown via an example of milling fixture design that this algorithm yields a design that is superior to the result obtained from either fixture layout or clamping force optimization alone.

Computer-aided fixture design system for comprehensive modular fixtures

Fixture design plays an important role at the planning stage before shop-floor production. A desired fixture design can be employed to hold the workpart securely so that slippage and excessive deformation can be prevented during machining. Therefore, appropriate fixturing contributes highly to machining quality. To reduce lead time and the human effort devoted to fixture planning, computer-aided fixture design (CAFD) is required. In this paper, a CAFD system consisting of three modules, i.e. Fixture Data Management, Fixture Element Selection and Fixture Layout Design, is developed. According to fixture feature recognition and classification, a comprehensive fixture database in the Fixture Data Management module is constructed to maintain efficiently the fixture-related data. The domain of the fixture database consists of modular mechanical fixtures, modular hydraulic fixtures and modular V-blocks. After expertise extraction, suitable fixture elements can be automatically selected according to the machining conditions in the Fixture Element Selection module. Finally, by integrating previous reasoning algorithms, fixturing locations and orientations are determined. Feasible fixture layouts that meet manufacturing and inspection specifications can be generated in the Fixture Layout Design module. The prototype system is implemented under commercial CAD and database management system (DBMS) software. Comprehensive fixture databases and a rule-based knowledge base are built to provide effective data management. The paper aims to propose a systematic CAFD framework and application system to provide efficient decision support for different types of fixture planning.

Experimental assessment of a clamp actuation intensity analysis model

The application of a clamp actuation intensity analysis (CAIA) model is a rough cut technique used to compute the minimum clamp pre-loads necessary to keep a workpiece from slipping within a fixture throughout a machining cycle. A CAIA model is based on the simplistic assumption that a fixture-workpiece behaves as a system of contacting rigid bodies subject to Coulomb friction at the joints. To date, little research has been carried out to ascertain how well these models predict minimum pre-loads for actual applications, or how their limitations can be overcome in order to improve their performance. This paper describes an experimental study that was used to the assess: (1) the impact of including all contact regions, regardless of rigidity, within a CAIA model, (2) the sensitivity of the CAIA model to known variations in coefficient of friction, and (3) the accuracy of predicted pre-loads for actual milling operations. The major conclusions drawn from this study are: (1) only the stiffest contact regions of a fixture-workpiece system should be included in a CAIA model, (2) there is nearly a one-to-one correspondence between the variation of the clamp pre-loads computed by the CAIA model and the variation of the inputted friction coefficients, (3) the clamp pre-loads computed by the CAIA model for a series of milling experiments were within 25% of the actual values for the majority of experiments, and (4) a reduction in the coefficient of static friction at fixture-workpiece joints appears to occur during the application of milling forces, this is especially true for planar tip fixture elements.

Externally resonated linear microvibromotor for microassembly

A new method for on-substrate fine positioning of microscale/mesoscale discrete components is presented, where component positions are finely adjusted using microlinear sliders and fixtures on the substrate. Each microlinear slider is actuated by vibratory impacts exerted by two pairs of microcantilever impacters. These microcantilever impacters are selectively resonated by shaking the entire substrate with a piezoelectric vibrator, requiring no need for built-in driving mechanisms such as electrostatic comb actuators, as reported previously. This selective resonance of the microcantilever impacters via an external vibration energy field provides with a very simple means of controlling forward and backward motion of the microlinear slider, facilitating assembly and disassembly of a microcomponent on a substrate. An analytical model of the device is derived in order to obtain, through the simulated annealing algorithm, an optimal design, which maximizes translation speed of the linear slider at desired external input frequencies. Prototypes of the externally resonated linear microvibromotor are fabricated using the three-layer polysilicon surface micromachining process provided by the Microelectronics Center of North Carolina, Research Triangle Park, NC, multiuser microelectromechanical processes service. These prototypes are tested for forward and backward motion via external vibration applied by an piezoelectric flexure vibrator, as well as the horizontal positioning and release of 500-/spl mu/m-square polysilicon chips against a reference fixture element anchored to the substrate.

IDEF0 Model of the Measurement Planning for a Workpiece Machined by a Machining Centre

A comprehensive analysis of the entire measuring operation for a workpiece machined by a machining centre should be conducted systematically before the application of a planning technique. For this purpose, an IDEF0 model is used in this paper to plan the measuring sequence and operation of a coordinate measuring system for a workpiece machined by a machining centre. Generally speaking, a machining centre can machine workpieces having complicated shapes. Therefore, the planning of measurement procedures and operations on a workpiece machined by a machine centre requires consideration of issues such as the position and measuring sequence of the measurement points, how to avoid probe collision during measuring, which fixture elements are required for measuring fixtures, and where the support points of fixtures and position of fixture locations should be.

The fixture planning of modular fixtures for measurement

A Computer Aided Fixturing System (CAFS) was used in this paper to study the planning of modular fixtures for measurement using a Coordinate Measuring Machine (CMM). This paper proposes fixturing planning of a complicated small supporting face and a large general supporting face. Group Technology (GT) was used to establish the coding database of the modular fixture element for use in the system. Several algorithms are developed to locate the appropriate fixture elements and their positions.

An Integrated Approach to Collision-Free Computer-Aided Modular Fixture Design

This paper describes a CAD-based methodology for developing a modular fixture design system using the Unigraphics (UG) solid modeller, integrated with a modular fixture element database, based on a hole-based IMAO modular fixturing system. A parametric modelling technique has been applied to construct the database. An integrated methodology is introduced in the system in which the functions of interactive, semi-automated and automated fixture design systems are combined collaboratively in a single environment. This provides the flexibility and functionality for making the design process more efficient. The interactive fixture design module helps the designer to select the fixturing faces, points and elements for building a fixture. Semi-automated and automated fixture design modules are built by transforming the designers' experience and knowledge into rules and algorithms to automate the selection of fixturing points and elements, More importantly, the system aims at producing a tool-collision-free fixture design using a machining interference detection submodule based on a cutter swept volume approach.

Analysis of Reactions and Minimum Clamping Force for Machining Fixtures with Large Contact Areas

This paper presents a model for analysing the reaction forces and moments for machining fixtures with large contact areas, e.g. a mechanical vice. Such fixtures transmit torsional loads in addition to normal and tangential loads and thus differ from fixtures using point or line contacts. The model is developed using a contact mechanics approach where the workpiece is assumed to be elastic in the contact region and the fixture element is treated as rigid. Closed-form contact compliance solutions for normal, tangential, and torsional loads are used to derive the elastic deformation model for each contact. A minimum energy principle is used to solve the multiple contact problem yielding unique predictions of the fixture-workpiece contact forces and moments due to clamping and machining forces. This model is then used to determine the minimum clamping force necessary to keep the workpiece in static equilibrium during machining. An example is given to demonstrate its effectiveness in analysing the clamping performance of a mechanical vice during machining.

Flexible multibody dynamics based fixture-workpiece analysis model for fixturing stability

The machining force and torque exerted on a workpiece vary as the cutter moves along the tool path, therefore a dynamic approach is essential for fixturing stability analysis. This paper presents a technique to dynamically model and analyze the fixture-workpiece system subjected to time-varying machining loads. Combining the advantages of FEA (Finite Element Analysis) and nonlinear rigid body dynamics, a flexible multibody dynamic model is formulated to incorporate the overall interaction (clamping forces, machining loads, and contact friction) between flexible workpiece and compliant fixture elements. Three major parameters affecting the fixturing stability, namely the magnitude, application sequence, and placement of fixturing clamps, are analyzed. Additionally, the time dependent deformation of a flexible workpiece under clamping and machining loads is estimated. A scaled engine block with the 3–2–1 fixturing scheme subjected to face milling operation is given as an example. Comparison between the simulation result and experimental data shows a reasonable agreement.

A Fast Analytical Method to Compute Optimum Stiffness of Fixturing Locators

Machining fixtures are used to rigidly hold and support workpieces during machining. The quality of the machined part directly depends on the combined stiffness of the workpiece and the fixture. Low fixture stiffness causes poor quality parts, while large fixture stiffness causes the fixtures to be expensive and cumbersome. Finite element models can be used to optimize the fixture stiffness; however these techniques are computationally expensive for complex workpiece geometries. This paper develops a fast analytical method for optimizing fixture locator stiffnesses for workpieces that are more rigid than the fixture elements. The developed methodology is validated through finite element simulations and experiments.

The fixture planning of modular fixtures for measurement

A Computer Aided Fixturing System (CAFS) was used in this paper to study the planning of modular fixtures for measurement using a Coordinate Measuring Machine (CMM). This paper proposes fixturing planning of a complicated small supporting face and a large general supporting face. Group Technology (GT) was used to establish the coding database of the modular fixture element for use in the system. Several algorithms are developed to locate the appropriate fixture elements and their positions.

An experimental evaluation of coefficients of static friction of common workpiece–fixture element pairs

Most machining fixtures utilize clamping forces and friction at fixture–workpiece joints to help prevent the workpiece from slipping out of the fixture during machining. The magnitudes of the clamping forces required are a direct function of the coefficients of static friction at the joints. Recently, analytical methods have been developed to predict minimum clamping forces. However, these methods require accurate estimates of the friction coefficients. One source of friction data are handbooks. However, these data are typically listed relative to the materials of the contacting elements and are otherwise completely generalized. This paper will illustrate that the coefficient of static friction for typical fixture–workpiece joints is not a simple function of the workpiece materials. Instead it is also a function of factors such as fixture element geometry, workpiece surface topography, clamping forces, the presence or absence of cutting fluids, and normal joint rigidity.

Mixed-Integer Programming Model for Fixture Layout Optimization

Workpiece deformation during machining is a significant source of machined feature geometric error. This paper presents a linear, mixed integer programming model for determining the optimal locations of locator buttons, supports, and their opposing clamps for minimizing the affect of static workpiece deformation on machined feature geometric error. This model operates on discretized candidate regions as opposed to continuous candidate regions. In addition it utilizes a condensed FEA model of the workpiece in order to minimize model size and computation expense. This model has two advantages over existing nonlinear programming (NLP) formulations. The first is its ability to solve problems in which fixture elements can be placed over multiple regions. The second is that a global optimal solution to this model can be obtained using commercially available software.

Finite element analysis and optimization in fixture design

Fixturing locating point synthesis considers the workpiece and the fixturing elements to be rigid, but however they are elastic and deformable. To ensure sustained quality of manufacture to meet the design tolerances, fixture design must be predictably repeatable. This paper is concerned with minimizing deformation of the workpiece due to machining loads about fixturing support positions, especially in thin castings. Finite element analysis is used in simulating the deformation of the workpiece at selected points. An optimization algorithm is developed to minimize deflections at these selected nodal points by considering the support and tool localtions as design variables. The resulting support locations and tool point designs ensure part support, kinematic closure and minimal workpiece deflections during machining.

Visibility Analysis and Synthesis for Assembly Fixture Certification Using Theodolite Systems

In automotive sheet metal assembly, part positioning and clamping is accomplished by fixtures consisting of fixture elements, such as pins and blocks. The locations of these elements are determined during process design and need to be certified during the construction and installation of an assembly line. Usually, theodolite systems are used to certify the locations of these elements by measuring the trihedron points on the fixture elements. However, no systematic method exists for the selection and placement of measuring systems. As a result, the current certification procedure is very time-consuming and is prone to error. This paper presents an algorithm for the optimal setup and placement of theodolite systems based on visibility analysis and synthesis. For a given tooling fixture, the visibility map is introduced to represent the set of potential measurement locations when a number of fixture elements are to be measured. From the set of potential measurement locations, an optimal setup will be selected based on minimizing the number of theodolite heads by optimally locating these theodolites. This approach will minimize measurement setups and improve measurement accuracy.