Samuel C Lorin

Combining Variation Simulation With Thermal Expansion Simulation for Geometry Assurance

In every set of assembled products, there are geometrical variations and deviations from nominal dimensions. This can lead to products that are difficult to assemble or products not fulfilling functional or aesthetical requirements. In several industries, variation simulation is used to predict assembly variation in the development phase. This analysis is usually done under room temperature conditions only. However, for some materials, such as plastics, the thermal expansion can be significant in the intended environmental span of the product. In an assembly, this can lead to thermal stresses and parts that will deform. To avoid this problem, locating schemes need to be designed to allow for the right behavior while exposed to varying temperatures. In this work, the effect of thermal expansion is studied in the context of variation simulation. A virtual tool for this purpose is also presented. Two case studies from the automotive industry are used where the combined effect of thermal expansion and assembly variation is analyzed. It is shown that it may not be sufficient to simply add the result from thermal analysis to assembly variation. Hence, to assure the geometrical and functional quality of assembled products during usage variation simulations need to be combined with thermal expansion simulation.

Efficient Contact Modeling in Nonrigid Variation Simulation

Virtual tools and methods are becoming increasingly important in order to predict the geometric outcome in early phases of the product realization process. Method of influence coefficients (MIC) in combination with Monte Carlo simulation (MCS) is a well-known technique that can be used in non-rigid variation simulation. In these simulations, contact modeling is important to ensure a correct result. Contact modeling simulates how mating surfaces are hindered from penetrating each other, giving rise to contact forces that contribute to the deformation of the parts when assembled and the final shape of the subassembly after springback. These contact forces have to be taken into consideration in each MCS-iteration. To secure reasonable response times, the calculation of the contact forces needs to be fast. In this paper, we formulate a quadratic programming(QP) problem to solve the contact problem. The case studies presented show that node-based contact modeling can be efficiently solved through QP.

SIMULATING PART AND ASSEMBLY VARIATION FOR INJECTION MOLDED PARTS

Final geometrical variation and deviation have often a negative effect on product functionality and aesthetics. In the automotive industry, design concepts are being evaluated and optimized to withstand variation in the early phase of product development. For this end, simulation tools are employed. Input to these simulations is requirements on parts and fixtures or measurements from previously manufactured parts. In the case of plastic components, parts are often manufactured in the injection molding process. Here, different materials and process settings can make it difficult to predict deviation and variation based on similar parts. In order to perform accurate assembly variation simulation, part variation simulation need, therefore, to be included. In this work a methodology is presented to simulate part and assembly variation, due to process noise, for plastic components manufactured in the injection molding process. The methodology is based on designed computer experiment and utilizes the concept of geometrical covariance and principal component analysis to relate process noise to variation patterns using regression analysis. Part and assembly variation are simulated combined using the distribution of these variation patterns. The model used for part variation simulation has been verified against commercial injection molding software showing good agreement. An industrial case from the automotive industry is used to elicit the proposed methodology.

Combining Variation Simulation With Thermal Expansion for Geometry Assurance

In every set of assembled products there are geometrical variation and deviations from nominal dimensions. This can lead to products that are difficult to assemble or products not fulfilling functional or aesthetical requirements. In several industries variation simulation is used to predict assembly variation in the development phase. This analysis is usually done under the condition of room temperature only. However, for some materials, such as plastics, the thermal expansion can be significant in the intended environmental span of the product. In an assembly, this can lead to thermal stresses and parts that will deform. To avoid this problem, locating schemes need to be designed to allow for the right behavior while exposed to varying temperatures. In this work the effect of thermal expansion is studied in the context of variation simulation. A virtual tool for this end is also presented. An example from the automotive industry is used where the combined effect of thermal expansion and assembly variation is analyzed. It is shown that it may not be sufficient to simply add the result from thermal analysis to assembly variation. Hence, to assure the geometrical and functional quality of assembled products, during its use, variation simulations need to be combined with thermal stresses.

Joining in Nonrigid Variation Simulation

Geometrical variation is closely related to fulfillment of both functional and esthetical requirements on the final product. To investigate the fulfillment of those requirements, Monte Carlo (MC)-based variation simulations can be executed in order to predict the levels of geometrical variation on subassembly and/or product level. If the variation simulations are accurate enough, physical tests and try-outs can be replaced, which reduce cost and lead-time. To ensure high accuracy, the joining process is important to include in the variation simulation. In this chapter, an overview of nonrigid variation simulation is given and aspects such as the type and number of joining points, the joining sequence and joining forces are discussed.

Welding Simulation of Non-Nominal Structures With Clamps

In any industrial assembly process, there are a number of sources of variation. Variation in the manufacturing process leads to component variation, which, together with fixture variation and variation stemming from the joining process, propagates to the final product. In order to analyze and diminish the effect of variation, it is important to identify and be able to simulate the phenomena contributing to final variation. In this paper, the focus is variation in welding distortion arising from non-nominal components that are joined. In the welding process, it has been shown that variation in components and in fixtures influences the size and distribution of weld-induced distortion. Hence, in order to accurately simulate geometric variation of an assembly joined by weld joints, variation simulation and welding simulation need to be performed in combination. Previous research that focused on the combination of variation simulation and welding simulation has not considered components that are clamped. Instead the components were treated as rigid bodies at non-nominal positions prior to welding. In many industrial applications, clamps are used when assemblies are welded, and it is therefore important to quantify the influence that clamping has on welding of non-nominal components. In this paper, we simulate the combination of variation in components and fixtures with welding, considering that the components are clamped prior to welding. Although clamps will force the components closer to their nominal positions along the weld joint, they also introduce a stress field in the structure, which together with the welding process may cause additional distortion. Two case studies are performed and analyzed: a T-weld joint and a butt-weld joint. The results show that welding distortion depends on fixture error even in the presence of clamps.

Simulation of non-nominal welds by resolving the melted zone and its implication to variation simulation

The prediction of geometric variation and its consequences is one important aspect of product development. For welded assemblies it has been shown that positioning errors of the parts prior to welding affects the weld-induced distortion. Therefore, to accurately predict geometric variation in welded assemblies, variation simulation and welding simulation need to be performed in combination. This is usually a very time consuming task, and therefore, the relatively fast SCV-method is utilized. This method is used to calculate welding distortion when positioning errors are present and it consists of the fol-lowing three steps: 1) a steady state computation of the thermal distribution during welding, 2) the melted zone along the full joint is encapsulated by sweeping a two-dimensional convex hull along the weld gun path, and 3) a uniform temperature is applied to all nodes inside this zone. The two-dimensional convex hull is computed so that when swept along the weld path, it will encapsulate the melted zone from the steady state temperature computation. The weld-induced distortion is obtained from the elastic volumetric shrinkage. In this article the focus is on the first step in this method; the temperature distribution computation. The positioning error can cause the connecting parts to have varying distances to each other at the joint, which cause the melted region to vary along the weld path. Therefore, it is not sufficient to capture the steady state temperature distribution at only one location. Depending on the geometry surrounding the weld path, several locations may be needed. In this new approach, the two-dimensional convex hull that is to be swept along the weld path, can vary along the weld path, and is computed from an interpolation of the multiple two-dimensional convex hulls obtained from the multiple steady state temperature computations. A comparison of the melted region using transient temperature calculation, a single steady state temperature calculation and this new approach has been made. Furthermore, the implication on distortion calculation has been studied.

On the Robustness of the Volumetric Shrinkage Method in the Context of Variation Simulation

Welding induces high temperatures that cause residual stresses and strains in the welded structure. With a welding simulation, these stresses and strains may be predicted. A full simulation implies performing a transient thermal and a quasi-static mechanical analysis. These analyses usually involve a large number of time steps that leads to long simulation times. For welding distortions, there are approximate methods that require considerably less time. This is useful when simulating large structures or for analyses that use an iterative approach common in optimization or variation simulation. One of these methods is volumetric shrinkage, which has been shown to give reasonable results. Here it is assumed that the driving force in welding distortion is the contraction of the region that has been melted by the weld. In volumetric shrinkage, the nodes that are inside the melted region are assigned a uniform temperature and the distortion is calculated using elastic volumetric shrinkage. Although this method has been shown to give reasonable predictions, we will show that it is sensitive to small perturbations, which is an essential part in variation simulation. We also propose a modification of the volumetric shrinkage method that addresses this lack of robustness; instead of defining the melted region by applying a uniform temperature to the nodes inside the zone, we formulate an optimization problem that finds a temperature distribution such that the local melted volume is preserved. A case study with application to variation simulation has been used to elicit the proposed method.

Minimizing Weld Variation Effects Using Permutation Genetic Algorithms and Virtual Locator Trimming

The mass production paradigm strives for uniformity, and for assembly operations to be identical for each individual product. To accommodate geometric variation between individual parts in such a process, tolerances are introduced into the design. However, for certain assembly operations this method can yield suboptimal quality. For instance, in welded assemblies, geometric variation in ingoing parts can significantly impair quality. When parts misalign in interfaces, excessive clamping force must be applied, resulting in additional residual stresses in the welded assemblies. This problem may not always be cost-effective to address simply by tightening tolerances. Therefore, under new paradigm of mass customization, the manufacturing approach can be adapted on an individual level. Since parts in welded assemblies are not easily disassembled and reused, interchangeability is not a relevant concern. This recognition means that each welded assembly can be adapted individually for the specific idiosyncrasies of ingoing parts. This paper focuses on two specific mass customization techniques; permutation genetic algorithms to assemble nominally identical parts, and virtual locator trimming. Based on these techniques, a six-step method is proposed, aimed at minimizing thing effects of geometric variation. The six steps are nominal reference point optimization, permutation GA configuration optimization, virtual locator trimming, clamping, welding simulation, and fatigue life evaluation. A case study is presented which focuses on one specific product; the turbine rear structure of a commercial turbofan engine. Using this simulation approach, the effects of using permutation genetic algorithms and virtual locator trimming to reduce variation are evaluated. The results show that both methods significantly reduce seam variation. However, virtual locator trimming is far more effective in the test case presented, since it virtually eliminates seam variation. This can be attributed to the orthogonality in fixturing. Seam variation is linked to weldability, which in turn has significant impact on estimated fatigue life. These results underscore the potential of virtual trimming and genetic algorithms in manufacturing, as a means both to reduce cost and increase functional quality.

Variation Simulation of Welded Assemblies Using a Thermo-Elastic Finite Element Model

Every series of manufactured products has geometric variation. Variation can lead to products that are difficult to assemble or products not fulfilling functional or aesthetical requirements. In this paper, we will consider the effects of welding in variation simulation. Earlier work that have been combining variation simulation with welding simulation have either applied distortion based on nominal welding conditions onto the variation simulation result, hence loosing combination effects, or have used transient thermo-elasto-plastic simulation, which can be very time consuming since the number of runs required for statistical accuracy can be high. Here, we will present a new method to include the effects of welding in variation simulation. It is based on a technique that uses a thermo-elastic model, which previously has been shown to give distortion prediction within reasonable accuracy. This technique is suited for variation simulations due to the relative short computation times compared to conventional transient thermo-elasto-plastic simulations of welding phenomena. In a case study, it is shown that the presented method is able to give good predictions of both welding distortion and variation of welding distortions compared to transient thermo-elasto-plastic simulations.