Kristina Wärmefjord

Tolerance Simulation of Compliant Sheet Metal Assemblies Using Automatic Node-Based Contact Detection

Tolerance simulation is a crucial tool for predicting the outcome in critical dimensions, used during early phases of product development in automotive industry. In order to increase the accuracy and the agreement with reality of the predictions even further, variation simulation software offer in some cases the possibility to perform compliant analysis, i.e. the parts are not restricted to be rigid. In the compliant analysis, contact modeling is an important tool to avoid that parts penetrate each other in the simulations. In this paper a simplified method for automatic contact detection, well suited for tolerance simulations, is suggested. The method is based on node to node contacts instead of contacts between a node and a surface, which is a common procedure. Using automatic contact detection can in many cases give rise to an excessively large number of contact pairs. Therefore, an algorithm for attenuation of the contact pairs is also presented. Traditionally, non-rigid variation simulations with contact modeling are very time consuming, but by using this kind of simplified contact modeling in combination with the Method of Influence Coefficient in the Monte Carlo simulations, the simulation times can be kept down. The method is tested on an industrial case study, with respect to both standard deviation and position. The correlation between simulated data and industrial inspection data is high and there is a considerable difference between simulations with and without contact modeling, showing that this is an important feature in non-rigid simulations. Inspection data is also compared to rigid simulations and to simulations with different number of contact pairs. The computational effort for the suggested node-node based contact modeling algorithm seems to be considerable less than when using traditional finite element software, but still, the agreement with inspection data is very good.

STRATEGIES FOR OPTIMIZATION OF SPOT WELDING SEQUENCE WITH RESPECT TO GEOMETRICAL VARIATION IN SHEET METAL ASSEMBLIES

During the assembly process of sheet metal parts, a lot of factors affect the final geometrical quality. It is important to have knowledge about the characteristics of as many as possible of those factors, not only to be able to reduce their effect, but also to be able to include those factors in variation simulations. Those tolerance simulations are crucial tools in early stages in automotive industry in order to predict the outcome in critical dimensions and it is of course important to have as good accuracy as possible in the simulations. One of the factors affecting the final geometry is the spot welding sequence. In this paper it is shown how the spot welding sequence affects the amount of geometrical variation in a sheet metal assembly. A method for including the welding sequence in tolerance simulations is described. Of course, it is desirable to find an optimal sequence, i.e. a sequence that minimizes the geometrical variation in the final assembly. Since this is a fast growing problem - the number of possible sequences for N welding points is N!, it is not practicable to test all possible sequences. In this work some different strategies for finding an optimal sequence are tested on several industrial case studies. The tested strategies are based on general guidelines, on minimizing variation in each welding step respectively calculations of the movements in unwelded points in each step. The strategies based on general guidelines was not successful, neither was the one based on minimization of the variation in each step. The strategy based on movements in the unwelded points seems however promising. It resulted in the best or one of the better sequences for all of the eight tested industrial case studies. ©2010 by ASME.

Combining Variation Simulation With Welding Simulation for Prediction of Deformation and Variation of a Final Assembly

In most variation simulations, i.e., simulations of geometric variations in assemblies, the influence from heating and cooling processes, generated when two parts are welded together, is not taken into consideration. In most welding simulations, the influence from geometric tolerances on parts is not taken into consideration, i.e., the simulations are based on nominal parts. In this paper, these two aspects, both crucial for predicting the final outcome of an assembly, are combined. Monte Carlo simulation is used to generate a number of different non-nominal parts in a software for variation simulation. The translation and rotation matrices, representing the deviations from the nominal geometry due to positioning error, are exported to a software for welding simulation, where the effects from welding are applied. The final results are then analyzed with respect to both deviation and variation. The method is applied on a simple case, a T-weld joint, with available measurements of residual stresses and deformations. The effect of the different sources of deviation on the final outcome is analyzed and the difference between welding simulations applied to nominal parts and to disturbed (non-nominal) parts is investigated. The study shows that, in order to achieve realistic results, variation simulations should be combined with welding simulations. It does also show that welding simulations should be applied to a set of non-nominal parts since the difference between deviation of a nominal part and deviation of a non-nominal part due to influence of welding can be quite large.

Method for Handling Model Growth in Nonrigid Variation Simulation of Sheet Metal Assemblies

In automotive industry, virtual tools and methods are becoming increasingly important to ensure robust solutions as early as possible in the development processes. Today, techniques exist that combine Monte Carlo simulations (MCS) with finite element analysis (FEA) to capture the parts nonrigid geometric behavior when predicting variation in a critical dimension of a subassembly or product. A direct combination of MCS with full FEA requires high computational power and the calculations tend to be very time consuming. To overcome this problem, the method of influence coefficients (MIC) was proposed by Liu and Hu in the late 1990s. This well-known technique has since then been used in several studies of nonrigid assemblies and sensitivity analysis of the geometric fault propagation in multistation assembly processes. In detailed studies of the resulting subassemblies and levels of variation, functionality for color plots and the ability to study the geometry in arbitrary sections are desired to facilitate the analysis of the simulation results. However, when including all part nodes in combination with methods for contact and spot weld sequence modeling, the required sensitivity matrices grow exponentially. In this paper, a method is proposed, describing how traditional MIC calculations can be combined with a separate detailed subassembly analysis model, keeping the model sizes down and thus facilitating detailed studies of larger assembly structures.

Including Assembly Fixture Repeatability in Rigid and Non-Rigid Variation Simulation

The repeatability of the assembly fixtures influences the geometrical outcome of an assembly. To control the fixtures, capability studies are conducted. Those studies give however just information about the variability in a number of inspection points. In this paper, a method for transforming the variation in inspection data to variation in the contacts between workpiece and locators is described. By doing this, the fault localizing of the fixture is facilitated. Further, the accuracy of the variation simulations used to evaluate different concepts and designs can be improved. Usually, when data from a repeatability study are used as input to a variation simulation, the tolerances are only applied in the points that actually were inspected. The suggested methodology makes it possible to transform the tolerances containing the repeatability of the fixture to tolerances on the locating scheme, and they are thereby affecting every point in the simulation model, not only the inspected ones. The method is tested on a case study and the effect of including fixture repeatability in a variation simulation is investigated. ©2010 by ASME.

Simulation of the effect of geometrical variation on assembly and holding forces

All assembly situations include joining of parts - by welding, riveting, bolting or using clip fasteners etc. Normally, the force needed to join two parts, i.e. the assembly force, is calculated under nominal conditions. Since all manufactured parts, as well as assembly fixtures, are afflicted with variation, the gap between two flanges that are to be joined may vary. Therefore, also the force needed to close the gap will vary as well as the remaining holding force. For a fixed force produced by a welding gun or an operator, also the remaining force after closing the gap will vary, which may lead to quality problems. In this paper, a simulation method for prediction of required assembly forces as well as holding forces due to initial gap is presented. Three different joining techniques are also discussed with respect to assembly and joining forces.

Evaluating genetic algorithms on Welding sequence optimization with respect to dimensional variation and cycle time

Spot welding is the predominant joining method in car body assembly. Spot welding sequences have a significant influence on the dimensional variation of resulting assemblies and ultimately on overall product quality. It also has a significant influence on welding robot cycle time and thus ultimately on manufacturing cost. In this work we evaluate the performance of Genetic Algorithms, GAs, on multi-criteria optimization of welding sequence with respect to dimensional assembly variation and welding robot cycle time. Reference assemblies are fully modelled in 3D including detailed fixtures, welding robots and weld guns. Dimensional variation is obtained using variation simulation and part measurement data. Cycle time is obtained using automatic robot path planning. GAs are not guaranteed to find the global optimum. Besides exhaustive calculations, there is no way to determine how close to the actual optimum a GA trial has reached. Furthermore, sequence fitness evaluations constitute the absolute majority of optimization computation running time and do thus need to be kept to a minimum. Therefore, for two industrial reference assemblies we investigate the number of fitness evaluations that is required to find a sequence that is optimal or a near-optimal with respect to the fitness function. The fitness function in this work is a single criterion based on a weighted and normalized combination of dimensional variation and cycle time. Both reference assemblies involves 7 spot welds which entails 7!=5040 possible welding sequences. For both reference assemblies, dimensional variation and cycle time is exhaustively calculated for all 5040 possible sequences, determining the optimal sequence, with respect to the fitness function, for a fact. Then a GA that utilizes Random Key Encoding is applied on both cases and the performance is recorded. It is found that in searching through about 1% of the possible sequences, optimum is reached in about half of the trials and 80-90% of the trials reach the ten best sequences. Furthermore the optimum of the single criterion fitness function entails dimensional variation and cycle time fairly close to their respective optimum. In conclusion, this work indicates that genetic algorithms are highly effective in optimizing welding sequence with respect to dimensional variation and cycle time.

Controlling Geometrical Variation Caused by Assembly Fixtures

In the auto body assembly process, fixtures position parts during assembly and inspection. Variation in the positioning process propagates to the final assembly. To control the assembly fixtures, repeatability studies are used. Those studies are, however, usually done with long intervals and the fixtures might be afflicted with variation between studies. There are also other sources of variation in the final assembly, such as variation in parts due to previous manufacturing steps. To separate variation caused by fixtures and the variation caused by previous manufacturing processes, a multivariate fixture failure subspace control chart is proposed.

GEOMETRY ASSURANCE INTEGRATING PROCESS VARIATION WITH SIMULATION OF SPRING-IN FOR COMPOSITE PARTS AND ASSEMBLIES

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Operator Related Causes for Low Correlation Between Cat Simulations and Physical Results

The objective of this study was to explore correlation between CAT (Computer Aided Tolerancing) simulation and physically measured results in running production with focus on operator dependant factors. Therefore, the manual assembly of 25 different system solutions (locating scheme, tolerances, fasteners etc for a part) was analyzed. The study has been performed in the automotive industry and the system solutions are from 3 different cars in 2 different factories, all manual assembly in a paced line. The analysis shows several interesting results; in running production 33% of the measurements are not ok although 28% had their tolerance zone adjusted according to the measured results to make them ok. The conclusion is that the CAT simulations do not predict all the variation and therefore additional factors need to be included to enable accuracy improvement. Further relationships between additional factors such as operator influence and bad geometrical quality can be proven. A short term solution is suggested as well as a long term solution involving the need for development of additional functions in CAT tools, the overall goal being to decrease the difference between simulation results and actual physical results.