Executive summary—Passenger-vehicle structural performance is extremely sensitive to welds and adhesive bonds. Traditionally, multidisciplinary optimization (MDO) has been performed largely using thickness, shape and material grade as variables. This project’s objective was to optimize the spot weld count and linear length of adhesives in the body while balancing vehicle structural performance and weight. Various optimization scenarios were carried out: maintain current structural performance but minimize weld count, adhesive length and body weight; maintain current weld count and adhesive length but maximize structural performance and minimize weight; and others. Including welds and adhesives as variables in the MDO process provided additional design space to improve structural performance and reduce cost through spot weld and adhesive minimization.
Specifically, in this project an automated weld and adhesive optimization process was developed at Ford to improve vehicle structural performance using a unique parametric technique developed by DEP, Inc. Variables included weld pitch and its alternative forms such as number of welds in a given weld line and percentage change to the weld count, type of welds, layers of adhesive bonds and adhesive bond dimensions. This process was implemented successfully on a passenger car currently in production with the primary objective of increasing modal frequency separation between body-in-prime (BIP) bending and torsional modes while maintaining the current number of total welds in BIP structure. The majority of the design variables were weld parameters at rocker, front and rear rails, roof liners, seat cross members, roof bows and sled runner locations. Parameters were automatically created using DEP’s MeshWorks software, which generates weld/adhesive lines automatically once parts are identified. Variables were created quickly, and DOE techniques were used to generate multiple designs by integrating the parametric model with SIMULIA’s Isight.
Over 1000 designs were generated rapidly and automatically, then evaluated across functions and attributes. Scripts were created for automatic post-processing of results. Subsequently an input/output matrix was tabulated, and response surface models were created using Isight’s RBF tool. Isight’s Pointer Algorithm was set to determine the optimal solution. The validated optimal design showed the required frequency separation with optimal placement of welds and adhesives. This process demonstrated the ability to execute weld and adhesive optimization with minimum resources to achieve optimum number of welds, placement of welds, and adhesive length in the fast turnaround time demanded by current product development cycles.
Introduction—Parametric CAE models are an essential part of any MDO process. For complex vehicle crash, NVH and durability models, the typical parameters considered are shape, gage, features and materials. Connector elements such as spot welds, seam welds and adhesives are typically not considered as design variables. By adding them to the MDO process, the design space can be further expanded.
During early stages of vehicle development when maximum design space freedom is available, all the above categories of design variables can be used for parametrization and subsequent optimization. However, as vehicle development progresses toward final design freeze, the design space reduces. For example, once the styling theme and vehicle packaging stages are complete, there is very limited applicability of shape parameters. Close to the end of the development cycle, the design variables used for MDO are primarily the gage, grade or connectors such as spot welds, seam welds and adhesives.
Even at the tail end of the vehicle development process, performance of the vehicle body can be improved while maintaining the weight targets by optimally placing the spot welds and adhesives at the right locations. Further, for a given level of performance, the number of spot welds and amount of adhesives can be minimized, which can significantly reduce manufacturing costs.
In this project, only spot welds and adhesives were addressed as design variables, and their impacts on vehicle performance, especially body static torsion and dynamic torsion and weight, were assessed. DEP’s MeshWorks software was used to create weld/adhesive parameters using a unique weld/adhesive line methodology.
Weld and adhesive optimization process
DOE-based optimization—The weld and adhesive optimization process developed in this project is depicted in Figure 1.
Full-vehicle stiffness, crash, NVH and durability models are required at the start of the process. Depending on the load cases to be considered for optimization, all or some of these models will be used for subsequent parametrization.
Using MeshWorks, the discrete spot welds are converted automatically into weld lines. The automated weld line creation takes into account parts that are welded together (both 2t and 3t) and whether they are at the flanges of the parts or in their interior. Other factors taken into account are (a) the relationship between the connecting part thicknesses and the weld nugget size and (b) the relationship between connecting part thicknesses, part materials and the weld failure forces. Figure 2a shows the typical spot welds in the body-in-prime of the vehicle. Figure 2b shows how the selected spot welds are automatically converted to weld lines. Besides creating weld lines using existing welds, there are also ways to create weld lines from CAD curves and 1D geometries.
Using MeshWorks, the above-generated weld lines are then converted into parameters whereby the number of spot welds in each weld line can be varied with the following methods: (a) spot weld pitch varying over a minimum to a maximum value within a weld line; (b) spot weld pitch of a group of weld lines being varied as a percentage of their original value; (c) explicitly the weld count in each weld line varying over a minimum to a maximum value. Using these methods, there is complete flexibility in generating a spectrum of parameters ranging from making every weld line an independent parameter to making all the weld lines into one single parameter. Figures 3a and 3b show welds created with different pitches (or count) at different locations of the vehicle body structure.
Adhesive lines are created in similar fashion, using the following methods: (a) existing adhesives can be converted automatically to adhesive lines; (b) existing weld lines can be used to create adhesive lines at the same locations; or (c) using CAD curves and 1D geometries.
Adhesive lines are then automatically converted to adhesive parameters whereby they take on a binary setting of whether to create adhesive elements or not when activated. When an adhesive parameter is defined, the width, thickness and material property of the adhesive are all specified as additional inputs. Further, the number of elements along the length, width and thickness of the adhesive are all specified as meshing conditions. Figures 4a and 4b show adhesive lines and their activated state respectively. As with the weld parameters, there is complete flexibility in generating a spectrum of parameters ranging from making every adhesive line an independent parameter to making all the adhesive lines into one single parameter.
Using Isight, a DOE matrix is generated considering the weld variables and their ranges, and the adhesive variables and their on/off settings.
For every design in the DOE matrix, MeshWorks automatically generates runnable structural FE models for crash, NVH and durability with weld elements with appropriate pitch and adhesive elements.
The models thus generated are then automatically submitted for solver runs in Nastran, Abaqus or LS-DYNA (depending on the load case) in an HPC resource.
All output responses such as body-in-prime torsional and bending stiffness, BIP frequencies, trimmed body frequencies, etc. are automatically extracted from the solver output files and tabulated as an input/output (I/O) table.
The above two steps of job submission and results extraction were highly automated through Ford custom scripts.
Chances are high that one or more designs with better performance (or alternately with reduced weld count but with baseline design performance) will be obtained from the I/O table of the DOE runs. To get to the true optimum, approximation models using RSM techniques are created using the I/O table. The RSM then provides sensitivities of the structural performance to various weld and adhesive lines.
Using the sensitivities obtained through the RSM, several optimization scenarios with appropriate objectives and constraints can be set up, using Isight to arrive at the final optimum. Typical optimization scenarios carried out are as follows:
- Set objective as improvement in performance while setting constraints on weld count and adhesive lengths.
- Set objective as minimize weld count and adhesive length while setting constraints as maintain baseline design performance.
Spot weld topology optimization—In addition to the DOE-based weld and adhesive optimization process described above, a unique MeshWorks-driven topology optimization process can be used to minimize weld count while maintaining baseline design performance. Key steps of this process are:
- The spot weld lines created in the process described above are realized with a pitch of 5mm, thereby producing densely packed weld elements next to each other. These spot weld hexa elements with 5mm pitch represent the design space for topology optimization. The rest of the model is considered as non-design space.
- Topology optimization is carried out with this model whereby constraints are set on frequencies, static stiffness, etc., while the objective is to minimize material in the design space, which in this case consists of the densely packed weld elements.
- The optimization will result in varying-density design space elements, indicating their effectiveness vs. ineffectiveness. Using these results and some manual fine-tuning, the final locations of spot welds are arrived at.
Weld/adhesive MDO process applied to vehicle program
Weld optimization on trimmed body for mode separation—The optimization process explained above was used on a sedan to improve its modal performance. The objective was to separate the trimmed-body vertical bending mode and torsion mode as much as possible from the baseline level of 0.1Hz, by maintaining or increasing the weld count. Figure 5 shows the frequency separation of the baseline trimmed body.
The parametric methodology developed by DEP and described above was used to optimize the vehicle body structure’s performance using spot weld pitch as a design variable. Spot weld lines were created and parametrized instantaneously using MeshWorks.
DOE-based optimization was performed with Isight, and a mode separation of 0.4Hz was achieved with a small increase in the number of spot welds. This is an appreciable improvement from the baseline design separation of 0.1Hz considering that it is done at the trimmed body level. Isight helped to rank order the spot weld lines based on sensitivity to the global trimmed body modes.
Adhesive optimization to improve body-in-prime (BIP) performance—The adhesive optimization process described above was used to improve the performance of the sedan BIP. The objective was to improve the baseline BIP performance in terms of global mode frequencies and static stiffness by adding a minimum number of adhesive bonds.
The spot weld lines at the ten most sensitive locations were selected based on the rank ordering obtained from the DOE-based optimization described above. Adhesive lines and realized adhesive bond elements were created at these ten locations automatically using the baseline BIP model. Figure 6 shows the adhesive bonds added.
Tables 1 and 2 show the improvement in BIP performance of the model where the adhesive bonds were added.
The results clearly indicate an appreciable performance improvement by adding adhesive bonds at a mere ten locations as suggested by the DOE-based optimization.
Spot weld topology optimization on body-in-prime (BIP)—The topology optimization process explained above was applied on the sedan BIP. The objective was to minimize the spot weld count by maintaining the baseline BIP performance in terms of global mode frequencies and static stiffness.
Spot weld lines were created automatically from the discrete spot weld points on the flanges using DEP’s MeshWorks software as shown in Figure 7. These spot weld lines were realized with a weld pitch of 5mm to generate the design space. Figure 8 shows the spot weld-based design space in the BIP and also enlarged views of local regions.
Spot weld hexa elements were used as the design space, and frequencies of BIP global modes and static stiffness values of the baseline design were used as constraints. The objective was to minimize the volume fraction of spot weld hexa elements.
Based on the topology optimization results, areas with high sensitivity to performance (smaller weld pitch) and areas with low sensitivity to performance (larger weld pitch) were automatically identified. Manual fine-tuning of the weld pitch was carried out using the topology results to arrive at the final design which resulted in a non-uniform weld pitch. Figures 9 and 10 show the change in the spot weld locations in specific regions of the BIP between baseline design, 5mm pitch design-space model, and optimized design.
This project identified the opportunity to reduce 268 spot welds while at the same time improving the structural performance of the BIP structure. Tables 3 and 4 show the improvement in BIP performance of the optimized design compared with the baseline design.
Results clearly indicate the ability of the spot weld topology optimization process to minimize welds while at the same time improving structural performance.
Conclusions—DOE- and topology-based optimization processes for spot weld and adhesive length minimization while balancing performance were developed and implemented in vehicle programs. The processes were implemented successfully on a passenger car currently in production, with the primary objective of increasing modal frequency separation between vehicle body bending and torsional modes while optimizing the number of welds and adhesive locations in the structure.
Weld and adhesive optimization processes developed in this study can be used for various optimization scenarios:
- Improving current structural performance while setting constraints on weld count and adhesive lengths.
- Minimizing spot weld count and adhesive lengths while maintaining current structural performance.
- Improving structural performance and minimizing spot weld count and adhesive lengths simultaneously.
This process can be used at any stage of vehicle development. Even in late design-freeze stages, when all other forms of design parameters such as shape, gage, etc. cannot be altered, weld and adhesive optimization can be carried out to improve structural performance and reduce manufacturing costs.
As shown in the project, spot welds with the addition of adhesive bonds at critical areas will improve body performance with little to no weight addition.
Manufacturing cost savings by way of reduced spot weld count and minimized adhesive lengths can be truly significant.
DEP’s MeshWorks software was used in this project to help generate the spot weld and adhesive bond lines with minimal complexity, and to parametrize the entire BIP very rapidly.
While this project focused on optimization processes with respect to body NVH performance, the methods developed are applicable to other attributes such as safety and durability as well as for multidisciplinary optimization.
Case study presented at SIMULIA Community Conference 2013: “Weld and Adhesive Optimization Process Development and Implementation on Vehicle Body Structure Development,” G. Nammalwar, B. Shahidi, A. Chator, L. Sivashankar, R. Frank, B. Barthelemy and N. Kochhar, Ford Motor Company; R. Krishnan and Rakesh K. D., DEP, Inc.