Damper design optimization to guarantee the highest load performance with lower mass

Industry: Transportation | Product: pSeven


Rubber-like materials are widely applied in vibration dampers and shock dampening in pumping units, shipyards equipment, railway transportation and other industries due to its hyperelasticity and deformation resilience (energy absorption).

The objective of this study is to find both a design with the highest load performance and with the lowest mass, keeping its loading performance as high as possible.


One of the challenges which the designers of the shock-absorbing devices face is to provide the necessary static load performance (force-displacement curve), resulting from the deformation process calculation. The load characteristics of the rubber-like damper are strictly nonlinear. These characteristics depend on the damper`s geometry parameters. Therefore searching for the optimal geometry to provide the necessary load performance is a sophisticated challenge which requires advanced methods of predictive modeling and optimization.

In some cases, damper mass is also an important criterion. The smaller mass of a product leads to materials economy and, as a result, to the cost-effective product. So, another challenge will be to get a set of optimal weight and load performing configurations (Pareto-frontier).


Single-objective problem – design optimization for the highest load performance

First, to define the geometry of the polyurethane damper, its size has to be selected to guarantee the maximum energy capacity for a given compression force and displacement. This design (picture on the right) allows receiving a wide range of load characteristics at the compact dimensions.

Next, 3D parametric model has to be constructed. Damper`s model was created in SolidWorks 3D CAD system. The simplified geometry of a damper is described by 6 parameters. For FEA-modeling, a 1/8 cyclic part (45º) was considered. FE simulation has been performed in ANSYS Mechanical. All the processes of FE modeling, boundary conditions setting, solution and results analysis were automated in pSeven.

To solve the problem, global optimization method was applied (Surrogate-Based Optimization, SBO). This method allows finding a global minimum of the function with the minimum of time-consuming calculations. 

Optimal geometry parameters were found and then analyzed up to ultimate load. This optimal configuration guarantees the best energy capacity. This was found as a ratio between the strain energies of the real and ideal dampers. The optimal configuration has the energy capacity  > 0.92, which is an excellent result.

Multiobjective design optimization for the lowest design mass, keeping its loading performance high

When the designer has a multi-objective task to handle, the SBO method can also be applied to get the result in the short timeframe. MO SBO — multi-objective surrogate-based optimization (SBO adapted to multi-objective tasks) — was applied in this case. This method implemented in pSeven allows building the frontier of optimal (by mass and load performance) options with the minimum referrals to the external solver (Pareto-Frontier). In this case, two criteria were subject to optimization (mass and load performance, M and J target functions), with six parameters describing the model selected and five constraints set. Only 600 calls to external solver were made. The chart below represents the results of the solution: all the J and M for all the configurations, red dots indicate the Pareto optimal points.

Damper design optimizationDamper design optimization

Five design configurations among the fifteen points within the Pareto-frontier represent the optimal proportion of mass and load performance of the damper. The chart shows that further mass decrease leads to a considerable loss in load performance. This means that the configurations with the parameters corresponding to these other points do not bring value to the manufacturer.

Still, it is up to the manufacturing company to decide what configuration they would select out of the five optimal ones since it depends on what criterion is more important. As we can see from the picture below, a smaller mass would give less efficiency of the configuration, and the manufacturer has to find a trade-off between these two parameters.

Damper design optimization

Other criteria, as a shock-absorber stroke, might be important depending on its field of application. This criterion can also be included in the solution in pSeven.


SBO method allows finding highly effective damper configurations and shock isolation systems made of a rubber-like material in a very short period of time. These configurations have the best elastic characteristics for the greatest dynamic energy absorption and resonance offset. In this particular test case, pSeven use allowed to get the energy capacity up to > 0.9.

Multi-objective optimization with mass as one of the criteria provides the designer with the necessary information when developing mass-sensitive shock-absorbing systems. Having an automated process integration and design optimization environment as a tool enables dampers manufacturers to customize the optimal configuration of the product for specific needs of customers quicker than ever.