# Mechanical calculations & simulations

Huygens Engineers performs the necessary calculations and simulations during the process of development and engineering. The share of calculation and simulation varies widely among projects. In some projects the share is 100%. We aim to keep analytical insight as the main driver for design, with subsequent confirmation through FEA.

Huygens Engineers delivers calculation and simulation services in the fields of mechanics, heat, fluid flow and electromagnetics. For mechanics, we have capabilities on the following subjects:

- Strength, stress and strain
- Fatigue calculations and damage calculations with complex loads
- Buckling analysis
- Modal analysis and harmonic response
- Geometry optimization
- Effect of tolerance spread on component-performance
- Body dynamics
- Writing software for cases that cannot be solved in standard simulation environments

## Strength, stress and strain

Analytical calculations are foundational in mechanical engineering and represent a significant portion of the analysis-hours. This is complemented by FEA simulations and Python modeling. The figure shows an example of an analytical calculation of stress in a conical spring and a linear stress simulation with non-linear contact simulation of a clamp-assembly for a highly pre-tensioned knife.

The figure below provides an illustration of the range of sizes of components on which Huygens Engineers performs work. The illustration includes an FEA analysis of a sizeable ground frame design (20 m in size) for a water turbine and, on the other side of the size-spectrum, an FEA analysis of a sensor body (20 mm in size) with a plate thickness of 1/10th mm.

For hyper-elastic and visco-elastic materials, a linear approximation of deformation is often inadequate. The video below shows a large deformation (non-linear) analysis of a hyper-elastic material assembly.

## Fatigue calculations and damage calculations with complex loads

In large mechanisms and in mechanisms with long service-life, criteria like transportability, cost-price, dynamic loading and size-restrictions often lead to fatigue-critical designs. Huygens has developed extensive expertise in fatigue assessment.

Fatigue calculations can be done analytically for normalized situations. The figure shows an excerpt of a shaft-fatigue calculation in MathCAD, according to DIN 743.

On the other end of the spectrum, regarding the complexity of fatigue calculations, lie situations where loads vary in intensity and in direction in complex patterns. This is, for example, the case in a tidal turbine where fatigue is assessed by adding damage of a set of recurring cycles (time-series), incorporating cycles stemming from rotation of the blades in a non-uniform flow, due to surface-waves, varying flow-strength, and non-uniform flow, in turn attributed to the boundary layer effects on the sea-floor. These types of challenges can be tackled with normal stress projections on planes at each node of the mesh, rainflow counting and a full damage assessment (typically through Palmgren-Miner). The figure shows a water turbine, shows the detailed meshing necessary at locations of stress-concentrations, shows an example of optimal local coordinates on each point of the mesh for cumulative fatigue analysis, and shows cumulative damage projected on a part of the surface resulting from a complex load pattern.

## Buckling analysis

For thin-plated designs, local buckling can sometimes be a concern. Utilization of linear buckling model can cause drastic overestimation of the buckling load-coefficient, which is why a non-linear buckling analysis and more accurate prediction of the load-coefficient are required. The process to create a non-linear buckling analysis consists of pre-stressing the model, creating deformed shapes and subsequently using these deformed shapes to introduce small imperfections in the model. A non-linear (large deformation and plastic material behavior) static structural analysis is performed to determine the point at which buckling really occurs. The figure and video below show a local buckling analysis of a wind-turbine mast around the access door.

## Modal analysis & harmonic response

An eigenfrequency is a frequency in which the object will transfer vibrational to kinetic energy with minimal losses. In modal analysis we determine the natural mode shapes and frequencies of an object during free vibration. An example of an object in which the eigenfrequency is an important characteristic is the mast of a wind turbine, as shown in the figure. If the rotor would operate in the eigenfrequency of the mast, this would lead to increasing vibrations, which in the end could lead to failure of the structure. The figure and video show you a modal analysis performed on a water turbine arm. The calculated eigenfrequencies in FEA were compared to the measured eigenfrequencies, with the goal of determining the damping characteristics of the water surrounding the turbine.

One step up from modal analysis, Huygens Engineers simulates the vibrational behavior of a structure or component as a result of a vibratory excitation. This is harmonic response.

## Geometry optimization

Instead of checking a shape using the traditional FEA methods, topology optimization takes a rough geometrical envelope, accompanied by design constraints (e.g. minimize the maximum Von-Mises stress and reduce mass by 50%), and determines the optimal shape. This often results in very ‘organic’ shapes, which is demonstrated by the illustration below, where optimization is applied to the situation of a bridge.

## Effect of tolerance spread on component-performance

Manufacturing tolerances and variations of temperature and/or load can have a big influence on the performance of a system, especially when the product is small compared to the magnitude of the tolerances. Instead of demanding higher precisions on a large number of dimensions in a product to reduce the part-to-part variation, Huygens Engineers focuses on a screening of the design to identify the ‘big fish’; the parameters with the largest impact on the system performance. With these parameters identified, the required tolerances can be calculated, or the system can be optimized using Monte Carlo simulations to change the design and reduce the effect of the parameters, allowing for wider tolerances and a reduced cost price for the part, as well as a better part-to-part performance. The figure shows an application of a Monte Carlo simulation for the effect of tolerance spread on a mechanical sensor.

## Body dynamics

With rigid body dynamics, the kinematics of a system of bodies that form a mechanism can be calculated. Variables include displacements, rotations, load, moments, and inertia. Subsequently, a part of this system (one or multiple bodies) can be taken out of the linked system and analyzed, using a static structural FEA analysis. The results from this analysis consist of displacement, stress, and strain values. With these outcomes it becomes possible to calculate the power required for the displacement of a body, and to manipulate the controls of e.g. a servo motor to optimize the speed of the motion, while reducing the maximum power requirement. The figure illustrates a movement analysis of a robot arm. The videos firstly show a moving simulation of the robot arm, as illustrated in the figure, and secondly a simulation of rigid/flexible body dynamics.

## Writing software for cases that cannot be solved in standard simulation environments

In some situations, the exact phenomena at play cannot be easily modeled in existing software. This then requires construction of a custom FEA model to both explain current behavior and predict the outcome of design changes.

When the cause of deviant performance or of system failure is not well understood, an extensive analysis on all possible interactions between the internal system elements and the external environment is sometimes unavoidable. The amount of work involved in this type of endeavor may vary widely.

Examples or work addressed in this manner by Huygens Engineers involves wrapping interaction in combination with either stick-slip effects due to variation of friction-coefficients under varying load or varying temperature or large-deformation caused leverage.

Specifically, in a cooling tower used in the food industry, tension build-up in the spiral belt in certain circumstances was not always well understood. The complex interactions between the elements in the tower, the occurrence of stick-slip phenomena and the influence of temperature changes required the use of Python to build a custom FEA model. The figure illustrates modeling of forces in a type of spiral cooler.

Thanking you for your interest, we welcome you to ask us any question, and invite you to consider whether we could mean something for you.