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Improving a Coffee Capsule Packaging Machine Using RecurDyn Multibody Simulation

Improving a Coffee Capsule Packaging Machine Using RecurDyn Multibody Simulation

Analysis Goal: Increase the production capacity by 25% without increasing overall costs and energy consumption.

Production capacity is one of the most important features of an automatic packaging machine. OPEM’s designers, in Parma, Italy, are constantly looking for new design solutions with increased capacity and reliability, attractive pricing, and small dimensions that will enhance their competitiveness. The main objective of this project was to increase the packaging capacity by 25% without affecting the general architecture, the size of parts and the energy efficiency of the machine. The objectives were achieved by optimizing the motion profiles of all of the actuators (cams and controlled electric drivers) because optimizing motion profiles is the way to achieve higher capacity without increasing the power demand and dynamic loads. At the same time the behavior of a complex chain mechanism had to be considered. A large number of RecurDyn multibody dynamics simulations were performed in order to check and verify the effects of the optimized motion profiles on the overall system behavior.

Espresso

Development Process

  1. Motion profiles are applied to all ideal motors equipping the machine. Motion profiles are designed and optimized to guarantee continuity and lowest possible accelerations, while achieving the desired displacements at the desired instants.
  2. The rigid multi-body model of the entire machine verifies that the motion profiles are properly synchronized. The same model also measures the power requirements, which determines the selection of the proper motors. Rigid multibody simulation is the best approach to verify motion profiles because each simulation runs quickly. Running multiple iterations to optimize the profiles is easy and can be done automatically. The RecurDyn Chain Toolkit allows for the easy modeling of the chain mechanism and the large number of contacts can be calculated quickly.
  3. This model includes a FullFlex representation of the thin film that is used to seal the capsules. Flexible multi-body (reduced ex and full ex) is necessary to check the effectiveness of the proposed design solutions. Although some components of the machine are largely flexible, the relative positioning of the capsule, film and tools must also be guaranteed in severe dynamic conditions.
  4. The multi-flexible body model of the entire machine is used to verify that the positions of tools and capsules are guaranteed even when the structures deform in dynamic conditions.
  5. This model also calculates the dynamic reaction forces at the constraints that connect each machine sub-system to the main frame.
  6. The loads obtained from the multi flexible body model are used for structural assessment (strength and fatigue) using finite element analysis software.
Cut and Weld
Film Feeder Flex
Cut Weld Flex
Structure

Gear Contacts in RecurDyn/DriveTrain, Including the Gear Meta Model

Basics of Modal Flexible Body Simulation

Review of RecurDyn/DriveTrain

RecurDyn/DriveTrain defines and simulates drivetrain components, including gears, bearings, and shafts (see toolkit icons in the figure). Users can easily simulate and analyze drivetrain systems with specialized user interfaces, a specialized solver, and dedicated post-processing.

The GearKS and BearingKS toolkits have been developed through a technical partnership with Gleason’s KISSsoft, and offers KISSsoft’s Gear Analytic Contact and tens of thousands of gear and bearing libraries. This allows RecurDyn users to accurately calculate a variety of results including transmission error for noise and vibration evaluation.

Gear Contact elements in RecurDyn/DriveTrain

In the GearKS toolkit the contact between gears is referred to as a gear force. GearKS supports 3 gear force types as shown in the image below: Inactivate, KISSsoft Force, and KISSsoft Force (Meta Model). These contacts are explained below, with a focus on the meta model option, because it is expected to be used frequently.

KISSsoft Force

Gear Force Types

Inactivate – If this type is selected, GearKS doesn’t calculate the gear contact. Instead, other contacts such as a gear involute contact or a geo contact must be defined. To use gear involute contact, first set the Gear Force Type to Inactivate and then create the gear involute contact using the RecurDyn/Gear Toolkit (different than the GearKS toolkit).

KISSsoft Force – The gear contact is calculated by the co-simulation between RecurDyn and the embedded KISSsoft solver. Each time step, RecurDyn transfers the updated position of the gears to KISSsoft and the KISSsoft solver embedded in RecurDyn calculates the gear contact. The reaction force/torque is transferred from KISSsoft to RecurDyn.

KISSsoft Force (Meta Model) – This method is generally recommended because it is very fast and has high accuracy. Unlike the KISSsoft Force (Direct Co-Simulation) option, KISSsoft Force (Meta Model) uses the pre-calculated Gear Meta Model in the simulation, which is the reason for its speed. The Gear Meta Model (*.gmm file) must be created using up to 6 parameters which are related to the location/ orientation of the gear pair before simulation. The generation of the Gear Meta Model requires from several minutes to several hours. The Gear Meta Model is reusable if the same gear pair is used for another model. The same Gear Meta Model can be used for the several gear pairs in the same model.

More About the Gear Meta Model

In general, meta models are also known as surrogate models, or approximate models. A meta model is prepared by running a series of analyses with varied values for some number of gear-related variables. The outputs of all of these analysis runs are used to construct an N-dimensional response surface that quickly predicts the outputs of interest as a function of a specific input case. Using the response surface, you can quickly obtain gear contact results that accurately consider transmission errors because the surface is generated from accurate KISSsoft gear contact data. The gear meta model is generated with a set of static analyses and the meta model data is stored in a *.gmm file.

The 6 gear variables that may be considered include Rotational Angle (most important), Penetration, Distance Error, Axial Offset, Twist, and Tilt. These variables are described in the figure below.

The default setting uses only 2 parameters: Rotational Angle and Penetration. The accurate simulation of gear vibrations requires an accurate calculation of the change in meshing stiffness. The meshing stiffness of a gear varies with several factors, and rotation is the most important variable for high-accuracy gear contact.

If the gears are constrained by revolute joints, the Distance Error, Twist, and Tilt parameters can be ignored. The Axial Offset can be ignored in many cases. Nonetheless, for the most accurate result, it is recommended to use all 6 parameters. The time to generate a Gear Meta Model (varies depending on the system) is as low as several minutes when 2 parameters are used but may require several hours when all 6 parameters are used.

Choosing the Right Contact Type for Your Model

Please refer to the table.

The KISSsoft Force (Meta Model) is recommended in most cases because of its high accuracy and speed. Even though it takes time to generate Gear Meta Model, Gear Meta Model is reusable. Another reason to use KISSsoft Force (Meta Model) is if the gear specification is already fixed.

While the KISSsoft Force (Direct) is a little more accurate, the benefit of faster simulation speed (>50x) with the KISSsoft Force (Meta Model) compensates for the slight loss of the accuracy. If you only need to run 1 or 2 simulations then the KISSsoft Force (Direct) option can be a good choice.

The Gear Involute Contact is a good choice if the focus of the model is on macro system behavior rather than the micro effects such as the transmission error or the effect of the micro geometry of the gear. Gear Involute Contact is very convenient because no pre-calculation is needed.

If you need to simulate a flexible gear then you should use the Geo Surface Contact because the KISSsoft Force and Gear Involute contacts don’t support flexible bodies.

Calculation of Mass Properties When merging bodies with different materials

When you merge rigid bodies using the Merge Body command, the mass properties of the merged body are automatically calculated and applied, using one of two methods. The first method described below is used when the “User Input in Material Input” option (highlighted in the figure) is not checked and the second method is used when this option is checked.

First Option: Use the physical properties of the target body

The mass properties of the merged body are based on the total solid volume and assuming the material type of the Target Body.

For example, let’s assume that the Target Body is Steel and that Body B (Aluminum) is merged into it. The newly merged body has a material type of steel and the mass properties are calculated on the total solid volume. On the other hand, if body B were the target body, the material type of the resulting body would be aluminum. Given this behavior, this option is only appropriate when merging bodies of the same material.

Second Option: User Input in Material Input

After calculating the mass and moment of inertia from each of the Source Bodies, combine their mass properties with the mass properties of the target body. Set the mass properties of the target body with these combined properties, using the Material Type mode of “User Input” in the body properties. In summary, use this option when merging bodies with different material types in order to obtain accurate mass properties for the combined body.

Basics of Modal Flexible Body Simulation

Basics of Modal Flexible Body Simulation

This article is intended to help beginners understand a principle that is included in RecurDyn, in this case the modal approximation to flexibility in the RFlex (‘Reduced Flexibility’) module. You can use this information to help others understand the work that you do. There are also some usage tips that might be useful to you.

Including the flexibility of a body can be important. For example, a person designing a ruler must determine the difficulty of bending the ruler as well as the difficulty of breaking the ruler.

For another example, consider a bridge. A truck driver could be concerned if heavy shaking occurs when his/her truck goes over the bridge. Since the bridge didn’t collapse even when a heavy truck went across, does that mean the design is acceptable?

No, it does not.

An engineer must consider how much of a load a bridge can handle as vehicles cross and how much deformation will occur. Whether or not a collapse will occur is a question of strength, and how much it will flex is a question of rigidity. While strength and rigidity are different types of standards, a design must satisfy both criteria.

Flex Ruler
Bridge

Simulations and Flexible Bodies

MeshComputer simulations can be used to check strength and rigidity before a physical prototype is built and tested. The same solid geometry that is created by the engineer during design can be used for simulation. The solid geometry itself only includes exterior shapes and mass properties, and cannot be used to define how much a body will flex.

However, if we subdivide the body geometry into very small blocks (‘elements’), and mathematically define springs between all of the corners of the elements then we can calculate how the body flexes when any type of load is applied. As shown in the figure, the collection of elements looks very much like a net and is called a ‘mesh’.

When using solid elements there are three translational equations that are used for each corner of each element. The mesh shown includes thousands of equations. Since a finite number of elements are used in a mesh, this simulation method is referred to as the finite element method.

Including all of the equations for the flex body in every timestep of a RecurDyn multibody dynamics simulation can take a lot of computational time. Is there a more efficient way to include a flexible body?

Vibration

Vibration is when a flexible body repeatedly switches between its default shape and a deformed shape. An example is a tuning fork. Vibration results in sound in the air when the frequency of the vibration is within the auditory range. The condition when a flexible body tends to vibrate at a certain frequency is known as a resonance or a natural frequency. Flexible bodies can have many natural frequencies, and each frequency is associated with a particular deformed shape of the body, known as a mode shape. Natural frequencies are also known as modal frequencies. A tuning fork is designed to vibrate at a consistent frequency when tapped on the side of one of the forks with a mallet.

Tuning Fork
Tuning Fork

A tuning fork, like all flexible bodies, can vibrate at different frequencies, depending on the energy or forces that are used to excite the vibration. The image on the left shows the vibration of the fork at its primary natural frequency, and the mode shape (magnified) shows that the tines of the fork are moving in and out. The image on the left shows a vibrational mode where the tines are moving front and back, and not synchronized.

The total vibration of a flexible body may include many separate vibrations. As the French physicist Fourier stated, “A single complex wave is actually the sum of multiple simple waves.” This statement means that no matter how complex the wave, it can always be divided up into multiple simple waves, and when these simple waves are combined together, they become identical to the complex wave. The image shows how a complex wave (C) is separated into the two simple waves (A) and (B). Fourier is well-known for his Fast Fourier Transform (FFT) which can separate the individual frequencies of an acoustic waveform.

Flexible Body Analysis Using Vibration Modes

The finite element method, mentioned above, can be used to calculate the modal frequencies and mode shapes of a flexible body. The principle of superposition is used to combine individual mode shapes with weighting factors in order to reproduce any deformed shape of a flexible body. The weighting factors are also known as modal participation factors. This approach to representing flexible bodies has been offered in many dynamic simulation software for over 35 years.

Component mode synthesis (CMS) is a substructuring method that uses mode shapes and frequencies to represent the structure. CMS was originally developed to solve complex structures in a reasonable time, when computers were much slower. With multibody dynamics we are solving the flexible body several times in each time step, so even though computers are much faster today we need fast techniques to do the millions of flexible body solves that may occur during a simulation.

The use of the CMS flexible body in a multibody dynamics simulation requires the identification of attachment nodes in the finite element mesh. Some attachment nodes are located at joints/constraints and other attachment nodes are located where applied loads occur. Using finite elements software (including RFlexGen in RecurDyn) there are two sets of load cases that are investigated. First the attachment nodes at constraints are assumed to be fixed and a constrained normal modes analysis is run. Second, unit loads for each of the six degrees of freedom at each of the force attachment nodes are applied to create a set of constraint modes, which are also referred to as Craig-Bampton modes.

Advantages of Using Vibrational Modes for Flexible Body Analysis

Reduced computational complexity

CMS was developed for the reduction of finite element models and reduced computational time. For example, a detailed model, simplified model, and reduced model can all be created for the same flexible body in accordance with the degree of desired computational complexity. The starting finite element analysis model for CMS does not need to be as detailed as a model that is calculating the effect of geometric detail, such as stress concentrations. Second, the CMS model contains a small number of modes as compared to the number of finite element equations in the simplified models. In terms of computational complexity, a model with 100,000 nodes may have 300,000 equations to solve while the corresponding CMS model only has 100 equations to solve as related to the calculation of the modal participation factors as described above. Consequently, the use of flexible bodies using modes greatly reduces computational complexity, resulting in shorter computation times when arriving at solutions.

Reduction in effort needed to create flexible bodies

CMSThe meshes used in simplified models allow for sufficiently accurate results even if they are not as fine (small elements) as the meshes used for strength analyses (detailed model). If the subject is high frequency noise or acoustics, then a detailed model may be needed, but in general, the frequencies at issue for machinery are often in the 0 ~ 100Hz range. In such cases, creating and using a mesh that properly expresses rigidity and mass alone is not a problem. In particular, bending and torsion is extremely accurate for the low frequencies that are most often used in common machinery, so flexible bodies created by the reduction of simplified models through CMS can be used to solve machinery vibration issues.

Limitations of Using Vibration Modes for Flexible Body Analysis

Linear Behavior

The deformation of a flexible body can be expressed as the combination of multiple mode shapes because of the principle of superposition, which only applies to linear systems. Simulation cases that are not linear systems include large overall deformations, hyper elastic materials such as rubber, and local plastic deformations. It is necessary to use RecurDyn FFlex in such cases where the flexible body behavior is nonlinear. Since generally there are small deformations involved when designing machines, most machine designs can be done with a linear analysis.

User Knowledge Required to Select Modes for MBD Simulation

The user selects the number of modes for the finite element analysis software to produce for the flexible body. In the RecurDyn multibody dynamics software the user has to decide which of the modes should be included in the model. If too many modes are included it can slow down the model run time. If too few modes are included, then the simulation results may be in error. Therefore, the user needs to make several runs initially in order to establish how many modes should be included for sufficient accuracy with a reasonable run time. This decision process is not needed when running FFlex.

Sliding and Rolling Contact

Much caution is needed when trying to include sliding or rolling contact with a modal flexible body. A contact applies a force to the body, but with sliding or rolling contact the force can’t be associated with a node because it is changing location. If the modal flexible body is quite stiff then it is possible to define such contacts if the treatment of the contact surface is carefully done.

Application of Modal Flexible Body Analysis

Flexible body analysis using vibrational modes can be used for many applications. This level of analysis is positioned between rigid body analysis that does not consider any body flexibility and complex, nonlinear flexible body analysis. A modal flexible body can produce useful results for system vibrations in the 100~200Hz range, such as might occur in the analyses of vehicle vibrations or passenger comfort. Other applications include automobiles, frames for operated machines such as construction equipment, frames for automated factory equipment, and other parts for machinery. The image portrays the simulation of an internal combustion engine with a flexible connecting rod.

Modal Flexible Body Analysis

Using Particleworks Coupled with RecurDyn to Simulate Water Behavior in Water Technology Products

By Chiaki Miyazawa (LIXIL Corporation) and Akiko Kondoh (Prometech Software)

An important line of business for the LIXIL Corporation, Japan’s largest building and equipment manufacturer, is water technology products such as baths, kitchens and toilets. LIXIL is in the process of introducing Particleworks (from Prometech Software, Inc.) and RecurDyn (from FunctionBay Inc.) in the research and development of these products. Particleworks is a meshless multiparticle simulation (MPS) computational fluid dynamics (CFD) tool and RecurDyn is a multibody dynamics tool.
Dr. Miyazawa of LIXIL’s Advanced Core Technology Division explains: “I am mainly in charge of digital technology fields such as CFD simulation and virtual reality (VR). Previously, we largely focused on airflow analysis using a finite volume method (FVM) simulation tool that was effective for airflow evaluation even when toilet water flow analysis was necessary. However, since FVM requires extensive computational resources, when it became necessary to evaluate many small droplets, such as for showers, I started looking for a suitable tool.

This was when I found Particleworks, which was introduced with the keywords “liquid splashing” and “mixing”. So, I started a trial of Particleworks. Currently, we are verifying the reproducibility of shower toilets and showerheads, water splashing phenomena in kitchens, and kitchen sink flow behavior, and have already begun using prototypes for research.”

RecurDyn-Particleworks Example #1: Simulation of a Shower Head

LIXIL’s “Ecoful Shower” is a shower head product (Fig. 1) that includes an impeller incorporated in the shower head that rotates at high speed and blocks half of the shower holes at a time. This mechanism increases the pressure inside the shower head, producing a regular shower sensation for the user, however the water consumption is 48% lower than that of the conventional water volume (10 L/minute). Besides conserving water, it is also important to optimize the water pressure and the size of the water drops to improve comfort. Particleworks was used for these evaluations.

In this shower head mechanism, the impeller rotates due to the water flow, and the number of rotations changes according to the flow velocity. Since Particleworks, when used by itself, is only able to provide a constant rotation speed, regardless of the water flow, we used a coupled simulation with the RecurDyn multi-body dynamics simulation software to confirm the effects of both stable rotation speed and rotation changes (Fig. 2).

The results of the fluid behavior simulation were generally good because they met LIXIL’s guidelines compared to the measured values. The rotation speed of the impeller gradually increased at first, decreased gradually after reaching the peak, and finally stabilized. The transition states obtained by simulation were roughly consistent with the measured values.

Regarding the internal pressure of the shower head, we verified that the results almost matched the measured values. The size of the particles was measured with a high-speed camera, and the difference from the calculated value was also within the company’s guidelines. Overall, it was evaluated as a good result for a shower head simulation. In summary Dr. Miyazawa said, “The Particleworks-RecurDyn co-simulation is a great advantage because it allows the behavior of the shower and the internal impellers to be easily reproduced.”

RecurDyn-Particleworks Example #2: Simulation of Waste Flushing in a Kitchen Sink

Kitchens are easier to use if they are easier to clean. To achieve this, it must be easier to flush waste from the bottom of the sink and into the drain.

LIXIL’s new sink product introduced the “Niagara Flow Type”, where the bottom of the sink slopes more from the left and right edges, preventing the water from spreading and helping it flow smoothly towards the drain. This allows for efficient drainage from anywhere in the sink. Particleworks was used to evaluate how effective the new shape is. The kitchen sink design was evaluated in tests based on a very large number of assumptions, including how to flush waste.

In the simulation, we first tried to use Particleworks by itself to reproduce how easy it was for waste placed at equal intervals to flow.

Initial simulations showed that the water flowed faster, slipped more, and spread less compared to the test. The waste was also flowing unnaturally. Therefore, a test was conducted on a simple shape to obtain parameters by associating the test results with the simulation results. In actual phenomena, a film of water penetrates under the waste and surrounds it making the waste slippery.

In the Particleworks calculations, particles didn’t penetrate below the waste as easily in the first trial. This was solved by making the particles smaller. However, this required a lot of computational resources.

To reduce the computational load and shorten the simulation times to less than a day, it was necessary to enlarge the particles to some extent. However, this caused some differences from the actual phenomenon. Therefore, several attempts were made to adjust the contact friction parameters to approximate the behavior of the waste particles.

It was found that it was easier to adjust the contact friction parameters by defining the waste with polygons in RecurDyn, so once again a simulation was performed by coupling Particleworks with RecurDyn.

Next, the frictional force and particle shape were defined to prevent the waste from moving before the water supply. A correlation was made by adjusting the frictional force and the transition speed.

Through trial and error, the reproduction of water spread and the behavior of the waste were improved compared to the first simulation, and could also be improved compared to the actual test.

LIXIL continues to refine their sink simulations in order to produce a final result that meets their standards of accuracy for correlation to physical test results.

Using the Enhanced EHD (Elasto-Hydrodynamic Lubrication) Toolkits

Using the Enhanced EHD (Elasto-Hydrodynamic Lubrication) Toolkits

Since the release of RecurDyn V9R1 an enhanced version of the EHD (Elasto-Hydrodynamic Lubrication) toolkit has been available to RecurDyn users. Now there are actually two EHD toolkits- the Rotational Lubrication toolkit and the Piston Lubrication toolkit. These toolkits enable RecurDyn to analyze the behavior of a lubricant film in the thin gap between rapidly-moving cylindrical surfaces and the hydrodynamic forces transmitted from the lubricant to the surfaces.The Rotational Lubrication toolkit is for modeling primarily rotational motion, such as the motion found in journal bearings. The Piston Lubrication toolkit is for modeling primarily translational motion. It also supports RFlex (Flexible) Body analysis.

EHD Overview

The goal of hydrodynamic lubrication is to have a lubricant that penetrates into the contact zone between rubbing solids and creates a thin liquid film. This film separates the surfaces from direct contact. In general, this reduces friction and can consequently reduce wear, since friction within the lubricant is less than between the directly contacting solids. The EHD toolkits consider viscosity and surface roughness and calculate the elastic hydrodynamic force as well as the asperity contact force. The EHD Force can be shown with a contour display and EHD results can be exported. The interactions between the mechanical model and the EHD solver is shown in the figure.

The history of lubrication theory goes back to 1886 when O. Reynolds published his famous equation of the fluid film flow in the narrow gap between two solids. The Reynolds equation carries his name and forms a foundation of the lubrication theory. The figure shows the consideration of shear stress in the fluid as a function of the relative velocity between the solid components.

The calculation of the behavior of the local fluid lubrication region is determined by the governing equations in the figure.

When considering the behavior of the lubrication region and the contact region there are two regimes of interest. A thin film is considered to have a height / roughness of less than 4 mm, and may have intermittent metal to metal contact. A thick film is considered to have a height / roughness of greater than 4 mm and the EHD lubrication should be stable. The figure graphically depicts these concepts.

The governing equations for the contact region are given in the figure below.

In the case of piston lubrication both the piston and the cylinder head are RFlex flexible bodies. The nodes in the piston mesh are mapped to nodes in the mesh grid of a virtual cylinder in order to detect interferences related to the contact modeling.

The EHD toolkits have their own license, so if you would like to use EHD Toolkit, please contact MotionPort to obtain a trial license. There is also a specific RecurDyn tutorial for the EHD toolkits, include pre-created example models:

Tips for mesh generation – Using the Gradation Factor and Chordal Error Ratio Parameters to Control the Mesh Density

Tips for mesh generation – Using the Gradation Factor and Chordal Error Ratio Parameters to Control the Mesh Density

When you mesh complex geometry, you can improve the simulation speed and accuracy by generating a non-uniform mesh, with varying mesh density. The guiding concept is that a higher mesh density should be used in regions of high stress (and high stress gradients) while a lower mesh density can be used in area of low stress (and low stress gradients).

Note: ‘Mesh density’ is defined as the number of elements per unit distance in a mesh. A high mesh density generally produces more accurate results while a low mesh density can be simulated faster.

The RecurDyn/Mesher provides several options to generate a variable mesh efficiently. This article introduces two important parameters, the Gradation Factor and the Chordal Error Ratio. These parameters, when used properly, cause the mesh to have the proper mesh densities at curved surfaces or small features.

The definitions of the two parameters are as follows (please also refer to the images):

  • Chordal Error Ratio: It is the error between ideal curve (arc) and the approximated mesh as compared to the segment length. A smaller value produces a denser mesh on curved geometry that is more accurate.
  • Gradation Factor: It defines the rate at which the mesh transitions between high mesh density and low mesh density. The default value is 2. If you use a smaller value, the element size will vary more slowly.

A comparison of the images in the top half of the figure above shows that the reduction of the Chordal Error Ratio by a factor of 10 results in high mesh density along all of the arcs along the perimeter of the Geneva wheel as well as the circle in the center. Then, looking at the images in the bottom half of the figure shows that an 80% reduction of the Gradation Factor results in a much slower transition from a high-density mesh to a low-density mesh.

The best practice is to adjust these two parameters such that the transition in mesh density matches the transition of strain energy in the structure, while keeping the total number of nodes and elements low enough to allow for reasonable simulation times.

Modeling Contacts

Modeling Contacts

Many mechanical systems include contacts and the simulation of contacts can use up a lot of calculation time. It is important to be able to calculate the contacts quickly while maintaining sufficient accuracy. RecurDyn provides a broad library of 3D and 2D contacts to choose from when creating a model, as shown in the figure.

3D Contact

A 3D contact defines the contact between two three-dimensional shapes. The solid contact (Solid) and geo surface (Geo Sur) contacts are widely used because they can be quickly defined between bodies with general geometry. We will discuss how to use these below as well as the Primitive3D contacts.

You can download a RecurDyn model using the link below to reference as you continue reading this guide.

3D Contact Example Model Download

 

An example use of a Solid Contact, which is a 3D Contact

 

2D Contact

A 2D contact is defined between two curves, although one or both of the curves can be a special case for a curve, a circle. Although RecurDyn models generally consider 3D assemblies, sometimes the mechanism in the assembly has 2D motion, as constrained by several joints. In this case contact between two bodies can be described using a 2D contact, which solves more quickly. A 3D contact may be preferred if there is interest is observing contact pressures.

The most widely used 2D contact is a geo curve (Geo Cur).

You can download a RecurDyn model using the link below to reference as you continue reading this guide.

2D Contact Example Model Download

A Model Expressed with a Curve-to-Curve Contact Object, which is a 2D Contact Object

Tip: You may use the curve constraints, PTCV and CVCV, in order to reduce the simulation time as compared to using 2D contacts. The disadvantage would be that the bodies would no longer have the ability to “lift off.” Please refer to the following FAQ “How can I reduce the time required to analyze a model that includes contacts (PTCV, CVCV)?” for more information about using the PTCV and CVCV contraints.

Using Contacts

Note: Contact objects can be used in a variety of ways depending on the entities in the model, such as its geometries and parameters. Therefore, the following information should be used as a basic guide to working with contacts. The contacts in a specific model may behave differently than described in this guide.

Solid Contact

Solid contacts are fast and accurate when contact occurs between two general convex surfaces or between a flat surface and a convex surface (examples shown in the figure to the right).

The figure below shows a model in which several small spheres exist inside a larger sphere.

In this example, contact occurs between the convex surfaces of the small spheres and the concave surface of the larger sphere.

However, as the contact occurs only in small portions of the spheres rather than large areas, solid contact objects may still be applied successfully because the concave contact surface of the large sphere is sufficiently flat to properly interact with the convex surfaces of the small spheres.

When you define a contact inside a shape, as shown above, you may need to adjust the Normal Direction in the Solid tab of the Properties dialog box (as highlighted).

Geo Surface Contact

Geo surface contact objects can be applied to almost any form of contact. If the contact occurs between two convex surfaces, however, a solid contact object will produce faster analysis results than a geo surface contact object. As we stated before, a geo surface contact object works better than a solid contact object when contact occurs between flat surfaces or contact occurs over a large area between a convex surface and a concave surface. The figure illustrates one such case, where the convex surface of the upper body fits tightly within the concave surface of the lower body.

Primitive 3D Contact Objects

The two contacts described above are good choices for bodies with general surfaces. In some cases a bodies may include a contact surface that can represented with an analytical shape, such as a sphere, box, or cylinder. An example of this would be the contact between a pin and a hole. This could be efficiently modeled with a cylinder-in-cylinder contact. The Primitive3D contacts, as shown in the figure, can be used to model these analytical contacts quickly and accurately. Please note the dash symbol (“-“) in the contact names can be replaced with the word “to.” The left parentheses can be replaced with the word “in.” Therefore the contact name Sph-Sph is a short version of “Sphere-to-Sphere” and Sph(Sph) is a short version of “Sphere-in-Sphere.”

The reason that the primitive contacts are fast, smooth, and accurate is that the contact surfaces can be expressed mathematically, so the RecurDyn solver needs to consider only a few equations in order to determine the accurate contact point and calculate the contact force.

The primitive 3D shapes may be created manually in RecurDyn or they will be created for you if you have the right option turned on when you import a CAD file. The option is “Convert Primitive Geometries when importing CAD Files” and it is found in the CAD dialog box that is shown when you click on the CAD option under the pull-down menu that includes the Display setting, within the Setting group of the ribbon under the Home tab. It can be worthwhile to invest some time to arrange to have primitive geometry in your RecurDyn model so that you can take advantage of Primitive 3D contacts.

For example, with the model described in the “Solid Contact” section, you could use a sphere-to-sphere contacts and sphere-in-sphere contacts to run simulations that are at least ten times faster than when solid contacts are used.

For piston models, you could use a cylinder-in-cylinder contact object. For bearing models, you could use a sphere-in-torus contact object.

Although general contact objects can be used regardless of the shape of the object and are needed to represent complex geometry, you may want to use primitive 3D contacts when possible to obtain fast and accurate analysis results.

Basics of the Contact Algorithm

Given the potential for contact analysis to occupy most of the calculations and to affect the simulation results, it is very important to understand the basics of the contact algorithm and contact parameters.

RecurDyn contact is based on the penalty method, which is of the most common contact algorithms. There are many possible ways to implement the penalty method, and the performance and accuracy depend on the implementation. Fundamentally, the key characteristic of the penalty method is that it uses the interference between the bodies in contact to calculate the contact force.

Let’s consider the figure to the right. The bodies are in contact with each other. In reality, the material of the two bodies are not overlapped, but the bodies deform in response to the contact force.

The penalty method uses the concept of the overlapped material (‘penetration’) and the concept of ‘penetration depth’ to define the equivalent of a deformed spring to calculate the contact force. This is the basic concept of the penalty method.

The Penalty Method calculates the contact force as if there is a spring between the ‘overlapped area’ and the spring is compressed by the penetration.

In other words, if the penetration is δ, the contact force f is calculated by f = kδ. (K is one of the contact parameters, Stiffness Coefficient.)

The equation for determining the contact force is shown in the figure to the right.

There are other factors that are considered as well, as shown in the figure. The damping portion of the contact force is a function of the relative velocity between bodies and always opposes the relative motion. The damping force is also a function of the penetration.

There are three exponents that can be used to tune the contact force in order to achieve the most realistic behavior. Many RecurDyn beginners use contacts without knowing the details of the contact force calculation. But you will be able to use RecurDyn contacts and set the contact parameters successfully if you understand the contact force calculation. You can also contact MotionPort for advice on selecting contacts and setting the contact parameters.

For bodies with complex geometry, the contact surface is divided into small, flat facets that are used to identify when interferences occur and to find the location contact point for that simulation time.

Consequently, a small deviation occurs between the actual shape of the geometry and the shape that is defined by the facets. RecurDyn will automatically place more (smaller) facets in area of high curvature. You can also control the size of the facets by adjusting properties of each contact surface.

Each type of contact has a Characteristic tab in the associated Properties dialog box.

The Stiffness and Damping Coefficients for the contact perform the same functions as the Stiffness and Damping Coefficients in the Spring Force dialog box, as shown in the figure below.

The explanation in this document is to help your understanding of the Penalty method. The MotionPort website has a collection of technical papers about contact modeling at https://motionport.com/resources/technical-papers/contact-modeling. Please refer to these papers for the theoretical description of the Penalty method as well as other contact techniques.)

Example Contact Calculation

In the example image below, we consider a sequence of four cases where the penetration increases until the external force and the contact force (f = kδ) reach equilibrium. Note that units are not specified for simplicity.

Case #1 – The weight of the upper box applies a force of 30, but there is no contact force because there is no penetration (δ=0). Consequently, the upper box moves downward.

Case #2 – There is penetration, δ=1, so a contact force of 10 occurs, but since the weight of the upper box (30) > 10, the box continues to move downward.

Case #3 – Since 30 > 20, so the box continues to move downward.

Case #4 Finally at a penetration of 3 the force equilibrium is achieved (30 = 30).

Note that the example values of δ are quite large in this example. This was done to help you visualize the contact calculation. However, with real models the value of δ is typically quite small.

Since the contact force f = kδ, if you set K (stiffness coefficient) too small, δ must be very big to achieve the force equilibrium. In fact, penetration (δ) is an artificial value so very small δ is reasonable. Therefore, it is good to use a big enough value for K. For example, the default K of the RecurDyn Geo Surface Contact and Solid Contact is 100,000 N/mm.)

In the below example, a box whose mass is 1Kg is put on a big box. In this case, the contact force is calculated to be approximately 10N (assuming that the gravitational acceleration is approximately 10m/s^2) and the penetration is 0.0001 mm when K = 100,000 N/mm.

If K is too big, since f = kδ, a small change of the penetration (δ) affects the magnitude of the contact force drastically. If the contact force changes a lot, it can make the RecurDyn solver unstable. High stiffness coefficients can result in high frequency vibrations in the system. Therefore, it is very important to use the appropriate K for each situation. In summary, if K is too small excessive penetration occurs and the result becomes inaccurate. But if K is too big, the large force variation affects the solver stability. When tuning the stiffness coefficient it is best to adjust the value higher or lower by no more that a faction of ten with each adjustment.

Example Contact Cases

Case #1:

In this figure, let’s assume that the blue (small) box is very heavy. The mass is 100 kg, and the downward force is approximately 1000 N)
– If K = 10N/mm, δ must be 100 mm to achieve a force equilibrium (when the contact force = 1000N).
– If the height of the red box is 10mm, δ cannot be 100mm. So, in this model the blue box will fall down through the red box because the force equilibrium is not achieved.

Solution #1:

Sometimes there is excessive penetration between the two bodies. Please remember that this is usually caused by too big external force or too small K. If you want to reduce the penetration, increase K. If you can predict the magnitude of the contact force, you can estimate the minimum K for the simulation (the appropriate K). For example, if you set K = 100,000 N/mm, then the force equilibrium can be achieved when δ=0.01mm.)

Case #2:

Numerical analysis uses the discrete time steps for the calculation. Therefore, when the time step is big (as in the figure) and the relative velocity between bodies is significant, contact may not occur between 2 bodies at the starting time step and then the 2 bodies can overlap excessively at the next time step. In the below model, at the first time step (t0), δ = 0, so only gravity is applied to the upper box and it moves downward.

If δ becomes 15 at t1, the upward force (contact force) becomes 150 and the downward force (gravity) is still 30. The net force becomes an upward force of 120 (150 – 30). As a result, the upper box can suddenly bounce upward because of the abrupt upward force that is applied to the upper box.

Solution #2:

To avoid this kind of trouble, you should use the sufficiently small time step size to prevent the sudden large penetration. You can use the RecurDyn solver parameter, Maximum Time Step to ensure a small time step. The experienced users can use Maximum Stepsize Factor in the Contact parameter dialog instead. This parameter uses a smaller time step when the contact between 2 bodies is active.

For example, consider a Maximum Stepsize Factor = 10 in the below (right-side) dialog. When 2 bodies are about to be contacted (as they approach each other), RecurDyn solver reduces the time step by a factor of 10 to prevent the excessive penetration by the sudden collision.

Case #3:

This case is similar to Case #1, where it is possible that the upper body just falls through the lower body instead of bouncing off.

This kind of result may be caused by the Maximum Penetration in the Contact parameter dialog. This parameter means that if the real penetration is bigger than this ‘Maximum Penetration’, the contact force is not calculated. This is needed to prevent false contacts when one body passed around and behind the other body.

In this case, if the Maximum Penetration is set to 5, since δ = 15 at t1, the contact force becomes 0 because 15 > 5. As a result, only the downward force (30) is applied to the upper box, and the upper box continues to fall down.

Solution #3:

The solution is also similar to the Solution #2, that the time step size needs to be reduced to prevent the excessive penetration. Technically, increasing the maximum penetration can prevent this kind of problem, but it is recommended to reduce the time step size in most cases because the smaller penetration produces the better result.

Again, please remember that the MotionPort website has a collection of technical papers about contact modeling at https://motionport.com/resources/technical-papers/contact-modeling.

How to use the 2D Belt

If a belt assembly in your product undergoes primarily 2D behavior, learn a faster way to simulate it using the 2D belt option of the RecurDyn/Belt toolkit. A second benefit of this option is that long belts with thousands of segments can be solved efficiently. The commands of the 2D Belt are found within the 2D Belt group of the Belt tab.

Read More

RecurDyn and Particleworks co-simulation: Washing machine

RecurDyn and Particleworks co-simulation: Washing machine

In another article, we shared a unique application of RecurDyn and Particleworks co-simulation on a clothes styler. In this article we would like to showcase the same type of co-simulation being used to simulate both a top-loading and a front-loading washer. The co-simulation illustrates the dynamic interaction of flexible bodies (representing clothes) and the moving impeller and/or drum in RecurDyn and the fluid particles of Particleworks that represent the water and detergent.

This example demonstrates the power of doing Multiphysics simulations with RecurDyn and partner software. In this case we consider the physics of multibody dynamics, nonlinear flexible bodies, and particle-based fluids. As we provide new combinations of simulation capabilities, the ability to simulate your systems of interest become broader and more accurate.

Some of the critical engineering questions that can be answered with this type of simulation are:

1. How does the motion of the fabric change with different levels of water, quantity of clothes in the drum, or different agitator motion?
2. How does the energy consumption of the washer change with different levels of water or different agitator motion?

Below are two videos showing the co-simulation between RecurDyn and Particleworks with a top-loading washer model and a front-loading washer model.

Top-loading Washer

Front-loading Washer

Other applications of this capability could be:

1. The transport of wet or dry product in flexible containers, including during stacking,
2. Effects of fuel sloshing in flexible containers during vehicle motion,
3. Response of flexible seals in motions to internal and external fluid flows.

Can you think of other examples where an accurate simulation requires the consideration of rigid bodies, nonlinear flexible bodies (with contact), and particle-based fluids?

MotionPort plans to create additional examples of this new capability, both with Particleworks and EDEM. If you have an application of interest, please let us know.  To send your examples, please enter them on our Contact Us page.

RecurDyn V9R2 capability to include FFlex bodies in co-simulations with Particleworks

RecurDyn V9R2 capability to include FFlex bodies in co-simulations with Particleworks

In earlier versions of RecurDyn and Particleworks the fluid particles could only interact with rigid bodies. Now, RecurDyn V9R2 has the capability to include FFlex bodies in co-simulations with Particleworks. An interesting tutorial uses the example of a styler steam clothing care system to teaches how to perform a co-simulation between RecurDyn and Particleworks. The co-simulation illustrates the dynamic interaction between the shaking mechanism and the flexible bodies (representing the clothes) in RecurDyn and the fluid particles of Particleworks that represent the steam.

The styler unit, shown in the image, is used to shake off the dust attached to cloth and to remove its wrinkles with steam. It also reduces the odors and allergens in the clothing.

The tutorial analyzes the dynamic interaction between an item of clothing, which is expressed as a flexible body, and the steam, which is expressed as particles.

After the co-simulation, an analysis is made of the stress in the clothing as the particles touch the flexible body, using the Contour function of RecurDyn.

To learn more about the styler unit, perform a search on your favorite search engine using the text: “styler steam clothing care system.”

The Styler co-simulation video covers the following topics (with time stamps): Creating walls (0:30), Exporting walls (1:55), Creating steam particles (2:16), Setting fluid properties (3:26), Co-simulation (7:32), Post-processing (8:45)

Click play below to watch the video (approx. 9:38).

More examples of RecurDyn and Particleworks co-simulation in action:

RecurDyn and Particleworks co-simulation: Washing machine