CREATION AND DEMONSTRATION OF JOINTS USING LS-DYNA

Objective:

To create various types of mechanical joints like revolute joint,spherical joint,cylindrical joint and translation joint using LS-DYNA.

Also to demonstrate their working mechanisms.

Mechanism:

Mechanism is a collection of bodies (links) that may be interconnected by joints to constrain their relative motions. They form a mechanical system with one body fixed, with the purpose of altering a given input motion to produce a different output motion.

The basic components of a mechanism can be characterized as follows:

• Body (link):

A mechanical body is a physical component that usually is considered rigid.

Its primary function is to hold fixed geometric relationships between its joint elements.

Links can be subdivided into categories depending on the number of joints incident with that link.

• Constraint (joints):

A joint is defined as a connection between two links. The primary kinematic function of a joint is to constrain the relative motions allowed between the connected bodies.

Because a joint connects two mechanical bodies, the joint is not a separate physical entity in itself, but the interface composed of the contact surfaces on the two connected bodies.

The two contact surfaces, when considered separately, are each referred to as a joint element and, when joined together, the surface of contact physically adds some constraint(s) to the relative motion between two links.

Revolute joint:

A revolute joint only allows rotation, between the paired elements, around a joint axis defined by the geometry.

The revolute joint has only one degree of freedom (DOF) and the joint variable is the relative rotation (Δθ) between the joint elements.

To create a revolute joint in LS-DYNA, we use two shell parts created from '4N shell' of shape mesher option, in which one of them is going to be fixed and other one would be in motion.

The shell in motion is modelled with rigid material MAT_20 and the fixed shell part is modelled with deformable material model.

A revolute joint is created between the two parts using the card *CONSTRAINED_JOINT_REVOLUTE by picking up the appropriate nodes of the parts that are coincident with each other.

A load curve LCID is defined to impose rotational displacement to the moving shell part.

Using *PRESCRIBED_MOTION_RIGID card, the rotational DOF and the created LCID are defined accordingly.

The simulation is finally defined with a suitable termination time and timestep using *CONTROL_TERMINATION and *CONTROL_TIMESTEP cards respectively.

The animation of the revolute joint simulation is obtained from the generated binary d3plot file.

Spherical joint:

A spherical joint is equivalent to three revolute joints intersecting at a central point and allows one element to rotate freely with respect to the other.

Hence, the spherical joint has three DOFs and the joint variables may be chosen as three angles Δθ, Δθ′, and Δθ′′.

To create a spherical joint in LS-DYNA, we use two spherical shells created from 'sphere shell' of shape mesher option in which one of them is going to be fixed and other one would be in motion.

The fixed sphere is cut half to demonstrate the spherical joint mechanism.

The spheres are modelled with rigid material MAT_20 and shell section.

Extra nodes are created at the centres of the shells to deploy the axis of rotational movement of joint using *CONSTRAINED_EXTRA_NODES card and they are included into the rigid constrained part.

A spherical joint is created between the two spheres using the card *CONSTRAINED_JOINT_SPHERICAL by picking up the centre nodes of the spheres that are coincident with each other.

A load curve LCID is defined to impose rotational displacement to the rotating sphere.

Using *PRESCRIBED_MOTION_RIGID card, the rotational DOF and the created LCID are defined accordingly.

The simulation is finally defined with a suitable termination time and timestep using *CONTROL_TERMINATION and *CONTROL_TIMESTEP cards respectively.

The animation of the spherical joint simulation is obtained from the generated binary d3plot file.

Translational joint:

A translational joint only allows relative axial translation, of the paired elements with respect to each other, defined by the geometry of the joint.

This type of joint has one DOF, and the joint variable is the relative axial translation (Δs) between the joint elements.

The translational joint is also known as 'prismatic joint'.

To create a translational joint in LS-DYNA, we use two shell boxes created from 'box shell' of shape mesher option in which one of them is going to be fixed and other one would be in motion.

The boxes are modelled with rigid material MAT_20 and shell section.

Extra nodes are created at the centres of the shells to deploy the axis of translational movement of joint using *CONSTRAINED_EXTRA_NODES card and they are included into the rigid constrained part.

A translational joint is created between the two boxes using the card *CONSTRAINED_JOINT_TRANSLATIONAL by picking up the centre nodes of the cylinders that are coincident with each other.

A load curve LCID is defined to impose rotational displacement to the rotating sphere.

Using *PRESCRIBED_MOTION_RIGID card, the rotational and translational DOFs, and the created LCID are defined accordingly.

The simulation is finally defined with a suitable termination time and timestep using *CONTROL_TERMINATION and *CONTROL_TIMESTEP cards respectively.

The animation of the translational joint simulation is obtained from the generated binary d3plot file.

Cylindrical joint:

A cylindrical joint is equivalent to a revolute joint in series with a prismatic joint with coaxial joint axes.

It permits rotation about, and independent translation along, the joint axis defined by the geometry of the joint.

Therefore, the cylindrical joint is a two DOFs joint and Δθ and Δs are both joint variables.

To create a cylindrical joint in LS-DYNA, we use two cylindrical shells created from 'cylinder shell' of shape mesher option in which one of them is going to be fixed and other one would be in motion.

The cylinders are modelled with rigid material MAT_20 and shell section.

Extra nodes are created at the centres of the shells to deploy the axis of translational and rotational movement of joint using *CONSTRAINED_EXTRA_NODES card and they are included into the rigid constrained part.

A cylindrical joint is created between the two shells using the card *CONSTRAINED_JOINT_CYLINDRICAL by picking up the centre nodes of the cylinders that are coincident with each other.

A load curve LCID is defined to impose rotational displacement to the rotating sphere.

Using *PRESCRIBED_MOTION_RIGID card, the rotational and translational DOFs, and the created LCID are defined accordingly.

The simulation is finally defined with a suitable termination time and timestep using *CONTROL_TERMINATION and *CONTROL_TIMESTEP cards respectively.

The animation of the cylindrical joint simulation is obtained from the generated binary d3plot file.

Conclusion:

Thus, various kinematic joints are created and their mechanisms have been demonstrated successfully.

However, there are options to input elastic stiffness and frictional moment coefficients for the joints and calculate their joint forces developed using *CONSTRAINED_STIFFNESS_GENERALIZED card in LS-DYNA.