week-11 Joint creation and Demonstration

OBJECTIVE:

Demonstration of spherical, revolute, cylindrical and translational joints using *CONSTRAINED_JOINT keyword.

PROCEDURE:

Mechanical joint is a mechanism which is used to connect one or more mechanical parts to another. The above-mentioned joints will be discussed in the following section.

1) Spherical Joint –

The spherical joint also called a ball joint is shown in figure 1.1. The nodal points 1 and 2 should coincide in the initial configuration. It allows a limited range of smooth movement in all the directions.

Fig 1.1: Spherical joint with the nodal point as 1 and 2 [1]

Fig 1.2: Spherical joint with nodal point as 4 and 5 created in LS-DYNA

Figure 1.2 depicts the simple spherical joint created in LS-PrePost. Part 1 and part 2 are fixed and moving single shell elements. Each of the shell element is created using shape mesher option available in element and mesh utility. This can be also done by create plane option present in surface utility. These elements are created with some distance apart. These shell elements are then translated to get coinciding points (point 4 and 5) to form a joint. *MAT_RIGID material card is assigned for defining rigid material properties for both the elements. One material is constrained in x, y and z displacements and rotation setting CON1/CON2 options as 7 and the other material is not constrained. This is done because we have two parts, part 1 is fixed and part 2 is moving. Shell section is assigned for the elements with thickness value 1mm. The parts are then assigned with respective section and material properties. Figure 1.3 shows the material card assignment. A pair of a common node can also be created for two parts. *CONSTRAINED_EXTRA_NODES or *CONSTRAINED_NODAL_RIGID_BODY can be used to assign the particular node to either rigid body or deformable-body.

Fig 1.3: Material card assignment for the shell elements

Node 6 and node 7 are given a load by *LOAD_NODE_POINT keyword. Figure 1.4 shows the load curves assigned for node 6 and 7. Curve 1 is assigned to node 7 and curve 2 is assigned to node 6.

Fig 1.4: Load curves used for loading node 6 and 7

Fig 1.5: Spherical joint created by *CONSTRAINED_JOINT_SPERICAL keyword

From figure 1.5 we can see that the node 4 and 5 are selected to form a spherical joint. These node points should coincide to form a joint. Control termination card is assigned with a termination time of 0.5. Control time-step keyword is used with the load curve to limit the maximum time-step size. The assigned constant maximum time-step is 4.15e-6. Figure 1.6 depicts the output results for the spherical joint.

Fig 1.6: Output for spherical joint in LS-PrePost

2) Revolute Joint –

Fig 1.7: Revolute joint with nodes 1, 2 as one pair and 3, 4 as another pair [1]

The revolute joint also called a hinge joint has one degree of freedom. This joint has pure rotation motion along a common axis. Figure 1.7 depicts a typical revolute joint with two nodal pairs formed by nodes 1, 2 and 3, 4. The nodal points 1 and 2 should coincide in the initial configuration, similarly, node 3 and 4 should satisfy this condition.

Fig 1.8: Revolute joint with nodes 3, 5 forming one pair and 4, 6 as another pair created in LS-DYNA

Figure 1.8 depicts the created revolute joint in LS-Prepost. The two parts are generated similarly as discussed for spherical joint, using shape mesher option available in element and mesh utility. This can be also done by create plane option present in surface utility. These elements are created with some distance apart. *MAT_RIGID material card is assigned for defining rigid material properties for both the elements. The material card assignment is similar to the revolute joint discussed above. One material is constrained in x, y and z displacements and rotation setting CON1/CON2 options as 7 and the other material is not constrained. This is done because we have two parts, part 1 is moving and part 2 is fixed. Shell section is assigned for the elements with thickness value 1mm. The parts are then assigned with respective section and material properties. The axis of rotation for this model is Y-axis. A point load is assigned to node 1 and 2 with *LOAD_NODE_POINT keyword. A constant load of 1 unit is given through the load curve definition.

Fig 1.9: Load curve assigned for applying point load on node 1 and 2

Fig 1.10: Local coordinate system defined by *DEFINE_COORDINATE_NODES

The local coordinate system is required to define generalize joint stiffness further. The coordinate system is defined with three nodes with first node (5) as local origin, the second node (7) located along the x-axis and third node (6) in the local XY plane. Joint stiffness generalized keyword is used to define joint stiffness.

Fig 1.11: Revolute joint created by *CONSTRAINED_JOINT_REVOLUTE keyword

Figure 1.11 depicts the keyword used to create the revolute joint. Two pairs of nodes as discussed above are considered to generate the joint. The nodes in the node pair 3, 4 and 4, 6 coincide with each other. Termination time assigned for this analysis is 0.02. Control time-step keyword is used with the load curve to limit the maximum time-step size. The assigned constant maximum time-step is 4.15e-6. Figure 1.12 depicts the post-processing result for a revolute joint.

Fig 1.12: Output for spherical joint in LS-PrePost

3) Cylindrical Joint –

Fig 1.13: Cylindrical joint with nodes 1, 2 as one pair and 3, 4 as another pair [1]

The cylindrical joint has two degrees of freedom, it can rotate about a single axis and translate along the single axis as well. Figure 1.13 shows the sketch of a cylindrical joint. Nodes 1, 2 and 3, 4 forms a pair and these nodes in a pair should coincide with each other. The inner cylinder can rotate about x and translate along the x-axis.

Fig 1.14: Cylindrical joint with nodes 10001, 10002 forming one pair and 10003, 10004 as another pair created in LS-DYNA

Figure 1.14 shows the created cylindrical joint in LS-PrePost. The axis of rotation and translation is the x-axis. Nodes from the nodal pair 10001, 10002 and 10003, 10004 coincide with each other. Here like previous examples these nodes are not a part or body but are located outside the respective bodies. These extra nodes are created by the element tool>Node editing option. So, a node-set is created where node 10001 and 10003 are grouped to fixed body and node 10002 and 10004 are grouped to a moving body. Further nodes of moving and fixed bodies are assigned to particular part by using *CONSTRAINED_EXTRA_NODES_SET. Figure 1.15 shows the constrained extra node assignment.

Fig 1.15: Respective nodes constrained to fixed and moving parts by using *CONSTRAINED_EXTRA_NODES_SET

Fig 1.16: Cylindrical joint created by *CONSTRAINED_JOINT_CYLINDRICAL keyword

Figure 1.16 depicts the nodes assigned to form a cylindrical joint. Node 10001 and 10003 belong to a fixed part that is the outer cylinder whereas nodes 10002 and 10004 belong to the moving part, the outer cylinder. Initial rotational velocity is given to the inner cylinder by using *INITIAL_VELOCITY_RIGID_BODY keyword. Figure 1.17 shows the rotational velocity assignment procedure.

Fig 1.17: Rotational velocity assigned to the inner cylinder

Figure 1.18, depicts the output in LS-PrePost. Termination time assigned for this analysis is 0.1. Control time-step keyword is used with the load curve to limit the maximum time-step size. The assigned constant maximum time-step is 4.15e-6. The inner cylinder rotates about x-axis while the outer cylinder is fixed.

Fig 1.18: Output for Cylindrical joint in LS-PrePost

4) Translational Joint –

Fig 1.19: Translational joint with nodes 1, 2 as one pair, 3, 4 as second pair and 5, 6 as third pair [1]

The translational joint allows a part to translate along one direction with respect to another part. It can only translate and cannot rotate. So, basically it has only one translational degree of freedom and zero rotational degree of freedom. The nodes in the nodal pair (1,2), (3,4) and (5,6) should coincide. Figure 1.20 depicts the geometry and the extra nodes generated to create the translational joint. The geometry has been designed in LS-PrePost by using Element and mesh>ShapeMesher>Box shell option. The opposite faces of the box are deleted at the end. The nodes of node pairs (1001,1002), (1003,1004) and (1005,1006) coincide respectively. The inner part has an X translational degree of freedom.

Fig 1.20: Translational joint with nodes 1001, 1002 forming one pair, 1003, 1004 as second pair and 1005, 1006 as the third pair created in LS-DYNA

Nodes 1001, 1003 and 1005 are referred to moving part which is the inner box. Nodes 1002, 1004 and 1006 are referred to the fixed part which is the outer box. This is done by creating a node-set ID and these nodes are constrained to respective parts by using *CONSTARINED_EXTRA_NODES_SET. This is done similar to the cylindrical joint. Figure 1.21 depicts the keyword definition for creating the translational joint.

Fig 1.21: Translational joint created by *CONSTRAINED_JOINT_TRANSLATIONAL keyword

The inner box is given displacement in the x-direction. The motion is defined by a load curve. Figure 1.22 shows the *BOUNDARY_PRESCRIBED_MOTION_RIGID card assignment used for defining displacement.

Fig 1.22: Displacement defined in the x-direction for the inner box

All the other setting are kept similar to other case setups. Termination time of 0.1 unit is defined. A Control time-step keyword is used with the load curve to limit the maximum time-step size. The assigned constant maximum time-step is 4.15e-6.

(a)

(b)

Fig 1.23: Output for Translational joint in LS-PrePost, (a) inner box translated along the x-direction, (b) the nodes in nodal pairs displaced apart after translation

CONCLUSION:

All the given joints, spherical, revolute, cylindrical, and translational have been demonstrated. Geometries for all the joints have been created in LS-PrePost and simulated with LS-DYNA software.

Reference:

[1] - LS-DYNA manuals, https://www.dynasupport.com/manuals