Automotive Trunk Lid Mechanism with Modified BISTOP Function and Motion Curve

Introduction:

Mechanism and Machine: A mechanism is a constrained kinematic chain. This means that the motion of any one link in the kinematic chain will give a definite and predictable motion relative to each of the others. Usually, one of the links of the kinematic chain is fixed in a mechanism. Whereas a  machine is a combination of rigid or resistant bodies, formed and connected so that they move with definite relative motions and transmit force from the source of power to the resistance to be overcome. A machine has two functions: transmitting definite relative motion and transmitting force. These functions require strength and rigidity to transmit the forces. Though all machines are mechanisms, all mechanisms are not machines.

Links, Frames and Kinematic chain:

A link is defined as a rigid body having two or more pairing elements which connect it to other bodies for the purpose of transmitting force or motion. In every machine, at least one link either occupies a fixed position relative to the earth or carries the machine as a whole along with it during motion. This link is the frame of the machine and is called the fixed link. The combination of links and pairs without a fixed link is not a mechanism but a kinematic chain.

Pairs, Lower Pairs and Higher Pairs:

A pair is a joint between the surfaces of two rigid bodies that keeps them in contact and relatively movable. Generally, there are two kinds of pairs in mechanisms, lower pairs and higher pairs. What differentiates them is the type of contact between the two bodies of the pair. Surface-contact pairs are called lower pairs. The point, line, or curve-contact pairs are called higher pairs. 

 In order to simulate the motion of an automobile trunk lid, it is necessary to build a four-bar mechanism where one link is fixed to the ground body and the other three links coupler, follower and input link are used to simulate the motion of an automobile trunk lid. The trunk lid is simulated by using the mechanism as shown below:

 It is necessary to create follower, coupler and input link in Altair's MotionView before importing the Body-In-White structure of the automobile.

1) Firstly, it is necessary to build a follower link which is a cylinder of radius 2mm between the points Point A (921, 580, 1124) and Point C (921, 580, 1104). 

2) In a four-bar mechanism, the coupler is attached to the endpoint of the follower. The coupler can be created with point E and F of coordinates Point E (878, 580, 1108) and Point F (878, 580, 1118). 

3) Using the Macros point feature in Motion solve, three points were created. One point (point 4) in between E and F along the vector and similarly another point (point B) in between A and C along the vector, Point 3 in between C and E along the vector. The created new points are equidistant from the other two points.

 4) Next, it is necessary to add bodies with mass and inertial properties at the newly created points through Macros command. The bodies were assigned to mass and inertial properties. Geometries (cylinders) are created.

5) Since the created individual bodies are not connected to each other and also in order to reduce the degrees of freedom of these bodies and make it a single body they should interlink with joints. A revolute joint will reduce 3 translational and 2 translational degrees of freedom of every individual body. 4 revolute joints are created between three newly created bodies and ground body along the global y-axis. Now the total degrees of freedom becomes 3. It means out of 18 degrees of freedom 15 degrees of freedom has been restrained. In order to remove the redundant constraints, the revolute joint is replaced by an 'inline joint' and thus the total number of redundant constraints becomes zero. And finally, the analysis becomes a kinematic simulation.

6) The next step is to create the input link as mentioned before, which is used to open and close the trunk lid. Three main points namely points G (830,580,1080), H(790, 580, 1088) and I(825,580,1109) are created and their corresponding cylinders were also created. Next, the Centre of Mass of the while input link (Body 1) which is previously at point 3 is shifted to point G as shown in the figure below. 

7)The input link is not associated with any kind of Joint / Motions. So it is necessary to import a motion curve which helps the input link to open and close the imported Trunk lid. In MotionView the imported Curves have the following features. 

Forces: nonlinear characteristics for the forces, e.g., spring force vs. deformation characteristic or a damping force vs. deformation velocity

Motions: displacements vs. time, velocity vs. time, and/or acceleration vs. time data.

Constraints: constraint paths for high-pair joint types (e.g., curve-to-curve joint)

8) A Motion curve file in excel(.csv) format is imported into the MotionView. This file contains two columns. The first column was assigned to the x-axis and the second column was assigned to the       y-axis. his completes the mechanism and is ready for simulation to test before importing the Trunk lid CAD model.

9) After creating the mechanism for the trunk lid, the BIW structure of the car was imported into MotionView. The trunk lid and the body of the car were provided as .hm files which were imported using the 'Import CAD or FE Using Hypermesh' feature. There are two ways by which the models can be imported.

`dot` Import each component of the geometry as an individual part with the centre of mass and                   inertias

`dot` Import the geometry without mass and inertia

Since the mass and inertial properties of the system are not of concern, the second option was selected. The student version of Altair does not support 'Allow Hypermesh to specify mesh options' feature and thus for that reason when the CAD file is imported, the Hypermesh window gets opened. To continue as usual 'Save and quit' would take back to MotionView. 

10) The automobile trunk lid was imported and the newly created four-bar input link is then attached to it. Later the BIW structure is also imported and it is connected to the ground body. Notice how the graphic cylinder is no longer visible after importing.

 11) The displacement motion which was initially added to the POINT F was replaced with the imported motion curve.

• Since the data in a curve is at discrete points, a function must be used to interpolate and/or extrapolate the data for times when there is no direct data point available in the curve.
• Interpolation can be done either using the AKIMA (AKISPL) , CUBIC (CUBSPL), or QUINTIC (QUISPL) interpolation method. These functions are supported in the MotionSolve expression language.
• The AKIMA fitting algorithm uses local methods to calculate the spline coefficients. No matrices are ever inverted. For this reason, it is preferred when the reference spline has many data points.

12) An output to measure the displacement of the input link with respect to the ground body was then added.

13) DX function computes the X-component of the relative translational displacement of marker I with respect to marker J, as resolved in the coordinate system of marker K. the Syntax is: DX (I,J,K)

I : marker whose displacement is to be computed.

J : marker with respect to which the displacement is to be computed.

K : resultant displacement vector is resolved in the coordinate system of the K marker. This argument is optional. If omitted, it defaults to the ground coordinate system.

In order to find the displacement of the ground body with respect to the input link was to be measured by using the following syntax: DX({B_Ground.cm.idstring},{b_1.cm.idstring})

14) This completes the model building for the trunk lid which was simulated in MotionView. As it can be observed that the trunk lid does not stop even if it starts hitting the BIW structure which is not at all acceptable. 

HyperView Collision Detection Algorithm 

• HyperView allows to view and detect collisions between the graphic objects of the current animation model during simulations.
• To access this panel, click on the Collision Detection button on the Tools toolbar, or select Collision Detection from the Tools menu.

• Option Highlights:

1.Collision Sets:

• The collision sets defined for the current model are listed in the Collision Sets list. A collision set is activated, or deactivated, using the radio button.
• Activating the Clear Collision Detection option clears the contour for the collision detection results, and deactivates all of the collision sets listed.
• Each collision set is defined by two groups, A and B. A group can contain more than one component.

 2. Selection:

• The Components input collector allows selecting the components that are required to add to the existing groups.
• Once the components are selected, click the appropriate Add to Group button to add the component to a specific group.

3.Proximity:

• Check Enable proximity checking to allow the objects to be detected at the distance specified in the Minimum Distance field.
• If Enable proximity checking is unchecked, the objects will collide at their actual collision point and will be displayed in the colour red.

4.Animation Event:

• Ignore Collisions: Continuos animation, which ignores the collision point. Under this option the results can be displayed either by elements or by components. When elements is selected, only those specific parts which are colliding are highlighted in red whereas the components option highlights the entire BIW structure of the automobile.
• Stop on Collision: Animation stops when a collision is detected.
• Stop on Proximity Violation: Animation stops when a defined proximity violation is detected.

The simulation of the motion of the trunk lid along with the three modes of collision detection are better described in the 3 videos below:

Ignore Collisions:

 Stop on Collision:

 Stop on Proximity Violation:

 15) However, the stop on collision option is not a very effective way of stopping the trunk lid motion. Instead, the BISTOP function or the Motion curve that was defined at the input link's mechanism needs to be modified. 

16) An alternative way to stop the trunk lid would be by modifying the motion curve that controls the movement of the input link. The curve that was provided had a negative peak too. If the negative values in the .csv file were made to zero then the trunk lid stops moving forward from that point onwards. The original curve and the .csv file are shown below

 17) After modifying the above curve's displacement values the negative peaks in the curve are now eliminated and the trunk lid stops exactly when it hits the BIW structure of the car.

The displacement of the input link with respect to ground body was measured as an output using the DX function.

Displacement of the Input Link With the Modified Motion Curve: The output of the DX function resembles the characteristics of the imported MotionCurve can be seen below when the negative displacements were eliminated, the DX curve flattens out.

BISTOP Function: 

The BISTOP function models a gap element. It can be used to model forces acting on a body while moving in the gap between two boundary surfaces. This can be used to limit the motion of a joint.

Syntax - Bistop`(x,dotx,x_1,x_2,k,e,c,d)`

The BISTOP function models a gap element. It can be used to model forces acting on a body while moving in the gap between two boundary surfaces. This can be used to limit the motion of a joint.

`x`- independent variable

`dotx` - The derivative of the independent variable

`x_1` - The lower bound of x

`x_2` - The upper bound of x

`k` – Stiffness of the boundary surface interaction

`e` – Exponent of the force deformation characteristic

`c`– Maximum damping coefficient

`d` – Penetration

The AZ and WZ functions are used as the independent varable and the derivative of the independent variable respectively within BISTOP function. The AZ and WZ measure the rotational displacement and velocity, respectively of a marker “I” with respect to the marker, “J”.

• AZ(I, J)

  I - The marker whose rotational displacement is to be computed

  J - The marker with respect to which the velocity is to be computed

• WZ(I, J, K)

  K - The resultant velocity vector is resolved in the coordinate system of the K marker

18) Modifying the BISTOP Function: The BISTOP function is added by clicking on the force icon from the client-specific toolbar. The force properties were specified as 'Rotational`and`Action- Reaction'. The action force would act on the 'Coupler' and the reaction force would act on the 'Ground Body'. The force was applied at the 'point A'. Under the Rotational properties tab, the expression was defined in the 'Ty' column since all the joints are aligned by the Global Y-axis. The syntax for the BISTOP curve used was:

BISTOP(AZ({j_0.joint_i.idstring},{j_0.joint_j.idstring}),WZ({j_0.joint_i.idstring},{j_0.joint_j.idstring}),-10*PI/180,10*PI/180,1e4,2,100,0.1)

 It can be seen that unlike the previous simulation where the trunk lid would continue moving below, in this case, the trunk lid now stops as soon as it strikes the BIW structure of the automobile.

All required Session files and Model files can be found here

https://drive.google.com/open?id=1eGIiZq0m7-n524kKG6hkiWNCF59wmnYl