S3-1 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation SECTION 3 SUSPENSION SYSTEM

S3-2 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation

S3-3 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation SPRING-DAMPER SYSTEM n Make use of differential equation elements and functions to represent a bushing failure and the degradation of shock performance in a suspension model. Also, use ADAMS/Linear to examine the model’s system modes. n What’s in this section: u STEP Function Review u Simulating an Impulsive Force u Function for a Square Wave u Tracking System Loads u Using ADAMS/Linear u Workshop 8: Suspension System

S3-4 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation STEP FUNCTION REVIEW n Definition u In MSC.ADAMS, the STEP function approximates an ideal mathematical step function without the discontinuities. u Avoid discontinuous functions because they lead to solution convergence difficulties. u The STEP function steps quantities, such as motions or forces, up and down, or on and off. Note: A STEP function is used when a value needs to be changed from one constant to another.

S3-5 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation STEP FUNCTION REVIEW (CONT.) n Syntax u STEP (q, q 1, f 1, q 2, f 2 ) where: u q - Independent variable; mainly used as independent varible, but can be any variable (other functions, etc.) u q 1 - Initial value for q u f 1 - Initial value for f u q 2 - Final value for q u f 2 - Final value for f Note: q 1 < q 2 n Example:

S3-6 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation SIMULATING AN IMPULSIVE FORCE n Following is an example of a function that will approximate an impulse (a theoretical mathematical model) with magnitude 500, duration 0.2 sec, at 2.1 seconds: n STEP(TIME, 2.0, 0.0, 2.1, +500) + STEP(TIME, 2.1, 0.0, 2.2, -500) n Here is the effect you get for the following periods in time:

S3-7 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation SIMULATING AN IMPULSIVE FORCE (CONT.) n As you can see, the impulse took 0.1 seconds to turn on ( =0.1 sec) and 0.1 seconds to turn off ( =0.1sec). You can modify this for your specific problem. Keep in mind, however, if you make it too sudden it will be harder for the integrator to solve. Sharp discontinuities will cause ADAMS/Solver to take very small time steps in order to resolve the behavior to your given error tolerance. You may also need to ask for more simulation steps if you want to see the impulse as it is happening during the simulation. n Also, an equivalent impulsive force can be achieved using a nested STEP function, like this: STEP(TIME-2.1, -0.1, 0, 0, (STEP(TIME-2.1, 0.0, 500, 0.1, 0)))

S3-8 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation SIMULATING AN IMPULSIVE FORCE (CONT.) n When dealing with short duration events, remember that you must consider the relative size of the impulse in relation to the time step. MSC.ADAMS uses a variable-time step size. If the size of time step grows larger than the impulse width, the integrator may jump over the impulse event. You can control the maximum size of the time step by using HMAX on the INTEGRATOR statement.

S3-9 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation FUNCTION FOR A SQUARE WAVE n You can use a STEP function with a sine function to create a square wave. The key lies in recognizing that the “independent variable” in the STEP function can be any valid MSC.ADAMS function expression. step(sin(2*pi*time),-0.01,-1,0.01,1) n When the value of the sine wave is positive, the STEP makes the function value +1; when the sine is negative, the STEP makes the function -1. The 0.01 values can be made smaller for sharper transitions between -1 and +1. n Enter this function in the Function Builder and use the plot button to see how it works.

S3-10 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation FUNCTION FOR A SQUARE WAVE (CONT.)

S3-11 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation TRACKING SYSTEM LOADS n MSC.ADAMS offers many functions which allow you to track loads throughout a simulation. n As a rule of thumb, for every force element that exists in the system, there is a corresponding function which will report and store that force’s value throughout the simulation. n These functions can be used within other model functions to perform a variety of modeling tasks. Examples include: u Friction modeling u Representation of failures u Output channel scaling/manipulation u Simulation control n EXAMPLE: General Force

S3-12 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation USING ADAMS/LINEAR n Overview u The LINEAR command linearizes the nonlinear system equations of motion and provides two basic capabilities: l An eigensolution l A state space matrix calculation. l The eigensolution option determines natural frequencies and mode shapes while the matrix calculation option computes the linear state space matrix that describes the mechanical system. You may issue this command following a static or a transient analysis. Depending on the options you specify, the results of the command are reported on the screen and written to the tabular output file, the results file, and, if required, the user-specified files.

S3-13 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation USING ADAMS/LINEAR (CONT.) n You can plot eigenvalues and mode shapes that ADAMS/Solver computes on a real-imaginary plot, and then animate them in MSC.ADAMS. In addition to verifying stability, eigendata is used for validating implementation of models with eigendata from other modeling approaches or experimental data. This is especially true if an elastic or control subsystem model has been implemented in ADAMS/Solver. n ADAMS/Linear outputs a state-space representation in a form suitable for importing into a matrix manipulation and control design package, such as MATRIX x and MATLAB. A state-space model representation is suitable for obtaining frequency response of the MSC.ADAMS model, verifying model control properties (ability to control and observe), and designing feedback controllers for MSC.ADAMS models. For more information, see the LINEAR command in the ADAMS/Solver online help.

S3-14 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation USING ADAMS/LINEAR (CONT.) n With ADAMS/Linear, you can compute eigenvalues and eigenvectors or export the state-space matrices that have been linearized about an operating point. n Eigenvalues/Eigenvectors

S3-15 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation USING ADAMS/LINEAR (CONT.) n State Space Matrices

S3-16 ADM703, Section 3, August 2005 Copyright  2005 MSC.Software Corporation USING ADAMS/LINEAR (CONT.) n Summary of Functionality u System-level linear modes visualization u Damping and frequency values of system modes u Model debug -- sanity check u Aids in controls modeling n Notes u ADAMS/Linear is a plugin to ADAMS/Solver and ADAMS/View. u The output is only a linearization of the system about a given point in the simulation. u Best used after equilibrium simulations or during steady state dynamics.