Using Adams/Solver - MD Adams 2010

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<p>1 About Adams/SolverAbout Adams/SolverAdams/SolverConventions2ConventionsThroughout the help, the following type styles are used as visual cues.Style: Indicates:Name A string that is a legal name for use in interface products. The following criteria must be met in order for a legal string to be defined: The name may only contain alpha numeric characters (upper and lower case). No white space in the name. No special characters in the name (e.g. @#$%^&amp;*). The exception to this rule is the underscore '_' character. Names must begin with an alpha character or an underscore. (e.g. 4bar is not legal, while _4bar is legal). x Arguments in Adams subroutines and functionsi Parameters that follow a statement, command, or argument:i = Integerr = Realc= Character string (alphanumeric)e = Function expressionv =Varying type (integer, real, or alphanumeric)id =Identifierx,y,z =Cartesian coordinate (real)a,b,c =Angular coordinate (real)PART Minimum abbreviations of statements, commands, and arguments{ } Selection you can make from a series of items[ ] Optional selection you can make from a series of items[[ ]] Combined selection you can make from a series of itemsA Two-dimensional matricesa One-dimensional matricesVectorsUnit vectorsR1x3 About Adams/SolverConventionsBest PracticesThis section contains general tips on advanced modeling with Adams/Solver. Discontinuities Units Dummy Parts Joints Motions Forces Contacts Subroutines Simulation/Integrators Debugging Miscellaneous Tips Discontinuities Discontinuities are the root cause of most simulation problems. Avoid them. Examples of discontinuous functions: MIN, MAX, DIM, MOD, IF. Discontinuous displacements and velocities cause corrector and integrator failures. Discontinuous accelerations cause integration failures (requires infinite force). Discontinuous forces cause corrector failures.Units Widely separated magnitudes in a matrix can cause numeric difficulties (conditioning problems). Be careful when using inconsistent units. Choose units so that model states (displacements and velocities) are reasonable values. For example, choosing "mm" for displacements of a rocket which travels thousands of kilometers is a poor choice. Choose units so that stiffness values are not very large. Choose time units appropriate to the phenomena being studied.Dummy Parts A dummy part is any part with zero or very small mass. Sometimes dummy parts are useful; but generally, avoid using them.Adams/SolverConventions4 Avoid connecting dummy parts with compliant connections (BEAMs, BUSHINGs, and so on). If the mass of the dummy part = 0, then the acceleration, a = F/m = F/0 = infinite. Even if the mass is very small, a = F/m = very large number. Therefore, small masses/moments of inertia introduce high frequencies into the system, which is usually undesirable since it has detrimental effects on the solver. If you must use dummy parts, then constrain all DOF, since with no DOF for the dummy part, a=F/m is not an issue. Dummy parts should be massless; 0.0 (or unassigned), not 1e-20.Joints Avoid using FIXED joints. A FIXED joint adds equations to your system that arent necessary when two or more parts can be combined or merged into a single part. Avoid using many FIXED joints to lock parts to ground. Enormous torques may develop due to large moment arms. If you must lock something to ground with a FIXED joint, consider assigning it a very large mass/inertia so that it can behave like ground, or consider merging it to ground (for more information, see Knowledge Base Article 7902). When possible, create a FIXED joint at the center-of-mass (cm) of the lightest part, to minimize the reaction forces/torques. Avoid redundant constraints. Adams eliminates them by looking at pivots in a constraint Jacobian, which are in no particular order. As a result, the physical meaning may be disregarded.Motions Ideally, motions should impose continuous accelerations. Avoid using splines in a motion (function based on time is ideal). If you must use splines as motion, use their velocity form (see Knowledge Base Article 9752 for more information). This is true for both GSTIFF and SI2_GSTIFF integrators. Avoid using motion as a function of variables (that is, states). In general, cubic splines (CUBSPL) may work better on motions than the Akima. The derivatives of the cubic are better than those of the Akima, so theyre more useful in forces than in motions (see Knowledge Base Article 7534 for more information).Forces If using data, approximate forces with smooth, continuous splines. Dont define a spring damper with spring length=0. Make sure velocities are correct in force expressions. For example, in this damping function:-c*vx(i,j,j ) the 4th term is missing --^5 About Adams/SolverConventionsThe 4th term defines the reference frame in which the time derivatives are taken, and this may be important.Contacts Contacts should penetrate before statics. Models with impacts should have slight penetration in model position when doing statics. All tires should penetrate the road. Models with tires should have slight penetration in model position when doing statics. For example, if only rear tires penetrate, the static position could be a handstand. Contact properties are model dependent. See the CONTACT statement, and Knowledge Base Article 10170 for a starting point. Adjustment of the properties to match experimental results is expected.Subroutines If possible, use an Adams function over a subroutine. If you receive errors in your model, eliminate user subroutines so theyre not the source of the errors. Verify that your compiler is compatible with the current version of Adams.Simulation/Integrators Perform initial static first, when applicable. Note that a static solution may be more difficult to find than a dynamic solution. If you care only about the dynamic solution and cannot find static equilibrium, then either increase your error tolerance or forget about the static simulation. 15-20 static iterations is suspect. If GSTIFF won't start, its most likely a problem with initial conditions. Don't let the integrator step over important events. Short duration events like an impulse can be captured by setting maximum time step, HMAX, to value less than impulse width. Use HMAX so that Adams/Solver acts as a fixed-step integrator. Spikes in results output may come from changes in step size. Reduce HMAX or try setting HINIT=HMAX. Run with SI2 instead. Adams/Solver uses a body 3-1-3 rotation sequence (psi, theta, phi). Theta=0d (or 180d) is bad (Euler singularity). If the z-axis of part cm is parallel to z-axis of ground, there will be a Euler singularity. For Euler Singularities, Theta=90D will have good pivots. Models will run better, and won't act like there is a discontinuity. Truncation (or round-off) errors accumulate when you let MAXIT go larger than 6. The theory of GSTIFF says 2-3 iterations is desirable; it breaks down if it uses more than 4 or 5.Debugging Try to understand mechanism from a physical standpoint.Adams/SolverConventions6 Use building blocks of concepts that worked in the past. Add enhancements to the model using crawl-walk-run approach. Test with a small model to isolate problems. Have graphics for visualizing motion. Look at damping terms as a source of errors. Incorrect sign and missing terms are typical mistakes. Turn on DEBUG/EPRINT. Turn gravity off, since it can accentuate modeling errors. Models should have no warnings during simulation (for example, redundant constraints, splines, and so on). Understand numerical methods (for example, understand your integrator). Look for results which become very large in magnitude; this could indicate a discontinuity.Miscellaneous Tips Avoid very large numbers and very small numbers. Be wary when your model contains numbers like 1e+23 or 1e-20. Choose the right set of units. Length units of millimeters may not be appropriate if youre modeling an aircraft landing on runway. Use a reasonable time scale. If duration of dynamic event time is short, consider using milliseconds units. Extend the range of spline data beyond the range of need. Dont write function expressions that can potentially divide by zero (for example, use the MAX function to prevent this: function =8/MAX(0.01,your_function). Add damping so frequencies can dissipate. Avoid very high damping rates. The high damping cause a rapid decay in response, which is difficult for an integrator to follow. Avoid toggles, dual solutions, or bifurcations. Dont use 1.0 for the exponent in IMPACT or BISTOP functions. This creates a corner (that is, a non-smooth function). Instead, try 2.2 for the exponent.Additional PublicationsYou might find it helpful to refer to the following resources when modeling mechanical systems.7 About Adams/SolverConventionsRecommended Publications:To learn about: See:Akima Method Akima, Hiroshi. A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures. Journal of the Association for Computing Machinery, Vol. 17, No. 4, pp. 589-602, New York: JACM, October, 1970.BDF Integration Algorithm Brayton, R. K., F. G. Gustavson, and G. D. Hatchel. A New Efficient Algorithm for Solving Differential-Algebraic Systems using Implicit Backward Differentiation Formulas. Proceedings of the IEEE, Vol. 60, No. 1, pp. 98-108. New York: Institute of Electrical and Electronics Engineers, 1972.Chebyshev Polynomial Carnahan, B., H.A. Luther, and J.O. Wilkes. Applied Numerical Methods. New York: John Wiley &amp; Sons, 1969.Cubic Curve Fitting Method Forsythe, G.E., M.A. Malcolm, and C.B. Moler. Computer Methods for Mathematical Computations. Englewood: Prentice-Hall, Inc., 1977.DASSL Computer Code Gear, W.C. Numerical Initial Value Problems in Ordinary Differential Equations. Englewood Cliffs: Prentice-Hall. 1971; and Brenan, K.E., S.L. Campbell, and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. New York: Elsevier Science, 1989.Gear Stiff Gear, W.C. Simultaneous Numerical solution of Differential-algebraic Equations. IEEE Transactions on Circuit Theory, Vol. CT-18, No. 1, pp. 89-95. New York: Institute of Electrical and Electronics Engineers, 1971.Numerical Stiffness Wielenga, T. The Effect of Numerical Stiffness on Mechanism Simulation. Proceedings from the 1986 International Computers in Engineering Conference, Vol. 1, pp. 369-378. New York: American Society of Mechanical Engineers, 1986.Rotational Coordinates Kane, T.R., P.W. Likins, and D.A. Levinson. Spacecraft Dynamics. Edited by D.D. Heibert and M. Eichberg, New York: McGraw-Hill Book Company, 1983.Standard Beam Stiffness Matrix Przemieniecki, J. S. Theory of Matrix Structural Analysis, p. 79. New York: McGraw-Hill, 1968.Timoshenko Beams Oden, J. T., and E. A. Ripperger. Mechanics of Elastic Structures, Second Edition, p. 351. New York: McGraw-Hill, 1981.Vehicle Technology Vehicle Dynamics Terminology, SAEJ670e. Warrendale, PA: Society of Automotive Engineers, Inc., 1978.Adams/SolverConventions8Adams/Solver GlossaryThis glossary defines terms that may be unfamiliar to you or that have meanings peculiar to the Adams/Solver documentation. The terms are listed alphabetically.AAction-Only ForceA force that has one point of action and has no points of reaction.Action-Reaction ForceA force that causes equal and opposite forces at its points of attachment BBase FrameA reference frame with respect to which you position and orient another reference frame. For example, if you define the position and orientation of a marker with respect to a body coordinate system (BCS), the BCS is the base frame.CCommandAny interactive instruction that Adams/Solver or the postprocessor accepts.Constitutive EquationA tensor equation that establishes a relation between statical and kinematical tensors. For example, the following constitutive equation for a field force relates the statical force tensor (Fi) to the kinematical displacement tensor (Uj) and velocity tensor (Vj) by means of stiffness (Kij) and damping (Cij) matrices, respectively:Fi = - (Kij * Uj) - (Cij * Vj)DDAEDifferential Algebraic EquationDIFSUB (integrator)An integrator written by C. W. Gear to solve stiff ODEs. MSC has modified this integrator to solve stiff DAEs. This integrator is unrelated to the Adams/Solver subroutine that is known by the same name. For more on the DIFSUB integrator, see:A B C D E F G H I J K L MN O P Q R S T U V W X Y Z9 About Adams/SolverConventions Gear, C.W. Numerical Initial Value Problems in Ordinary Differential Equations. New Jersey: Prentice-Hall. Discrete FunctionA function that you define with a set of data points rather than with a continuous equation.Dynamic AnalysisAn analysis, performed over time, of a system that relies on inertial effects to determine motion.EEuler SingularityA singular matrix that results when the second Euler angle is zero. Therefore, the first and third Euler angles are not uniquely defined, and this results in a singular Jacobian matrix.FForceAn effect that has magnitude and direction and that causes motion of a rigid part when there is no other external effect on the rigid part. In Adams/Solver, force sometimes refers to both translational and rotational forces.HHolonomicAn adjective associated with system constraints. A holonomic constraint equation is an equality configuration constraint equation that can be expressed in the form F(q,t) = 0, where q denotes the system generalized coordinates and t is time. The function need not be a function of time.IIntegration StepThe steps at which Adams/Solver integrates. Adams/Solver varies the size of these steps as necessary to obtain an accurate solution, to stay within the error limits you specify (if any), and to converge to a solution.JJointA system element that connects two parts and allows relative motion of one part with respect to another. You must assign each joint to exactly two markers that are not in the same part.KKinematic AnalysisAdams/SolverConventions10An analysis of a mechanical model with zero degrees of freedom. Adams/Solver calculates the reaction and applied forces as well as the motion of the model.LLocal Body Reference FrameThe local body reference frame is an orthogonal triad attached to and moving with the body. It acts as the sole reference for defining any collection of markers that move with the body.LU FactorizationThe process of redefining a matrix, A, as a product of a lower triangular matrix, L, and an upper triangular matrix, U:LU = AL and U are the factors of A.MMarkerA system element you use to mark the center of mass in a part, the inertia axis of a part, a boundary of a part, the point at which a joint connects a part to another part, a point of action in a force field, or any other point that is significant to the analysis or to the graphics output of the model. Every marker in an Adams/Solver model has a coordinate system associated with it. Adams/Solver fixes each marker with respect to a part...</p>