The problem of understanding and modeling the complicated physics underlying the action and response of the interfaces in typical structures under dynamic loading conditions has occupied researchers for many decades. This handbook presents an integrated approach to the goal of dynamic modeling of typical jointed structures, beginning with a mathematical assessment of experimental or simulation data, development of constitutive models to account for load histories to deformation, establishment of kinematic models coupling to the continuum models, and application of finite element analysis leading to dynamic structural simulation. In addition, formulations are discussed to mitigate the very short simulation time steps that appear to be required in numerical simulation for problems such as this. This handbook satisfies the commitment to DOE that Sandia will develop the technical content and write a Joints Handbook. The content will include: (1) Methods for characterizing the nonlinear stiffness and energy dissipation for typical joints used in mechanical systems and components. (2) The methodology will include practical guidance on experiments, and reduced order models that can be used to characterize joint behavior. (3) Examples for typical bolted and screw joints will be provided.
The paper describes the preliminary evaluation of a 6 degree of freedom electrodynamic shaker system. The 8 by 8 inch (20.3 cm) table is driven by 12 electrodynamic shakers producing motion in all 6 rigid body modes. A small electrodynamic shaker system suitable for small component testing is described. The principal purpose of the system is to demonstrate the technology. The shaker is driven by 12 electrodynamic shakers each with a force capability of about 50 lbs (220 N). The system was developed through an informal cooperative agreement between Sandia National Laboratories, Team Corp. and Spectral Dynamics Corporation. Sandia provided the laboratory space and some development funds. Team provided the mechanical system, and Spectral Dynamics provided the control system. Spectral Dynamics was chosen to provide the control system partly because of their experience in MIMO control and partly because Sandia already had part of the system in house. The shaker system was conceived and manufactured by TEAM Corp. Figure 1 shows the overall system. The vibration table, electrodynamic shakers, hydraulic pumps, and amplifiers are all housed in a single cabinet. Figure 2 is a drawing showing how the electrodynamic shakers are coupled to the table. The shakers are coupled to the table through a hydraulic spherical pad bearing providing 5 degrees of freedom and one stiff degree of freedom. The pad bearing must be preloaded with a static force as they are unable to provide any tension forces. The horizontal bearings are preloaded with steel springs. The drawing shows a spring providing the vertical preload. This was changed in the final design. The vertical preload is provided by multiple strands of an O-ring material as shown in Figure 4. Four shakers provide excitation in each of the three orthogonal axes. The specifications of the shaker are outlined in Table 1. Four shakers provide inputs in each of the three orthogonal directions. By choosing the phase relationships between the shakers all six rigid body modes (three translation, and three rotations) can be excited. The system is over determined. There are more shakers than degrees of freedom. This provided an interesting control problem. The problem was approached using the input-output transformation matrices provided in the Spectral control system. Twelve accelerometers were selected for the control accelerometers (a tri-axial accelerometer at each corner of the table (see Figure 5). Figure 6 shows the nomenclature used to identify the shakers and control accelerometers. A fifth tri-axial accelerometer was placed at the center of the table, but it was not used for control. Thus we had 12 control accelerometers and 12 shakers to control a 6-dof shaker. The 12 control channels were reduced to a 6-dof control using a simple input transformation matrix. The control was defined by a 6x6 spectral density matrix. The six outputs in the control variable coordinates were transformed to twelve physical drive signals using another simple output transformation matrix. It was assumed that the accelerometers and shakers were well matched such that the transformation matrices were independent of frequency and could be deduced from rigid body considerations. The input/output transformations are shown in Equations 1 and 2.
This paper discusses issues that arise in controlling high quality mechanical shock inputs for mock hardware in order to validate a model of a bolted connection. The dynamic response of some mechanical components is strongly dependent upon the behavior of their bolted connections. The bolted connections often provide the only structural load paths into the component and can be highly nonlinear. Accurate analytical modeling of bolted connections is critical to the prediction of component response to dynamic loadings. In particular, it is necessary to understand and correctly model the stiffness of the joint and the energy dissipation (damping) that is a nonlinear function of the forces acting on the joint. Frequency-rich shock inputs composed of several decayed sinusoid components were designed as model validation tests and applied to a test item using an electrodynamic shaker. The test item was designed to isolate the behavior of the joint of interest and responses were dependent on the properties of the joints. The nonlinear stiffness and damping properties of the test item under study presented a challenge in isolating behavior of t4he test hardware from the stiffness, damping and boundary conditions of the shaker. Techniques that yield data to provide a sound basis for model validation comparisons of the bolted joint model are described.
The dynamic response of critical aerospace components is often strongly dependent upon the dynamic behavior of bolted connections that attach the component to the surrounding structure. These bolted connections often provide the only structural load paths to the component. The bolted joint investigated in this report is an inclined lap-type joint with the interface inclined with respect to the line of action of the force acting on the joint. The accurate analytical modeling of these bolted connections is critical to the prediction of the response of the component to normal and high-level shock environmental loadings. In particular, it is necessary to understand and correctly model the energy dissipation (damping) of the bolted joint that is a nonlinear function of the forces acting on the joint. Experiments were designed and performed to isolate the dynamics of a single bolted connection of the component. Steady state sinusoidal and transient experiments were used to derive energy dissipation curves as a function of input force. Multiple assemblies of the bolted connection were also observed to evaluate the variability of the energy dissipation of the connection. These experiments provide insight into the complex behavior of this bolted joint to assist in the postulation and development of reduced order joint models to capture the important physics of the joint including stiffness and damping. The experiments are described and results presented that provide a basis for candidate joint model calibration and comparison.
When embarking on an experimental program for purposes of discovery and understanding, it is only prudent to use appropriate analysis tools to aid in the discovery process. Due to the limited scope of experimental measurement analytical results can significantly complement the data after a reasonable validation process has occurred. In this manner the analytical results can help to explain certain measurements, suggest other measurements to take and point to possible modifications to the experimental apparatus. For these reasons it was decided to create a detailed nonlinear finite element model of the Sandia Microslip Experiment. This experiment was designed to investigate energy dissipation due to microslip in bolted joints and to identify the critical parameters involved. In an attempt to limit the microslip to a single interface a complicated system of rollers and cables was devised to clamp the two slipping members together with a prescribed normal load without using a bolt. An oscillatory tangential load is supplied via a shaker. The finite element model includes the clamping device in addition to the sequence of steps taken in setting up the experiment. The interface is modeled using Coulomb friction requiring a modest validation procedure for estimating the coefficient of friction. Analysis results have indicated misalignment problems in the experimental procedure, identified transducer locations for more accurate measurements, predicted complex interface motions including the potential for galling, identified regions where microslip occurs and during which parts of the loading cycle it occurs, all this in addition to the energy dissipated per cycle. A number of these predictions have been experimentally corroborated in varying degrees and are presented in the paper along with the details of the finite element model.
MicroElectricalMechanical Systems (MEMS) were subjected to a vibration environment that had a peak acceleration of 120g and spanned frequencies from 20 to 2000 Hz. The device chosen for this test was a surface-micromachined microengine because it possesses many elements (springs, gears, rubbing surfaces) that may be susceptible to vibration. The microengines were unpowered during the test. The authors observed 2 vibration-related failures and 3 electrical failures out of 22 microengines tested. Surprisingly, the electrical failures also arose in four microengines in the control group indicating that they were not vibration related. Failure analysis revealed that the electrical failures were due to shorting of stationary comb fingers to the ground plane.