D. Geoff Rideout

Analytical Target Cascading in Automotive Vehicle Design

Target cascading in product development is a systematic effort to propagate the desired top-level system design targets to appropriate specifications for subsystems and components in a consistent and efficient manner. If analysis models are available to represent the consequences of the relevant design decisions, analytical target cascading can he formalized as a hierarchical multilevel optimization problem. The article demonstrates this complex modeling and solution process in the chassis design of a sport-utility vehicle. Ride quality and handling targets are cascaded down to systems and subsystems utilizing suspension, tire, and spring analysis models. Potential incompatibilities among targets and constraints Throughout the entire system can he uncovered and the trade-offs involved in achieving system targets under different design scenarios can he quantified.

A Review of Proper Modeling Techniques

A dynamic system model is proper for a particular application if it achieves the accuracy required by the application with minimal complexity. Because model complexity often—but not always—correlates inversely with simulation speed, a proper model is often alternatively defined as one balancing accuracy and speed. Such balancing is crucial for applications requiring both model accuracy and speed, such as system optimization and hardware-in-the-loop simulation. Furthermore, the simplicity of proper models conduces to control system analysis and design, particularly given the ease with which lower-order controllers can be implemented compared to higher-order ones. The literature presents many algorithms for deducing proper models from simpler ones or reducing complex models until they become proper. This paper presents a broad survey of the proper modeling literature. To simplify the presentation, the algorithms are classified into frequency, projection, optimization, and energy based, based on the metrics they use for obtaining proper models. The basic mechanics, properties, advantages, and limitations of the methods are discussed, along with the relationships between different techniques, with the intention of helping the modeler to identify the most suitable proper modeling method for a given application.

Systematic Identification of Decoupling in Dynamic System Models

pling among elements of a dynamic system model, and to partition models in which decoupling is found. The method can validate simplifying assumptions based on decoupling, determine when decoupling breaks down due to changes in system parameters or inputs, and indicate required model changes. A high-fidelity model is first generated using the bond graph formalism. The relative contributions of the terms of the generalized Kirchoff loop and node equations are computed by calculating and comparing a measure of their power flow. Negligible aggregate bond power at a constraint equation node indicates an unnecessary term, which is then removed from the model by replacing the associated bond by a modulated source of generalized effort or flow. If replacement of all low-power bonds creates separate bond graphs that are joined by modulating signals, then the model can be partitioned into driving and driven subsystems. The partitions are smaller than the original model, have lower-dimension design variable vectors, and can be simulated separately or in parallel. The partitioning algorithm can be employed alongside existing automated modeling techniques to facilitate efficient, accurate simulation-based design of dynamic systems. DOI: 10.1115/1.2745859

Coupled transverse vibration modeling of drillstrings subjected to torque and spatially varying axial load

Predicting and mitigating unwanted vibration of drillstrings is an important subject for oil drilling companies. Uncontrolled vibrations cause premature failure of the drillstring and associated components. The drillstring is a long slender structure that vibrates in three primary coupled modes: torsional, axial and transverse. Among these coupled modes, the transverse mode is the major cause of drillstring failures and wellbore washout. Modal analysis of drillstrings reveals critical frequencies and helps drillers to avoid running the bit near critical modes. In this article, the coupled orthogonal modes of transverse vibration of a drillstring in the presence of torque and spatially varying axial force (due to mud hydrostatic effect, self-weight and hook load) are derived and the mode shapes and natural frequencies are determined through the expanded Galerkin method. The results are verified by the nonlinear finite element method. Modal mass participation factor, which represents how strongly a specific mode contributes to the motion in a certain direction, is used to determine the appropriate number of modes to retain so that computational efficiency can be maximized.

Extension and application of an algorithm for systematic identification of weak coupling and partitions in dynamic system models

Abstract This paper reviews and extends a technique to detect weak coupling (one-way coupling or complete decoupling) among elements of a dynamic system model, and to partition and reduce models in which weak coupling is found. The ability to partition a model increases the potential for physical-domain model reduction, and allows parallel simulation of smaller individual submodels that can reduce computation time. Negligible constraint equation terms are identified and eliminated in a bond graph by converting inactive power bonds to modulated sources. If separate bond graphs result, between which all modulating signals move from a “driving” subgraph to a “driven” one, then one-way coupling exists in the model and it can be separated into driving and driven partitions. Information flow between the subgraphs is one-way. In this paper the algorithm is extended to models in which two-way information flow from modulating signals precludes complete partitioning. It is shown for several classes of modulating signals that, under certain conditions the signal is “weak” and therefore can be eliminated. Removal of weak signals allows partitioning of the longitudinal and pitch dynamics of a medium-duty truck model. The intensity of dynamic coupling and the potential for model reduction are shown to depend on the magnitude of system parameters and the severity of inputs such as road roughness.

Bond graph dynamic modeling and stabilization of a quad-rotor helicopter

Four-rotor/quad-rotor helicopters are emerging as a popular unmanned aerial vehicle configuration because of their simple construction, easy maintenance and high payload capacity. A quadrotor is an under-actuated mechanical system with six degrees of freedom and four lift-generating propellers arranged in cross configuration. Maneuvers are executed by varying the speed of the propellers, which causes moments that affect attitude control; and by varying thrust, which affects altitude control. This makes stabilization challenging. This work presents a dynamic model of such a vehicle using bond graphs. Both an open loop unstable model and a closed loop stable model using different controllers are demonstrated in this paper. The Newton-Euler formalism with body fixed coordinates is used to model the dynamics of the platform. Rotor drag torque is assumed proportional to thrust of the rotor. The graphical nature and explicit power flow paths inherent in the bond graph formalism facilitated model construction and troubleshooting. Existing commercial bond graph software allowed simultaneous modeling and control implementation. The model results for different maneuvers and combinations of propeller thrust agree with existing theoretical results. Open loop simulation shows an uncontrolled revolving effect with increasing linear speed which results in instability of the system. The closed loop PID-controlled result nicely demonstrates the stabilization of the system from an initial roll, pitch, yaw and altitude to the desired steady state configuration.

Model Complexity Requirements in Design of Half Car Active Suspension Controllers

This paper investigates the appropriate level of model complexity when designing optimal vehicle active suspension controllers using the Linear Quadratic Regulator (LQR) method. The LQR method requires the formulation of a performance index with weighting factors to penalize the three competing objectives in suspension design: suspension travel (rattle space), sprung mass acceleration (ride quality) and tire deflection (road-holding). The optimal control gains are determined from the solution of a matrix Riccati equation with dimension equal to the number of state variables in the model. A quarter car model with four states thus poses a far less onerous formulation problem than a half or full car model with eight or more states. However, half and full car models are often assumed to be more accurate than quarter car models, and necessary for capturing and controlling degrees of freedom such as pitch and roll motion which are not directly available from a quarter car. The vertical acceleration, pitch acceleration and roadholding of a pitch plane vehicle are controlled in this paper using both quarter and half car-based controllers. First, optimal gains are calculated for each of the front and rear actuators assuming that the front and rear of the vehicle can be separately modeled as quarter cars with four states each. Then, half car-based optimal gains, based on feedback of eight states for the entire vehicle, are computed. Using quarter car-based controllers at the front and rear of a half car gives superior performance in reducing sprung mass inertial acceleration, and can effectively control pitch motion even when interactions between front and rear suspensions are not decoupled. Minimizing vertical motion of the front and rear ends indirectly regulates pitch motion. Improvements resulting from the additional complexity of the half car-based controller are seen only when the weighting factor for pitch suppression is very high in the performance index.Copyright

Systematic Assessment of Rigid Internal Combustion Engine Dynamic Coupling

Accurate estimation of engine vibrations is essential in the design of new engines, engine mounts, and the vehicle frames to which they are attached. Mount force prediction has traditionally been simplified by assuming that the reciprocating dynamics of the engine can be decoupled from the three-dimensional motion of the block. The accuracy of the resulting one-way coupled models decreases as engine imbalance and cylinder-tocylinder variations increase. Further, the form of the one-way coupled model must be assumed a priori, and there is no mechanism for generating an intermediate-complexity model if the one-way coupled model has insufficient fidelity. In this paper, a new dynamic system model decoupling algorithm is applied to a Detroit Diesel Series 60 in-line sixcylinder engine model to test one-way coupling assumptions and to automate generation of a proper model for mount force prediction. The algorithm, which identifies and removes unnecessary constraint equation terms, is reviewed with the aid of an illustrative example. A fully coupled, balanced rigid body model with no cylinder-to-cylinder variations is then constructed, from which x, y, and z force components at the left-rear, right-rear, and front engine mounts are predicted. The decoupling algorithm is then applied to automatically generate a reduced model in which reciprocating dynamics and gross block motion are decoupled. The amplitudes of the varying components of the force time series are predicted to within 8%, with computation time reduced by 55%. The combustion pressure profile in one cylinder is then changed to represent a misfire that creates imbalance. The decoupled model generated by the algorithm is significantly more robust to imbalance than the traditional one-way coupled models in the literature; however, the vertical component of the front mount force is poorly predicted. Reapplication of the algorithm identifies constraint equation terms that must be reinstated. A new, nondecoupled model is generated that accurately predicts all mount components in the presence of the misfire, with computation time reduced by 39%. The algorithm can be easily reapplied, and a new model generated, whenever engine speed or individual cylinder parameters are changed. DOI: 10.1115/1.2795770

A review of proper modeling techniques

A dynamic system model is proper for a particular application if it achieves the accuracy required by the application with minimal complexity. Because model complexity often — but not always — correlates inversely with simulation speed, a proper model is often alternatively defined as one balancing accuracy and speed. Such balancing is crucial for applications requiring both model accuracy and speed, such as system optimization and hardware-in-the-loop simulation. Furthermore, the simplicity of proper models conduces to control system analysis and design, particularly given the ease with which lower-order controllers can be implemented compared to higher-order ones. The literature presents many algorithms for deducing proper models from simpler ones or reducing complex models until they become proper. This paper presents a broad survey of the proper modeling literature. To simplify the presentation, the algorithms are classified into frequency-, projection-, optimization-, and energy-based, based on the metrics they use for obtaining proper models. The basic mechanics, properties, advantages and limitations of the methods are discussed, along with the relationships between different techniques, with the intention of helping the modeler to identify the most suitable proper modeling method for their application.Copyright

Elastodynamic and finite element vibration analysis of a drillstring with a downhole vibration generator tool and a shock sub

Applying high-frequency axial oscillation into an oilwell drillstring in the “bottom-hole assembly” (BHA) has the potential to enhance drilling efficiency in extended reach wells. Downhole vibration generator tools such as agitators reduce the drillstring–wellbore friction and enhance the rate of penetration. However, introducing controlled vibrations into the drillstring can result in undesired vibration waves propagating along the drillstring, leading to inefficient drilling and catastrophic fatigue failure of the BHA components, “measurement-while-drilling” tools, and mud motors. A dynamic model of the entire drillstring, including vibration generators and shock subs, is required to study the effect of vibration generators on the complex nonlinear coupled axial-lateral dynamics of a drillstring inside a wellbore, to study the effect of vibration tools on the developed cutting force at the bit, and to facilitate simulation-based design of shock subs. A dynamic finite element model (FEM) and an analytical elastodynamic model, both including the vibration generator tool and a shock sub, have been developed. The “Bypassing PDEs” method was implemented on the Lagrangian of the system to develop the analytical equations. A multi-mode expanded Galerkin’s approximation, in conjunction with a multi-span BHA and Hertzian contact assumption, allowed analysis of multiple BHA contact points and, thus, more realistic estimates of drilling rotary speeds that can cause excessive vibration. The models also include torque, mud damping, spatially varying axial force, geometric nonlinearity, and axial stiffening. While the analytical model has fast running time and symbolic solution, the FEM model enables easy reconfiguration and future extensions of model geometry, interactions, and modified BHA configurations. There is agreement between the analytical and FEM simulation results for the vibration suppression ability of the shock sub, dynamic amplification of the vibrating tool force, critical rotary speeds, axial force along the drillstring, axial and lateral displacements, and the contact locations and severity.