Development of a Powerplant Hybrid Model at Toyota Motor Corporation

In order to reduce engine development times new and innovative approaches have to be used - where use of virtual prototyping techniques are made, and existing information reused in a methodical way. In a first step, a hybrid model is built by coupling experimental models of existing powertrain components with numerical models of newly designed components. Then, an experimental indirect force identification scheme is used to estimate realistic loads for the virtual prototype. In the final step, the virtual prototype is exploited to predict the effect of structural modifications on operational vibration response for the first six engine orders.

A process scheme covering the FE-experimental hybrid modeling, the force identification and the forced response calculation is shown here. In this case, the engine dynamics model combined an FE model of the cylinderblock and experimental models for other (existing) parts. 

The FE cylinderblock model was first validated by free-free experimental modal analysis, which showed good correlation of resonance frequencies and MAC values up to 3kHz. 

Modal model-based substructuring and FRF-based substructuring methods were considered for coupling the FE models with the experimentally obtained component models into a hybrid model.

The assembly dynamic behavior is calculated from the free-free modes of the single components. These modes originate from Normal Modes Analysis (MSC NASTRAN) and experimental modal analysis (LMS CADA-X). The assembly calculations are performed in LMS CADA-X Modal Design software environment. The experimental modes can be real or complex in nature, but to avoid loss of physical relevance during the design modification phase, real-valued modeshapes are used. In the case of the powerplant model assembly, most components are bolted together: the interface is therefore modeled as a sparse constant stiffness matrix, linking 10 node pairs. Free-free modes up to 3kHz are taken into account in order to minimize the effect of out-band higher frequency modes.

The inertia parameters of the free-free model are important parameters for accurate coupling calculations, as are the modal truncation effects. For FE modeled components, these parameters are easily calculated. For experimentally characterized components, however, these inertia characteristics need to be determined by additional analysis. Using the LMS Rigid Body Calculator to derive estimates based on measured broadband FRFs proved very accurate for both the Moment of Inertia and Center of Gravity.

For the FE cylinderblock, the result of the NASTRAN normal mode analysis is converted to modal model form by LMS Gateway. To save memory and calculation time, the grid density and the modal vector size are reduced.1 Six rigid body modes are shifted to non-zero frequencies, and 0.1% damping value is assigned for 33 modes up to 3kHz.1 The powerplant components are dynamically characterized by standard experimental modal analysis techniques and 6 deformation modes are estimated up to 2kHz and 6 rigid body modes are synthesized from FRF-based estimations of inertial parameters.

The results of coupling calculation is in good agreement with validation measurements.

FBS predicts the frequency response function matrix after assembly, and gives force transmissibility between the two coupled substructures. By definition, the component models are FRF matrices [Hij], relating a response vector {Xi} to a forcing vector {Fj}. The basic assumption of FBS puts no restrictions on the origin of the composing FRF matrices. Whether they come from measurements, FEA, multibody simulations, or acoustic radiation predictions, the formulation remains unchanged. 

The resulting assembly FRF model can be exploited to evaluate design changes on any of the components or in the interface stiffness.

The FRF matrices from the components modeled by FE can be immediately synthesized in LMS Gateway from the MSC NASTRAN Sol.103 modal model, after having assigned a set of appropriate modal damping values. Should the frequency range covered by the FEA modal model be insufficient to avoid truncation effects, a dynamic compensation algorithm can be used. For the FE cylinderblock, a 60x60 FRF matrix is synthesized from 6 FEA rigid body modes based on FEA and shifted to non-zero frequencies and 33 FEA deformation modes up to 3kHz. The same DOF are considered as modal model based substructuring.

Both the modal model and FBS coupling algorithms have been evaluated for a series of subassembly calculations. Similar results were found for both methods for all evaluated sub-assemblies. The major advantage of FBS remains the very limited component model size and the small CPU time, if the number of coupling DOF is small. The major disadvantage of FBS comes from the stringent requirements during data acquisition in terms of FRF matrix size and quality. The above considerations make the FBS approach very well adapted to facilitate and fasten the design process of auxiliary components. In these cases, the mounting zone on the engine can be described by a FRF matrix of limited size. The application of an FBS scheme using this engine-interface matrix offers the design engineer the possibility to evaluate the auxiliary component in real-life conditions. For the application of substructuring techniques to assemble a high number of components into a single virtual powerplant model, the modal based method is more suitable, merely because of the reduced measurement effort.

The modal model-based techniques are applied to assembling the virtual model of the engine. The experimental models consist of the cylinderhead, intake & exhaust manifolds, exhaust pipe subassembly, the alternator, the airconditioner-pump, the fully assembled transmission, and the engine mount brackets. A model of the final prototype is shown.

To evaluate performance in terms of absolute NVH levels the virtual prototype needs to be loaded by realistic excitation forces. These are estimated by joint analysis of experimentally obtained operational vibrations and FRFs: the force-set includes combustion forces of each cylinder, inertia forces of the connecting rod and the crankshaft, piston slap forces and forces acting on the crank bearings.
All of these engine forces are calculated simultaneously by an indirect estimation using TPA (Transfer Path Analysis). The basic equation is:

A series of operational vibration measurements were performed on the powerplant on an engine test bench during run-up sequences from 3000 to 5000rpm, with a load of 150Nm. These data were converted to order cuts from 0.5th to 8th order and processed to rank peak dynamic phenomena for force identification and running mode analysis. A 173x24 FRF matrix was derived by synthesis from the modal parameters resulting from the hybrid assembly model. For validation purposes, the same matrix is measured on the passive part of the powerplant, after removal of the moving components.

The straightforward estimation of a force vector by multiplication of the inverted FRF-matrix with operational response order cuts, leads to a minimal energy solution, because of the least square algorithm. However, such a minimal energy force vector is incompatible with the physical forces acting in an engine. Therefore, the indirect force estimation process is enhanced introducing the a priori knowledge of the force components.

By multiplication of the estimated force vector with the FRF-matrix calculated from the hybrid engine model, the identification procedure can be validated - good correlation was observed.

A large aluminum stiffener was selected as a benchmark modification. Assuming invariance of the excitation forces, a prediction can be made of the operational vibration levels after the structural modification. The estimated operational force vectors are multiplied by a newly synthesized FRF matrix, based on the hybrid model with stiffener. 

You can see the measured and predicted operational 3.5th order vibration levels with and without stiffener. Although a shift is observed between the predicted and measured peak speed, the speed tendency for increase and decrease of vibration levels clearly correlates between measurement and prediction. This is confirmed by other response DOF evaluations for all orders in the frequency band of interest.