A crankshaft system model for structural dynamic analysis of internal combustion engines

Abstract

A system model for analyzing the dynamic behavior of an internal combustion engine crankshaft is described. The model couples the crankshaft structural dynamics, the main bearing hydrodynamic lubrication and the engine block stiffness using a system approach. A two-level dynamic substructuring technique is used to predict the crankshaft dynamic response based on the finite-element method. The dynamic substructuring uses a set of load-dependent Ritz vectors. The main bearing lubrication analysis is based on the solution of the Reynold's equation. Comparison with experimental results demonstrates the accuracy of the model. Numerical results also show the capabilities and significance of the model in engine crankshaft design.

Introduction

Legislative and market pressures on internal combustion engine design call for increased engine power, reduced engine size and improved fuel economy, simultaneously. Also, efforts to reduce engine vibration and radiated noise while improving durability and reliability have become increasingly important to the automotive industry due to more stringent requirements for higher performance, lighter weight, low cost and fast-to-market engine designs. Optimized engine components are therefore required if competitive designs must be realized. Sophisticated analytical tools can greatly enhance the understanding of the physical phenomena associated with the operation of vital engine components. This is particularly true of crankshafts, one of the most analyzed engine components. Many sophisticated crankshaft analysis methods have been reported in the past. This has been mostly facilitated by the use of the finite-element method on high speed computers and the availability of elaborate finite-element preprocessors which can construct complex finite-element mesh models.

In recent years, noise, vibration and harshness (NVH) of automotive engines is becoming an integral part of the design process along with the traditional issues of durability and performance. NVH is strongly related to how customers perceive the quality of the engine; affecting, therefore, its competitiveness in the market place. Extensive static and dynamic analyses have been performed on vital engine components as crankshafts and engine blocks in order to improve their durability [1], [2], [3], [4] and NVH performance [5], [6], [7], [8]. The engine is a fine-tuned system of individual components. An optimum engine design requires a system approach since the performance of each component can be strongly dependent on the performance of the other components. This is particularly true for the crankshaft–block subsystem [9], [10], [11], [12].

A crankshaft–block subsystem consists of the crankshaft and the engine block coupled by the hydrodynamically lubricated main bearings. The loading on the system comes from the cylinder pressure and the piston–connecting rod inertia. The cylinder pressure applied on the piston crown is transmitted to the crankpin through the piston–connecting rod assembly. The inertia of the piston–connecting rod provides a load on the crankpin as well. The crankpin loads deform the crankshaft and are transmitted to the engine block at the main bearing locations through the main bearing hydrodynamics. Both the deformation of the crankshaft and the engine block affect the main bearing film thickness and therefore, the bearing hydrodynamics. For this reason, the mathematical model of the engine system requires three individual models which are coupled together; a structural model of the crankshaft, a structural model of the engine block and a lubrication model of the main bearings.

The large number of studies reported in the literature on the crankshaft–block interaction problem indicates its significance to the industry. A representative sample is given in Refs. [2], [10], [11], [12], [13], [14], [15], [16], [17]. Due to the complexity of the problem, many simplifying assumptions have been used. The first attempt to solve the problem is reported in Refs. [9], [18] where a calculation of bearing performance in statically indeterminate crankshaft systems is described. A static (not dynamic) crankshaft analysis is used and the block elasticity is represented by linear springs. The mobility method [19] describes the oil-film hydrodynamics neglecting, therefore, the important effects of journal misalignment and bearing design attributes as oil grooves and oil holes. The oil-film hydrodynamics have been almost exclusively represented by either the mobility method [10], [12], [13], [14] or simple spring–damper combinations [15], [16], [17]. In some cases the oil-film is completely neglected [11].

The significance of the crankshaft–block interaction problem in internal combustion engine design is due to a variety of reasons. First, the engine crankshaft is a finely optimized component with significant resonances (both torsional and bending) within its normal operating range. These resonances affect, among others, the dynamic stress distribution on crankshafts, bearing caps and engine bulkheads [2], [4] and the noise of the engine lower end [3], [7], [10]. The accurate prediction of dynamic stress levels is important for durability, low weight and high fatigue life [2]. The crankshaft dynamic response is also needed for optimizing crankshaft accessories as pulleys [16], [17] and flywheels [4]. Also the consideration of the oil-film hydrodynamics in the crankshaft–block interaction problem provides an enhanced bearing load prediction [4]. This allows for the design of more durable bearings with less friction and therefore, better fuel economy [20], [21]. Furthermore, the motion of each journal within the bearing clearance is needed for predicting the magnitude and duration of bearing impacts which normally occur during bearing load reversals. Such a prediction is essential for reducing the emitted noise from the engine lower end [10], [22].

This paper describes a crankshaft–block interaction methodology called CRANKSYM ($\text{Crank}$shaft $\text{Sy}$stem $\text{M}$odel). Section 2 gives an overview of the proposed crankshaft system model where all the features and assumptions are described in detail. Subsequent sections describe the crankshaft structural dynamic analysis and the engine block representation, the developed main bearing hydrodynamic analysis, and the coupled crankshaft–engine block model. The accuracy and efficiency of the crankshaft structural dynamic analysis is demonstrated in Ref. [23]. Comparison with experimental results shows the good accuracy of the proposed methodology. Finally, the capabilities and significance of the proposed crankshaft–engine block system model in engine design are illustrated using a V-shape six-cylinder engine.