Optimization Study of Shaft System Vibration and Broken Tooth Fault Under the Influence of 3D Mixed Lubrication of Marine Diesel Engine Timing Gear System

Abstract

Purpose

The timing gear drive mechanism serves as the fundamental transmission component of a diesel engine, encompassing a sophisticated elastic mechanical system comprising gears, multi-branch drive shafts, and various loads. The increasing demand for reduced vibration in modern diesel engines poses greater challenges to timing gear systems which must now withstand more extreme loads and operating conditions. This paper presents a coupled analytical model that integrates three-dimensional mixed lubrication and multi-branch shaft system vibration for the timing gear system of marine diesel engines. Additionally, it investigates broken tooth failure occurrence using an improved method and proposes an optimization scheme.

Methods

This paper focuses on the marine 20 V diesel engine timing gear and conducts research on the vibration characteristics of its shaft system, as well as optimization of broken teeth failure while considering the influence of three-dimensional mixed lubrication. Firstly, a 3D mixed lubrication analytical model is established and the validation of lubricant film stiffness and friction excitation is conducted. Based on this, the gear train is modeled with lumped-parameterized bending-torsion coupling dynamics, incorporating time-varying oil film stiffness and friction excitation. The vibration characteristics of the shaft system are analyzed by establishing an analytical model, which takes into account the comprehensive excitation from both internal and external factors in the multi-branch transmission shaft system. The accuracy of this model is then verified through actual diesel engine testing experiments. The conventional tooth root bending stress load spectrum is finally corrected, and the faulty gear is calibrated. Furthermore, a vibration optimization design scheme is proposed based on practical engineering experience.

Results

The accuracy of the coupled lubrication model developed in this study has been validated through comparisons with literature results and equivalent simulation tests. Furthermore, the precision of the vibration model has been confirmed through real-machine testing for both free and forced vibrations. Notably, during both calculation and experimentation, it was observed that the peak vibration energy at the oil pump shaft exceeded that at the flywheel end by a factor of 5.2; these poor vibration characteristics were identified as a primary cause of frequent tooth breakage in timing gears located near the oil pump shaft position. By improving the bending stress algorithm, we conducted a calibration of the bending fatigue strength for the timing gear that frequently experiences tooth breakage faults during diesel engine durability tests. The resulting minimum safety coefficient of 1.31 falls within the range of general reliability; however, it does indicate a susceptibility to tooth breakage faults. To address this issue in practical engineering applications, we propose an optimization scheme involving the addition of a vibration damper. This scheme increases the minimum safety factor to 1.64, effectively preventing occurrences of tooth breakage.

Conclusion

The study results unveil the failure mechanism of broken teeth in timing gears from a dynamics perspective, offering theoretical guidance for accurate prediction of tooth root bending stress and performance optimization as well as providing theoretical support for vibration response analysis of diesel gear shaft systems and vibration and noise reduction.

Appendices

Appendix A

See Tables 6 and 7.

Table 6 Support stiffness of the transmission system

Table 7 Simplified table of total shafting torsion lumped parameters of diesel engine

Appendix B

Cylinder Excitation Calculation

The excitation force of the cylinder is primarily composed of burst pressure and reciprocating inertia force. Figure 21 provides a force analysis of the crankshaft connecting rod mechanism.

In Fig. 21, A is the piston centroid; B is the crank centroid; L is the connecting rod; S is the piston stroke; OB is the radius; β is the swing angle; α is the angle.

Fig. 21

Force diagram of crank connecting rod mechanism

The tangential torque generated by the tangential force of the crankshaft is

$$ M_{g} = \frac{\pi }{4}D^{2} RP_{{\text{T}}} , $$

where $D$ is the cylinder diameter; $R$ is the crank radius; $P_{{\text{T}}}$ is the tangential force of gas.

The reciprocating inertia force of the moving parts in the cylinder of a diesel engine is concentrated on the crank pin. As the crankshaft rotates periodically, this reciprocating inertia moment is expressed as:

$$ M_{{\text{I}}} {\kern 1pt} = - mR^{2} \omega^{2} \left( {\frac{\lambda }{4}\sin \alpha - \frac{1}{2}\sin 2\alpha - \frac{3}{4}\lambda \sin 3\alpha - \frac{{\lambda^{2} }}{4}\sin 4\alpha } \right) $$

Camshaft Excitation Calculation

The camshaft excitation in this paper is primarily categorized into valve cam excitation and oil supply cam excitation [38]. The valve train must maintain the timeliness of its valve opening and closing while ensuring proper intake and exhaust functions. Figure 

Fig. 22

Valve cam force diagram

22 illustrates the torque balance.

In the Fig. 22, P is the action point; O is the center of the circle; e is the distance between the center of the cam circle and the action point; R is the radius of the base circle; h is the lift; w is the angular velocity; T is torque; F_s is friction; F_z is the cam force. Its equilibrium formula is

$$ T - F_{z} \cdot e - F_{s} \cdot \left( {h + R} \right) = 0. $$

The fuel supply system of the diesel engine differs from the high pressure common rail system in that it employs an auxiliary pump injection structure, as illustrated in Fig. 

Fig. 23

Oil supply cam force diagram

23.

In Fig. 23, F1 is the normal force between the roller and the cam; F₂ is the plunger lateral force; r₁ is the roller radius; r₀ is the radius of cam base circle; h is the cam lift. The load torque of the cam is

$$ T = F_{1} \cdot l = F_{z} (r_{0} + r_{1} + h) \cdot \tan \alpha , $$

where $r_{1}$ is the radius of the roller; $\alpha$ is the angle between the force of the cam roller contact point and the normal force.