Fig. 1. A four-gear chain model

Contact phase shifting of successive gear pairs for Improvement of NVH characteristics of powertrain systems

This study presents some guidelines to decrease the non-demanded excitations from the bearings and therefore to optimize the NVH characteristics of a gear reducer. The effect of the position of the contact of successive gear pairs (so-called contact phase shifting) and the resulting reduction of dynamic meshing contact forces is presented. A four-stage gear chain model is considered as a typical model for this investigation. The whole process including calculation of the optimal contact angle positions, system contact analysis, and finally the forced response analysis is executed in KISSsoft.
 

1. Model description

A four-stage gear chain model with one input and two outputs is shown in Fig. 1. The model consists of four gears G1 to G4, and nine bearings B1 to B9. The input torque = 183 Nm (CW), and output torques T1=30 Nm (CW) and T2=82 Nm (CCW) are applied at the coupling positions to the shafts.

Table 1. Contact position angles of gear pairs for three models

2. Optimal contact phase shifting

Three variants of the model are considered in this study. Table 1 reports the contact angle positions of the three gear pairs of these variants. The first case is the original model with nominal contact angle positions. The contact angle positions in the other two models are calculated to achieve optimal dynamic behavior by reducing the dynamic meshing contact forces. Consequently, this will lead to the reduction of dynamic bearing forces and improves the NVH characteristics of the system. The transient bearing forces are the main source of excitation from a powertrain system to the housing which generates noise.

Fig. 2. Variation of the transmission errors

The calculation of the optimum contact phase shifting is based on analytical geometry formulas, implemented in a so-called script. The script programming is a very fast and simple method in KISSsoft to solve such problems. The proposition of this approach is based on the shifting of the start of contact by half a pitch in order to avoid accumulation of high contact forces with respect to the rotation angle of gears. This simple approach, based on the gear geometry according to ISO 21771, can then be refined with the system contact analysis in KISSsoft. To evaluate if the contact phasing is ‘good’ or ‘bad’, graphics with variation of the torsional shaft deviations and the transmission errors are very useful. The torsional shaft deviation plot shows the torsional rotation of each shaft of the system. The torsional shaft deviation starts at the reference shaft with zero rotation, and then varies due to the transmission error effect from one shaft to another. The smaller the rotation is at the last shaft, the better the meshing pairs are with respect to the contact phase shifting.
 

3. System contact analysis

The system contact analysis is a newly developed module in KISSsoft which considers the coupling effect of all gear pairs and shaft deformations to perform the overall contact analysis. The results of the system contact analysis are shown in Figures 2 and 3 for three variants of the model. In both figures, for the original model, the peak values of the transmission error and torsional shaft deviation are ‘synchronized’. This means that their peak values occur at the same rotation angle. Therefore, it is assumed that the original model is the worst case regarding the NVH specifications. In the other variants Opt1 and Opt2, the highest values of the transmission errors and torsional shaft deviations are shifted (by 25% for Opt1 and by 50% for Opt2) with respect to the original model to decrease the resulting meshing contact forces. It is important to notice that in the Opt2 model, the transmission error of the gear pair G2-G3 is shifted in a way that a non-synchronization of the highest amplitudes of gear pairs G1-G2 and G2-G3 is evident. The models Opt1 and Opt2 are supposed to have superior performance in NVH characteristics when compared to the original model. In the next section, the forced response analysis is followed to clearly evaluate the performance improvement of these two models.

Fig. 3. Variation of the torsional shaft deviations

Fig. 4. Variation of the dynamic factors

4. Forced response analysis

In KISSsoft, as a newly developed tool, the calculation of the forced response is implemented. Based on the static transmission error of the gears, shaft imbalances, etc., the transient bearing loads are calculated considering the inertias and masses. The results of the forced response analysis are shown in Figs. 4 to 6. The procedure is based on the frequency response analysis where all excitations and responses are represented in terms of the excitation frequencies together with their corresponding amplitudes and phase angles [1]. Within this tool, a comprehensive list of different settings and options are provided which enable the user to precisely investigate the vibration characteristics of the system. The representation of the dynamic factor and meshing contact forces for the models Opt1 and Opt2 show that among the three variants, Opt2 has the lowest contact forces which implies that it has the best performance in NVH characteristics. In addition, the amplitude of the bearing force variations |F| among all bearings are calculated and shown in Fig. 6. According to the color legend scale of Fig. 6 and the results of Table 2, the model Opt2 contains the lowest maximum bearing force variations which clearly confirms that the contact phase shifting in this model results in the best dynamic behavior compared to the other two variants.

Fig. 5. Variation of the Meshing contact forces (max value-min value)

Fig. 6. Campbell diagram (amplitude of the maximum bearing forces |F| among all bearings)

Table 2. Amplitude of the maximum bearing forces |F|

References

[1] Beermann, S.: Simulation der Schwingungen von Stirnradgetrieben unter Verwendung der Spektralsimulation (in German), PhD Thesis, Karlsruhe, 2000, Fortschrittberichte VDI, Reihe 11, Schwingungstechnik, Nr. 288, VDI-Verlag, Düsseldorf, 2000.

Authors

Dr. Saeed Ebrahimi is currently working in KISSsoft for developing the forced response module in power train systems. He was previously an associate professor of mechanical engineering at Yazd University in Iran. He received his Ph.D. in mechanical engineering from Stuttgart University in Germany in 2007 and completed his post-doctoral fellowship at the Center for Intelligent Machines (CIM), McGill University, in 2008. His research interests include vibration analysis of powertrain systems and NVH simulation of gearboxes for acoustic optimization.

Dr. Ulrich Kissling was born in Zurich. He studied Machine Engineering at the Swiss Technical University (ETH). He continued his academic career with a doctorate. In 1981 he started his professional career as calculation engineer in a Gearbox Manufacturing Company in Zurich, continued then as Technical Manager and Managing Director.

As calculation engineer for gearbox design, he started to develop software for gear, bearing and shaft layout. In 1985 he named this software ‘KISSsoft’ and started to market it. In 1986 the first license was sold. In 1998 he founded his own company, KISSsoft AG, to take care of the software activities. Since then, the staff of KISSsoft AG is growing constantly from 3 people in 1998 to over 40 in 2022. Currently Dr. Kissling is together with his partner Dr. Beermann managing director of KISSsoft AG, with Dipl.-Ing. Hanspeter Dinner as Deputy Managing Director. Today the software is the leading drive train design software, used by more than 3500 companies on all continents.

As gear expert Dr. Kissling is actively participating in different Work Groups of ISO for the development of international standards.

Source: The image rights for all figures are held by KISSsoft