Keywords

1 Introduction

A non-Pneumatic tire (NPT, airless tire) has been used in specialized applications such as all-terrain vehicles. The previous study mentioned that the application of the NPT to standard passenger needs consideration of potential performances such as noise, vibration, harshness and rolling resistance [1]. In the previous research [2], an NPT structure with a circular deformable shear beam which has an advantage in reducing energy loss during impacting a cleat is proposed. The vibration analysis induced by discrete spokes was reported in the study [3]. However, estimating the vehicle vibration characteristics of NPT involving the nonlinear behavior of the tire and its interaction with other chassis components is not conducted very well, although it is crucial for vehicle development and chassis control. The main goals of the present work are to investigate and improve the vibration characteristics of a passenger car equipped with NPT. In the present study, tire finite element (FE) analysis combined with a multibody quarter-car model is performed. The vibration characteristics is investigated on a specific NPT construction in comparison to a pneumatic tire by using the method.

2 The Detail of NPT Structure

Figure 1 shows the specific structure of the NPT, based on the concept proposed in the previous work [4]. The spoke is made of elastomer with relatively low-hysteresis-loss properties compared to the rubber used for conventional pneumatic tire to mitigate the rolling resistance. The spoke geometry has an advantage of transferring stress concentration in tire bottom region to entire region by connecting angled spokes. The geometry helps reduce strain energy which is proportional to square of stress when linear elastic material property is assumed. The tread ring is composed of tread rubber, steel belts, and elastomer layer. The elastomer layer enables shear deformation of the tread ring, allowing the NPT to have a contact length comparable to that of a pneumatic tire. The steel belts are designed to transfer stress in the circumferential direction and positioned outside the elastomer layer to accommodate deformation of the spokes, which have relatively low-hysteresis-loss to reduce the rolling resistance.

The geometry is configured to provide comparable vertical static stiffness and footprint length with the tolerance of 10% to those of a similar size pneumatic tire as shown in Fig. 2, specifically 165/70R14.

Fig. 1.
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Structure of NPT in this study

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Fig. 2.
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Contact properties of NPT in comparison to pneumatic tire

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3 Modeling Description and Computational Process

3.1 Computational Process

In this study, a methodological approach based on finite element structural analysis is employed. Linear frequency-domain finite element analysis involving rolling effect is widely used to simulate rolling tire. However, as the tread ring of the NPT undergoes large deformations during rolling over a cleat, it is crucial to consider geometric nonlinearity of the structure. Additionally, the vibration caused by rotating discrete spokes contacting road surface also needs to be considered. For these reasons, nonlinear (rolling) tire simulation is employed in this study.

3.2 Modeling Description

The schematic diagram of the model is described in Fig. 3. In this study, a combination of a FE tire model and a multibody quarter-car model is employed. This approach is suitable when the input forces between the left and right wheels are in-phase, such as in case of a cleat impact, to directly capture the tire-suspension interaction and the nonlinear behavior of the NPT while mitigating computational cost.

The quarter-car model consists of tire and suspension link FE models, rigid car body, joints, and bushings. The physical properties of the model are determined based on a specific front suspension of a B-segment car. The material properties used in the tire FE model such as elasticity and viscoelasticity are determined based on the laboratory material tests.

As shown in Fig. 3, the calculation assumes the condition to roll over a 10 mm high step-shaped cleat. In this study, the spindle forces under speed of 10 km/h, 40 km/h and 60 km/h are calculated and compared between the NPT and the pneumatic tire. Once the spindle forces are calculated, they can be utilized as input information for vibration predictions analysis of the entire vehicle system.

Fig. 3.
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Schematic diagram of simulation model

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4 Results and Discussions

4.1 Vibration Characteristics of NPT

Time and frequency domain response of the spindle force in vertical direction is described in Fig. 4 and 5, respectively. At 10 km/h condition, the time domain spindle force of the NPT shows a similar tendency compared to that of the pneumatic tire and has a dip after the initial impact of the cleat. The dip can be explained by the bending deformation of the tread ring during rolling over the cleat, which is commonly referred to the envelope property. As the spindle force during cleat crossing at lower speed is influenced by enveloping and footprint length properties [5], the NPT is considered to have the envelope property similar to that of the pneumatic tire. The major difference at 57 Hz can be attributed to the vibration generated while the individual spoke hits the road surface. The vibration around 190 Hz is a result of the characteristic vibration caused by the mass and stiffness of the spokes themselves, as shown in Fig. 6. This type of vibration can be referred to spring surge in general.

At 40 km/h condition, the time-domain spindle force exhibits the unsprung mass vibration around 10–20 Hz and the first-order vertical vibration mode around 90 Hz as shown in Fig. 6. The NPT shows the major difference in the vibration amplitude around 90 Hz compared to the pneumatic tire while the amplitudes of lower frequency are at the same level. Since the NPT has the envelope property similar to that of the pneumatic tire, the frequency characteristics of the input force generated when rolling over the cleat can be assumed to be qualitatively equivalent, and the difference in the spindle force can be attributed to the difference in the vibration characteristics of the tire structure. One possible factor is that the spokes of the NPT are composed of low-hysteresis-loss materials, which may explain the higher gain in this frequency range.

At 60 km/h condition, vibration amplitude of NPT is comparable to that of the pneumatic tire. It is well- known that tire vertical force resulting from cleat impact depends on the speed, as the frequency characteristics of the input force vary with the speed during cleat crossing.

Fig. 4.
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Time domain spindle force

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Fig. 5.
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Frequency domain spindle force

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Fig. 6.
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Mode shapes affecting spindle force

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In summary, significant differences were observed in the high frequency range such as the vibration caused by the rotating discrete spokes, the spoke surge, and the tire characteristic vibration at certain vehicle speed while the overall trends are similar. While these trends can potentially change through innovative designs of the spoke shape, the fundamental tendencies are estimated to remain the same. Addressing these differences would require improvements in both vehicle and tire construction.

4.2 Vibration Characteristics Between Different Structure

The results introduced in the previous section show the vibration characteristics of the NPT. However, these results are based on the examination of a specific structure. In particular, the NPT has an opportunity to change the vibration characteristic around 90 Hz by adjusting the enveloping property to change the frequency characteristics of input force during rolling over the cleat, leveraging its design flexibility. To verify this, a study was conducted by individually adjusting the elastic modulus of the spokes and elastomer layer to maintain the constant vertical stiffness while changing the envelope property.

In this study, two NPT models with almost identical vertical stiffness were examined, with different design properties as shown in Table 1. Spec A has the same specification as discussed in the previous section while the tread groove is omitted for simplicity. Figure 7 illustrates the contact properties of tires. Spec B, the construction with a tread ring of higher rigidity exhibits the shorter contact length, indicating the lower envelope property.

Table 1. Elastic modulus and vertical stiffness of NPTs for parametric study
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Fig. 7.
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Contact properties of NPT

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Figures 8 and 9 compare the time and frequency domain spindle force in vertical direction, respectively. For the NPT with the higher rigidity of the tread ring (Spec B), the characteristic vibration around 90 Hz at 40 km/h is reduced compared to Spec A. This result suggested that the frequency characteristics of the input force during rolling over the cleat has a peak close to the eigen frequency of the first-order vertical vibration mode of Spec A, which is qualitatively similar behavior to pneumatic tires [6], while it is separated for Spec C. However, the vibration around this frequency range is larger at 60 km/h. This can be explained by the speed dependency of the frequency characteristics of input force generated during cleat crossing.

As mentioned above, the trend of the NPT in this study, which exhibits a larger amplitude of high-frequency vibration, remains consistent across different structures. However, it can be described that the NPT has design flexibility to change the vibration characteristics at a specific speed by adjusting the envelope property.

Fig. 8.
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Time domain spindle force between different construction

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Fig. 9.
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Frequency domain spindle force between different construction

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5 Conclusion

In the present study, the vibration characteristics of a specific NPT construction was evaluated within a comprehensive vehicle simulation, considering the nonlinear behavior of the tire. The spindle force was investigated in comparison to the pneumatic tire and found that the NPT has high-frequency characteristic vibrations, although overall trends are similar. However, it was also described that the NPT possesses the design flexibility to change the frequency characteristics at a specific speed by adjusting the envelope property. Future efforts will focus on exploring performance improvements including the tire and the vehicle design properties.