**3. Case study**

With Eq. (36), it is possible to obtain a better vehicle stability representation and

To simplify the solution of the system of equations in Eq. (30), the following

• the lateral load transfer of the trailer model is controlled through the torsional moment of the chassis (spherical joints 27 and 28 (Eqs. (15) and (16))).

*Fx*<sup>1</sup> *Fy*<sup>1</sup> ⋮ *Tx*<sup>5</sup> *Tx*<sup>11</sup> *Tx*<sup>21</sup> *Tx*<sup>27</sup> *Tx*<sup>28</sup> *FT*<sup>2</sup> *FT*<sup>4</sup> *FT*<sup>18</sup> *FT*<sup>20</sup> *FLS*<sup>6</sup> *FLS*<sup>9</sup> *FLS*<sup>22</sup> *FLS*<sup>25</sup> *FFW*<sup>12</sup> *FFW*<sup>17</sup> *Fz*<sup>1</sup> *Fz*<sup>3</sup> *Fz*<sup>19</sup> *Fz*<sup>17</sup> *Px Py Pz*

*:*

½ � 0 <sup>135</sup>�<sup>1</sup>

(38)

Eq. (38) shows the final static system for the stability analysis, solving this system using the Gauss-Jordan elimination method, all secondary variables are a function of primary variables, (*Px*—force acting on the *x*-axis, *Py*—force acting on

• in the majority of *LCVs*, the load on the trailers is uniformly distributed

the *SRT*3*Dψϕφ* factor value attainments closer to reality.

*Numerical and Experimental Studies on Combustion Engines and Vehicles*

the *y*-axis, and *Pz*—force acting on the z-axis).

hypotheses were considered:

(Eq. (20));

*Cut* 1

⋮

*Cut* 22

*Eq:*ð Þ 20 *Eq:*ð Þ 15 *Eq:*ð Þ 16

In this study, a B-train trailer with two axles on front and three axles on the rear is analysed. This model has a suspension system with a tandem axle, and its parameters depend on the construction materials. Another important parameter of the model is the dynamic rolling radius or loaded radius*li*. The proposedmodel considersMichelin XZA® [36] radial tyres. **Table 5** shows the parameters of the trailer used in this analysis [32, 38].

To calculate the *SRT* factor, the inertial force is increased until the lateral load transfer in the rear axle is complete (the entire load is transferred from the rear inner tyre to the rear outer tyre when the model makes a turn). The reduction in the *SRT* factor (Eq. (36) and the solution of the system of Eq. (38)) results from the combined action of the trailer systems, which allows a body roll angle of the trailer model (**Figure 33**) [32]. In this figure, it can be seen how the stability factor varies according to the influence of some of the parameters of the developed model.

When the model considers all parameters, the *LLT* coefficient on the front axle is approximately 70% of the *LLT* coefficient on the rear axle [21]. Applying this concept, the *SRTall* factor reduces to *0.3364 g*. Finally, the proposed model shows how the lateral offset of the cargo (*d1* = 0.1 m) influences the *SRToff* factor: 2 cm of lateral offset corresponds to a loss of stability of around *0.01 g* a reduction similar to that reported by Winkler [20, 32].

Additionally, the proposed model shows how a change in the lateral separation between the springs (*b*) influences the *SRT* factor. Some *LCVs* with tanker trailers have a greater lateral separation between the springs, which leads to a decrease in the roll angle and thus an increase in the *SRT* factor: 1 cm of lateral separation between the springs corresponds to a gain or loss of stability of around *0.001 g,* as shown in **Figure 33b** [32].

This model also allows the determination of the lateral (*h1*) and vertical (*h2*) *CG* location (**Figure 34**).

Finally, if we consider the recommended maximum lateral load transfer ratio for the rear axle of 0.6 [39, 40], and also include the recommended bank angle and longitudinal slope of the road [41, 42], we can calculate the *SRT* factor for a trailer model on downhill and uphill corners. **Table 6** shows a trailer model with different trailer/trailer angles (*ψ*) [32].

**Figure 33.** *(a) Roll angle of the trailer (*θ*). (b) Change in the* SRT *factor.*

## *Numerical and Experimental Studies on Combustion Engines and Vehicles*

An analysis of **Table 6** leads to the following conclusions for the critical condi-

• when the trailer is in downhill corners, a 1% slope angle corresponds to a loss of

• the trailer/trailer angle is inversely proportional to the *SRT* factor since when the trailer makes a horizontal curve with a small radio, and the trailer/trailer

This study demonstrates that the longitudinal characteristics of a trailer model have an essential influence on the *SRT* factor calculation. In this case, the *SRT* factor is approximately 38% lower than the previously reported standard value. This value is very close to that reported by Winkler [20] (i.e. 40%), which suggests that the

This model also shows that the change in the lateral separation between the springs (*b*) plays an important role, and thus it should be considered in the design and construction of trailers. Greater lateral separation between the springs will

We also found that the parameters of the road, such as the bank angle and the longitudinal slope angle, can affect vehicle stability. This situation is closer to the actual problem: when the road is not planar, the lateral and the longitudinal load transfer play an important role in reducing the stability. On the other hand, this provides a very important warning, because some simplifications carried out when estimating the *SRT* factor can lead to a considerably higher stability value. This is a point of concern, leading to the perception that our roads are safer than they really

• a 1% bank angle corresponds to gain in the stability of around 0.01 *g*;

angle and inertial force are large, the *SRT* factor is lower.

*Stability Analysis of Long Combination Vehicles Using Davies Method*

tions of the trailer:

**4. Conclusions**

are [32].

**157**

stability of around 0.0021 *g*;

*DOI: http://dx.doi.org/10.5772/intechopen.92874*

proposed model provides consistent results [32].

increase the trailer model stability [32].

**Figure 34.** *(a) Lateral* CG *location. (b) Vertical* CG *location.*


#### **Table 6.**

*Static rollover threshold (SRT) of the trailer model with trailer/trailer angle.*

In the worst-case scenario, the trailer model, for a downhill corner with a bank angle of 0%, the longitudinal slope of the road of 8%, and a trailer/trailer angle of 20° can reduce the *SRT* factor of the model by 59.6%, using *0.4511 g* as a reference [32].

*Stability Analysis of Long Combination Vehicles Using Davies Method DOI: http://dx.doi.org/10.5772/intechopen.92874*

An analysis of **Table 6** leads to the following conclusions for the critical conditions of the trailer:

