# Exploring the Potential of Camber Control to Improve Vehicles’ Energy Efficiency during Cornering

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## Abstract

**:**

## 1. Introduction

## 2. Power Loss during Cornering

#### 2.1. Tyre Kinetics with Camber Control

_{w}, Y

_{w}and Z

_{w}are coordinates of the tyre. While keeping the same camber angle during driving, the direction of $T$ is perpendicular to the wheel plane. The equation of motion can then be written as

#### 2.2. The Power for Propulsion of the Wheels

^{2}).

#### 2.3. The Power for Controlling Camber Angles

## 3. Tyre Model

#### 3.1. Longitudinal Force

#### 3.2. Lateral Force

#### 3.3. Overturning Moment

#### 3.4. Aligning Moment

## 4. Energy Saving with Camber Control

#### 4.1. Path Design

#### 4.2. Driver Model

_{1}= T

_{2}= T

_{3}= T

_{4}. The steering controller is based on the multiple-preview point steering theory [20,21,22]. Figure 8 shows a basic schematic diagram of this steering controller. As shown in the figure, the controller has three inputs: the lateral offset Δy

_{1}between the vehicle and the road at the current position, the yaw angle offset Δψ between the vehicle yaw angle ψ

_{v}and the road heading angle ψ

_{r}and the lateral offset Δy

_{2}at preview distance l ahead of the vehicle. The l is the product of preview time t

_{p}and the vehicle forward speed V

_{x}, i.e., l = V

_{x}t

_{p}. The front steering angle ${\delta}_{f}$ can be determined as

_{f}is $[0,{25}^{\xb0}]$. The camber angles of both front wheels, ${\gamma}_{1}$ and ${\gamma}_{2}$, are set to the same value, and so are also the camber angles of both rear wheels, ${\gamma}_{3}$ and ${\gamma}_{4}$, i.e., ${\gamma}_{1}$ = ${\gamma}_{2}$ and ${\gamma}_{3}$ = ${\gamma}_{4}$. For the control of the camber angle, the relationships between camber angles and front steering angle are defined as:

#### 4.3. Analysis of Components of Power Loss

_{all}changes, the simulation model is implemented in Matlab and Dymola. The simulation setups presented in Table 5 are used. The path parameters L = 60 m and R = 100 m are adopted; two lateral accelerations at steady-state cornering 3 m/s

^{2}and 6 m/s

^{2}are used and corresponding velocities are calculated; three different combinations of K

_{12}and K

_{34}are simulated. The P

_{all}can be a function of K

_{12}and K

_{34}under a given path and velocity.

^{3}. In [23], it was shown that the effect of camber on ${f}_{rr}$ is low, so in this paper it is kept constant and is given a value of ${f}_{rr}=0.01$.

_{all}, P

_{camber}, P

_{w}and the components of P

_{w}are shown in Figure 10 and Figure 11.

_{w}are aerodynamic loss, rolling resistance loss and lateral slip loss. Although controlling camber can cost power, which is shown in Figure 10d and Figure 11d, the total power loss can still be reduced while entering the corner, which is shown in Figure 10c K

_{12}= K

_{34}= 4, 9 and Figure 11c K

_{12}= K

_{34}= 4, 9. From Figure 10g and Figure 11g, implementing positive camber control coefficients can greatly reduce lateral slip loss. The reduction of this part of power loss can be explained by studying Figure 6b. It is evident that keeping the same lateral force, the camber thrust can reduce the absolute value of slip angle and consequently, the lateral slip loss is reduced.

_{zi}sinγ

_{i}can have different influences on rolling resistance loss in different slip angle regions. From Figure 12, for R = 100 m, V

_{x}= 62.3 km/h and a

_{y}= 3 m/s

^{2}, the slip angles are comparatively small. Compared to K

_{12}= K

_{34}= 4, the slip angles are further reduced by K

_{12}= K

_{34}= 9 and then all aligning moments become positive, which increases the rolling resistance substantially and greatly weakens the camber’s contribution to power reduction. However, from Figure 13, for R = 100 m, V

_{x}= 88.18 km/h and a

_{y}= 6 m/s

^{2}, the slip angles are seen to be comparatively large. Consequently, further increasing the camber angle, $\sum _{i=1}^{4}{M}_{zi}\mathrm{sin}{\gamma}_{i}$ does not increase much and the reduction of lateral slip loss still plays a dominant role in energy saving.

## 5. Controller Design for Camber

_{x}= 62.3 km/h and a

_{y}= 3 m/s

^{2}, when ${K}_{12}={K}_{34}=4$, the camber angles at steady-state cornering are found to be 6.5

^{0}and $\eta $ is 8.31%; for R = 100 m, V

_{x}= 88.18 km/h and a

_{y}= 6 m/s

^{2}, when ${K}_{12}={K}_{34}=9$, the camber angles at steady-state cornering are 15

^{0}and $\eta $ is 19.11%.

^{2}) at steady-state cornering are studied and corresponding velocities are deducted.

_{z}introduced in Section 4.3, at low accelerations higher camber angle settings might increase rolling resistance loss considerably as can be seen from Figure 14a–c, Figure 15a–c and Figure 16a–c. For 6 m/s

^{2}, the results show that for larger values of K

_{12}and K

_{34}, more energy can be saved. But for the rest of the lateral accelerations there are maximum energy saving points. Above all, these points are not singular and many combinations of K

_{12}and K

_{34}can be chosen for energy saving control.

_{12}= K

_{34}. To study these assumptions, the combinations of K

_{12}and K

_{34}are chosen and the camber angles during the steady-state cornering part are also shown in Table 8. These combinations are the optimal points or near the optimal ones. It can be seen that for certain a

_{y}during the steady-state cornering, the efficient camber angles are approximately equal.

_{y}. A controller which uses a

_{y}as criteria for the camber control is shown in Figure 17 and the mean value of the three camber angles in Table 8 for each lateral acceleration a

_{y}is used. Although, at high lateral accelerations such as 6m/s

^{2}and above, camber setting larger than 15° may save more energy, the average driver generally drives below 4 m/s

^{2}and 6 m/s

^{2}or higher only occurs in extreme situations [25]. Also with the concern of suspension working space, 15° camber angle is still chosen for lateral acceleration higher than 6 m/s

^{2}in this work.

_{f}and a

_{y}for each constant velocity can be regarded to be unchanged. Therefore, a feedforward camber controller based on the information δ

_{f}and V

_{x}is designed for simulation purposes. With the designed camber controller, the percentages of energy saving for the chosen driving scenarios defined in Table 7 are shown in Figure 18. The results show that the designed camber controller has a very promising application prospect for energy saving.

## 6. Conclusions

_{12}and K

_{34}, two designed paths and two velocities are primarily studied. With camber control, the components of total power loss, which includes the power for controlling camber, are studied and from the results it is concluded that the three main components are aerodynamic loss, rolling resistance loss and lateral slip loss. For chosen combinations of K

_{12}and K

_{34}, camber control can reduce lateral slip loss but can also cause different changes in rolling resistance loss. In Section 5, different combinations of K

_{12}and K

_{34}, three paths and six velocities (corresponding to six accelerations at steady-state cornering) for each path are further studied.

_{12}and K

_{34}that can have a positive impact. The strategy of implementing the same camber angles for all tyres is chosen to be adopted. From Table 8, for each lateral acceleration the efficient camber angles are almost equal even if the velocities are different. The camber controller based on lateral acceleration is then developed and the effectiveness of the controller is evaluated. The results show that the proposed control algorithm is promising to save energy during cornering.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Active wheel corner module [8].

**Figure 9.**Rear views of the vehicle with different settings on camber control coefficient K

_{12}and K

_{34}.

Coefficient | Value | Coefficient | Value | Coefficient | Value | Coefficient | Value |
---|---|---|---|---|---|---|---|

${p}_{Cx1}$ | 1.579 | ${p}_{Ex3}$ | 0 | ${p}_{Kx3}$ | −0.4098 | ${r}_{Ex1}$ | −0.4403 |

${p}_{Dx1}$ | 1.0422 | ${p}_{Ex4}$ | 0.001719 | ${p}_{Vx1}$ | 0 | ${r}_{Ex2}$ | −0.4663 |

${p}_{Dx2}$ | −0.08285 | ${p}_{Hx1}$ | 0 | ${p}_{Vx2}$ | 1.0568 ×10^{−4} | ${r}_{Hx1}$ | −9.968 × 10^{−5} |

${p}_{Dx3}$ | 1 | ${p}_{Hx2}$ | 0.0011598 | ${r}_{Bx1}$ | 13.046 | ||

${p}_{Ex1}$ | 0.11113 | ${p}_{Kx1}$ | 21.687 | ${r}_{Bx2}$ | 9.718 | ||

${p}_{Ex2}$ | 0.3143 | ${p}_{Kx2}$ | 13.728 | ${r}_{Bx3}$ | 0 |

Coefficient | Value | Coefficient | Value | Coefficient | Value | Coefficient | Value |
---|---|---|---|---|---|---|---|

${p}_{Cy1}$ | 1.338 | ${p}_{Hy2}$ | 0.00352 | ${p}_{Vy3}$ | −0.162 | ${r}_{By3}$ | 0.002037 |

${p}_{Dy1}$ | 0.8785 | ${p}_{Ky1}$ | −15.324 | ${p}_{Vy4}$ | −0.4864 | ${r}_{By4}$ | 0 |

${p}_{Dy2}$ | −0.06452 | ${p}_{Ky2}$ | 1.715 | ${r}_{Vy1}$ | 0.05187 | ${r}_{Ey1}$ | 0.3148 |

${p}_{Dy3}$ | 0 | ${p}_{Ky3}$ | 0.3695 | ${r}_{Vy2}$ | 4.853 × 10^{−4} | ${r}_{Ey2}$ | 0.004867 |

${p}_{Ey1}$ | −0.8057 | ${p}_{Ky4}$ | 2.0005 | ${r}_{Vy3}$ | 0 | ${r}_{Hy1}$ | 0.009472 |

${p}_{Ey2}$ | −0.6046 | ${p}_{Ky5}$ | 0 | ${r}_{Vy4}$ | 94.63 | ${r}_{Hy2}$ | 0.009754 |

${p}_{Ey3}$ | 0.09854 | ${p}_{Ky6}$ | −0.8987 | ${r}_{Vy5}$ | 1.8914 | ||

${p}_{Ey4}$ | −6.697 | ${p}_{Ky7}$ | −0.23303 | ${r}_{Vy6}$ | 23.8 | ||

${p}_{Ey5}$ | 0 | ${p}_{Vy1}$ | 0 | ${r}_{By1}$ | 10.622 | ||

${p}_{Hy1}$ | 0 | ${p}_{Vy2}$ | 0.03592 | ${r}_{By2}$ | 7.82 |

Coefficient | Value | Coefficient | Value | Coefficient | Value | Coefficient | Value |
---|---|---|---|---|---|---|---|

${q}_{sx1}$ | 0 | ${q}_{sx4}$ | 4.912 | ${q}_{sx7}$ | 0.7104 | ${q}_{sx10}$ | 0.2824 |

${q}_{sx2}$ | 1.1915 | ${q}_{sx5}$ | 1.02 | ${q}_{sx8}$ | −0.023393 | ${q}_{sx11}$ | 5.349 |

${q}_{sx3}$ | 0.013948 | ${q}_{sx6}$ | 22.83 | ${q}_{sx9}$ | 0.6581 |

Coefficient | Value | Coefficient | Value | Coefficient | Value | Coefficient | Value |
---|---|---|---|---|---|---|---|

${q}_{Bz1}$ | 12.035 | ${q}_{Dz1}$ | 0.09068 | ${q}_{Dz10}$ | 0 | ${q}_{Hz2}$ | 0.0024087 |

${q}_{Bz2}$ | −1.33 | ${q}_{Dz2}$ | −0.00565 | ${q}_{Dz11}$ | 0 | ${q}_{Hz3}$ | 0.24973 |

${q}_{Bz3}$ | 0 | ${q}_{Dz3}$ | 0.3778 | ${q}_{Ez1}$ | −1.7924 | ${q}_{Hz4}$ | −0.21205 |

${q}_{Bz5}$ | −0.14853 | ${q}_{Dz4}$ | 0 | ${q}_{Ez2}$ | 0.8975 | ${s}_{Sz1}$ | 0.00918 |

${q}_{Bz6}$ | 0 | ${q}_{Dz6}$ | 0 | ${q}_{Ez3}$ | 0 | ${s}_{Sz2}$ | 0.03869 |

${q}_{Bz9}$ | 34.5 | ${q}_{Dz7}$ | −0.002091 | ${q}_{Ez4}$ | 0.2895 | ${s}_{Sz3}$ | 0 |

${q}_{Bz10}$ | 0 | ${q}_{Dz8}$ | −0.1428 | ${q}_{Ez5}$ | −0.6786 | ${s}_{Sz4}$ | 0 |

${q}_{Cz1}$ | 1.2923 | ${q}_{Dz9}$ | 0.00915 | ${q}_{Hz1}$ | 0.0014333 |

L (m) | R (m) | V_{x} (km/h) | a_{y} (m/s^{2}) | K_{12} | K_{34} |
---|---|---|---|---|---|

60 | 100 | 62.3 | 3 | 0 | 0 |

60 | 100 | 62.3 | 3 | 4 | 4 |

60 | 100 | 62.3 | 3 | 9 | 9 |

60 | 100 | 88.1 | 6 | 0 | 0 |

60 | 100 | 88.1 | 6 | 4 | 4 |

60 | 100 | 88.1 | 6 | 9 | 9 |

Parameters | Values | Parameters | Values |
---|---|---|---|

m | 1500 kg | I_{w} | 1 kgm^{2} |

I_{z} | 1700 kgm^{2} | C_{ar} | 0.3 |

l_{f} | 1.2 m | A | 2 m^{2} |

l_{r} | 1.5 m | R_{0} | 0.3 m |

t_{w} | 1.65 m | h | 0.48 m |

R (m) | a_{y} (m/s^{2}) | V_{x} (km/h) | R (m) | a_{y} (m/s^{2}) | V_{x} (km/h) | R (m) | a_{y} (m/s^{2}) | V_{x} (km/h) |
---|---|---|---|---|---|---|---|---|

50 | 1 | 25.4 | 100 | 1 | 36 | 150 | 1 | 44 |

2 | 36 | 2 | 50.9 | 2 | 62.35 | |||

3 | 44 | 3 | 62.35 | 3 | 76.3 | |||

4 | 50.9 | 4 | 72 | 4 | 88.1 | |||

5 | 56.9 | 5 | 80.4 | 5 | 98.5 | |||

6 | 62.35 | 6 | 88.1 | 6 | 108 |

a_{y} (m/s^{2}) | R (m) | V_{x} (km/h) | K_{12} = K_{34} | γ_{1} = γ_{2} = γ_{3} = γ_{4} (degree) | η (%) |
---|---|---|---|---|---|

1 | 50 | 25.4 | 0.8 | 2.49 | 1.54 |

100 | 36 | 1.5 | 2.35 | 1.49 | |

150 | 44 | 2 | 2.11 | 1.40 | |

2 | 50 | 36 | 1.5 | 4.70 | 5.35 |

100 | 50.9 | 3 | 4.77 | 4.70 | |

150 | 62.35 | 4 | 4.31 | 4.24 | |

3 | 50 | 44 | 2 | 6.33 | 9.68 |

100 | 62.35 | 4 | 6.47 | 8.31 | |

150 | 76.3 | 6 | 6.60 | 7.30 | |

4 | 50 | 50.9 | 3 | 9.53 | 13.62 |

100 | 72 | 6 | 9.78 | 10.75 | |

150 | 88.1 | 8.5 | 9.51 | 10.12 | |

5 | 50 | 56.9 | 4.4 | 13.96 | 17.63 |

100 | 80.4 | 8.5 | 13.88 | 15.20 | |

150 | 98.5 | 12.5 | 13.98 | 13.31 | |

6 | 50 | 62.35 | 5 | 15.00 | 21.92 |

100 | 88.1 | 9 | 15.00 | 19.10 | |

150 | 108 | 13 | 15.00 | 16.89 |

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## Share and Cite

**MDPI and ACS Style**

Sun, P.; Stensson Trigell, A.; Drugge, L.; Jerrelind, J.; Jonasson, M. Exploring the Potential of Camber Control to Improve Vehicles’ Energy Efficiency during Cornering. *Energies* **2018**, *11*, 724.
https://doi.org/10.3390/en11040724

**AMA Style**

Sun P, Stensson Trigell A, Drugge L, Jerrelind J, Jonasson M. Exploring the Potential of Camber Control to Improve Vehicles’ Energy Efficiency during Cornering. *Energies*. 2018; 11(4):724.
https://doi.org/10.3390/en11040724

**Chicago/Turabian Style**

Sun, Peikun, Annika Stensson Trigell, Lars Drugge, Jenny Jerrelind, and Mats Jonasson. 2018. "Exploring the Potential of Camber Control to Improve Vehicles’ Energy Efficiency during Cornering" *Energies* 11, no. 4: 724.
https://doi.org/10.3390/en11040724