Study on the interaction of electric vehicle roll and battery pack stability

Battery safety of electric vehicles is important for the application of electric vehicles. The performance of the battery pack determines the development of electric vehicle. Domestic and overseas media have reported electric vehicle explosion accidents so many times. Battery safety of electric vehicles mainly contains three aspects: electrical safety, thermal balance and vibration, the vibration of the battery pack is especially important. Vibration will lead to the declination of battery performance, the change of contact resistance, even the arc and uncontrollable thermal under driving condition. These may cause a fire or an explosion. The performance of battery pack not only depends on the BMS (Battery Management System) that makes the battery pack charges and discharges more reasonably, but depends on the stability of the battery pack. The vehicle steering characteristic is changed because of the ground roughness, and it influences the movement of the battery pack. To improve the ride performance of the vehicle and battery pack, it is essential to study the interaction of electric vehicle roll and battery pack stability [1]-[3].


Introduction
Battery safety of electric vehicles is important for the application of electric vehicles.The performance of the battery pack determines the development of electric vehicle.Domestic and overseas media have reported electric vehicle explosion accidents so many times.Battery safety of electric vehicles mainly contains three aspects: electrical safety, thermal balance and vibration, the vibration of the battery pack is especially important.Vibration will lead to the declination of battery performance, the change of contact resistance, even the arc and uncontrollable thermal under driving condition.These may cause a fire or an explosion.The performance of battery pack not only depends on the BMS (Battery Management System) that makes the battery pack charges and discharges more reasonably, but depends on the stability of the battery pack.The vehicle steering characteristic is changed because of the ground roughness, and it influences the movement of the battery pack.To improve the ride performance of the vehicle and battery pack, it is essential to study the interaction of electric vehicle roll and battery pack stability [1]- [3].

9-DOF vehicle roll model
The uneven road can affect the stability of the vehicle body and battery pack.Considering the vehicle yaw velocity and lateral velocity, a 9-DOF vehicle roll model includes the battery pack was developed (Fig. 1) [4,5].The 9-DOF as follows: vehicle lateral displacement, vertical displacement, pitch, roll, vehicle yaw velocity, and movement of the vertical direction of four wheels.
where   The relationship of position vector P in inertial system and vehicle coordinate system was obtained by using the instantaneous velocity of the rigid body.It can be expressed as: G is the ground reference system for vehicle motion, S as the body-fixed coordinate frame, the coordinate system of the vehicle has the angular velocity , and the synthetic velocity . Taking the derivative of the Eq. 2, we can get: Taking the derivative of the Eq. ( 3) again and substituting in the formula of acceleration composition, the acceleration of the centroid of the inertial system is obtained.
According to Eq. (1) and Eq. ( 4), the acceleration as was decomposed in the vehicle body coordinate system, and the lateral acceleration of the center of mass is obtained: Due to 0, 0 sin sin   , the Eq. ( 5) is simplified.

The moment equation of the vehicle body
Matrix Euler equation: where J is the inertia tensor matrix of the body in the satellite reference system, it can be represented as: ω is the angular velocity coordinate array:  is the antisymmetric coordinate matrix of ω: M is the torque coordinate array: Substituting the Eqs.( 7)-( 9) into the Eq. ( 6), we can rearrange the equations.
Torque around the x axis of the body: Torque around the y axis of the body: Torque around the z axis of the body:

Dynamic equations
The body vertical equation: are the supporting forces of four suspensions.

   
The vertical displacement of the upper end of the four suspensions can be obtained from the geometric relation in the Fig. 1 when there is a little roll angle and the pitching angle, we can get: The vertical motion equation of four tires: where qi is the vertical input of the ground, kti is the tire stiffness.
The vehicle pitching movement equation: The vehicle roll movement equation: The vehicle yaw angle movement equation: Regard the battery as four parts, there are: The geometric relations are obtained from the Fig. 3: The vertical motion equation of the mass center of battery pack: The pitch motion equation of the battery pack: The roll motion equation of the battery pack: The vibration attenuation of battery can be calculated by the above equations under the circumstance of vehicle vertical input , vertical, roll and pitch motion of battery and vibration transmission of road surface.

The establishment and calculation of roll simulation model
Table 1 shows the parameters from a remodeled vehicle and its battery pack.White noise is the input signal for the simulation.Road roughness is the Power Spectral Density (PSD) Class E. The front wheels slowly turned 0.1 rad.The results are shown in Fig. 7-9.We can draw conclusions from the Figs.7-9.When the steering angle slowly increases to a certain value, then the roll angle of the battery pack increases to a certain value too.It shows that the vehicle operates in a steady-state circular motion in stable state.If the speed of vehicle is not changed, then the battery pitch angle is unchanged.The vertical displacement of the battery changes little with the increase of the steering angle.It is because the steering angle is set to a smaller upper limit value during the simulation, and there is no large deviation in results.
And it can be known from Figs. 10-12, adding damping of front and rear suspensions will bulk up the vertical vibration amplitude of the battery, but the increment is relatively small.The pitch angle also increase, but in the meanwhile the roll angle has reduced, because the increase of suspension stiffness leads to the increase of roll angle stiffness.From the view of simulation results, the stiffness of the suspension is increased by configuring a high performance shock absorber and a short spring.Although it will inhibit roll, simply increasing the hardness of the shock absorber and spring will cause a lot of negative effects.On the one hand, the comfort of vehicles on the uneven roads is poor; on the other hand, as the suspensions cannot eliminate the road ups and downs, too many bounces of wheels lead to the loss of adhesion.So the stability of the battery pack has declined.

Conclusions
In this paper, the interaction of electric vehicle roll and battery pack stability was analyzed.When all of these impacts of automotive steering and vibration on body and battery pack are considered together, a full vehicle roll model of 9-DOF and Simulink model have been built to analysis the problem.The influence of the suspension parameters was simulated by increasing the four suspensions stiffness values.According to the calculated results, the suspension stiffness is a critical influence factor for the battery pack.When increased the four suspensions stiffness, the stability of the battery pack has declined.And the vibration is uncontrolled.Results obtained from this study are summarized as follows: 1.The stability of the vehicle body and the battery pack can reach an optimum value by the reasonable selection of the parameters of the suspension and the bracket; 2. Equipping vehicles with an active roll control system, a new type of suspension control system.It has become one of the hot spots in the development of automobile techniques.

Fig. 1 9 -
Fig. 1 9-DOF full vehicle roll model 2.1.The lateral acceleration of the vehicle body The point O is the intersection of vertical line passing through the centroid of vehicle and roll axis.Based on the vehicle coordinate system with the origin at the point O, the centroid position vector with respect to the point O can be written as [6]-[9]: hr cos cos -hr cos sin hr sin .

Fig. 2 2 . 5 .
Fig. 2 The schematic diagram of vehicle steering The geometric relations are obtained from the Fig. 2.

Fig. 3
Fig. 3 Top view of model The forces of four corners of the battery pack   1, 2, 3, 4

XFig. 4
Fig.4The full vehicle and battery roll model

Fig. 7
Fig. 7 Battery pack vertical displacement curve Fig. 8 shows the curve of battery pack pitch angle, X coordinate axle represents time (s).Y coordinate axle

Fig. 8
Fig. 8 Battery pack pitch angle curve Fig. 9 shows the curve of battery pack roll angle, X coordinate axle represents time (s).Y coordinate axle

Fig. 9
Fig. 9 Battery pack roll angle curve The four suspensions stiffness values increased by 5000N/m, the results are shown in Figs.10-12.The dotted line in Figs.10-12 stands for the situation after the suspen-

Fig. 10
Fig. 10 comparison of vertical displacement of battery pack