A braking control method for electric vehicles that combines economy and comfort

Abstract

The application is suitable for the field of automobile braking technology, and provides an electric vehicle braking control method combining economy and comfort, which comprises the following steps: step one, longitudinal-vertical dynamics modeling; step two, tire model modeling; step three, comfort factor: combining the longitudinal-vertical dynamics model and the tire model, analyzing the factors influencing comfort from the longitudinal and vertical angles, extracting important influencing factors, and interacting the longitudinal and vertical influencing factors to analyze the factors influencing comfort from the longitudinal-vertical coupling angle; step four, economy factor: ensuring that the vehicle uses regenerative braking to the maximum extent and reduces tire wear as much as possible within the range allowed by the motor power and torque and under the premise of related vehicle component constraints; and step five, ensuring the comfort and economy of the electric vehicle during braking through the comfort factor and the economy factor, so that the economy and braking safety of the vehicle are ensured.

Description

A braking control method for electric vehicles that combines economy and comfort Technical Field

[0001] This invention relates to the field of automotive braking technology, specifically to a braking control method for electric vehicles that integrates economy and comfort. Background Technology

[0002] In recent years, electric drive has become an inevitable main power source for automobiles. External factors driving this change include the global energy and environmental crises, while internal factors include the continuous development and progress of technologies such as motors and batteries, propelling electric vehicles into the practical application stage. Currently, the main obstacles to the development of electric vehicles include: short driving range, limited charging infrastructure coverage, and high cost, short lifespan, and low energy density of batteries.

[0003] Improving the fuel economy of electric vehicles requires not only increasing the energy recovered during braking but also minimizing tire wear. Studies show that in urban driving conditions, 30%–50% of the energy directly driving a vehicle is consumed during braking. Therefore, recovering and utilizing this braking energy is crucial for increasing the vehicle's driving range. Braking force causes longitudinal deformation of the tires, and the energy loss resulting from this deformation leads to tire wear. Tire wear not only causes economic losses but also affects vehicle braking safety. Therefore, tire wear is also vital to the fuel economy and safety of electric vehicles.

[0004] During vehicle braking, longitudinal movement causes vehicle pitch, and road surface excitation leads to vertical vibration, resulting in decreased ride comfort and a reduced driving experience. Existing research often considers energy recovery during electric vehicle braking or incorporates longitudinal comfort into energy recovery control, addressing comfort through braking force distribution. However, this approach only considers a single economic factor, neglecting the impact of tire wear on vehicle economy and safety, as well as the influence of vertical control on comfort and economy. Therefore, there is an urgent need to provide an electric vehicle braking control method that integrates economy and comfort to overcome the shortcomings in current practical applications. Summary of the Invention

[0005] The purpose of this invention is to provide a braking control method for electric vehicles that integrates economy and comfort, aiming to solve the problems in the background art mentioned above.

[0006] This invention is implemented as follows: a braking control method for electric vehicles that integrates economy and comfort, the method comprising the following steps:

[0007] Step 1: Longitudinal-Vertical Dynamics Modeling: Select a five-degree-of-freedom half-vehicle model with longitudinal-vertical coupling. Based on the half-vehicle model, derive the longitudinal and vertical dynamic models of the vehicle, thereby coupling the vehicle's vertical suspension system with the longitudinal dynamic system.

[0008] Step 2: Tire Model Building: Select the Magic Tire Model;

[0009] Step 3: Comfort Factors: Combining the longitudinal-vertical dynamics model and the tire model, we analyze the factors affecting comfort from both longitudinal and vertical perspectives, extract the important influencing factors, and interact the longitudinal and vertical influencing factors to analyze the factors affecting comfort from the perspective of longitudinal-vertical coupling.

[0010] Step 4: Economic Factor: The total energy loss is obtained by superimposing the various energy losses. Braking force is then distributed to the front and rear and left and right wheels of the vehicle. The distribution result ensures that, within the allowable range of motor power and torque and under the constraints of relevant vehicle components, the vehicle can use regenerative braking to the maximum extent and minimize tire wear.

[0011] Step 5: By using comfort and economy factors, ensure that the amplitude of vehicle body vibration, energy loss and tire wear are minimized. Use model predictive control algorithm to optimize the distribution of front and rear suspension forces and front and rear wheel braking forces to ensure the comfort and economy of electric vehicle braking.

[0012] As a further aspect of the present invention: In step one, the five degrees of freedom of motion of the half-vehicle model include the longitudinal rigid body motion of the whole vehicle, the vertical motion and pitch motion of the vehicle body, and the rotational motion of the front wheel and the rear wheel about their respective axes.

[0013] As a further aspect of the present invention: In step one, starting from the vertical motion, the loads on the front and rear wheels are as follows:

[0014]

[0015] Where m x m wf m wr These are respectively half the vehicle's mass, the mass of the front wheels, and the mass of the rear wheels, w mf w mr These represent the motor speeds of the front and rear wheels, respectively, in L. f L r k represents the distance from the center of gravity to the front and rear axles, respectively. twf k twr These represent the vertical stiffness of the front and rear wheels, respectively; L is the wheelbase; and z is the vehicle braking intensity. fw z rwThese represent the vertical displacements of the unsprung mass at the front and rear, respectively.

[0016] The dynamic load caused by vertical motion can be considered as an equivalent force applied to the front and rear wheels, and the equivalent force values ​​are as follows:

[0017]

[0018] Where h xd The height of the vehicle's center of gravity;

[0019] The front and rear suspension forces resulting from the combined effects of longitudinal braking motion and road surface excitation are as follows:

[0020]

[0021] Where k sf k sr These are the front suspension spring stiffness and the rear suspension spring stiffness, respectively, c sf c sr These are the front suspension damping coefficients and the rear suspension damping coefficients, respectively. x The vertical displacement of the vehicle body, θ is the height of the vehicle's center of gravity, z fx z rx These are the vertical displacements of the front and rear vehicle bodies, respectively. sfc F src These are the front controllable damping force and the rear controllable damping force, q f q r These are the vertical disturbance input displacement signals of the road surface at the location of the preceding vehicle and the following vehicle, respectively. These displacement signals are derived from the road surface power spectral density G. q (f) is represented, and road surface roughness is divided into eight levels (AH) using power spectral density values, G q The formula for calculating (f) is as follows:

[0022]

[0023] Where f is the reciprocal of the wavelength, i.e., the spatial frequency, f0 is the reference spatial frequency, and G q (f0) is the road surface roughness coefficient, and n is the frequency exponent;

[0024] The equations of motion and rotation for the front and rear wheels are as follows:

[0025]

[0026] Where I wf I wrF represents the moment of inertia of the front and rear wheels about their respective axes of rotation. xf F xr The longitudinal braking forces of the front and rear wheels, T, are respectively. df T dr The braking torques of the front and rear wheels are w, respectively. wf w wr These are the rotational speeds of the front and rear wheels, respectively.

[0027] The equations of motion for the vehicle body's vertical direction and the dynamic equations for its pitch angle are as follows:

[0028]

[0029]

[0030] When the vehicle starts moving longitudinally, the equation of motion during the braking process is as follows:

[0031] F b +F f +F w +F i =δma v ;

[0032] Where F b For vehicle braking force, F f For rolling resistance, F w For wind speed drag, F i For ramp resistance, δ is the vehicle rotational mass conversion factor, and a is the slope resistance. v For vehicle acceleration, the braking intensity formula is z = -a v / g;

[0033] The relationship between the hydraulic braking torque and wheel cylinder pressure of the front and rear axles is as follows:

[0034]

[0035] Where T phf T phr These are the actual hydraulic braking torques of the front and rear wheels, respectively, p wf p wr Do not use the actual cylinder pressure of the front and rear wheels, K zf K zr The braking coefficients D for the front and rear axle brakes, respectively. zf D zr These are the diameters of the front and rear wheel brake cylinders, R. zf R zr Let be the effective radii of the front and rear brake discs, respectively; then the total braking torque applied to the wheels is as follows:

[0036] T di =T hi +T mi i = f, r

[0037] T ref =2(T) hf +T hr +T mf +T mr ).

[0038] As a further aspect of the present invention: In step one, the motor is the key to energy recovery, and during braking, the power P transmitted by the motor to the battery is... b And the power P transmitted to the battery by the front and rear motors. bf P br as follows:

[0039] P b =P bf +P br

[0040] P bf =T mf w mf η mf / 9550

[0041] P br =T mr w mr η mr / 9550;

[0042] Where T mf T mr P represents the torque of the front motor and the rear motor, respectively. bf P br η represents the power transmitted to the battery by the front and rear motors, respectively. mf η mr These are the conversion efficiencies of the front and rear motors, respectively.

[0043] In the transmission system, the relationship between the torque at the motor end and the wheel end and the rotational speed is shown below:

[0044]

[0045] Where w wf w wr T represents the rotational speeds of the front and rear wheels, respectively. mdf T mdr i represents the braking torque applied by the front motor and the rear motor to the front and rear wheels, respectively. f i r These are the reduction ratios of the front and rear transmissions, respectively.

[0046] The formulas for the battery open-circuit voltage E and the battery recovered energy Q are as follows:

[0047] E = U + Ir b

[0048] |P bf +P br |=|EI|+I 2 r b

[0049] Q = ∫EIdt;

[0050] Where U and I are the charging voltage and charging current, respectively, and r b If we consider the internal resistance of the battery during charging, then the expression for battery charging is as follows:

[0051] C bttry =∫Idt / 3600

[0052] C max =f bttry (temp)

[0053]

[0054] Where C bttry For discharge capacity, C max To maximize battery energy usage, f bttry (temp) is a function related to temperature.

[0055] As a further aspect of the present invention: In step two, during vehicle braking, the tire slip ratio is calculated using the following formula:

[0056]

[0057] Where u w1 u w2 These are the center velocities of the front and rear wheels, respectively, r. r0 v is the radius of free rolling of the wheel. x For vehicle speed;

[0058] Under steady-state braking conditions, the formula for calculating the longitudinal force is as follows:

[0059] F xi =D sin{Carctan[Bs-E(Bs)} j -arctan(Bs j ))]}j=1,2i=f,r;

[0060] Among them, parameter D determines the peak value of the curve and is the peak factor; C affects the shape of the curve and is the shape factor; B is the stretch curve factor, corresponding to the stiffness coefficient of the linear segment; and E affects the characteristic shape around the peak value of the curve and is the curvature factor.

[0061] As a further aspect of the present invention: In step three, by combining the formulas for front suspension force and rear suspension force, the front controllable damping force and rear controllable damping force are optimized, thereby optimizing the front suspension force, rear suspension force, and braking intensity. This balances the changes in front and rear wheel loads caused by braking and the vertical vibration of the vehicle body caused by road surface excitation. The calculation formula is as follows:

[0062] Z = (|z fx |-|z rx |)+(|z fw |-|z rw |)+|z x |+|θ|.

[0063] As a further aspect of the present invention: In step four, the energy equation of the vehicle during braking is as follows:

[0064] E r =E0-E loss1 -E loss2 -E loss3 -E f ;

[0065] Among them, E r The energy recovered from the battery, E0 is the kinetic energy of the vehicle at the start of the braking process, E loss1 E is the energy loss caused by slope drag and air drag. loss2 Energy loss caused by internal components of the hub motor, E loss3 Energy loss due to mechanical friction in hydraulic systems, E f The kinetic energy of the vehicle at the end of the braking process;

[0066] When the starting and ending speeds of the braking process are determined, the energy that needs to be recovered from the battery is maximized, thus minimizing the energy loss at each stage, or minimizing the sum of energy losses at each stage. The formulas for calculating each energy loss are as follows:

[0067]

[0068]

[0069]

[0070] E loss =E loss1+E loss2 +E loss3 ;

[0071] Where F a For slope resistance, F s For air resistance, t s For sampling time, w mf w mr These represent the speeds of the front and rear motors, respectively, in W. wf w wr T represents the rotational speeds of the front and rear wheels, respectively. hf T hr These are the hydraulic braking torques for the front and rear wheels, respectively.

[0072] As a further aspect of the present invention: In step four, the wear amount I of the tire tread during tire braking... a The calculation formula is as follows:

[0073]

[0074] To reduce unnecessary tire wear during braking, the torque differences between the front and rear wheels, and between the left and right wheels, need to be reduced as follows:

[0075] ΔT=(T mf -T mr )+(T hr -T hr );

[0076] To ensure the vehicle meets overall braking requirements, the magnitude of the product of slip ratio and vertical load, ΔI, needs to be reduced as follows:

[0077] ΔI=(s f ×F zf +s r ×F zr )×10 -3 ;

[0078] The total component of the tire wear factor is obtained as Δ = ΔT + ΔI.

[0079] As a further aspect of the present invention: In step five, in the model predictive control algorithm, x is used as the state variable, U as the control variable, and J as the objective function, with the relevant expressions as follows:

[0080]

[0081] Where α, β, and γ are the weights of the energy recovery factor, tire wear factor, and comfort factor, respectively. To achieve the control requirements, the relevant vehicle parameters must also meet their associated constraints.

[0082]

[0083] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0084] 1. The braking comfort of the vehicle has been optimized from the perspective of longitudinal-vertical coupling. During longitudinal braking, the vehicle's deceleration, braking intensity, and road input will all cause changes in the load and pitch angle of the front and rear wheels. The vertical load of the wheels will also affect the longitudinal braking force of the wheels to a certain extent. The two are coupled and interact with each other, which is closer to the working conditions faced by the vehicle during actual braking and better meets the requirements of vehicle braking comfort.

[0085] 2. The braking economy of a vehicle includes not only the driving range affected by energy recovery, but also the tire wear caused by the distribution of braking force. The longitudinal braking force of the wheels not only causes tire deformation and energy loss, but also tire wear, which in turn affects the safety of the vehicle during braking. Analyzing tire wear ensures both the economy and the braking safety of the vehicle.

[0086] 3. This invention performs longitudinal-vertical coupled modeling of the vehicle; analyzing the vehicle solely from the longitudinal or vertical direction cannot accurately describe the vehicle's dynamics. The vehicle's braking intensity and braking deceleration always affect the vertical load of the wheels, the vehicle's vertical vibration, and pitch angle. The vertical load of the wheels affects the longitudinal braking force of the wheels, which in turn affects the wheel wear. Establishing a longitudinal-vertical coupled dynamic model can comprehensively consider the vehicle's braking requirements and improve the accuracy of braking force optimization. Attached Figure Description

[0087] Figure 1 shows a five-degree-of-freedom half-vehicle model with longitudinal-vertical coupling of the wheels;

[0088] Figure 2 shows the internal resistance model commonly used in batteries;

[0089] Figure 3 is a diagram showing the energy flow during vehicle braking. Detailed Implementation

[0090] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0091] Please refer to Figures 1-3. An embodiment of the present invention provides a braking control method for electric vehicles that integrates economy and comfort. The method includes the following steps:

[0092] Step 1: Vertical-Longitudinal Dynamics Modeling

[0093] First, based on the vehicle's motion characteristics and the research features of this invention, a five-degree-of-freedom half-vehicle model with longitudinal-vertical coupling is selected as the vehicle model for this invention. This half-vehicle model includes five degrees of freedom: longitudinal rigid body motion of the whole vehicle, vertical motion and pitch motion of the vehicle body, and rotational motion of the front and rear wheels around their axes. Based on this model, the wheel load changes caused by braking intensity are considered.

[0094] As shown in Figure 1, starting from the vertical motion of the vehicle, the loads on the front and rear wheels are as follows:

[0095]

[0096] Where m x m wf m wr These represent half the vehicle's mass, the mass of the front and rear wheels, and w, respectively. mf w mr These represent the speeds of the front and rear wheel motors, respectively, in L. f L r kt represents the distance from the center of gravity to the front and rear axles, respectively. wf kt wr These represent the vertical stiffness of the front and rear wheels, respectively; L is the wheelbase; and z is the vehicle braking intensity. fw z rw These represent the vertical displacements of the unsprung mass at the front and rear, respectively.

[0097] Since longitudinal braking causes vehicle vibration, the dynamic load changes of the front and rear wheels can be equivalently represented by equivalent forces applied to the front and rear wheels, respectively. The magnitudes of the equivalent forces applied to the front and rear wheels are as follows:

[0098]

[0099] Where h xd The vehicle's center of gravity height. The front and rear suspension forces resulting from the combined effects of longitudinal braking motion and road surface excitation are as follows:

[0100]

[0101] Where k sf k sr These are the front and rear suspension spring stiffnesses, respectively, c sf csr These are the damping coefficients for the front and rear suspensions, respectively. x The vertical displacement of the vehicle body, θ is the height of the vehicle's center of gravity, z fx z rx These represent the vertical displacements of the front and rear vehicle bodies, respectively, F efc F src These are the front and rear controllable damping forces, q f q r The vertical disturbance input displacement signals of the road surface at the front and rear vehicle locations are respectively given by the road surface power spectral density G. q (f) is represented, and road surface roughness is divided into eight levels (AH) using power spectral density values, G q The formula for calculating (f) is as follows:

[0102]

[0103] Where f is the reciprocal of the wavelength, i.e., the spatial frequency, f0 is the reference spatial frequency, and G q (f0) is the road surface roughness coefficient, and n is the frequency exponent. The equations of motion and rotation of the front and rear wheels are as follows:

[0104]

[0105] Where I wf I wr F represents the moments of inertia of the front and rear wheels about their axes of rotation, respectively. xf F xr The longitudinal braking forces of the front and rear wheels are T, respectively. df T dr The braking torques of the front and rear wheels are respectively, w wf w wr These represent the rotational speeds of the front and rear wheels, respectively.

[0106] As shown in Figure 1, the equations of motion for the vehicle body's vertical direction and the dynamic equations for its pitch angle are as follows:

[0107]

[0108]

[0109] Starting from the longitudinal motion of the vehicle, the equation of motion for the vehicle braking process is as follows:

[0110] F b +F f +F w +F i =δma v ;

[0111] Where F b For vehicle braking force, F f For rolling resistance, F w For wind speed drag, F i For ramp resistance, δ is the vehicle rotational mass conversion factor, and a is the slope resistance. v For vehicle acceleration, the braking intensity formula is z = -a v / g;

[0112] Since the wheel cylinder is directly related to the generation of mechanical (hydraulic) braking force, the hydraulic braking system model can be approximated by the wheel cylinder model. Assuming that the left and right brakes on the front axle are the same, and the left and right brakes on the rear axle are the same, the relationship between the hydraulic braking torque and the wheel cylinder pressure on the front and rear axles is as follows:

[0113]

[0114] Where T phf T phr These are the actual hydraulic braking torques of the front and rear wheels, respectively, p wf p wr Do not use the actual cylinder pressure of the front and rear wheels, K zf K zr These are the braking factors of the front and rear axle brakes, D respectively. zf D zr These are the diameters of the front and rear wheel brake cylinders, R. zf R zr Let be the effective radii of the front and rear brake discs, respectively. The total braking torque applied to the wheels is then shown below:

[0115] T di =T hi +T mi i = f, r

[0116] T ref =2(T) hf +T tr +T mf +T mr ).

[0117] The motor is key to energy recovery, and its relevant calculation formula is as follows:

[0118] P b =P bf +P br

[0119] P bf =T mf w mf η mf / 9550

[0120] P er =T mr w mr η mr / 9550;

[0121] Where P b T represents the power transmitted from the motor to the battery during braking. mf T mr These represent the torques of the front and rear motors, P. bf P br These represent the power transmitted to the battery from the front and rear motors, respectively, in W. mf w mr These represent the front and rear motor speeds, η. mf η mr These represent the conversion efficiencies of the front and rear motors, respectively. The relationship between the torque at the motor end and the wheel end and the rotational speed in the transmission system is shown below:

[0122]

[0123] Among them, w wf w wr These represent the rotational speeds of the front and rear wheels, respectively, T. mdf T mdr i represents the braking torque applied by the front and rear motors to the front and rear wheels, respectively. f i r These are the reduction ratios of the front and rear transmissions, respectively.

[0124] As shown in Figure 2, the relevant battery formulas are as follows:

[0125] E = U + Ir b

[0126] |P bf +P br |=|EI|+I 2 r b

[0127] Q = ∫EIdt;

[0128] Where E is the battery open-circuit voltage, U and I are the charging voltage and charging current respectively, and r b Let Q be the internal resistance of the battery during charging, and Q be the energy recovered by the battery. The relevant expressions for battery charging are as follows:

[0129] C bttry =∫Idt / 3600

[0130] C max =f bttry (temp)

[0131]

[0132] Where C bttry For discharge capacity, C max To maximize battery energy usage, f bttry (temp) is a temperature-related function;

[0133] Step 2: Tire Model Building:

[0134] Assuming that the radii of the four wheels (front, rear, left, and right) are all r and that they are all the same, and since the Magic tire model is a semi-empirical model that can reflect the interaction with the road surface and is suitable for the dynamic simulation of a car, the Magic tire model is selected in this invention.

[0135] The formula for calculating tire slip ratio during vehicle braking is as follows:

[0136]

[0137] Where u w1 u w2 These are the center velocities of the front and rear wheels, r and r, respectively. r0 v is the radius of free rolling of the wheel. x Let be the vehicle speed. Under steady-state braking conditions, the formula for calculating the longitudinal force is as follows:

[0138] F xi =D sin{Carctan[Bs-E(Bs)} j -arctan(Bs j ))]}j=1,2i=f,r;

[0139] Among them, parameter D determines the peak value of the curve and is the peak factor; C affects the shape of the curve and is the shape factor; B is the tensile curve factor, corresponding to the stiffness coefficient of the linear segment; and E affects the characteristic shape around the peak value of the curve and is the curvature factor (note that in the above calculation formula, the unit of longitudinal force is N, and the unit of wheel vertical load is KN). Their relevant values ​​can be obtained from the table.

[0140] Step 3: Comfort Factors

[0141] When a vehicle brakes, there are two phases that can cause discomfort to the occupants: the sudden increase in braking force causing the vehicle to lurch forward and the sudden loss of inertial force causing the vehicle to pitch backward. To improve the comfort during braking, the braking force should be distributed as much as possible to meet the braking requirements of the vehicle, and the load change between the front and rear wheels should be minimized as much as possible, thereby reducing the absolute value of the vehicle's pitch angle.

[0142]

[0143] According to the equation expressing suspension force, the front and rear suspension forces and braking intensity can be optimized by optimizing the controllable damping forces at the front and rear. This balances the changes in front and rear wheel loads caused by braking and the vertical vibration of the vehicle body caused by road excitation. Therefore, Z is used as part of the subsequent optimization objective function, and its calculation formula is as follows:

[0144] Z = (|z fx |-|z rx |)+(|z fw |-|z rw |)+|z x |θ|;

[0145] Step 4: Economic Factors:

[0146] 1. One way to improve the economy of a vehicle is to maximize the energy recovery from braking while ensuring the safety of vehicle braking, and to optimize the combined braking strategy of regenerative braking and friction braking. Specifically, this can be summarized as: how to distribute the electric motor torque and hydraulic braking torque on each wheel.

[0147] As shown in Figure 3, the energy equation of the vehicle during braking is as follows:

[0148] E r =E0-E loss1 -E loss2 -E loss3 -E f ;

[0149] Among them, E r The energy recovered from the battery, E0 is the kinetic energy of the vehicle at the start of the braking process, E loss1 E is the energy loss caused by slope drag and air drag. loss2 Energy loss caused by copper losses, iron losses, etc. inside the hub motor, E loss3 Energy loss due to mechanical friction in hydraulic systems, E f This represents the vehicle's kinetic energy at the end of the braking process. If the starting and ending speeds of the braking process are fixed, then to maximize the energy recovered from the battery, the energy loss at each stage must be minimized, or the sum of the energy losses at each stage must be minimized. The formulas for calculating each energy loss are as follows:

[0150]

[0151]

[0152]

[0153] E loss =E loss1 +E loss2 +E loss3 ;

[0154] Where F a For slope resistance, F s For air resistance, t s For sampling time, w mf w mr These represent the front and rear motor speeds, respectively, in W. wf w wr These represent the rotational speeds of the front and rear wheels, respectively, T. hf T hr The hydraulic braking torques for the front and rear wheels are respectively (due to the limited torque of the motor, it is sometimes insufficient to meet the braking needs of the vehicle, so hydraulic torque is used for compensation), and E loss As part of the objective function of subsequent optimization algorithms;

[0155] 2. In the initial stage of tire braking, the tire tread undergoes longitudinal deformation under the braking force. If only the distribution of motor and hydraulic torque between the front and rear wheels is considered when improving fuel economy, it may lead to severe tire wear, which will not only reduce the vehicle's fuel economy but also affect the safety of the vehicle in subsequent driving.

[0156] Tire tread wear I during tire braking a The calculation formula is as follows:

[0157]

[0158] Where C1 and C2 are parameters related to road surface roughness, and k M Here are parameters related to tire materials, where σ is the vertical ground stress of the tread and dl is the tire contact patch. Existing research has proposed a correction formula for tire wear as follows:

[0159]

[0160] Where C0 represents fatigue wear, G0 represents the rated load, n represents the vertical load exponent, and b x b y These represent the relative wear coefficients for longitudinal and lateral forces, respectively. l0 is the standard distance, l is the actual distance, and α is the slip angle. When the vehicle tire material is fixed, C0, n, and b... x b yThe effect on tire wear is fixed. When the road surface is known, the effect of A on tire wear is also known. Therefore, when the tire and road conditions remain unchanged, without considering the changes in tire contact marks with the transfer of braking load, the amount of tread wear is approximately proportional to the product of the slip ratio and the vertical load, that is, approximately proportional to the braking force.

[0161] The greater the difference in braking force between the front and rear wheels and between the left and right wheels, the greater the difference in tire wear, which is detrimental to tire maintenance and driving safety. Therefore, considering the economic factors caused by tire wear, the difference in braking torque between the front and rear wheels should be minimized as much as possible. ΔT is then used as part of the objective optimization function, and its calculation formula is as follows:

[0162] ΔT=(T mf -T mr )+(T hf -T hr );

[0163] During vehicle deceleration and braking, the slip ratio varies considerably with changes in braking intensity, leading to increased vertical load on the wheels. Furthermore, tire wear is related to (s×F) z The slip ratio is directly proportional to the vertical load, therefore the tire wear factor is also large. Thus, the control strategy should ensure that the vehicle meets the overall braking requirements while minimizing the product of the slip ratio and vertical load. Therefore, ΔI is also included as part of the objective optimization function.

[0164] ΔI=(s f ×F zf +s r ×F zr )×10 -3 ;

[0165] And Δ = ΔT + ΔI is taken as the total component of the tire wear factor in the objective optimization function;

[0166] When braking an electric vehicle, excessive braking force should be avoided as much as possible. Once the braking force is determined, the difference in braking force between the front and rear wheels, as well as the product of the slip ratio and vertical load of the front and rear tires, should be minimized. Otherwise, it will not only affect comfort but also increase tire wear.

[0167] Step 5: Optimization Strategy

[0168] Through the analysis of comfort and economy factors, it is clear that in order to ensure the comfort and economy of electric vehicles during braking, it is necessary to minimize the amplitude of vehicle body vibration and the energy loss. Therefore, model predictive control algorithms can be used to optimize the distribution of front and rear suspension forces and front and rear wheel braking forces to achieve the requirements.

[0169] In the model predictive control algorithm, x is taken as the state variable, U as the control variable, and J as the objective function. The relevant expressions are as follows:

[0170]

[0171] Where α, β, and γ are the weights of the energy recovery factor, tire wear factor, and comfort factor, respectively. To achieve the control requirements, the relevant vehicle parameters must also meet their associated constraints.

[0172]

[0173] The above steps can be used to implement a control strategy for electric vehicles that balances economy and comfort.

[0174] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A braking control method for electric vehicles that integrates economy and comfort, characterized in that, The method includes the following steps: Step 1: Longitudinal-Vertical Dynamics Modeling: Select a five-DOF half-vehicle model with longitudinal-vertical coupling. Derive the longitudinal and vertical dynamic models of the vehicle based on the half-vehicle model, thereby coupling the vehicle's vertical suspension system with the longitudinal dynamic system; Step 2: Tire Model Modeling: Select the Magic tire model; Step 3: Comfort Factors: Combining the longitudinal-vertical dynamics model and the tire model, analyze the factors affecting comfort from both longitudinal and vertical perspectives, extract important influencing factors, and interact the longitudinal and vertical influencing factors to analyze the factors affecting comfort from the perspective of longitudinal-vertical coupling; Step 4: Economy Factors: Superimpose various energy losses to obtain the total energy loss, and apply braking force to the front, rear, left, and right wheels of the vehicle. The allocation is determined to ensure that, within the limits of motor power and torque and under the constraints of relevant vehicle components, the vehicle utilizes regenerative braking to the maximum extent possible while minimizing tire wear. Step five: Using comfort and economy factors, the amplitude of vehicle body vibration, energy loss, and tire wear are minimized. Model predictive control algorithms are used to optimize the distribution of front and rear suspension forces and front and rear wheel braking forces to ensure both comfort and economy during braking of the electric vehicle. In step one, the five degrees of freedom of the half-vehicle model include the longitudinal rigid body motion of the entire vehicle, the vertical motion and pitch motion of the vehicle body, and the rotational motion of the front and rear wheels about their respective axes. In step one, starting from the vertical motion, the loads on the front and rear wheels are as follows: ;in 、 These are respectively half the vehicle's mass, the mass of the front wheels, and the mass of the rear wheels. These represent the motor speeds of the front and rear wheels, respectively. These are the distances from the center of gravity to the front and rear axles, respectively. These are the vertical stiffnesses of the front and rear wheels, respectively. Wheelbase For vehicle braking strength, These represent the vertical displacements of the unsprung masses at the front and rear, respectively. The dynamic load resulting from the vertical motion can be considered as an equivalent force applied to the front and rear wheels, with the equivalent force values ​​as follows: ;in The vehicle's center of gravity height; the front and rear suspension forces resulting from the combined effects of longitudinal braking motion and road surface excitation are as follows: ;in These are the front suspension spring stiffness and the rear suspension spring stiffness, respectively. These are the damping coefficients of the front suspension and the rear suspension, respectively. Vertical displacement of the vehicle body, For the height of the vehicle's center of gravity, These are the vertical displacements of the front and rear vehicle bodies, respectively. These are the front controllable damping force and the rear controllable damping force, respectively. These are the vertical disturbance input displacement signals of the road surface at the location of the preceding vehicle and the location of the following vehicle, respectively. These displacement signals are derived from the road surface power spectral density. The road surface roughness is represented and classified into eight levels (A, H) using power spectral density values. The calculation formula is as follows: ;in It is the reciprocal of the wavelength, i.e., the spatial frequency. For reference spatial frequency, This is the road surface roughness coefficient. The frequency index is used; the equations of motion and rotation for the front and rear wheels are as follows: The equations of motion for the vehicle body's vertical direction and the dynamic equations for its pitch angle are as follows: When the vehicle starts moving longitudinally, the equation of motion during the braking process is as follows: ;in For vehicle braking force, For rolling resistance, For wind speed drag, For slope resistance, The formula for vehicle acceleration and braking intensity is: The relationship between the hydraulic braking torque and wheel cylinder pressure of the front and rear axles is as follows: The total braking torque applied to the wheels is as follows: 。 2. The electric vehicle braking control method integrating economy and comfort according to claim 1, characterized in that, In step one, the motor is key to energy recovery; during braking, the power transferred from the motor to the battery is... and the power transmitted to the battery by the front and rear motors. as follows: ;in These are the torques of the front and rear motors, respectively. These represent the power transmitted to the battery by the front and rear motors, respectively. The conversion efficiencies of the front and rear motors are shown below. In the transmission system, the relationship between the torque at the motor end and the wheel end and the rotational speed is as follows: Battery open-circuit voltage E and battery recovered energy The formula is as follows: ;in These are the charging voltage and the charging current, respectively. If we consider the internal resistance of the battery during charging, then the expression for battery charging is as follows: ;in For discharge capacity, To maximize battery energy utilization It is a function related to temperature.

3. The electric vehicle braking control method integrating economy and comfort according to claim 1, characterized in that, In step two, the tire slip ratio is calculated using the following formula during vehicle braking: ;in Let the radius be the radius of free rolling of the wheel. Let be the vehicle speed; under steady-state braking conditions, the formula for calculating the longitudinal force is as follows: ; parameters Determine the peak value of the curve, which is the peak factor. The shape factor affects the shape of the curve. This is the tension curve factor, corresponding to the stiffness coefficient of the linear segment. The curvature factor is the characteristic shape that influences the area around the peak of the curve.

4. The electric vehicle braking control method integrating economy and comfort according to claim 1, characterized in that, In step three, by combining the formulas for front and rear suspension forces, the front and rear controllable damping forces are optimized, thereby optimizing the front and rear suspension forces and braking intensity. This balances the changes in front and rear wheel loads caused by braking and the vertical vibration of the vehicle body caused by road excitation. The calculation formula is as follows: 。 5. The electric vehicle braking control method integrating economy and comfort according to claim 1, characterized in that, In step four, the energy equation for the vehicle during braking is as follows: ;in, Energy recovered at the battery end, This represents the vehicle's kinetic energy at the start of the braking process. Energy loss is caused by slope resistance and air resistance. Energy loss caused by internal components of the hub motor Energy loss caused by mechanical friction in hydraulic systems This represents the vehicle's kinetic energy at the end of the braking process. When the starting and ending speeds of the braking process are determined, the energy that needs to be recovered from the battery is maximized, thus minimizing the energy loss at each stage, or minimizing the sum of energy losses at each stage. The formulas for calculating each energy loss are as follows: ;in For slope resistance, For air resistance, Sampling time, These are the speeds of the front and rear motors, respectively. These are the rotational speeds of the front and rear wheels, respectively. These are the hydraulic braking torques for the front and rear wheels, respectively.

6. The electric vehicle braking control method integrating economy and comfort according to claim 5, characterized in that, In step four, the amount of tread wear during tire braking. The calculation formula is as follows: To reduce unnecessary tire wear during braking, the torque differences between the front and rear wheels, and between the left and right wheels, need to be reduced as follows: To ensure the vehicle meets overall braking requirements, the product of the slip ratio and vertical load must be reduced. as follows: ； Obtain the total component of the tire wear factor 。 7. The electric vehicle braking control method integrating economy and comfort according to claim 6, characterized in that, In step five, the model predictive control algorithm will... As a state variable, As a control variable, The relevant expression for the objective function is as follows: ;in These are the weights for the energy recovery factor, tire wear factor, and comfort factor, respectively. To achieve the control requirements, the relevant vehicle parameters must also meet their associated constraints. 。

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