Calculation method and application of understeering angle

Abstract

This application provides a method and application for calculating tire understeer angle, belonging to the field of tire design; the calculation method includes calculating lateral acceleration; selecting lateral acceleration; and calculating understeer angle based on the selected lateral acceleration, wherein the calculation of understeer angle includes plotting two sets of selected lateral accelerations, which can respectively obtain the front axle lateral acceleration and sideslip angle curve A. f -α and rear axle lateral acceleration versus sideslip angle curves A r -α; curve A f -α and curve A r -α were fitted with polynomials respectively, and A was obtained respectively. f The relationship with α and A r The relationship with α; then solve for the same acceleration A (A = A f =A r Front axle slip angle α f and rear axle side slip angle α r Furthermore, the understeer angle δu = α for different lateral accelerations A is obtained. f -α r .

Description

Technical Field

[0001] This application belongs to the field of tire design and relates to a method for calculating tire understeer angle and its application. Background Technology

[0002] Vehicle handling stability is one of the most important characteristics of a driving vehicle, and studying vehicle handling stability is an important means of improving overall vehicle performance. Understeer is one aspect of evaluating vehicle handling stability. Factors affecting understeer primarily include the vehicle's center of gravity position, the mass of the springs and unsprings, the roll center positions of the front and rear suspensions, variations in the vehicle's toe and roll angles, and tire stiffness. It can be seen that understeer is partly controlled by the vehicle itself and partly influenced by tire characteristics. However, when evaluating overall vehicle handling stability, the same vehicle is typically used with tires of the same specifications but different structural designs. Therefore, when evaluating different tires, the influence of other vehicle factors can be ignored, and the analysis can focus solely on the impact of tire characteristics on understeer.

[0003] For vehicles on the road, the total steering angle δ is partly due to the motion steering angle δk generated by the road curvature and vehicle suspension characteristics, and partly due to the understeer angle δu of the tires, i.e., δ = δk + δu. When evaluating vehicle characteristics, the same vehicle is being evaluated, so the motion steering angle δk is the same, and it is reasonable to consider only the understeer angle δu. The lateral stiffness of the front and rear axle tires is an important factor affecting the understeer characteristics of a vehicle. During actual cornering, the tire lateral angle increases, resulting in greater lateral force and lateral acceleration. Due to the difference in load and lateral angle between the front and rear axles, the driver needs to input an additional steering angle to compensate for the difference in lateral angle to ensure stable vehicle driving and avoid large oversteer and understeer. This additional steering angle is the understeer angle. Therefore, the understeer angle is the difference in lateral angle generated by the front and rear axle tires under the same lateral acceleration.

[0004] Existing research on understeer characteristics mainly falls into two categories: one is to simply compare the lateral stiffness of a single tire under load, evaluating the overall understeer characteristics of the vehicle based on the magnitude of the lateral stiffness; the other requires the use of a suspension K&C test bench to consider the influence of various vehicle parameters, including the mass of the springs and non-springs, and the position of the center of gravity, on the overall understeer characteristics. The first method is rather general in its study of overall vehicle understeer characteristics. In actual vehicle operation, the vertical forces on the left and right tires constantly change, leading to changes in tire lateral forces and lateral stiffness. Therefore, analyzing only the lateral stiffness under a single load ignores load variations and the theoretical basis for understeer angle generation. The second method utilizes a vehicle K&C test bench, but this method is expensive to install and not widely available. Summary of the Invention

[0005] This application provides a method for calculating the understeer angle of a tire, including the following steps:

[0006] Calculation of lateral acceleration: Based on the first axle load, set multiple vertical force percentages Fz (%) and measure the corresponding vertical force Fz, then obtain other vertical force percentages Fz (%) and their vertical forces Fz by linear fitting; wherein, the first axle is one of the front axle and the rear axle of the vehicle, and the second axle is the other of the front axle and the rear axle; set multiple sideslip angles α to obtain each Fz (%) and its Fz and the lateral force Fy under each α; calculate the lateral acceleration A according to formula (3):

[0007] A = Fy / Fz*g(3)

[0008] Where g is the acceleration due to gravity;

[0009] This yields a table of lateral acceleration data for different Fz (%) and under Fz, as well as under multiple sideslip angles α;

[0010] Selection of lateral acceleration A: Select the required sideslip angle from the set sideslip angles; set the percentage of vertical force after the first axle load transfer when the vehicle turns through a sideslip angle of n°; set the load ratio of the first axle to the second axle to determine the percentage of vertical force after the second axle load transfer; select two sets of lateral acceleration A from the obtained lateral acceleration data table based on these settings.

[0011] Calculation of understeer angle: By plotting the two selected sets of lateral accelerations A, the curves A of front axle lateral acceleration and sideslip angle can be obtained respectively. f -α and rear axle lateral acceleration versus sideslip angle curves A r -α; will curve A f -α and curve A r -α were fitted with polynomials respectively to obtain A.f The relationship with α and A r The relationship with α; then solve for the same acceleration A (A = A f =A r Front axle slip angle α f and rear axle side slip angle α r Furthermore, the understeer angle δu = α for different lateral accelerations A is obtained. f -α r .

[0012] In some embodiments of this application, more specifically, in the calculation step of lateral acceleration, multiple sideslip angles α are set, and the set Fz(%) and the lateral force Fy under Fz and the set sideslip angle α are measured; for other Fz(%) and the lateral force under Fz, the measured lateral force Fy is linearly or nonlinearly fitted according to α≤5° or α>5°; thereby obtaining each Fz(%) and the lateral force Fy under Fz and each α.

[0013] In some embodiments of this application, in the calculation step of lateral acceleration, multiple sideslip angles α are set to 1°, 2°, 3°, 4°, 5°, 6°, and 7°.

[0014] In some embodiments of this application, in the step of calculating lateral acceleration, a six-component force test bench can be used to measure the vertical force Fz and calculate the lateral acceleration A.

[0015] In some embodiments of this application, in the step of selecting the lateral acceleration A, the percentage of vertical force after the transfer of the first axle load is set to 10% when the vehicle turns through a sideslip angle of n = 1°.

[0016] In some embodiments of this application, the first axis is the front axis and the second axis is the rear axis; in the step of selecting the lateral acceleration A, the load ratio of the front axis to the rear axis is set to 50:40, thereby determining the vertical force corresponding to 80% of the reference vertical force of the front axis, and then determining the percentage of the vertical force after the load transfer of the second axis, wherein the reference vertical force of the front axis is Fz corresponding to Fz (100%).

[0017] In some embodiments of this application, in the understeer angle calculation step, curve A is... f -α and curve A r -α were fitted with cubic polynomials, and then solved using univariate methods to obtain the front and rear axle slip angles α. f and α r .

[0018] In some embodiments of this application, the method for calculating the understeer angle of the tires also includes the application of the understeer angle: the understeer angle δu of different lateral accelerations A is plotted to obtain the understeer curve A-δu; the understeer state of the vehicle can be judged or compared through the curve A-δu.

[0019] In some embodiments of this application, in the understeer angle application step, the understeer curve is divided into three parts: ① when the lateral acceleration A is in the range of 0-0.3g, the vehicle is in a normal driving state; ② when the lateral acceleration A is in the range of 0.3-0.6g, it is a non-linear region of vehicle driving; ③ when the lateral acceleration A is above 0.6g, the vehicle is prone to understeer.

[0020] The second embodiment of this application provides an application of a method for calculating tire understeer angle in tire testing, which adopts the method for calculating tire understeer angle described in any of the preceding technical solutions.

[0021] Compared with the prior art, the beneficial effects of this application are as follows:

[0022] The understeer angle calculation method provided in at least one embodiment of this application is based on a two-degree-of-freedom vehicle model. It treats the left and right tires on the front axle and the left and right tires on the rear axle as a single unit. Utilizing the principle that the understeer angle is generated by the difference in sideslip angle between the front and rear axles, and employing only objective data obtained from a low-speed six-component force test bench, it considers the lateral load transfer generated by the left and right tires during actual vehicle cornering. By utilizing the different loads on the front and rear axles, it obtains the different sideslip angles generated by the front and rear axle tires under the same lateral acceleration, thus yielding the difference in sideslip angle between the front and rear axles, which is the understeer angle. This method fully utilizes theoretical knowledge, considers the actual cornering conditions of the vehicle, is simple to operate, has a clear and straightforward testing and calculation process, and is low-cost.

[0023] The method for calculating tire understeer angle provided in at least one embodiment of this application can calculate tire understeer angle and predict vehicle understeer characteristics, and calculate the magnitude of understeer angle under the same lateral acceleration A under different loads on the front and rear axles of the vehicle. Attached Figure Description

[0024] Figure 1 This is a curve showing the front and rear axle lateral acceleration versus sideslip angle in one implementation method;

[0025] Figure 2 This is a deficiency turning curve in one implementation method;

[0026] Figure 3 This is another implementation of the front axle lateral acceleration and sideslip angle curve;

[0027] Figure 4 This is another implementation of the rear axle lateral acceleration versus sideslip angle curve;

[0028] Figure 5 This is another implementation of the front and rear axle lateral acceleration and sideslip angle curves;

[0029] Figure 6 This is an alternative implementation of the inadequate steering curve;

[0030] Figure 7 It is a curve representing the shortcomings of different implementation schemes superimposed on each other; Detailed Implementation

[0031] The technical solutions of this application are described in detail below with reference to specific embodiments. However, it should be understood that, without further description, the elements, structures and features in one embodiment can also be beneficially incorporated into other embodiments.

[0032] When a vehicle turns, it generates centrifugal force. To ensure that the vehicle travels along the path, it generates a corresponding centripetal force. However, when a vehicle actually turns, the tires do not steer towards the path, but rather towards the inside of the wheel. This causes the vehicle's direction of motion to differ from the steering plane of the wheel. The centripetal force is decomposed into a force that propagates along the vehicle's direction and a lateral force Fy.

[0033] When a vehicle turns, because the tires are elastic, they undergo elastic deformation during the turn, causing the vehicle's speed direction to differ from its orientation. This creates an angle between the two directions, known as the tire's slip angle α. This angle then generates a reaction force from the ground on the tire, called the lateral force Fy. When the slip angle α ≤ 5°, the lateral force Fy has a linear relationship with the slip angle α, calculated using the formula Fy = k t *α(k t (This refers to the tire's lateral stiffness). When the slip angle α > 5°, the slip angle and the lateral force exhibit a non-linear relationship. As the slip angle increases, the lateral force increases less and less.

[0034] Due to the different loads on the front and rear axles, the vertical force Fz on the front and rear axles (Fz on the front axle) is different. f Rear axle vertical force Fz r The uneven distribution of lateral force Fy generated by the front and rear tires (front axle lateral force Fy) f Rear axle lateral force Fy r The magnitudes are also different; the lateral acceleration A (front axle lateral acceleration A) is different. f lateral acceleration A of the rear axle r They are not the same. The front axle lateral acceleration is the ratio of the front axle lateral force to the front axle load, i.e., A. f =Fy f / mf The lateral acceleration of the rear axle is the ratio of the lateral force on the rear axle to the load on the rear axle, i.e., A. r =Fy r / m r Therefore, under the same lateral acceleration A, the front axle slip angle α f Rear axle side slip angle α r The difference between the front and rear axle slip angles is called the understeer angle δu = α. f -α r .

[0035] This embodiment provides a method for calculating the understeer angle δu of a tire. In this method, a six-component force test bench can be used as the test equipment to conduct steady-state force and torque tests under multiple loads and multiple sideslip angles.

[0036] 1. Calculation of lateral acceleration A

[0037] In this embodiment, the six-component force test bench is used for testing in accordance with the general standard GMW15204. As required, the test air pressure is set to the actual vehicle test air pressure, and the rated vertical force percentage (100%) is set as the reference vertical force of the vehicle's front axle. The vertical force Fz(N) corresponding to the vertical force percentage Fz(%) is mg (g is the gravitational acceleration 9.8N / kg).

[0038] Multiple vertical force percentages Fz (%) are set based on the actual front axle load, and the corresponding front axle vertical force Fz is measured. Then, other vertical force percentages Fz (%) and vertical forces Fz are obtained by linear fitting.

[0039] For example, set Fz (100%) and measure the corresponding Fz, as well as Fz (20%) and its Fz, Fz (50%) and its Fz, Fz (80%) and its Fz, Fz (130%) and its Fz, and Fz (160%) and its Fz. Based on these six sets of data, the data processing template (built-in software) of the six-component force test bench will increase the vertical force percentage from Fz (100%) to Fz (160%) at certain intervals (e.g., 5%), and decrease the vertical force percentage to Fz (40%), and calculate the corresponding vertical force Fz (N).

[0040] It is worth noting that this embodiment uses the front axle load as the calculation object to obtain the percentage of front axle vertical force and the front axle vertical force. In actual operation, the rear axle load can also be selected. Generally, the front axle load is selected, and this embodiment will mainly describe the front axle load.

[0041] Furthermore, for a specific tire being tested, multiple slip angles α (e.g., slip angles α between integers 1 and 10) are set during steady-state force and torque tests with multiple loads and slip angles on a six-component force test bench. Once the slip angle α is set, the sensors on the six-component force test bench can automatically measure the corresponding lateral force Fy under each Fz (%) and its corresponding Fz values ​​when testing the tire.

[0042] Since the six-component force test bench only measures the set Fz (%) and the sideslip angle α under Fz, the lateral force Fy under these set values ​​can be directly obtained. For other Fz (%) and the lateral force Fy corresponding to the sideslip angle α under Fz, it can be obtained by linear or nonlinear fitting of the set Fz (%) and the lateral force Fy under Fz. As mentioned above, when the sideslip angle α ≤ 5°, the lateral force Fy has a linear relationship with the sideslip angle α and can be obtained by formula or linear fitting of the set Fz (%) and the lateral force Fy under Fz; when the sideslip angle α > 5°, the lateral force Fy has a nonlinear relationship with the sideslip angle α and can be obtained by nonlinear fitting of the set Fz (%) and the lateral force Fy under Fz. For example, given the previously defined Fz(20%) and its Fz, Fz(50%) and its Fz, Fz(80%) and its Fz, Fz(100%) and its Fz, Fz(130%) and its Fz, and Fz(160%) and its Fz, the lateral force Fy corresponding to each of these six Fz(%) and each α under Fz can be directly measured using a six-component force test bench. Each α corresponds to six Fy values. For the other Fz(%) and the lateral force Fy under Fz obtained through fitting, linear or nonlinear fitting can be performed respectively based on α≤5° or α>5° when the previous six Fy values ​​are obtained; thus obtaining the lateral force Fy under each other Fz(%) and its Fz and each α. More specifically, for example, when α = 2° (α ≤ 5°), the six Fy values ​​measured by the sensor at α = 2° can be linearly fitted based on the six sets of data: Fz(20%) and its Fz, Fz(50%) and its Fz, Fz(80%) and its Fz, Fz(100%) and its Fz, Fz(130%) and its Fz, and Fz(160%) and its Fz. Alternatively, the formula Fy = k can be used. t *α is used for calculation to obtain the other Fz (%) and the lateral force Fy under Fz when α = 2°. When α = 7° (α > 5°), the six Fy values ​​measured by the sensor at α = 7° can be obtained by nonlinear fitting based on the six sets of data: Fz (20%) and its Fz, Fz (50%) and its Fz, Fz (80%) and its Fz, Fz (100%) and its Fz, Fz (130%) and its Fz, and Fz (160%) and its Fz.

[0043] Based on the lateral forces Fy obtained at each sideslip angle α, and combined with the vertical forces Fz, the corresponding lateral acceleration A is calculated. Specifically,

[0044] As mentioned above, because:

[0045] A=Fy / m(1)

[0046] In the formula: Fy is in N, and m is in N / (ms) -2 Therefore, the unit of A is m / s. 2 .

[0047] Dividing both sides of equation (1) by the gravitational acceleration g, we get:

[0048] A / g=Fy / mg=Fy / Fz(2)

[0049] Right now:

[0050] A = Fy / Fz*g(3)

[0051] According to formula (3), by combining the vertical force percentage Fz (%) and its corresponding vertical force Fz (N), as well as the sideslip angle α and its corresponding lateral force Fy, we can obtain the vertical force percentage Fz (%) and vertical force Fz (N), and the lateral acceleration A corresponding to different sideslip angles α; as shown in Table 1, the values ​​of one embodiment are calculated.

[0052] Table 1:

[0053]

[0054] As described above, firstly, in Table 1, the Fz(100%) and its Fz, Fz(20%) and its Fz (not shown), Fz(50%) and its Fz, Fz(80%) and its Fz, Fz(130%) and its Fz, and Fz(160%) and its Fz in the left two columns were set and measured; then, Fz(%) and its Fz between 20% and 160% were obtained at 5% intervals. Secondly, α was set to integers between 1 and 10°, and the lateral force Fy under the first six groups of Fz(%) and its Fz was measured under each α. Thirdly, according to different ranges of α, the lateral force Fy under other Fz(%) and its Fz was obtained through linear or nonlinear fitting. Finally, the lateral acceleration A in Table 1 (i.e., the lateral acceleration data table) was calculated using formula (3).

[0055] 2. Selection of lateral acceleration A

[0056] The gear ratio of a vehicle is generally 15-20. During the turning process, the steering wheel angle is generally in the range of 100° to 180°, and the tire slip angle is generally 7-8°. Therefore, in the actual data processing process, the maximum slip angle setting is 7°.

[0057] Considering the vehicle's actual turning state, as the sideslip angle changes, there is a lateral load transfer between the front and rear axles and the left and right tires, thus allowing us to obtain the percentage of vertical force after the front axle load transfer. This data can be set according to the actual vehicle conditions, with a lower percentage for conventional passenger cars and a higher percentage for heavy trucks. In this embodiment, it is set that when the vehicle turns through a 1° sideslip angle, the percentage of vertical force after the front axle load transfer (i.e., the lateral load on the left and right tires) is transferred by 10%.

[0058] During the six-component force test, the vertical force percentage Fz (100%) was set as the front axle reference vertical force. The typical front-to-rear axle load ratio for a vehicle is 50:40. The rear axle reference vertical force was set as the vertical force corresponding to 80% of the front axle reference vertical force. If the vertical force corresponding to 80% is not the rear axle reference vertical force, it needs to be selected based on the actual front-to-rear axle load ratio of the vehicle, choosing the one closest to the vehicle's rear axle vertical force as the rear axle reference vertical force.

[0059] Based on the above description, during cornering, the sideslip angle α is selected as 1°, 2°, 3°, 4°, 5°, 6°, and 7°, and the percentage of vertical force after front axle load transfer is 100%, 110%, 120%, 130%, 140%, 150%, and 160% (i.e., 10% of the lateral load is transferred between the left and right tires), and the percentage of vertical force after rear axle load transfer is 80%, 90%, 100%, 110%, 120%, 130%, and 140% (i.e., the rear axle reference vertical force is 80% of the front axle reference vertical force), or selected according to the actual front and rear axle load ratio, for example, the rear axle reference vertical force is 75% of the front axle reference vertical force.

[0060] Therefore, based on the sideslip angle α, the percentage of vertical force after the front axle load transfer, and the percentage of vertical force after the rear axle load transfer, the corresponding lateral acceleration value A can be selected from Table 1, as shown by the dark markings in Table 2.

[0061] Table 2:

[0062]

[0063] 3. Calculation of understeering angle

[0064] Plot the data (two sets, seven data points each) obtained from Table 2 to obtain curves A of front axle lateral acceleration and sideslip angle. f-α and rear axle lateral acceleration versus sideslip angle curves A r -α; such as Figure 1 As shown.

[0065] Curve A f -α and curve A r -α were fitted with polynomials respectively to obtain A. f The relationship with α and A r The relationship with α; then solve for the same acceleration A (A = A f =A r Front axle slip angle α f and rear axle side slip angle α r When the lateral acceleration A is 0, the lateral force and sideslip angle are also 0. Therefore, the front and rear sideslip angles for lateral accelerations A of 0, 0.2, 0.4, 0.6, 0.8, and 0.9 can be obtained. Under heavy front axle loads, the front axle sideslip angle α is used. f Rear axle side slip angle α r The difference can be used to obtain the understeer angle δu = α for different lateral accelerations A. f -α r .

[0066] For example, it can be used for Figure 1 Curve A in f -α and curve A r -α were fitted with cubic polynomials to obtain A f =a1*α 3 +b1*α 2 +c1*α and A r =a2*α 3 +b2*α 2 +c2*α, and then use single-variable calculation to obtain the front and rear axle slip angles α under the same lateral acceleration A. f and α r Finally, we obtain δu = α f -α r .

[0067] 4. Application of understeering angle

[0068] By plotting the understeer angle δu calculated above for different lateral accelerations A, we can obtain the understeer curve A-δu, as shown below. Figure 2 As shown in the figure, the understeer angle δu increases with increasing lateral acceleration A, indicating understeer. When the understeer angle decreases with increasing lateral acceleration, the vehicle is in oversteer.

[0069] The understeer curve is divided into three parts: ① When the lateral acceleration A is in the range of 0-0.3g, the vehicle is in a normal driving state, and there is no sharp turning. ② When the lateral acceleration A is in the range of 0.3-0.6g, it is the non-linear region of vehicle driving, which is important for the lateral load transfer of the vehicle. ③ When the lateral acceleration A is above 0.6g, the vehicle is in a cornering situation and is more prone to understeer, so studying the magnitude of the understeer angle in this stage is of great significance.

[0070] In ③, when the lateral acceleration A is above 0.6g, the larger the understeer angle of the tire, the worse the front axle stability, front and rear axle balance and ultimate stability of the vehicle. The quality of the vehicle's understeer characteristics can be predicted based on the size of the understeer angle when the lateral acceleration A is above 0.6g in the A-δu curve.

[0071] The following detailed description, in conjunction with embodiments, will facilitate a better understanding of this application.

[0072] Comparative Example: Using lateral stiffness as an existing parameter for evaluating understeer characteristics, lateral stiffness tests were conducted on different schemes of the 2355019 tire produced by Sentury Tire Co., Ltd. The obtained lateral stiffness data was processed, and the linear region of the curve was selected for calculation to obtain the lateral stiffness. Then, the magnitude of the lateral stiffness of different schemes was compared to obtain the ranking of the understeer characteristics of different schemes. This evaluation process has several problems: (1) It simply uses lateral stiffness for comparison and qualitative analysis, lacking theoretical support; (2) The angular range for calculating lateral stiffness is relatively small, and the lateral acceleration is also relatively small. It belongs to the method of evaluating straight driving and small steering, ignoring the understeer that occurs under large lateral acceleration; (3) The load transfer that occurs during the actual vehicle steering process is not considered when calculating lateral stiffness, and it is not combined with reality. Therefore, such an evaluation method will result in inaccurate evaluation results of actual vehicles, poor consistency between objective data and subjective evaluation, and is not conducive to guiding tire performance development.

[0073] Example 1:

[0074] The process of calculating the understeer angle of different schemes using the method provided in this embodiment is as follows.

[0075] (1) Taking one tire as an example, the calculation process for other schemes is the same as above. After completing the multi-load and multi-lateral deflection angle test using a six-component force test bench, the data in Table 3 are obtained. Due to the different vehicle models, the front and rear axle loads are different, and the reference load for lateral load transfer is different. Therefore, it can be set according to different vehicle models.

[0076] Table 3:

[0077]

[0078] (2) Based on the data in Table 3, obtain the curves of lateral acceleration and sideslip angle under different vertical forces on the front and rear axles, i.e., the A-α curves, as shown below. Figure 5 As shown, this includes Figure 3 The curve A showing the front axle lateral acceleration versus sideslip angle f -α and Figure 4 The rear axle lateral acceleration versus sideslip angle curve A shown is shown below. r -α.

[0079] Based on the A-α curve, polynomial fitting was used to obtain A... f The relationship with α and A r Using the relationship with α, calculate the front axle sideslip angle α under the same lateral acceleration A. f and rear axle side slip angle α r The understeer angle δu is the front and rear axle slip angles α. f α r The difference, thus further yielding δu=α f -α r Specifically, A is obtained by fitting a cubic polynomial. f =0.0037*α3-0.0658α2+0.4194*α+0.0001,A r =0.0044*α³ - 0.0764α² + 0.4652*α + 0.0021, and then using the single-variable solution method, the front and rear axle slip angles α under different lateral accelerations A are obtained. f α r The understeering angle δu is obtained by subtracting the values.

[0080] Furthermore, the lateral acceleration A and understeer angle δu are plotted to obtain the understeer curve, as shown below. Figure 6 As shown.

[0081] Repeat the above steps to calculate the understeer curves for other tires, and then superimpose the understeer curves of the different schemes onto the... Figure 6 In the middle, thus obtaining Figure 7 .

[0082] from Figure 7 Multiple curves reveal the understeer angles of different schemes under significant lateral acceleration, thus predicting the order of front axle stability, front-rear axle balance, and ultimate stability in real-world vehicle handling evaluation. Under the same condition A, a smaller understeer angle is better, meaning Case 2 yields the best result, while Case 3 yields the worst.

[0083] The calculation principle of understeer angle has been explained in detail above. Based on this principle, the understeer angle of the tire is calculated using objective bench data. In future studies, different front and rear axle lateral load transfer ratios can be considered based on the fundamental principle of understeer angle, and the transfer ratios can be readjusted to improve the consistency with real-vehicle evaluation. Compared with existing understeer evaluation methods, the method provided in this application is simple to calculate, easy to operate, and has high predictive accuracy. It can reduce the number of real-vehicle tests, lower testing costs, and improve the consistency between objective data and subjective evaluation, which is of great significance for research on the consistency between subjective and objective factors.

[0084] Compared to current methods for studying understeer characteristics, this implementation fully utilizes the generation and calculation principles of the understeer angle. Based on theory, it fully considers the lateral load transfer between the left and right tires during actual cornering, and then uses the different loads on the front and rear axles to obtain the different slip angles generated by the front and rear axle tires under the same lateral acceleration. This allows for the determination of the difference in slip angles between the front and rear axles, i.e., the understeer angle, thus combining theoretical support with practical application. Furthermore, the required raw data can be obtained using only a low-speed six-component force test bench, resulting in low cost and simple equipment operation. Once the front and rear axle loads are obtained, calculations can be performed, and the calculation process is clear and straightforward, avoiding waste of time and human resources.

[0085] This implementation method does not simply use the lateral stiffness of a single tire under load to compare understeer characteristics, nor does it use the expensive K&C suspension test bench; instead, it ensures the accuracy of the calculation results based on the theoretical basis and the source of the understeer angle, and also considers the actual driving conditions of the vehicle in the calculation process. The combination of theory and practice better reflects the correlation between the calculation results and performance evaluation.

[0086] In combination, the experimental method provided by this implementation method is simple, the calculation process is simple and reliable, and the theoretical knowledge and actual situation ensure the correctness, practical applicability and simplicity of the entire calculation, which is conducive to long-term sustainable development.

[0087] The described embodiments are merely preferred embodiments of this application and are not intended to limit the scope of this application. Any modifications and improvements made by those skilled in the art to the technical solutions of this application without departing from the spirit of this application should fall within the protection scope defined by the claims of this application.

Claims

1. A method for calculating tire understeering angle, characterized in that, Includes the following steps: Calculation of lateral acceleration: Based on the first axle load, set multiple vertical force percentages Fz (%) and measure the corresponding vertical force Fz, then obtain other vertical force percentages Fz (%) and their vertical forces Fz by linear fitting; wherein, the first axle is one of the front axle and the rear axle of the vehicle, and the second axle is the other of the front axle and the rear axle; set multiple sideslip angles α to obtain each Fz (%) and its Fz and the lateral force Fy under each α; calculate the lateral acceleration A according to formula (3): A=Fy / Fz*g (3) Where g is the acceleration due to gravity; thus, we obtain a table of lateral acceleration data for different Fz (%) and under Fz, as well as under multiple sideslip angles α; Selection of lateral acceleration A: Select the required sideslip angle from the set sideslip angles; set the percentage of vertical force after the load transfer on the first axle when the vehicle turns through a sideslip angle of n°; set the load ratio of the first axle to the second axle to determine the percentage of vertical force after the load transfer on the second axle; select two sets of lateral acceleration A from the obtained lateral acceleration data table based on these settings; Calculation of understeer angle: By plotting the two selected sets of lateral accelerations A, the curves A of front axle lateral acceleration and sideslip angle can be obtained respectively. f -α and rear axle lateral acceleration versus sideslip angle curves A r -α; will curve A f -α and curve A r -α were fitted with polynomials respectively to obtain A. f The relationship with α and A r The relationship with α; then solve for the same acceleration A (A=A f =A r Front axle slip angle α f and rear axle side slip angle α r Furthermore, the understeer angle δu=α for different lateral accelerations A is obtained. f -α r .

2. The method for calculating tire understeer angle according to claim 1, characterized in that, In the calculation of lateral acceleration, more specifically, multiple sideslip angles α are set, and the set Fz (%) and the lateral force Fy under Fz and the set sideslip angle α are measured. For other Fz (%) and the lateral force under Fz, the measured lateral force Fy is linearly or nonlinearly fitted according to α≤5° or α>5°, so as to obtain each Fz (%) and the lateral force Fy under Fz and each α.

3. The method for calculating tire understeer angle according to claim 1, characterized in that, In the calculation of lateral acceleration, multiple sideslip angles α are set as 1°, 2°, 3°, 4°, 5°, 6°, and 7°.

4. The method for calculating tire understeer angle according to any one of claims 1-3, characterized in that, In the calculation of lateral acceleration, a six-component force test bench is used to measure the vertical force Fz and calculate the lateral acceleration A.

5. The method for calculating tire understeer angle according to claim 3, characterized in that, In the step of selecting the lateral acceleration A, the percentage of vertical force after the transfer of the first axle load is set to 10% when the vehicle turns through a sideslip angle of n=1°.

6. The method for calculating tire understeer angle according to claim 5, characterized in that, The first axis is the front axis, and the second axis is the rear axis. In the step of selecting the lateral acceleration A, the load ratio between the front axis and the rear axis is set to 50:40, thereby determining that the vertical force corresponding to 80% of the vertical force corresponding to the reference vertical force of the front axis is the vertical force, and then determining the percentage of the vertical force after the load transfer of the second axis, wherein the reference vertical force of the front axis is Fz corresponding to Fz (100%).

7. The method for calculating tire understeer angle according to any one of claims 1-4, characterized in that, In the calculation step of the understeering angle, for curve A f -α and curve A r -α were fitted with cubic polynomials, and then solved using univariate methods to obtain the front and rear axle slip angles α. f and α r .

8. The method for calculating tire understeer angle according to any one of claims 1-4, characterized in that, It also includes the application of understeer angle: the understeer angle δu of different lateral accelerations A is plotted to obtain the understeer curve A-δu; the understeer state of the vehicle can be judged or compared through the curve A-δu.

9. The method for calculating tire understeer angle according to claim 8, characterized in that, The understeer curve is divided into three parts: ① When the lateral acceleration A is in the range of 0-0.3g, the vehicle is in a normal driving state; ② When the lateral acceleration A is in the range of 0.3-0.6g, it is the non-linear region of vehicle driving; ③ When the lateral acceleration A is above 0.6g, the vehicle is prone to understeer.

10. The application of the method for calculating tire understeer angle according to any one of claims 1-9 in tire testing.

Images