CN110929340B - Method for calculating slip angle caused by steering trapezium of front wheel driving automobile - Google Patents

Method for calculating slip angle caused by steering trapezium of front wheel driving automobile Download PDF

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CN110929340B
CN110929340B CN201911215236.6A CN201911215236A CN110929340B CN 110929340 B CN110929340 B CN 110929340B CN 201911215236 A CN201911215236 A CN 201911215236A CN 110929340 B CN110929340 B CN 110929340B
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slip angle
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苗立东
曲宝军
张剑罡
徐希翼
张允明
许梁
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Shandong University of Technology
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Abstract

A method for calculating the slip angle of an automobile wheel in a non-Ackerman steering relation relates to a design calculation method for the steering performance of an automobile, in particular to a method for calculating the slip angle of the wheel aiming at the conditions of double-axle, four-wheel automobiles, front wheel driving and movement under a low-speed large-rotation angle. According to the invention, the numerical solution meeting the precision requirement is obtained by an iteration method based on the stress balance condition and the motion coordination condition of the automobile. The method is proved to be effective and feasible by comparing the solving example with the actual experimental phenomenon. The method provides a method for calculating the wheel slip angle in the steering process of the vehicle type, can more accurately predict the motion characteristics of the vehicle in the product design stage, and can also provide a theoretical basis for calculating simulation software development.

Description

Method for calculating slip angle caused by steering trapezium of front wheel driving automobile
Technical Field
The invention relates to a design calculation method of automobile steering performance, in particular to a calculation method of wheel slip angle caused by double axles, front wheel driving and steering trapezoids which do not meet an Ackerman steering relation.
Background
With the improvement of the speed of a modern automobile, wheels are always subjected to certain and sometimes larger lateral force when the automobile turns, certain side deflection angles are generated by the wheels, an Akerman steering structure is not ideal any more, and an ideal state is a steering state between Akerman steering and parallel steering, namely an under-Akerman steering structure, which is also the structure adopted by most of the current automobiles; however, when the automobile with the structure is turned at a low speed and a large turning angle, the centrifugal force is very small and can be usually ignored due to low speed, but the motion interference among wheels, particularly among front turning wheels, can cause the tires to generate a certain and even larger cornering angle to form cornering force, which has a certain influence on the running performance of the automobile, such as the aligning performance and the maneuvering performance, and if the influence is not considered, the error of the calculation result is relatively large, and the opposite result can be possibly obtained. In addition, when some calculation simulation software is developed, calculation is required for this case, and therefore, when the correlation analysis is performed on the automobile, it is necessary to perform analysis calculation on the cornering angle and the cornering force in this case.
Disclosure of Invention
Aiming at the situation, the invention provides a method for solving the problem of calculating the slip angle caused by the owaxman steering structure.
When calculating, the relevant structural parameters of a given automobile are needed: front treadB 1 Rear trackB 2 WheelbaseLDistance between two main pin axis grounding points of front wheelKCornering stiffness of each wheelk i (subscript)i=1, 2,3,4 represent the front inner wheel, front outer wheel, rear inner wheel, rear outer wheel, lower same), the rotation angle α of the front inner wheel and the rotation angle β of the front outer wheel, respectively, the wheel rotation axis being orthoprojected on the supporting ground on which the vehicle is traveling during analysis. The calculation process needs iterative solution, and the specific process is as follows:
(1) Determining the back inner wheel slip angle gamma at the beginning of an iteration 3 Is defined by the range of (2); calculating the intersection point of the rotation center lines of the front inner wheel and the front outer wheel according to the given conditionsO FR Intersection point of front inner wheel rotation center line and rear axle axisO 1 Intersection point of front outer wheel rotation center line and rear shaft axisO 2 . After passing the rear wheel ground center (tire ground center, the same applies below) pointP T3 AndO FR and (5) making a straight line, and calculating an included angle phi between the straight line and the axis of the rear axle. Taking gamma 3 Is a minimum value gamma of (2) 3min =0, take γ 3 Is the maximum value gamma of (2) 3max =φ;
(2) Determination of gamma 3 Taking gamma 3 =(γ 3min3max )/2;
(3) At gamma 3 Timing determination of rear outer wheel slip angle gamma 4 Is not limited in terms of the range of (a). Ground center point of rear inner wheelP T3 Making straight lineL 3 Perpendicular to rear inner wheel center speedu 3 According toGeometrical relationshipL 3 The included angle between the rear axle axis and the rear axle is the side deflection angle gamma of the rear inner wheel 3L 3 Intersecting the axis of rotation of the front inner wheelP 1L 3 Intersecting the axis of rotation of the front outer wheelP 2P 1 Point and rear outer wheel grounding centerP T4 The included angle between the connecting line of the (E) and the axis of the rear axle is the back outer wheel slip angle gamma 4 Is a minimum value gamma of (2) 4_MIN By the following constitutionP 2 Point and rear outer wheel grounding centerP T4 The included angle between the connecting line of the (E) and the axis of the rear axle is the back outer wheel slip angle gamma 4 Is the maximum value gamma of (2) 4_MAX . Iterative calculation, initial gamma extraction 4min =γ 4_MIN ,γ 4max =γ 4_MAX
(4) Determination of gamma 4 Taking gamma during calculation 4 =(γ 4min4max )/2;
(5) From the slip angle gamma 3 、γ 4 To obtain instantaneous center of (1)O u Is a position of (2);
(6) Based on the instant centerO u Obtaining the front inner wheel slip angle gamma from the geometric relationship 1 Angle of front outer wheel slip gamma 2
(7) Obtaining the lateral force, and obtaining the lateral force born by each wheel according to the cornering stiffness of each wheel respectively asF 1F 2F 3F 4 And calculateF 3 And (3) withF 4 Is of the total force of (2)F 34F 34 Acting on the rear axle axis;
(8) Driving force determinationF x1F x2 . For a common differential mechanism, the differential mechanism is provided with a plurality of differential gears,F x1F x2F x . The front inner wheel is subjected to lateral forceF 1 And driving forceF x1 Is of the total force of (2)F 1H Lateral force exerted by the front outer wheelF 2 And driving forceF x2 Is of the total force of (2)F 2HF x Minimum value of (2)F xmin When=0, whenF 2H Crossing pointO 1 In the time-course of which the first and second contact surfaces,F x take the maximum valueF xmax Calculated according to the force vectorF xmax . Taking outF x =(F xmin +F xmax ) Performing iterative calculation for initial value of/2, and calculatingF 1H AndF 2H is the resultant force intersection point of (2)O FF . If it isO FF Is positioned behind the rear axle, to makeF xmin =F x The method comprises the steps of carrying out a first treatment on the surface of the If it isO FF Is positioned in front of the rear axle, to makeF xmax =F x Performing iterative calculation in the step (8) again until the pointO FF Is positioned on the axis of the rear axle;
(9) Calculating the force resultant force of four wheelsyResultant force in axial directionF yHxResultant force in axial directionF xH And processing the calculation result in sequence according to the following different conditions:
(A) If gamma is 4 =γ 4_MAX Or gamma 4 =γ 4_MIN Currently taken gamma 3 、γ 4 Neither satisfies the condition; if it isF yH > 0, let gamma 3min =γ 3 Conversely, let gamma 3max =γ 3 Returning to the step (2) for iterative computation;
(B) If (A) is not satisfied, then judgingF yH If (3)F yH < 0, let gamma 4min =γ 4 The method comprises the steps of carrying out a first treatment on the surface of the If it isF yH > 0, let gamma 4max =γ 4 Returning to the step (4) for iterative computation;
(C) If (A) and (B) are not satisfied, then judgingF xH If (3)F xH < 0, let gamma 3max =γ 3 If (3)F xxH > 0, let gamma 3min =γ 3 Returning to the step (2) for iterative computation; if it isF xH =0, specify γ 3 The condition is also satisfied, and the calculation is finished;
(10) And outputting the slip angle of each wheel.
In actual calculation, the error limit is set according to the use requirement and the computer precision when judging and comparing by means of computer programming calculation.
The principle on which the calculation method is based is that the cornering characteristics of the tire, the motion coordination and the dynamic balance of the automobile are adopted. When the wheels are laterally deviated by lateral force, the lateral force acted on the wheels by the ground is perpendicular to the central plane of the wheels and coincides with the orthographic projection line of the rotation center line of the wheels, and when the automobile makes a curvilinear motion, the automobile rotates around the instant center, and the perpendicular line of the speed of the centers of the wheels is intersected with the instant center at one point.
The invention has advantages over the prior art.
At present, the automobile steering performance is studied, and the cornering angle and cornering force caused by steering trapezoids are generally calculated through simulation software such as Carsim, and the like, but no calculation method is disclosed. There are also studies on the driving condition of the rear wheels, but the driving force conditions of the front wheels are different from those of the rear wheels, and the calculation method cannot be used.
The invention provides a calculation method for calculating the wheel slip angle caused by interference of steering trapezium of a front wheel driving and front wheel steering automobile, and the calculation result is consistent with the observed phenomenon, thus the method is effective.
Drawings
FIG. 1 is a schematic representation of the computational kinetic analysis of the present invention.
FIG. 2 is a flow chart of the calculation of the present invention.
Fig. 3 and 4 show test results.
In the figure, 1 is the footprint of the front outer wheel on the ground, and 2 is the footprint of the front inner wheel on the ground.
Description of the embodiments
The invention is further described with reference to fig. 1 and 2.
The wheelbase of the automobile isL=2.46 m, equal track pitch front and rear,B 1 =1.465 m,B 2 distance between two front wheel kingpin ground points =1.448 mK=B 1 Front wheel steering is adopted. When the maximum rotation angle of the front inner wheel is 0.5847 rad (33.5 °), the corresponding maximum rotation angle of the front outer wheel is 0.5206 rad (29.83 °). The tires of the four wheels of the vehicle are the same, the cornering stiffness is the same, and the value is 20000N/rad. The coordinate system is established at the midpoint of the rear axleO RxThe positive direction of the shaft is forward,yall positions, such as the positions of the various points, of the axis in the forward direction of the axis to the left are represented in a projected relationship projected onto the support plane of the vehicle.
(1) Determining the back inner wheel slip angle gamma at the beginning of an iteration 3 Is defined by the range of (2); firstly, calculating the intersection point of the rotation center lines of two front wheels according to the given conditionsO FR The coordinates are (-3.8236, 10.2260), the coordinates are m, and the same will not be described below; intersection point of front inner wheel rotation center line and rear axleO 1 (0,4.4492) intersection point of front outer wheel and rear axleO 2 (0,3.5577). Ground center point of rear inner wheelP T3 AndO FR and (3) making a straight line, and calculating an included angle phi= 0.3826 rad between the straight line and the axis of the rear axle. Taking gamma 3 Is a minimum value gamma of (2) 3min =0rad, take γ 3 Is the maximum value gamma of (2) 3max =φ;
(2) Determination of gamma 3 Taking gamma 3 =(γ 3min3max )/2=0.1913 rad;
(3) According to the principle of kinematics, at gamma 3 Timing determination of rear outer wheel slip angle gamma 4 Is not limited in terms of the range of (a). Ground center point of rear inner wheelP T3 Making straight lineL 3 Perpendicular tou 3 According to physical relationsL 3 Included angle gamma with axis of rear axle 3L 3 Intersecting the axis of rotation of the front inner wheelP 1 The coordinates are (-1.0198,5.9898),L 3 intersecting the axis of rotation of the front outer wheelP 2 The coordinates are (-0.8286,5.0028).P 1 Point and rear outer wheel grounding centerP T4 An included angle between the connecting line of the (E) and the axis of the rear axle is gamma 4 Is the most significant of (3)Small value gamma 4_MIN = 0.1437 rad, byP 2 Point and rear outer wheel grounding centerP T4 And the included angle between the connecting line of the (E) and the axis of the rear axle is determined to be gamma 4 Is the maximum value gamma of (2) 4_MAX = 0.1507 rad. Iterative calculation, initial gamma extraction 4min =γ 4_MIN ,γ 4max =γ 4_MAX
(4) Determination of gamma 4 Taking gamma during calculation 4 =(γ 4min +γ 4max )/2= 0.1472 rad;
(5) From the slip angle gamma 3 、γ 4 To obtain instantaneous center of (1)O u Is (-0.9165,5.4569);
(6) Based on the instant centerO u Obtaining the front inner wheel slip angle gamma from the geometric relationship 1 =0.0358 rad, front outer wheel slip angle γ 2 = 0.0212 rad;
(7) The lateral force is obtained, and the lateral force born by each wheel is the product of the lateral deflection angle and the lateral deflection rigidity respectively, which isF 1 = 716.8514 N、F 2 =424.4061 N、F 3 =3825.8 N、F 4 = 2944.3N, and calculateF 3 And (3) withF 4 Is of the total force of (2)F 34 = 6770.0 N,F 34 The position is on the axis of the rear axle;
(8) Driving force determinationF x1F x2 . For a common differential mechanism, the differential mechanism is provided with a plurality of differential gears,F x1F x2F x . The front inner wheel is subjected to lateral forceF 1 And driving forceF x1 Is of the total force of (2)F 1H Lateral force exerted by the front outer wheelF 2 And driving forceF x2 Is of the total force of (2)F 2HF x Minimum value of (2)F xmin When=0, whenF 2H Crossing pointO 1 In the time-course of which the first and second contact surfaces,F x take the maximum valueF xmaxF xmax 32.9088N can be obtained by a force vector calculation method. Taking outF x =(F xmin +F xmax ) For the initial value,/2= 16.4544N, iterative calculation is performed to calculateF 1H AndF 2H is the resultant force intersection point of (2)O FF The coordinates are (-0.6306,5.1768). If it isO FF Is positioned behind the rear axle, to makeF xmin =F x The method comprises the steps of carrying out a first treatment on the surface of the If it isO FF Is positioned in front of the rear axle, to makeF xmax =F x This calculationO FF Is positioned behind the rear axle, to makeF xmin =F x = 16.4544N; iterative calculation is carried out again in the step (8) until the pointO FF On the axis of the rear axle, to obtainF x = 24.2658N; the step error limit is set to 0.00001 m;
(9) Calculating the force resultant force of the wheelsyResultant force in axial directionF yH =-6974.2 N,xResultant force in axial directionF xH = 225.8308N, the calculation results are processed sequentially according to the following different cases:
(A) If gamma is 4 =γ 4_MAX Or gamma 4 =γ 4_MIN Currently taken gamma 3 、γ 4 Neither satisfies the condition; if it isF yH > 0, let gamma 3min =γ 3 Conversely, let gamma 3max =γ 3 Returning to the step (2) for iterative computation; according to the calculation result, gamma is calculated at the first iteration 4 ≠γ 4_MAX ,γ 4 ≠γ 4_MIN Proceeding to the next step (B); the angular error limit value at the time of judgment in this step is set to (gamma) 4_MAX -γ 4_MIN )/65536;
(B) If (A) is not satisfied, then judgingF yH If (3)F yH < 0, let gamma 4min =γ 4 The method comprises the steps of carrying out a first treatment on the surface of the If it isF yH > 0, let gamma 4max =γ 4 Returning to the step (4) for iterative computation; according to the calculation result; according to the above calculation junctionFruit, first iterationF yH < 0, let gamma 4min =γ 4 = 0.1472 rad, returning to the iterative calculation of step (4); when the judgment is made in this step, the error limit value of the force is 0.1N;
(C) If neither (A) nor (B) is satisfied, ifF xH < 0, let gamma 3max =γ 3 If (3)F xxH > 0, let gamma 3min =γ 3 Returning to the step (2) for iterative computation; otherwise, explain gamma 3 The condition is also satisfied, and the calculation is finished; when the judgment is made in this step, the error limit value of the force is 0.1N;
(10) And outputting the slip angle of each wheel.
Through repeated iterative calculation, the slip angles of the four wheels are calculated as follows: gamma ray 1 =0.0377 rad,γ 2 =0.0489 rad,γ 3 =0.0075 rad,γ 4 =0.0054 rad。
The vehicle in the embodiment is adopted for testing, the vehicle runs at the lowest stable speed, the speed is between 4 km/h and 5 km/h, the front wheel rotates to the maximum rotation angle position, and after the vehicle rotates on the ground for 4 circles, the test results are shown in fig. 3 and 4; the wheel leaves a footprint on the ground, the footprint 1 of the front outer wheel is more visible than the footprint 2 of the front inner wheel, and the footprints of the two rear wheels are difficult to observe, which is consistent with the calculation results.

Claims (1)

1. A method for calculating a slip angle caused by a steering trapezoid of a front wheel drive automobile comprises the following steps of knowing relevant structural parameters of the automobile: front treadB 1 Rear trackB 2 WheelbaseLDistance between two main pin axis grounding points of front wheelKCornering stiffness of each wheelk i Subscript ofiThe method is characterized in that the orthographic projection of the wheel rotation axis is calculated on the supporting ground of the automobile, and is solved by the following steps:
(1) Determining the back inner wheel slip angle gamma at the beginning of an iteration 3 Is defined by the range of (2); firstly, calculating the intersection point of the rotation center lines of the front inner wheel and the front outer wheel according to the structural parametersO FR Intersection point of front inner wheel rotation center line and rear axle axisO 1 Intersection point of front outer wheel rotation center line and rear shaft axisO 2 The method comprises the steps of carrying out a first treatment on the surface of the Ground center point of rear inner wheelP T3 AndO FR making a straight line, and calculating an included angle phi between the straight line and the axis of the rear axle; taking gamma 3 Is a minimum value gamma of (2) 3min =0, take γ 3 Is the maximum value gamma of (2) 3max =φ;
(2) Determination of gamma 3 Taking gamma 3 =(γ 3min3max )/2;
(3) At gamma 3 Timing determination of rear outer wheel slip angle gamma 4 Is defined by the range of (2); ground center point of rear inner wheelP T3 Making straight lineL 3 Perpendicular to rear inner wheel center speedu 3 According to geometrical relationsL 3 The included angle between the rear axle axis and the rear axle is the side deflection angle gamma of the rear inner wheel 3L 3 Intersecting the axis of rotation of the front inner wheelP 1L 3 Intersecting the axis of rotation of the front outer wheelP 2P 1 Point and rear outer wheel grounding centerP T4 The included angle between the connecting line of the (E) and the axis of the rear axle is the back outer wheel slip angle gamma 4 Is a minimum value gamma of (2) 4_MIN By the following constitutionP 2 Point and rear outer wheel grounding centerP T4 The included angle between the connecting line of the (E) and the axis of the rear axle is the back outer wheel slip angle gamma 4 Is the maximum value gamma of (2) 4_MAX The method comprises the steps of carrying out a first treatment on the surface of the Iterative calculation, initial gamma extraction 4min =γ 4_MIN ,γ 4max =γ 4_MAX
(4) Determination of gamma 4 Taking gamma during calculation 4 =(γ 4min4max )/2;
(5) From the slip angle gamma 3 、γ 4 To obtain instantaneous center of (1)O u Is a position of (2);
(6) Based on the instant centerO u Obtaining the front inner wheel slip angle gamma from the geometric relationship 1 Angle of front outer wheel slip gamma 2
(7) Obtaining the lateral force, and obtaining the lateral force born by each wheel according to the cornering stiffness of each wheel respectively asF 1F 2F 3F 4 And calculateF 3 And (3) withF 4 Is of the total force of (2)F 34F 34 Acting on the rear axle axis;
(8) Driving force determinationF x1F x2 The method comprises the steps of carrying out a first treatment on the surface of the For a common differential mechanism, the differential mechanism is provided with a plurality of differential gears,F x1F x2F x the method comprises the steps of carrying out a first treatment on the surface of the The front inner wheel is subjected to lateral forceF 1 And driving forceF x1 Is of the total force of (2)F 1H Lateral force exerted by the front outer wheelF 2 And driving forceF x2 Is of the total force of (2)F 2HF x Minimum value of (2)F xmin When=0, whenF 2H Crossing pointO 1 In the time-course of which the first and second contact surfaces,F x take the maximum valueF xmax Calculated according to the force vectorF xmax The method comprises the steps of carrying out a first treatment on the surface of the Taking outF x =(F xmin +F xmax ) Performing iterative calculation for initial value of/2, and calculatingF 1H AndF 2H is the resultant force intersection point of (2)O FF The method comprises the steps of carrying out a first treatment on the surface of the If it isO FF Is positioned behind the rear axle, to makeF xmin =F x The method comprises the steps of carrying out a first treatment on the surface of the If it isO FF Is positioned in front of the rear axle, to makeF xmax =F x Performing iterative calculation in the step (8) again until the pointO FF Is positioned on the axis of the rear axle;
(9) Calculating the force resultant force of four wheelsyResultant force in axial directionF yHxResultant force in axial directionF xH And processing the calculation result in sequence according to the following different conditions:
(A) If gamma is 4 =γ 4_MAX Or gamma 4 =γ 4_MIN At presentTaking gamma 3 、γ 4 Neither satisfies the condition; if it isF yH > 0, let gamma 3min =γ 3 Conversely, let gamma 3max =γ 3 Returning to the step (2) for iterative computation;
(B) If (A) is not satisfied, then judgingF yH If (3)F yH < 0, let gamma 4min =γ 4 The method comprises the steps of carrying out a first treatment on the surface of the If it isF yH > 0, let gamma 4max =γ 4 Returning to the step (4) for iterative computation;
(C) If (A) and (B) are not satisfied, then judgingF xH If (3)F xH < 0, let gamma 3max =γ 3 If (3)F xxH > 0, let gamma 3min =γ 3 Returning to the step (2) for iterative computation; if it isF xH =0, specify γ 3 The condition is also satisfied, and the calculation is finished;
(10) And outputting the slip angle of each wheel.
CN201911215236.6A 2019-12-02 2019-12-02 Method for calculating slip angle caused by steering trapezium of front wheel driving automobile Active CN110929340B (en)

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