Methods for calculating tire center height changes during steering based on kingpin inclination and caster

Abstract

This invention discloses a method for calculating the tire center height change during steering under kingpin inclination and caster conditions. The method includes the following steps: Step 1, calculating the vertical displacement of the tire center on the ground under kingpin inclination conditions; Step 2, the method for calculating the tire center height change during steering; Step 3, calculating the tire center height change based on the vertical displacement of the tire center on the ground and the vertical displacement of the outer lower side of the tire under kingpin inclination conditions. This calculation method not only helps engineers understand the system better but can also be applied to the development of automotive chassis, such as the calibration of power steering systems. Furthermore, the calculation formula can be programmed and embedded into vehicle dynamics simulation software, making the simulation results more accurate.

Description

Technical Field

[0001] This invention belongs to the field of vehicle measurement technology and relates to a method for calculating the tire center height change during steering due to kingpin inclination and kingpin caster. Background Technology

[0002] The kingpin inclination and caster angles have a significant impact on a vehicle's steering, handling, and safety, and are essential parameters to adjust during four-wheel alignment. When steering, the tire rotates around the kingpin. Due to the inclination or caster of the kingpin, the tire tends to move towards the ground. However, since the ground doesn't actually sink to accommodate the tire's movement, the relative displacement between the tire and the ground doesn't disappear. Under the reaction force of the ground, this relative displacement manifests as an upward displacement of the tire.

[0003] Currently, there are few specific formulas for calculating this displacement. Some related formulas exist in journal articles, but they are not precise enough. Classic books such as *Automotive Theory* provide qualitative descriptions, but do not offer specific derivations. Therefore, in order to accurately calibrate the power steering system during automotive power steering system development and assist engineers in automotive chassis development, there is an urgent need to research a more quantitative and precise method for calculating the kingpin inclination angle and caster angle. Summary of the Invention

[0004] The purpose of this invention is to propose a method for calculating the tire center height change during steering under kingpin inclination and caster conditions, thereby addressing the problem of insufficient accuracy in existing calculation formulas. This method provides calculation techniques for the displacement change of the tire center in the direction perpendicular to the ground when the tire rotates at a certain angle under both kingpin inclination and caster conditions. This clarifies the change in tire center height relative to the ground and can be used for power steering system calibration during development.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] In a first aspect, the present invention provides a method for calculating the change in tire center height during steering due to kingpin inclination, comprising the following steps:

[0007] Step 1: Calculate the vertical displacement of the tire centerline on the ground when turning under kingpin inclination conditions.

[0008] Kingpin inclination angle is the angle between the projection line of the kingpin axis onto the normal plane of the vehicle axis and the perpendicular line to the horizontal plane, denoted as . In the normal plane of the vehicle's axial direction, let the kingpin offset be... Kingpin offset is the point where the kingpin intersects the ground and the tire's center of gravity. The distance of the projection point on the ground; assuming the tire's center of gravity. The distance to the main sales outlet is Tire heart The vertical projection on the main pin is ;

[0009] The angle by which the tire rotates around the kingpin during steering is denoted as . If the tire radius is R, then the tire center of gravity during steering is... The vertical displacement on the ground is:

[0010]

[0011] in, ,

[0012] When the rotation angle hour,

[0013] ;

[0014] Step 2: Calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination.

[0015] Let the tire width be W, and the vertical displacement of the lower outer side of the tire on the ground be:

[0016]

[0017] When the rotation angle hour, ;

[0018] Step 3: Calculate the change in tire center height based on the vertical displacement of the tire center on the ground and the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination.

[0019] Furthermore, in step 3, the change in tire center height... The calculation formula is as follows:

[0020] .

[0021] Secondly, the present invention provides a system for calculating the change in tire center height during steering due to kingpin inclination, comprising the following modules:

[0022] The first displacement calculation module is used to calculate the vertical displacement of the tire center on the ground when turning under kingpin inclination conditions.

[0023] The second displacement calculation module is used to calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination conditions.

[0024] The tire center height change calculation module is used to calculate the tire center height change based on the vertical displacement of the tire center on the ground and the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination.

[0025] Thirdly, the present invention provides an electronic device, the electronic device comprising:

[0026] Memory, used to store executable instructions;

[0027] When the processor executes executable instructions or computer programs stored in the memory, it implements the method for calculating the change in tire center height during steering as provided in the first aspect above.

[0028] Fourthly, the present invention provides a computer-readable storage medium storing executable instructions or a computer program, wherein the executable instructions, when executed by a processor, implement the method provided in the first aspect of the present invention.

[0029] Fifthly, the present invention provides a method for calculating the change in tire center height during steering due to caster, comprising the following steps:

[0030] Step 1: Calculate the vertical displacement of the tire centerline on the ground when turning under caster conditions.

[0031] The caster angle is the angle between the projection of the kingpin axis onto the normal plane along the vehicle's longitudinal direction and the perpendicular line to the horizontal plane, denoted as . In the longitudinal normal plane of the vehicle, let the kingpin trailing distance be... Kingpin trail is the distance between the kingpin and the ground and the tire's center of gravity. The distance of the projection point on the ground; assuming the tire's center of gravity. The distance to the main sales outlet is Tire heart The vertical projection on the main pin is ;

[0032] The angle by which the tire rotates around the kingpin during steering is denoted as . If the tire radius is R, then the tire center of gravity during steering is... The vertical displacement on the ground is:

[0033]

[0034] in, ,

[0035] When the rotation angle hour,

[0036] ;

[0037] Step 2: Calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination.

[0038] Calculate the vertical displacement of point A on the ground:

[0039] ;

[0040] Calculate the vertical displacement of point B on the ground:

[0041]

[0042] in, ;

[0043] Calculate the vertical displacement of the outer underside of the tire on the ground:

[0044] ;

[0045] Step 3: Calculate the change in tire center height based on the vertical displacement of the tire center on the ground and the vertical displacement of the lower outer side of the tire on the ground when turning under caster conditions.

[0046] Furthermore, in step 3, the change in tire center height... The calculation formula is as follows:

[0047] .

[0048] Sixthly, the present invention provides a system for calculating the change in tire center height during steering due to caster, specifically including the following modules:

[0049] The displacement calculation module 1 is used to calculate the vertical displacement of the tire center on the ground when turning under kingpin inclination conditions.

[0050] The second displacement calculation module is used to calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin tilt conditions.

[0051] The tire center height change calculation module is used to calculate the tire center height change based on the vertical displacement of the tire center on the ground and the vertical displacement of the lower outer side of the tire on the ground when turning under caster conditions.

[0052] In a seventh aspect, the present invention provides an electronic device, the electronic device comprising:

[0053] Memory, used to store executable instructions;

[0054] When the processor executes executable instructions or computer programs stored in the memory, it implements the method for calculating the change in tire center height during steering as provided in the fifth aspect above.

[0055] Eighthly, the present invention provides a computer-readable storage medium storing executable instructions or a computer program, wherein when the executable instructions are executed by a processor, they implement the method for calculating the change in tire center height during steering as provided in the fifth aspect above.

[0056] Compared with the prior art, the present invention has the following technical effects:

[0057] This invention proposes a calculation expression for the vertical displacement of the tire center on the ground when the tire rotates around the kingpin under kingpin inclination and caster conditions. The expression is illustrated graphically with examples of how the displacement changes with the rotation angle. This calculation method not only helps engineers understand the technology better but can also be applied to the development of automotive chassis, such as the calibration of power steering systems. Furthermore, the expression can be programmed and embedded into vehicle dynamics simulation software such as TruckSim or CarSim, resulting in more accurate simulation results. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the tire rotating around the kingpin with the kingpin inclined. The left image is a projection of the steering tire directly in front, and the right image is an unfolded analysis diagram of the steering wheel after rotating around the kingpin by a certain angle.

[0059] Figure 2 This is a schematic diagram of the tire rotating around the kingpin with the kingpin inclined. The left image is a projection of the steering tire directly in front, and the right image is a diagram of the tire's lower outer side after the steering wheel has rotated 180° around the kingpin.

[0060] Figure 3 This describes how the tire center height changes with the rotation angle when the kingpin is inclined.

[0061] Figure 4 This is a schematic diagram of the tire rotating around the kingpin under kingpin tilt conditions. The left image is a projection of the steering tire directly in front, and the right image is an unfolded analysis diagram of the steering wheel after rotating around the kingpin by a certain angle.

[0062] Figure 5 This is a schematic diagram of the tire rotating around the kingpin with the kingpin tilted back. The left image is a projection of the steering tire directly in front, and the right image is a diagram of the position of the tire's outer lower side after the steering wheel has rotated 180° around the kingpin.

[0063] Figure 6 This describes how the tire center height changes with the rotation angle when the tire is caster.

[0064] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. Detailed Implementation

[0065] The following two examples illustrate how to calculate the displacement of the tire's geometric center in the direction perpendicular to the ground when the tire rotates by a certain angle, under the conditions of kingpin inclination and kingpin caster.

[0066] Example 1

[0067] This embodiment provides a method for calculating the height change of the tire's geometric center due to the kingpin inclination during steering, including the following steps:

[0068] Step 1: Calculate the vertical displacement of the tire centerline on the ground when turning under kingpin inclination conditions.

[0069] like Figure 1 As shown, the kingpin inclination angle refers to the normal plane from the projected kingpin axis to the vehicle axis (the direction viewed from the front to the rear or from the rear to the front). Figure 1 Within the plane bb), the angle between its projection line and the perpendicular line to the horizontal plane is shown in the figure. Figure 1 In In the bb plane, let the kingpin offset be... Kingpin offset is the point where the kingpin intersects the ground and the tire's center of gravity. The distance of the projection point on the ground; assuming the tire's center of gravity. The distance to the main sales outlet is Tire heart The vertical projection on the main pin is .

[0070] Assuming the tire rotates around the kingpin during steering... Angle (see rotating plane) Figure 1 (the aa plane), that is, the tire center of gravity within the aa plane. With a rotation radius of From the circle Point A travels along the arc to point A. Since plane aa and plane bb are perpendicular, let point B be the projection of point A onto plane bb. Then, in plane aa... The movement of a point along the arc to point A is equivalent to moving from point A to point B in the bb plane. The point moves along a straight line to point B. Let the tire radius be R, then the tire center... The vertical displacement on the ground is:

[0071]

[0072] in, ,

[0073] When the rotation angle hour,

[0074] .

[0075] Step 2: Calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination.

[0076] Let the tire width be W, and the lower outer side of the tire be point D, see... Figure 2 .

[0077] The vertical displacement of the lower outer side of the tire on the ground is:

[0078]

[0079] When the rotation angle hour, .

[0080] Step 3: Calculate the change in tire center height based on the vertical displacement of the tire center on the ground and the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination.

[0081] Assuming that during steering, the tire rotates around the kingpin... If the angle (i.e., the tire steering angle) is such that the ground does not collapse when the tires turn, then the displacement is... Under the reaction force of the ground, it shifted upwards and in the opposite direction towards the ground. Tire center height change The calculation formula is as follows:

[0082]

[0083]

[0084] It can be seen that the change in tire heart height is related to tire width, tire radius, kingpin inclination angle, and tire steering angle.

[0085] In this embodiment, 275 / 80R22.5 tires are used, with a tire radius of... Tire width Kingpin inclination angle Kingpin offset ,but Follow See the changes Figure 3 .

[0086] It can be seen that as the tire rotates around the kingpin at an increasing angle, the height of the tire center also increases.

[0087] Example 2

[0088] This embodiment provides a method for calculating the change in tire geometric center height due to caster during steering, including the following steps:

[0089] Step 1: Calculate the vertical displacement of the tire centerline on the ground when turning under caster conditions.

[0090] like Figure 4 As shown, the kingpin caster angle refers to the normal plane projected from the kingpin axis to the longitudinal direction of the vehicle. Figure 3 Within the cc plane, the angle between its projection line and the perpendicular line to the horizontal plane is shown in [reference needed]. Figure 3 In In the cc plane, let the kingpin trailing distance be... Kingpin trail is the distance between the kingpin and the ground and the tire's center of gravity. The distance of the projection point on the ground; let the distance from the tire center to the kingpin be... fetal heart rate The vertical projection on the main pin is .

[0091] Assuming the tire rotates around the kingpin during steering... Angle (see rotating plane) Figure 3 (the aa plane), that is, the fetal heart in the aa plane. With a rotation radius of From the circle Point A travels along the arc to point A. Since plane aa and plane cc are perpendicular, let point B be the projection of point A onto plane cc. Then, in plane aa... The movement of a point along the arc to point A is equivalent to moving from point A to point C in the cc plane. The point moves along a straight line to point B. Let the tire radius be R, then the tire center... The vertical displacement on the ground is:

[0092]

[0093] in, ,

[0094] When the rotation angle hour,

[0095] .

[0096] Step 2: Calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination.

[0097] Calculate point A (see) Figure 4 The vertical displacement on the ground is:

[0098] ;

[0099] Calculate point B (see) Figure 4 The vertical displacement on the ground is:

[0100]

[0101] in, ;

[0102] Calculate the vertical displacement of the outer underside of the tire on the ground:

[0103] .

[0104] Step 3: Calculate the change in tire center height based on the vertical displacement of the tire center on the ground and the vertical displacement of the lower outer side of the tire on the ground when turning under caster conditions.

[0105] Assuming the tire rotates around the kingpin during steering... If the angle is such that the ground does not collapse when the tires turn, then the displacement... Under the reaction force of the ground, it shifted upwards and in the opposite direction towards the ground. Let the change in tire center height be... ,

[0106]

[0107] It can be seen that the change in tire heart height is related to the tire radius, caster angle, kingpin trail, and tire steering angle.

[0108] In this embodiment, 275 / 80R22.5 tires are used, with a tire radius of... Kingpin caster angle Main tail distance ,but Follow See the changes Figure 6 .

[0109] It can be seen that as the tire rotates around the kingpin at an increasing angle, the tire center height also increases.

[0110] In summary, when the kingpin is tilted inward or outward, as the tire's rotation angle around the kingpin increases, the tire's center height also increases, meaning the vehicle body is raised, which requires overcoming more gravitational potential energy. When the steering wheel is released, the tire will straighten somewhat under the influence of gravitational potential energy, thus improving the vehicle's straight-line driving ability.

[0111] Understanding the effects of caster and kingpin inclination on steering is helpful for developing steering systems. Products related to steering systems on the market include mechanical hydraulic power steering, electric power steering, electro-hydraulic power steering, steer-by-wire, and future intelligent steering. Regardless of the type of steering system developed, the driver's hand force and assist torque are amplified by the reduction gear to overcome steering resistance. The hand force provided by the driver when operating the steering wheel is essentially a constant. This is to avoid a feeling of inconsistent steering wheel weight, which would affect driving quality. Besides factors such as vehicle speed, the required assist torque is related to the real-time steering wheel angle. A larger steering wheel angle requires more assist torque because more gravitational potential energy needs to be overcome. Conversely, when returning the steering wheel to center, less assist torque is needed because gravitational potential energy does positive work. When developing steering control software, it is necessary to calibrate the required assist torque based on real-time feedback of vehicle speed, steering wheel angle, steering wheel angular acceleration, and hand torque. Due to the presence of kingpin inclination and caster, at the same steering wheel angle, the assist torque calibrated further away from the steering wheel zero position is greater than that calibrated closer to the steering wheel zero position. The method of this invention can provide some theoretical guidance for calibrating basic assist and return-to-center assist. Furthermore, this calculation formula can be programmed and embedded into vehicle dynamics simulation software such as TruckSim or CarSim, which involves secondary development of the vehicle dynamics software, thereby making the simulation results more accurate.

Claims

1. A method for calculating the change in tire center height during steering due to kingpin inclination, characterized in that, Includes the following steps: Step 1: Calculate the vertical displacement of the tire centerline on the ground when turning under kingpin inclination conditions. Kingpin inclination angle is the angle between the projection line of the kingpin axis onto the normal plane of the vehicle axis and the perpendicular line to the horizontal plane, denoted as . In the normal plane of the vehicle's axial direction, let the kingpin offset be... Kingpin offset is the point where the kingpin intersects the ground and the tire's center of gravity. The distance of the projection point on the ground; assuming the tire's center of gravity. The distance to the main sales outlet is Tire heart The vertical projection on the main pin is ; The angle by which the tire rotates around the kingpin during steering is denoted as . If the tire radius is R, then the tire center of gravity during steering is... The vertical displacement on the ground is: in, , When the rotation angle hour, ； Step 2: Calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination. Let the tire width be W, and the vertical displacement of the lower outer side of the tire on the ground be: When the rotation angle hour, ; Step 3: Based on the vertical displacement of the tire centerline on the ground and the vertical displacement of the tire's outer lower side on the ground during steering with kingpin inclination, calculate the change in tire centerline height. : 。 2. A system for calculating the change in tire center height during steering when the kingpin inclination is induced, characterized in that, Includes the following modules: The first displacement calculation module is used to calculate the vertical displacement of the tire center on the ground when turning under kingpin inclination conditions. Kingpin inclination angle is the angle between the projection line of the kingpin axis onto the normal plane of the vehicle axis and the perpendicular line to the horizontal plane, denoted as . In the normal plane of the vehicle's axial direction, let the kingpin offset be... Kingpin offset is the point where the kingpin intersects the ground and the tire's center of gravity. The distance of the projection point on the ground; assuming the tire's center of gravity. The distance to the main sales outlet is Tire heart The vertical projection on the main pin is ; The angle by which the tire rotates around the kingpin during steering is denoted as . If the tire radius is R, then the tire center of gravity during steering is... The vertical displacement on the ground is: in, , When the rotation angle hour, ； The second displacement calculation module is used to calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination conditions. Let the tire width be W, and the vertical displacement of the lower outer side of the tire on the ground be: When the rotation angle hour, ; The tire center height change calculation module is used to calculate the tire center height change based on the vertical displacement of the tire center on the ground and the vertical displacement of the tire's outer underside on the ground during steering with kingpin inclination. : 。 3. An electronic device, characterized in that, The electronic device includes: Memory, used to store executable instructions; A processor, when executing executable instructions or computer programs stored in the memory, implements the method as described in claim 1.

4. A computer-readable storage medium storing executable instructions or a computer program, characterized in that, When the executable instructions are executed by the processor, they implement the method as described in claim 1.

5. A method for calculating the change in tire center height during steering due to caster, characterized in that, Includes the following steps: Step 1: Calculate the vertical displacement of the tire centerline on the ground when turning under caster conditions. The caster angle is the angle between the projection of the kingpin axis onto the normal plane along the vehicle's longitudinal direction and the perpendicular line to the horizontal plane, denoted as . In the longitudinal normal plane of the vehicle, let the kingpin trailing distance be... Kingpin trail is the distance between the kingpin and the ground and the tire's center of gravity. The distance of the projection point on the ground; assuming the tire's center of gravity. The distance to the main sales outlet is Tire heart The vertical projection on the main pin is ; The angle by which the tire rotates around the kingpin during steering is denoted as . If the tire radius is R, then the tire center of gravity during steering is... The vertical displacement on the ground is: in, , When the rotation angle hour, ； Step 2: Calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin inclination. Calculate the vertical displacement of point A on the ground: ； Calculate the vertical displacement of point B on the ground: in, ; Calculate the vertical displacement of the outer underside of the tire on the ground: ； Step 3: Based on the vertical displacement of the tire centerline on the ground and the vertical displacement of the tire's outer underside on the ground during steering under caster conditions, calculate the change in tire centerline height. : 。 6. A system for calculating the change in tire center height during steering due to caster, characterized in that, Specifically, it includes the following modules: The displacement calculation module 1 is used to calculate the vertical displacement of the tire center on the ground when turning under kingpin inclination conditions. The caster angle is the angle between the projection of the kingpin axis onto the normal plane along the vehicle's longitudinal direction and the perpendicular line to the horizontal plane, denoted as . In the longitudinal normal plane of the vehicle, let the kingpin trailing distance be... Kingpin trail is the distance between the kingpin and the ground and the tire's center of gravity. The distance of the projection point on the ground; assuming the tire's center of gravity. The distance to the main sales outlet is Tire heart The vertical projection on the main pin is ; The angle by which the tire rotates around the kingpin during steering is denoted as . If the tire radius is R, then the tire center of gravity during steering is... The vertical displacement on the ground is: in, , When the rotation angle hour, ； The second displacement calculation module is used to calculate the vertical displacement of the lower outer side of the tire on the ground when turning under kingpin tilt conditions. Calculate the vertical displacement of point A on the ground: ； Calculate the vertical displacement of point B on the ground: in, ; Calculate the vertical displacement of the outer underside of the tire on the ground: ； The tire centerline height change calculation module is used to calculate the tire centerline height change based on the vertical displacement of the tire centerline on the ground and the vertical displacement of the tire's outer underside on the ground during steering under caster conditions. : 。 7. An electronic device, characterized in that, The electronic device includes: Memory, used to store executable instructions; A processor, when executing executable instructions or computer programs stored in the memory, implements the method as described in claim 5.

8. A computer-readable storage medium storing executable instructions or a computer program, characterized in that, When the executable instructions are executed by the processor, they implement the method as described in claim 5.

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