Road surface speed bump optimization design method based on vehicle-road coupling vibration response

Abstract

The invention belongs to the technical field of speed bump design, and discloses a road surface speed bump optimization design method based on vehicle-road coupling vibration response, which comprises the following steps of: determining asymmetric segmented curve design of a speed bump; resolving analytic expressions of curves of different structural sections of the deceleration strip; establishing a speed bump combination curve scheme, and combining the cosine segment and the parabolic segment according to different horizontal projection lengths; establishing a coupling model among the wheels, the suspension system, the vehicle body and the road surface; the height of the speed bump is set to obtain different working conditions under various curve combination schemes; and screening an optimal speed bump scheme according to a vibration response result. According to the invention, the traditional speed bump design is broken through, and technical optimization is realized on multiple aspects such as speed reduction control, driving comfort and retrograde driving warning.

Description

Technical Field

[0001] The present invention relates to the technical field of speed bump design, and in particular to a road speed bump optimization design method based on vehicle-road coupled vibration response. Background Art

[0002] In recent years, with the rapid growth of road traffic volume, speed bumps, as a mandatory deceleration facility, have played an important role in ensuring pedestrian safety and reducing accident risks. The People's Republic of China Transportation Industry Standard JT / T713-2008 "Road Rubber Speed ​​Bumps" stipulates that the cross-sectional shape of speed bumps should be approximately trapezoidal. This requirement leads to the traditional speed bumps usually adopting a symmetrical trapezoidal or circular arc cross-sectional design, and their design methods are mainly based on engineering experience and experimental data. However, this design method may still cause severe impact vibration and poor driving comfort when vehicles pass at the required low speed. In addition, traditional symmetrical speed bumps are difficult to effectively curb wrong-way behavior and lack a targeted punishment effect on illegal vehicles.

[0003] Ren Chenglong et al. used simulation and experimental methods to study the effects of speed bumps with various cross-sections on vehicle ride smoothness and safety, finding that trapezoidal speed bumps had the greatest impact. Jia Changming studied the effects of symmetrical circular speed bumps on vehicle vibration and found that circular cross-sections exerted greater impact on vehicles. Based on these studies, it is clear that existing speed bump cross-sectional shapes are difficult to effectively match vehicle dynamics, resulting in severe vibrations even when vehicles pass within the speed limit, which in turn affects driving comfort and cargo safety. Furthermore, traditional static experimental methods cannot fully characterize the dynamic coupling effects between the vehicle and the road surface, resulting in a lack of systematic and quantitative theoretical basis for speed bump design. Current research has largely focused on experimental testing and improvements in parameters such as aspect ratio, such as Zhang Wei et al.'s "The Effect of Road Speed ​​Bumps on Vehicle Ride Comfort and Safety" and Hou Chenyuan et al.'s "Analysis of the Dynamic Response of Vehicles Passing Over Speed ​​Bumps." Furthermore, the article "A Review of Academic Research in China's Transportation Engineering, 2016" points out that the use of speed bumps in China is often blind and arbitrary. For example, current research primarily relies on field testing to obtain vehicle vibration response data to optimize speed bump design. However, this method has limitations such as long testing cycles, high costs, and poor data reproducibility. Furthermore, it struggles to reveal the dynamic interaction between the vehicle system and the speed bump. Currently, the optimization design of speed bump shapes still lacks systematic theoretical support.

[0004] Therefore, fully considering the vehicle-road coupled vibration response, breaking the limitations of traditional symmetrical section design, and establishing a speed bump optimization design method based on the vehicle-road coupled vibration response have become the key technical path to improve the comprehensive performance of speed bumps. Summary of the Invention

[0005] In order to solve the deficiencies in the prior art, the present invention proposes a road speed bump optimization design method based on vehicle-road coupled vibration response.

[0006] This paper discloses a method for optimizing the cross-sectional shape of speed bumps based on the vehicle-road coupled vibration response. This method aims to balance smooth passage of forward-traveling vehicles with effective interference with oncoming vehicles. By constructing an asymmetric curve and combining it with wheel-road coupled vibration simulation analysis, it achieves quantitative optimization of the speed bump shape. This method is highly systematic, has clear physical implications, and possesses excellent engineering applicability.

[0007] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0008] The implementation steps of the method of the present invention include the following aspects:

[0009] Step 1: Clarify the speed bump structure and coupling mechanism modeling requirements

[0010] The speed bump width used in this study is set at L = 400mm. By constructing a wheel-road coupling model related to wheel size and the dynamic response of the suspension system, a systematic study is conducted on the vehicle vibration response caused by different speed bump cross-section shapes. Traditional symmetrical cross-sections (such as arcs or trapezoids) cannot achieve both forward driving comfort and reverse driving deterrence during driving. Therefore, this method adopts an asymmetric piecewise curve design concept, using a combination of cosine function segments and parabola segments to describe the speed bump cross-section curve.

[0011] Step 2: Design the speed bump cross-section curve piecewise function

[0012] Based on the vehicle's driving direction and the order of tire contact, the following curve combination scheme is designed: the AB segment (the part where the wheels first contact) adopts a cosine function segment with a relatively gentle curvature, which is conducive to mitigating the initial impact of the vehicle; the BC segment (the latter segment) adopts a parabola function with an appropriately increased curvature to increase the discomfort when the wrong-way vehicle passes and achieve a punitive effect; to ensure the smoothness of the transition, the first-order derivatives of the two function curves are guaranteed to be continuous (i.e., differentiable continuity) at the connection point B, that is, the curve maintains a smooth transition both visually and structurally; while meeting the curve continuity conditions, the specific expression of the BC segment parabola is solved by solving the parameters of the curve function.

[0013] Step 3: Construct a combined curve change group plan

[0014] Keep the overall width of the speed bump constant at L = 400mm and set different horizontal projection lengths L for the AB segments. AB And the corresponding BC segment horizontal projection length L BC , gradually increase L AB The proportion of the components is used to reduce the initial impact and form different combination shapes. They are divided into the following four groups:

[0015] Solution 1: The wavelength of cosine is T = 400 mm, L AB =L / 2=200mm, L BC =LL AB =200mm as the control group.

[0016] Solution 2: The wavelength of the cosine is T = 479.5 mm, and the cosine segment is L AB =T / 2+T / 8=5T / 8=299.7mm, parabola segment L BC =LL AB =100.3mm.

[0017] Solution 3: The wavelength of the cosine is T = 456.1 mm, and the cosine segment is L AB =T / 2+2T / 8=3T / 4=342.1mm, parabola segment L BC =LL AB =57.9mm.

[0018] Solution 4: The wavelength of cosine is T = 427.4 mm. The cosine segment L AB =T / 2+3T / 8=7T / 8=373.9mm, parabola segment L BC =LL AB =26.1mm.

[0019] Through this parameter variation process, the optimization model from symmetrical speed bumps to asymmetrical curvature control can be gradually transformed, providing sample data for subsequent coupled vibration response analysis.

[0020] Step 4: Build a wheel-road coupling simulation model that considers tire size effects

[0021] Finite element methods are used to construct a coupled model between the wheels, suspension, body, and road surface. Specifically, a wheel-road coupling element developed by the authors, which accounts for wheel size effects, is used to simulate the dynamic interaction between the wheels and the road surface during driving. The simulation should meet the following conditions:

[0022] Considering the nonlinear deformation characteristics of tires;

[0023] The model should include boundary conditions such as tire radius, vehicle speed, and vehicle load;

[0024] The cross sections of the speed bumps are introduced into the simulation platform according to different combination schemes;

[0025] Output indicators include vertical acceleration and wheel-road contact force;

[0026] Forward and reverse simulation analyses were performed to evaluate comfort and reverse interference capabilities.

[0027] Step 5: Set different height schemes to simulate multiple working conditions

[0028] To evaluate the impact of different speed bump heights on the vehicle's vibration response, three different heights were set for each curve combination: H = 20 mm, H = 30 mm, and H = 40 mm. This yielded a total of 12 operating conditions, including four curves and three different heights. Simulations were performed to determine the peak vertical vibrations of the vehicle body and wheels under each condition.

[0029] Step 6: Select the optimal solution based on the vibration response results

[0030] Compare 12 sets of simulation results and select the optimal solution that takes into account the following performance:

[0031] The vehicle vibration response is minimal during forward driving;

[0032] The vertical impact is significant when driving in the opposite direction;

[0033] The curve is continuous and the shape is simple, which is convenient for engineering implementation;

[0034] The comprehensive evaluation indicators of comfort, traffic guidance and wrong-traffic punishment are the best.

[0035] Finally, the optimal speed bump cross-section design is formed, achieving dual optimization of structure and dynamic response.

[0036] Furthermore, the asymmetric segmented curve design of the speed bump structure includes a combined design of a cosine curve and a parabola curve, but is not limited to these two curve shapes.

[0037] Furthermore, the combination curve change group scheme includes four existing schemes, but is not limited to the combination of these four horizontal projection lengths.

[0038] Furthermore, the dimensions of the speed bump include different combinations of width L=400 mm, height H=20 mm, H=30 mm, and H=40 mm, but are not limited to these dimensions.

[0039] Furthermore, the wheel-road coupling unit that considers the wheel size effect needs to calculate the actual travel trajectory through the speed bump according to the actual size of the wheel, that is, the size of the wheel must be considered.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1) The asymmetric segmented curve is used to achieve optimized design, significantly improving the overall performance of the speed bump.

[0042] This invention constructs an asymmetric speed bump cross-sectional curve by smoothly connecting cosine function segments with parabola segments while maintaining continuity of the first-order derivative. This asymmetric surface not only meets the requirements for low-speed deceleration, but also significantly reduces impact vibrations on the vehicle, improving ride comfort. It is particularly suitable for vibration-sensitive areas such as schools and hospitals, ensuring traffic safety while reducing unnecessary vibration interference.

[0043] 2) It has the feature of reverse interference, effectively improving the road traffic management capabilities.

[0044] The asymmetric cross-sectional structure of this invention provides a smooth transition during forward travel to reduce vibration, while a sudden curvature intensifies the vehicle's vibration response during reverse travel, providing a dynamic warning to the driver. Compared to traditional symmetrical speed bumps, this new structure offers a certain degree of interference with reverse driving, effectively reducing illegal reverse driving. This prevents reverse driving in one-way streets, intersections, and restricted areas without relying on physical barriers, thereby improving road efficiency and conserving space.

[0045] 3) Improve design efficiency and accuracy based on the optimization method of vehicle-road coupled vibration model.

[0046] This paper uses a vehicle-road coupled dynamics model that accounts for tire nonlinearities and suspension system dynamics to simulate and analyze the vehicle's vibration response under speed bump excitation using different combinations of curves. Compared to traditional trial-and-error methods that rely on field testing, this method can predict vehicle dynamic behavior during the design phase, effectively reducing development time and testing costs, improving data repeatability and engineering reliability, and providing a scientific basis for optimizing speed bump structural parameters.

[0047] 4) Support frequency domain characteristic analysis and enhance vehicle dynamics compatibility.

[0048] The vehicle-road coupling model constructed by this invention can determine the dominant vibration frequency of a vehicle passing over different speed bump structures, facilitating analysis of the coupling relationship between the speed bump and the vehicle's natural frequency. During the design phase, excitation frequencies close to the vehicle's vertical modal frequency are avoided, mitigating resonance risks at the source and improving vehicle safety and speed bump compatibility. This approach is particularly suitable for roads with mixed traffic of different vehicle types. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1This is a flow chart of a method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response in the present invention;

[0051] Figure 2 is a three-dimensional schematic diagram of the vehicle model in the present invention;

[0052] Figure 3 Schematic diagram of the wheel-road coupling unit in the present invention;

[0053] Figure 4 It is a schematic diagram of the three-dimensional structure of the novel speed bump in the present invention;

[0054] Figure 5 is a comparison diagram of the vehicle body vertical peak acceleration under different working conditions in an embodiment of the present invention;

[0055] Figure 6 is a comparison diagram of the dynamic load coefficients of the wheelset 2 under different working conditions in an embodiment of the present invention;

[0056] Figure 7 1 is a comparison diagram of the vertical acceleration amplitude spectrum of the tractor under the optimal working condition in an embodiment of the present invention;

[0057] Figure 8 1 is a comparison diagram of the vertical acceleration amplitude spectrum of the trailer under the optimal working condition in an embodiment of the present invention;

[0058] Figure 9 1 is a comparison diagram of the vertical peak acceleration of the vehicle when traveling in the forward and reverse directions under the optimal working conditions in an embodiment of the present invention;

[0059] Figure 10 3 is a comparison diagram of the dynamic load coefficients of the wheelset 2 when the vehicle is traveling in the forward and reverse directions under the optimal working conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0061] 110 , the present invention provides a method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response, comprising the following steps:

[0062] Step 1: Determine the asymmetric segmented curve design of the speed bump, and choose to describe the cross-sectional curve of the speed bump by combining cosine function segments and parabola segments (such as Figure 4 As shown, they correspond to the AB segment and BC segment of the ABC curve respectively).

[0063] Step 2: Calculate the analytical expressions for the speed bump's different structural segments. The front segment AB uses a cosine function, while the rear segment BC uses a parabola function. The first-order derivatives of these two function segments at their connection point B are continuous (i.e., differentiable). This ensures a smooth transition, both visually and structurally. While satisfying the curve continuity requirements, calculate the specific expressions for the different function segments AB and BC.

[0064] Step 3: Create a speed bump combination curve scheme, combining the above cosine function segment and parabola function segment with different horizontal projection lengths. Set the width of the speed bump model to L = 400mm, and set different AB segment horizontal projection lengths L AB And the corresponding BC segment horizontal projection length L BC , gradually increase L AB The proportion of the components is used to reduce the initial impact and form different combination shapes. They are divided into the following four groups:

[0065] Solution 1: The wavelength of the cosine function is T = 400 mm, and the length of the cosine segment is half of the total length of the speed bump. AB =T / 2=200mm, parabola segment L BC =LL AB =200mm as the control group.

[0066] Solution 2: The wavelength of the cosine is T = 479.5 mm, and the cosine segment is L AB =T / 2+T / 8=5T / 8=299.7mm, parabola segment L BC =LL AB =100.3mm.

[0067] Solution 3: The wavelength of the cosine is T = 456.1 mm, and the cosine segment is L AB =T / 2+2T / 8=3T / 4=342.1mm, parabola segment L BC =LL AB =57.9mm.

[0068] Solution 4: The wavelength of cosine is T = 427.4 mm. The cosine segment L AB =T / 2+3T / 8=7T / 8=373.9mm, parabola segment L BC =LL AB =26.1mm.

[0069] By combining two curve segments with different lengths, four different asymmetric segmented curve sections can be obtained.

[0070] Step 4: Establish a coupling model between wheels, suspension system, vehicle body and road surface. A wheel-road coupling unit that takes into account the wheel size effect is used to simulate the dynamic interaction between the wheel and the road surface during driving. This unit is simulated using the Opensees finite element platform. During simulation, tire deformation is considered nonlinear; the vehicle model should include parameters such as tire radius R, spring parameter k and damping parameter c of the suspension system, vehicle speed v, and vehicle load G, where the vehicle load includes the vehicle body load (tractor gravity load G1 and trailer gravity load G2) and the gravity load G of each wheel pair. 轮对1 ~G 轮对4 ; Add the speed bump cross-sectional shape files of each scheme to the simulation platform respectively; calculate and output the vehicle body vertical acceleration and wheel-road contact force; simulate and analyze the optimization of the speed bump in forward and reverse directions respectively, and evaluate the comfort and reverse interference capability.

[0071] Step 5: Set the speed bump height to obtain different operating conditions under various curve combinations. Three speed bump heights were set: H = 20 mm, H = 30 mm, and H = 40 mm. This yielded 4 curves x 3 heights = 12 operating conditions. The speed bump position parameters, vehicle position parameters, and vehicle travel distance were set. Following the simulation process in the previous step, the peak vertical vibration values ​​of the vehicle body and wheels were determined for each operating condition.

[0072] Step 6: Select the optimal speed bump design based on vibration response results. Comparing the results of 12 simulation conditions, the team determined the following: Minimum vehicle vibration response during forward travel; significant vertical impact during reverse travel; continuous curves and simple shapes for easy engineering implementation; and optimal overall comfort, traffic guidance, and reversal deterrence. By considering all these requirements, the optimal design was selected, ultimately resulting in the optimal speed bump cross-section design.

[0073] Example:

[0074] In the embodiment of the present invention, a cosine curve and a parabola curve are selected to design the shape of the speed bump in combination with the above method.

[0075] Reference Figure 2 The vehicle model consists of a tractor head and a trailer body, with a total of four wheel pairs. The wheel radius is R = 0.52m, the tractor mass is set to m1 = 6.8t, the trailer mass is fully loaded m2 = 25t, and the vehicle body and wheels are connected by different spring damping systems. The starting position of the speed bump is x = 10.85m, the starting position of the rear wheel is x = 0, and the vehicle travels along the positive direction of the x-axis at six different speeds of 10 to 60km / h. The vehicle travels a distance of 21.9m;

[0076] Reference Figure 3,The wheel-road coupling unit consists of a road surface node and a mobile wheel node. ,Two road surface nodes are set at the initial position x=0 and the end position x=100, ,covering the entire area that the vehicle passes through.

[0077] Reference Figure 4 The speed bump width was set to L = 400 mm, and an asymmetric speed bump model was established, combining cosine function segments and parabolic function segments of different heights. The heights were set to H = 20 mm, H = 30 mm, and H = 40 mm, respectively. Considering the smooth continuity of the speed bump, the two curve segments were continuously differentiable at the junction.

[0078] The specific expressions of the two curve segments of the control group of Scheme 1 are:

[0079]

[0080] The specific expressions of the two curve segments in Scheme 2 are:

[0081]

[0082] Among them, x0 is 1 / 8 of the wavelength T of the cosine function segment, that is,

[0083] The specific expressions of the two curve segments in Scheme 3 are:

[0084]

[0085] Among them, x0 is 1 / 4 of the wavelength T of the cosine function segment, that is,

[0086] The specific expressions of the two curve segments in Scheme 4 are:

[0087]

[0088] Among them, x0 is 1 / 8 of the wavelength T of the cosine function segment, that is,

[0089] In the above expressions, equation (1) is the analytical expression of the cosine function segment, and equation (2) is the analytical expression of the parabola function segment. The specific shape of the speed bump can be changed by adjusting the height value H.

[0090] Reference Figure 5The figures include two sub-figures: the left figure shows the peak acceleration of the tractor at different speeds, and the right figure shows the peak acceleration of the trailer under the same conditions. The figures illustrate the effects of four combinations of speed bump cross-sectional curve designs (Schemes 1–4) and three heights (H = 20 mm, 30 mm, and 40 mm) on the vehicle's peak acceleration response. At a height of 20 mm, the peak acceleration of the tractor and trailer varies little with increasing speed under each scheme. At 30 mm and 40 mm, peak acceleration remains low when the vehicle passes over the speed bump at speeds ≤30 km / h. However, when the vehicle speed reaches or exceeds 40 km / h, peak acceleration increases significantly under each scheme, demonstrating a significant speed amplification effect. Further comparison of the vibration responses at 30 mm and 40 mm heights reveals that even when the vehicle passes over the speed bump at low speeds (≤30 km / h), the 40 mm high speed bump still induces relatively high peak acceleration, while the 30 mm high speed bump induces significantly less acceleration.

[0091] At the same height, the impact of different cross-section curve schemes on the vehicle's peak acceleration response also varies significantly. Scheme 2 exhibits the lowest peak acceleration at all heights. Taking a 30km / h speed limit as an example, Scheme 2 reduces the tractor's peak acceleration by approximately 24.3%, 25.7%, and 25.6% compared to a conventional symmetrical trapezoidal cross-section at heights of 20mm, 30mm, and 40mm, respectively. This optimization significantly reduces vehicle vibration during normal low-speed travel over speed bumps, helping to improve driving comfort and cargo transportation safety.

[0092] In summary, we can preliminarily conclude that when the speed bump height is 30mm and the cross-sectional curve design corresponding to Scheme 2 is used, it can effectively stimulate the speed amplification effect, demonstrating good speed limit control capabilities, while also significantly reducing vibration response when vehicles pass at the specified low speed, balancing driving comfort and traffic safety. Therefore, this combination demonstrates excellent overall performance in this research example and has the potential to be applied as an ideal speed bump optimization design solution.

[0093] Reference Figure 6 The results are the comparison of the dynamic load coefficient of wheelset 2 when the vehicle passes through 12 different speed bumps. Figure 2 The second wheel set of the vehicle model shown in the x-direction has the largest static gravity load, with a single wheel gravity load of 62.91 kN. The dynamic load coefficient is calculated as:

[0094]

[0095] Among them, G is the gravity load of the wheel, F maxis the peak contact force between the wheel and the road when the wheelset passes through the speed bump. The ratio of the two can intuitively feel the dynamic effect of the speed bump on the wheel. Figure 6 At three different heights and six speeds, Scheme 2 exhibits the lowest dynamic load coefficient when the vehicle passes over the speed bump. This indicates that Scheme 2's speed bump design minimizes the dynamic effects on the wheels. The wheel-road dynamic response during forward vehicle travel further confirms that Scheme 2 is the optimal design.

[0096] Reference Figure 7 The results are a comparison of the vertical acceleration amplitude spectra of the tractor when the vehicle passes over the speed bump in Scheme 2. For speed bumps of different heights, the main vibration frequency of the tractor body when the vehicle passes is mainly concentrated in the range of 2 to 4 Hz.

[0097] Reference Figure 8 The results are a comparison of the vertical acceleration amplitude spectra of the trailer when the vehicle passes over the speed bump in Scheme 2. For speed bumps of different heights, the main vibration frequency of the trailer body when the vehicle passes is mainly concentrated in the range of 1 to 3 Hz.

[0098] Reference Figure 9 The figure shows the peak acceleration responses of the tractor and trailer when traveling in both forward and reverse directions over speed bumps in Scheme 2 (corresponding to three heights, H = 20mm, 30mm, and 40mm). As can be seen from the figure, under all operating conditions, the peak acceleration generated by the vehicle traveling over the speed bump in reverse direction is generally higher than that in forward direction. Taking a vehicle speed of 30 km / h as an example, the peak acceleration of the tractor in reverse direction increases by approximately 22.5%, 15.9%, and 8.6% compared to the forward direction for speed bump heights of 20mm, 30mm, and 40mm, respectively. This trend is also reflected in the trailer. Despite its overall lower acceleration level, its impact response in reverse direction is significantly enhanced. The cross-sectional design of Scheme 2 ensures the comfort of normal-traveling vehicles while exerting a stronger stimulus on vehicles traveling in the opposite direction, effectively enhancing their interference and disciplinary effects. This demonstrates the potential of this scheme in curbing reverse-traveling vehicles and provides support for deceleration optimization design to achieve differentiated traffic control and improve road safety.

[0099] Reference Figure 10, showing the changing trends in the dynamic load coefficient of wheelset 2 when a vehicle passes over a speed bump in Scheme 2 (heights of 20mm, 30mm, and 40mm, respectively) in both forward and reverse directions at different speeds. The figure clearly shows that the dynamic load coefficient increases linearly with vehicle speed, indicating that the higher the speed, the more significant the impact of the speed bump on the vehicle wheelset. Furthermore, at the same height and speed, the dynamic load coefficient generated by reverse travel is consistently higher than that generated by forward travel, further verifying that reverse travel exerts a more intense excitation on the vehicle structure. Taking a vehicle speed of 30 km / h as an example, at heights of 20mm, 30mm, and 40mm, the dynamic load coefficient of wheelset 2 in the reverse condition is approximately 34.1%, 14.5%, and 13.9% higher than that in the forward condition, respectively. This difference demonstrates that for speed bumps of any height, reverse travel significantly enhances the vertical wheel-rail impact.

[0100] In summary, the cosine segment L of Scheme 2 AB =299.7mm and parabola segment L BC =100.3mm combined cross-section is the optimal design shape. This cross-sectional shape not only minimizes the vehicle's vibration response during forward travel, but also significantly reduces vertical impact during reverse travel. This solution also ensures curve continuity and provides a specific functional expression for easy engineering implementation. It achieves the best overall comfort, traffic guidance, and counter-traffic deterrence among the four solutions.

[0101] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A road speed bump optimization design method based on vehicle-road coupled vibration response, characterized in that: The following steps are involved: (1) Determine the asymmetric segmented curve design of the speed bump; (2) Solve the analytical formula of the curves of different structural sections of the speed bump; (3) Establish a speed bump combined curve scheme by combining the above cosine segments and parabola segments with different horizontal projection lengths; (4) Establish a coupling model between wheels, suspension system, vehicle body and road surface; (5) Setting the height of the speed bump to obtain different working conditions under various curve combination schemes; (6) Select the optimal speed bump solution based on the vibration response results.

2. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 1, characterized in that: The asymmetric segmented curve design of the speed bump structure in step (1) includes a combined design of a cosine curve and a parabola curve.

3. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 1, characterized in that: In step (2), the front AB segment of the speed bump adopts a cosine function segment, and the rear BC segment adopts a parabola function segment, and the first-order derivatives of the two function segments at the connection point B are continuous. While meeting the curve continuity condition, the specific expressions of different function segments AB and BC are calculated.

4. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 1, characterized in that: The combination curve change group schemes in step (3) include four schemes, but are not limited to combinations of four horizontal projection lengths.

5. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 1, characterized in that: The dimensions of the speed bump in step (3) include different combinations of width L=400 mm, height H=20 mm, H=30 mm, and H=40 mm.

6. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 4, characterized in that: The first option: The wavelength of the cosine function is T = 400mm, and the length of the cosine segment is half of the total length of the speed bump. AB =T / 2=200mm, parabola segment L BC =LL AB =200mm as the control group.

7. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 4, characterized in that: The second solution: the wavelength of the cosine is T = 479.5 mm, and the cosine segment L AB =T / 2+T / 8=5T / 8=299.7mm, parabola segment L BC =LL AB =100.3mm.

8. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 4, characterized in that: The third solution: the wavelength of cosine is T = 456.1 mm, and the cosine segment is L AB =T / 2+2T / 8=3T / 4=342.1mm, parabola segment L BC =LL AB =57.9mm.

9. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 4, characterized in that: The fourth solution: the wavelength of cosine is T = 427.4 mm, and the cosine segment L AB =T / 2+3T / 8=7T / 8=373.9mm, parabola segment L BC =LL AB =26.1mm.

10. The method for optimizing the design of road speed bumps based on vehicle-road coupled vibration response according to claim 1, characterized in that: The wheel-road coupling unit that considers the wheel size effect in step (4) needs to calculate the actual travel trajectory through the speed bump based on the actual size of the wheel.

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