A multi-modal topology-optimized electric race car chain drive system

Abstract

This invention relates to the field of vehicle transmission system technology and provides a multimodal topology-optimized electric racing car chain drive system, including a transmission assembly, a differential, a bearing assembly, and a wheel assembly. The transmission assembly consists of a large sprocket, a small sprocket, and a chain. The large sprocket, initially a solid, un-drilled structure, is optimized through multimodal topology to form a three-layer radially hollow structure. The small and large sprockets both have a pitch of 15.875 mm, a roller diameter of 10.16 mm, and a gear ratio of 43:11. The differential is a Drexler differential, connected to the large sprocket. The bearing assembly includes cylindrical roller bearings adapted to the motor output shaft and deep groove ball bearings adapted to the differential and wheel hub, both lubricated and sealed with lithium-based grease. The wheel assembly is connected to the differential via a titanium alloy hollow half-shaft. This invention achieves a precise balance between lightweight sprockets and structural strength, resulting in high transmission efficiency and fast handling response.

Description

Technical Field

[0001] This invention belongs to the field of vehicle transmission system technology, and particularly relates to a multimodal topology-optimized electric racing car chain drive system. Background Technology

[0002] In electric racing car transmission systems, chain drives are widely used due to their advantages such as accurate average transmission ratio, low required tension, and low bearing friction loss. As the core component of the main reducer, the sprocket needs to ensure stable power transmission under heavy load conditions. With the development of electric racing cars towards lightweight design and high dynamic performance, the requirements for compactness and weight reduction in transmission systems are increasing. Current chain drive system design mainly focuses on sprocket parameter matching, structural strength verification, and lightweighting of wheel-side components, with sprocket hollowing optimization being one of the key methods for weight reduction.

[0003] Existing lightweight solutions for racing car chain drives typically employ simple, uniform circular hollowing or topology optimization methods based on static loads to reduce the structural weight of the sprocket. The basic design process involves: establishing an initial solid model of the sprocket, setting static or quasi-static load boundary conditions, generating material removal areas using topology optimization software, and then shaping the hollowed-out structure. Meanwhile, the spokes and hub in the wheel assembly are mostly made of conventional aluminum alloy, and deep groove ball bearings are typically used uniformly for the motor output shaft, differential, and hub.

[0004] Existing chain drive systems have shortcomings in their overall performance regarding lightweighting and structural strength. Specifically: the hollowing-out optimization of the sprockets fails to fully consider the coupling effect of high-frequency vibrations and dynamic loads during actual racing, leading to stress concentration and reduced fatigue life of the optimized sprockets under dynamic conditions; key sprocket parameters rely heavily on experience-based selection, lacking precise calculations based on core mechanical design formulas, thus affecting transmission smoothness; insufficient weight reduction of the wheel-side components results in excessive unsprung mass, reducing the racing car's handling response speed; and bearing selection fails to differentiate and adapt to the stress characteristics of each component, affecting the overall reliability and service life of the transmission system. Summary of the Invention

[0005] The purpose of this invention is to provide a multimodal topology-optimized electric racing car chain drive system, which aims to solve the problems existing in the background art.

[0006] This invention is implemented as follows: a multimodal topology-optimized electric racing car chain drive system, including a transmission component, wherein the multimodal topology-optimized electric racing car chain drive system includes:

[0007] The transmission assembly consists of a large sprocket, a small sprocket, and a chain. The two ends of the chain mesh with the large sprocket and the small sprocket, respectively. The large sprocket is initially modeled as a solid structure without holes, and then undergoes multimodal topology optimization to form a three-layer radial hollow structure. The pitch of the small sprocket and the large sprocket are both 15.875 mm, the roller diameter is both 10.16 mm, and the tooth ratio is 43:11.

[0008] The Drexler differential is connected to the large sprocket drive;

[0009] A hollow titanium alloy half-shaft is connected to the Drexler differential.

[0010] The wheel-side assembly is connected to the hollow titanium alloy half-shaft;

[0011] The bearing assembly includes cylindrical roller bearings adapted to the motor output shaft and deep groove ball bearings adapted to the Drexler differential and wheel hub. All bearings are lubricated and sealed with the same type of lithium-based grease.

[0012] Furthermore, the large sprocket is made of 7075-T6 aluminum alloy, and the three-layer radial hollow structure includes an outer oblong hollow, a middle approximately circular hollow, and an inner rounded triangular hollow. The corners of each hollow are rounded by 5mm. After optimization, the weight reduction rate of the large sprocket is 38%~42%, the maximum stress is ≤245MPa, the safety factor is ≥1.5, and the maximum deformation is ≤0.5mm.

[0013] Furthermore, the pitch circle diameter of the large sprocket is calculated using the formula d=p / sin(π / Z), and the actual pitch circle diameter of the large sprocket is 217.4797mm, the addendum circle diameter is 225.2810mm, and the dedendum circle diameter is 207.3197mm. The small sprocket is made of 42CrMo, and its pitch circle diameter is 56.3478mm, the addendum circle diameter is 64.4388mm, and the dedendum circle diameter is 46.1878mm. The key parameters of both the large and small sprockets are calculated based on the core formula of chain drive.

[0014] Furthermore, the implementation process of the multimodal topology optimization includes the following steps: 1) establishing an initial three-dimensional model of the large sprocket based on the core parameters of the chain drive; 2) performing modal analysis to extract the resonant frequency; 3) performing multimodal topology optimization analysis based on ANSYS Workbench software; 4) performing shape trimming and curve fitting on the optimized model; 5) verifying through strength simulation to finally form a hollow structure with uniform stress and smooth stress curve.

[0015] Furthermore, the number of the outer layer oblong hollows is 6, the central angle is 60°, the radial dimension ranges from 18 to 22 mm, and they are evenly distributed circumferentially along the outer radial end of the large sprocket; the number of the middle layer approximately circular hollows is 6, located between two adjacent outer layer oblong hollows, and the center of each hole is evenly distributed circumferentially to ensure the mechanical continuity of the wheel structure; the number of the inner layer rounded triangular hollows is 6, located at the inner radial end of the large sprocket and between two adjacent middle layer approximately circular hollows, and their side contours are consistent with the tangent direction of the adjacent middle layer approximately circular hollows to ensure the structural strength at the connection with the Drexler differential.

[0016] Furthermore, the wheel assembly includes spokes, a hub, and a carbon fiber rim. Both the spokes and the hub are made of 7075-T6 aluminum alloy and are compatible with 10-inch carbon fiber rims. The hub is equipped with a 45 steel inner liner, and the safety factor of the front and rear hubs is ≥2.0 under transient conditions of straight-line start, emergency braking, and rapid steering.

[0017] Furthermore, the center distance between the large sprocket and the small sprocket is 201.4 mm, which meets the 120° wrap angle requirement of the small sprocket. This center distance is determined based on the chain drive meshing characteristics and the space constraints of the rear compartment of the race car.

[0018] The present invention provides a multimodal topology-optimized electric racing car chain drive system, which has the following beneficial effects:

[0019] This invention achieves a precise balance between lightweighting and structural strength of the large sprocket through comparative screening of multiple optimization methods and simulation verification under multiple working conditions, combined with core mechanical design formulas. After multimodal topology optimization, the weight reduction rate of the large sprocket reaches 46.0%, which is more than 15% higher than that of traditional optimization methods, and the stress uniformity and dynamic stability are significantly improved. The three-layer radial hollow structure of the large sprocket, combined with the rounded corner design, effectively reduces stress concentration, and the outer elongated hollow increases the circumferential heat dissipation area, achieving a three-dimensional balance of weight reduction, strength, and heat dissipation. The overall transmission efficiency of the transmission system reaches more than 92%, and the lightweight wheel-side design reduces the unsprung mass of the entire vehicle by 5.1 kg, shortens the 0-75m acceleration time by 0.61s, and improves the handling response speed by 12%. The performance redundancy of each component is sufficient to meet the usage requirements of the high-intensity racing environment of Formula Student racing cars. Attached Figure Description

[0020] Figure 1 Schematic diagrams of the large sprocket structure under three optimization schemes, where a-simple uniform circular hollow, b-static load topology optimization, and c-multimodal topology optimization;

[0021] Figure 2 Stress distribution cloud maps of the three optimization schemes;

[0022] Figure 3Deformation contour map of the large sprocket under extreme driving conditions;

[0023] Figure 4 Detailed cross-sectional view of the best hollow structure;

[0024] Figure 5 Overall assembly drawing of the chain drive system;

[0025] Figure 6 Schematic diagram of the connection structure between the wheel-side assembly and the differential;

[0026] Figure 7 Assembly drawing of wheel rim assembly;

[0027] Figure 8 Simulation diagram of spoke strength;

[0028] Figure 9 Simulation diagram of transient working condition strength of front and rear wheel hubs.

[0029] In the attached diagram: 1. Spoke; 2. Hub; 3. Hub bearing; 4. Half shaft; 5. Dust cover for the ball cage; 6. Ball cage; 7. Large sprocket; 7.1. Long oval hole with rounded ends; 7.2. Nearly circular hole; 7.3. Inner layer hole; 8. Chain; 9. Small sprocket; 10. Differential; 13. Hub liner; 14. Three ball pins. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0031] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0032] like Figure 1 As shown, in an embodiment of the present invention, a multimodal topology-optimized electric racing car chain drive system includes:

[0033] The transmission assembly consists of a large sprocket 7, a small sprocket 9, and a chain 8. The two ends of the chain 8 are respectively engaged with the large sprocket 7 and the small sprocket 9. The initial model of the large sprocket 7 is a solid structure without holes, and it is formed into a three-layer radial hollow structure through multimodal topology optimization.

[0034] A Drexler differential 10 is connected to the large sprocket 7 for transmission. A titanium alloy hollow half-shaft 4 is connected to the Drexler differential 10, and a wheel-side assembly is connected to the titanium alloy hollow half-shaft 4.

[0035] The bearing assembly includes cylindrical roller bearings and deep groove ball bearings, wherein the cylindrical roller bearings are adapted to the motor output shaft and the deep groove ball bearings are adapted to the Drexler differential 10 and wheel-side assembly.

[0036] In this embodiment, the pitch p of both the large sprocket 7 and the small sprocket 9 is selected from the standard specification of 10A chain, with p = 15.875 mm and roller diameter d1 = 10.16 mm. The tooth ratio is set to 43:11, that is, the number of teeth of the large sprocket 7 Z1 = 43 and the number of teeth of the small sprocket 9 Z2 = 11. The key parameters of the sprockets are shown in Table 1.

[0037] Table 1 Key Parameters of Large Sprocket 7 and Small Sprocket 9

[0038]

[0039] According to the formula for the pitch circle diameter in the chain drive foundation design standard GB / T1243-2006:

[0040] ;

[0041] The calculated diameters of the large sprocket's 7-pitch circle are d1 = 15.875 / sin(π / 43) ≈ 217.4797 mm and the small sprocket's 9-pitch circle diameter are d2 = 15.875 / sin(π / 11) ≈ 56.3478 mm.

[0042] According to the formula for the tip circle diameter Formula for tooth root circle diameter The calculated addendum circle diameter of the 7th tooth of the large sprocket is 225.2810 mm and the dedendum circle diameter is 207.3197 mm; the addendum circle diameter of the 9th tooth of the small sprocket is 64.4388 mm and the dedendum circle diameter is 46.1878 mm.

[0043] The tooth thickness s is taken as 6.0 mm, the tooth groove radius r1 is taken as 5.1554 mm, and the working section radius r2 is taken as 13.2834 mm. The solid mass m0 of the large sprocket 7 is calculated as 0.743 kg by multiplying the volume of the three-dimensional model by the material density (ρ=2.81 g / cm³).

[0044] The above parameters were verified by chain drive meshing simulation. The meshing process of chain 8 with large sprocket 7 and small sprocket 9 was smooth, without jamming or chain slippage. The transmission ratio error was ≤0.5%, which met the design requirements.

[0045] To determine the optimal sprocket lightweighting solution, this embodiment systematically compares three optimization methods:

[0046] Option 1: Simple, uniform circular cutout;

[0047] Option 2: Static load topology optimization;

[0048] Option 3: Multimodal topology optimization.

[0049] The schematic diagrams of the large sprocket structure for the three optimization schemes are as follows: Figure 1 As shown in Table 2 (a-simple uniform circular hollow, b-static load topology optimization, c-multimodal topology optimization), the performance comparison results of each scheme are shown in Table 2.

[0050] Table 2 Performance Comparison of Three Lightweight Optimization Methods

[0051]

[0052] As shown in Table 2, Scheme 3 (multimodal topology optimization) significantly outperforms the other two schemes in all performance indicators: the weight reduction rate is 34.6% higher than Scheme 1 and 52.6% higher than Scheme 2; the maximum stress is reduced by 9.8%~12.5%; and the stress uniformity and dynamic stability are optimal. Its core advantage lies in fully considering the high-frequency vibration and dynamic load coupling characteristics of the sprocket during race car operation, avoiding the stress concentration problem of single-mode optimization at non-design frequencies, and conforming to the design principles of structural optimization under dynamic loads.

[0053] Operating parameters and simulation results for multimodal topology optimization:

[0054] For Scheme 3 (multimodal topology optimization), three typical operating conditions were set to simulate the actual running state of the race car, including straight-line start, high-speed driving, and emergency braking. The parameters and simulation results for each operating condition are shown in Table 3.

[0055] Table 3. Operating parameters and performance simulation results for multimodal topology optimization.

[0056]

[0057] Simulation results show that the maximum stress of the large sprocket 7 is ≤394.48MPa under all working conditions, the safety factor is ≥1.45, and the maximum deformation is ≤0.0052mm, all meeting the design constraints. The performance is optimal under high-speed driving conditions, while the stress and deformation are greatest under the extreme straight-line start-up condition, but still within the material's reliable range, verifying the stability and reliability of the multimodal topology optimization structure under complex working conditions. The deformation cloud diagram of the large sprocket under extreme driving conditions is shown below. Figure 3 As shown (unit: mm).

[0058] Optimal hollow structure design and performance verification:

[0059] Based on multi-condition simulation results, the optimal hollow structure of the large sprocket 7 was determined to be a three-layer radially distributed design through iterative optimization, as follows:

[0060] Outer layer hollow 7.1: There are 6 in total. They are elongated oval holes (waist-shaped holes) with rounded ends. They are evenly distributed around the outer end of the large sprocket 7 radially, with a central angle interval of 60° and a radial dimension range of 18~22mm. The outer contour of the hole is rounded without sharp corners, which can increase the circumferential heat dissipation area and improve the heat dissipation effect during high-speed operation.

[0061] The middle layer has six perforations, which are approximately circular holes located between any two adjacent outer layer elongated holes 7.1. They are evenly distributed circumferentially to ensure the mechanical continuity of the wheel structure.

[0062] The inner layer has six perforations, which are triangular holes with rounded ends. They are evenly distributed along the inner circumference of the large sprocket 7 and located between two adjacent middle layer circular holes 7.2 to ensure the structural strength of the connection between the large sprocket and the differential.

[0063] Each openwork corner has a 5mm rounded corner. The optimal openwork structure cross-sectional details are as follows: Figure 4 As shown.

[0064] The final performance verification results of the optimal hollow structure are as follows:

[0065] quality: =0.40kg, weight loss rate =46.0%, which meets the design target of 38%~42%;

[0066] Strength performance: Maximum stress 381.33MPa, safety factor 1.50, which just reaches the design threshold of 1.5, meeting the requirements of high-intensity working conditions in the competition;

[0067] Deformation performance: Maximum deformation is 0.0041mm, with a design constraint of ≤0.5mm to ensure transmission accuracy;

[0068] Heat dissipation performance: The circumferential linear heat dissipation area is 42% larger than that of a solid sprocket, effectively reducing the accumulation of frictional heat during high-speed operation.

[0069] Wheel rim assembly and other component design:

[0070] To enhance handling agility, this embodiment employs a short wheelbase and small tire configuration, paired with 10-inch carbon fiber rims. Based on the rim and hub connection points and after eliminating interference, and following strength simulation verification, a spoke 1 made of 7075-T6 aluminum alloy was designed, significantly reducing wheel rim mass. On average, each wheel is 2.55 kg lighter, reducing the race car's unsprung mass and improving its responsiveness and handling performance. Simultaneously, due to the reduced rim size, the matching 7075-T6 aluminum alloy hub 2 was also correspondingly reduced in size, further reducing wheel rim mass.

[0071] The design process of the custom-made wheel spokes is as follows: Custom-made wheel spoke design: Based on the wheel track and et value, and considering the carbon fiber rim (without integrated spokes), hub, and central locking nut, as well as eliminating interference with the brake calipers, the shape of the longitudinal section of the spokes was initially determined. After rotating to obtain the spoke model, it was imported into ANSYS Workbench. Strength simulation was performed based on the stress conditions of the spokes during racing. Based on the simulation results, hollowing out areas with lower stress and using a curved transition to reduce stress concentration resulted in the final spoke model. The spoke strength simulation diagram is shown below. Figure 8 As shown.

[0072] Wheel hub design: The tire continues the fixing method of "four brass pins for positioning and central outer nut for locking". Due to the use of 10-inch rims and the removal of the wheel-side reducer, the wheel hub size is greatly reduced. To further reduce weight, the upper boss is hollowed out, and the bottom of the front wheel hub is further material-removed according to the different functions of the front and rear wheel hubs. In addition, to address the issue of easy wear due to direct contact between the rear wheel hub and the three ball joint 14, a wheel hub liner 13 made of 45 steel was designed. To ensure the reliability of the structure, after obtaining the model, ANSYS Workbench was used. After the static structural strength verification was passed, simulations were performed on the front and rear wheel hubs under three transient conditions: straight-line start, emergency braking, and rapid steering. A safety factor greater than 2.0 was guaranteed for each condition. The transient performance verification results of the front and rear wheel hubs are shown in Table 4, and the strength simulation diagram is shown in... Figure 9 As shown.

[0073] Table 4. Transient Performance Verification Table for Front and Rear Wheel Hubs

[0074]

[0075] Differential, bearings and wheel center distance:

[0076] Differential 10 uses a Drexler differential, which adopts a high-precision gear meshing design. While meeting the cornering differential requirements of racing cars, it has a transmission efficiency of ≥95%, which is suitable for the power transmission characteristics of electric racing cars.

[0077] The bearing assemblies are selected based on the stress characteristics of each component: the motor output bearing is subjected to a large radial load, so a cylindrical roller bearing with a radial rated dynamic load ≥8kN is selected; the differential 10 and hub 2 mainly rotate at high speeds, so deep groove ball bearings with a limiting speed ≥8000r / min are selected. All bearings are uniformly lubricated and sealed with lithium-based grease (dropping point ≥180℃) to ensure consistent lubrication and service life of all components.

[0078] The center distance between the large sprocket 7 and the small sprocket 9 was determined to be 201.4 mm through SolidWorks assembly simulation correction. This dimension satisfies the space constraints of the rear compartment and ensures the 120° wrap angle requirement of the small sprocket 9, avoiding the risk of chain derailment during the engagement of the chain 8.

[0079] The overall assembly of the chain drive system is as follows Figure 5 As shown, the connection structure between the wheel-side assembly and the differential is as follows: Figure 6 As shown, the wheel rim assembly is assembled as follows: Figure 7 As shown.

[0080] In summary, the multimodal topology-optimized electric racing car chain drive system of this embodiment has an overall transmission efficiency of over 92%. The lightweight wheel-side design reduces the unsprung mass of the entire vehicle by 5.1 kg, shortens the 0-75m acceleration time by 0.61 s, and improves the handling response speed by 12%, fully meeting the usage requirements of the high-intensity racing environment of Formula Student racing.

[0081] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multimodal topology-optimized electric racing car chain drive system, characterized in that, The multimodal topology-optimized electric racing car chain drive system includes: The transmission assembly consists of a large sprocket (7), a small sprocket (9) and a chain (8). The two ends of the chain (8) are engaged with the large sprocket (7) and the small sprocket (9) respectively. The initial model of the large sprocket (7) is a solid structure without holes, and a three-layer radial hollow structure is formed through multimodal topology optimization. Drexler differential (10) is connected to the large sprocket (7) for transmission. A titanium alloy hollow half shaft (4) is connected to the Drexler differential (10), and a wheel-side assembly is connected to the titanium alloy hollow half shaft (4). The bearing assembly includes cylindrical roller bearings and deep groove ball bearings, the cylindrical roller bearings being adapted to the motor output shaft, and the deep groove ball bearings being adapted to the Drexler differential (10) and wheel-side assembly.

2. The multimodal topology-optimized electric racing car chain drive system according to claim 1, characterized in that, The large sprocket (7) is made of 7075-T6 aluminum alloy. The three-layer radial hollow structure includes an outer oval hollow (7.1), a middle approximately circular hollow (7.2), and an inner rounded triangular hollow (7.3). The weight reduction rate of the optimized large sprocket (7) satisfies: ； in, To reduce the weight of the large sprocket, Due to the lack of optimization of the solid sprocket quality, Mass of the large sprocket after multimodal topology optimization; The safety factor S satisfies: ， ； in, The maximum equivalent stress of the sprocket, This represents the maximum dynamic load that the sprocket can withstand. To optimize the effective load-bearing cross-sectional area of ​​the sprocket, The allowable stress for 7075-T6 aluminum alloy is... This is for the safety factor.

3. The multimodal topology-optimized electric racing car chain drive system according to claim 1, characterized in that, The pitch circle diameter of the large sprocket (7) Based on the formula: ； Tooth tip circle diameter Based on the formula: ； Tooth root circle diameter Based on the formula: ； in The pitch circle diameter, For chain pitch, This represents the number of teeth on the sprocket.

4. The multimodal topology-optimized electric racing car chain drive system according to claim 1, characterized in that, The implementation process of the multimodal topology optimization includes: 1) Establish an initial three-dimensional model of the large sprocket (7) based on the core parameters of the chain drive; 2) Perform modal analysis to extract resonant frequencies; 3) Perform multimodal topology optimization analysis on the initial 3D model using ANSYS Workbench software; 4) Perform shape trimming and curve fitting on the optimized initial 3D model; 5) Through strength simulation verification, a three-layer radial hollow structure with uniform stress and smooth stress curve is formed.

5. The multimodal topology-optimized electric racing car chain drive system according to claim 2, characterized in that, The number of the outer layer oblong hollow (7.1) is 6, the central angle is 60°, the radial dimension range is 18~22mm, and they are evenly distributed along the radial outer end of the large sprocket (7); The number of the approximately circular perforations (7.2) in the middle layer is 6, located between two adjacent oblong perforations (7.1) in the outer layer, and the centers of each hole are evenly distributed around the perimeter. The number of inner rounded triangular cutouts (7.3) is 6, located at the radial inner end of the large sprocket (7) and between two adjacent middle layer approximately circular cutouts (7.2), and their side contours are consistent with the tangent direction of the adjacent middle layer approximately circular cutouts (7.2).

6. The multimodal topology-optimized electric racing car chain drive system according to claim 1, characterized in that, The wheel assembly includes a spoke (1), a hub (2) and a carbon fiber rim, wherein the spoke (1) and the hub (2) are both made of 7075-T6 aluminum alloy. The wheel hub (2) is provided with a steel inner liner (13), and the safety factor of the front and rear wheel hubs (2) is ≥2.0 under the transient conditions of straight-line start, emergency braking and rapid steering. The deep groove ball bearing is adapted to the Drexler differential (10) and the wheel hub (2).

7. The multimodal topology-optimized electric racing car chain drive system according to claim 1, characterized in that, The center distance between the large sprocket (7) and the small sprocket (9) is determined based on the chain drive meshing characteristics and the space constraints of the rear compartment.

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