A bridge-type damping ridge rib layered constrained damping wheel

Abstract

The present invention relates to a bridge-type damping ridged rib layered constrained damping wheel, comprising a wheel and a constrained damping layer, wherein the constrained damping layer comprises an inner constraining layer, an elastic damping layer, and an outer constraining layer, wherein the inner constraining layer is bonded to the side of the wheel, and the elastic damping layer is tightly bonded to the inner constraining layer and the outer constraining layer, respectively; an annular protrusion is provided on the inner constraining layer, and a cavity is formed between the inner constraining layer and the spoke plate on both sides of the annular protrusion; a ridged rib is provided on the elastic damping layer, and the ridged rib is tightly bonded to the groove of the annular protrusion in the direction of the elastic damping layer. Compared with the prior art, the inner constraining layer in the present invention is provided with an annular protrusion at the spoke plate, which increases the thickness of the elastic damping layer at this location to form a ridged rib, and forms a cavity between the entire constrained damping layer and the spoke plate, thereby reducing the constraint on the elastic damping layer at the ridged rib, increasing the shear deformation capacity of the elastic damping layer, and enhancing the effect of the elastic damping layer in converting vibration mechanical energy into heat energy and dissipating the vibration energy of the system, thereby reducing the vibration noise generated by the wheel.

Description

Technical Field

[0001] The present invention relates to the technical field of damping, vibration reduction and noise reduction, in particular to a bridge-type damping ridge rib layered constrained damping wheel. Background Art

[0002] At present, my country's urban rail transit industry is developing rapidly. Urban rail transit is loved by residents of various cities in my country because of its high speed, high capacity and high punctuality. It has become an indispensable means of transportation for residents' daily travel. However, the vibration and noise pollution generated by the operation of urban rail transit is also a major problem that urban rail transit urgently needs to solve.

[0003] In urban rail transit, where vehicle speeds are relatively low, wheel-rail noise dominates the overall vibration noise. Installing damping devices on the wheels is an effective active vibration and noise reduction method. Currently, there are three main types of damping devices installed on wheels: layered constrained damping, damping rings, and tuned mass dampers. Of these damping devices, damping rings only effectively suppress squeal noise in curved sections, while tuned mass dampers only effectively suppress noise with a narrow bandwidth. Furthermore, both damping devices affect the wheel shape, making them less optimal.

[0004] Layered constrained damping (LCD) is simply adhered to the wheel surface, secured to the spokes with a rigid plate, and filled between them with a thin layer of high-damping viscoelastic material. The shear deformation of the damping layer converts vibration energy into heat and dissipates it, achieving vibration and noise reduction. This method is applicable over a wide noise reduction bandwidth, is simple to manufacture, and does not alter the wheel shape, making it readily applicable. However, the shear deformation of the damping layer is limited, and the vibration and noise reduction effectiveness of LCD still needs to be further optimized. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a bridge-type damping ridge layered constrained damping wheel. The inner constrained layer is provided with an annular protrusion at the spoke plate, and the thickness of the elastic damping layer at this location is increased to form a ridge. A cavity is formed between the entire constrained damping layer and the spoke plate, thereby reducing the constraint on the elastic damping layer at the ridge, increasing the shear deformation capacity of the elastic damping layer, and enhancing the effect of the elastic damping layer in converting vibration mechanical energy into heat energy and dissipating the vibration energy of the system, thereby reducing the vibration noise generated by the wheel.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A bridge-type damping ridge-rib layered constrained damping wheel comprises a wheel and a constrained damping layer tightly bonded to a side surface of the wheel, wherein the wheel is a spoke-plate wheel, and the constrained damping layer comprises an inner constraining layer, an elastic damping layer, and an outer constraining layer, wherein the inner constraining layer is bonded to the side surface of the wheel, the elastic damping layer is tightly bonded to the inner constraining layer, and the outer constraining layer is tightly bonded to the elastic damping layer;

[0008] The outer edge of the inner constraint layer is in close contact with the rim of the wheel, and the inner edge of the inner constraint layer is in close contact with the hub of the wheel. The inner constraint layer is provided with an annular protrusion facing the spoke plate and coaxial with the wheel. A cavity is formed between the inner constraint layer and the spoke plate from the annular protrusion to the outer edge or inner edge of the inner constraint layer.

[0009] The annular protrusion on the inner constraint layer is a groove in the direction of the elastic damping layer. The elastic damping layer is provided with a ridge rib, which is an annular convex block coaxial with the wheel. The annular convex block is tightly fitted with the groove.

[0010] Preferably, the constrained damping layer is in close contact with the outer side of the wheel.

[0011] Preferably, the cross-section of the cavity is approximately triangular.

[0012] Preferably, between the rim and the hub, the cross-section of the constrained damping layer is approximately bridge-shaped.

[0013] Preferably, the wheel is a straight-spoke wheel or a curved-spoke wheel.

[0014] Preferably, the inner constraint layer is glued to the side of the wheel, the elastic damping layer is glued to the inner constraint layer, and the outer constraint layer is glued to the elastic damping layer.

[0015] Preferably, the inner constraint layer and the outer constraint layer are constraint layers made of aluminum, steel or carbon fiber materials.

[0016] Preferably, the elastic damping layer is a damping layer made of a high-damping viscoelastic material with a material loss factor greater than 0.3.

[0017] Preferably, the thickness of the inner constraining layer is in the range of 0.5 to 5 mm, and the thickness of the outer constraining layer is in the range of 0.5 to 5 mm.

[0018] Preferably, the inner constraining layer and the outer constraining layer have the same thickness.

[0019] Preferably, the thickness of the elastic damping layer is in the range of 0.5 to 10 mm.

[0020] Preferably, the elastic damping layer has the same thickness at all locations except the ridge ribs.

[0021] Preferably, the cross section of the ridge rib is rectangular, the size of the rectangle is a*b, side a is parallel to the spoke plate, side b is perpendicular to the spoke plate, the length of a ranges from 2 to 20 mm, and the length of b ranges from 1 to 15 mm.

[0022] Preferably, an outer annular groove is provided at the connection between the spoke plate and the rim, and an inner annular groove is provided at the connection between the spoke plate and the hub. The contact point between the annular protrusion on the inner constraint layer and the spoke plate is marked as P. The distance between P and the inner annular groove is greater than L×1 / 5, and the distance between P and the outer annular groove is greater than L×1 / 5, where L represents the radial length of the spoke plate.

[0023] Preferably, the distances between the annular protrusion and the inner annular groove and the outer annular groove are determined according to the following steps:

[0024] S1: The steady-state responses of the rigid wheel and the layered constrained damping wheel under periodic simple harmonic load excitation are calculated by harmonic response analysis, and the velocity admittance diagrams of the rigid wheel and the layered constrained damping wheel are obtained;

[0025] S2: Analyze the velocity admittance diagram to find the frequency point set when the velocity admittance of the layered constrained damping wheel is greater than that of the rigid wheel. Then, find the frequency f from the frequency point set when the difference in velocity admittance between the layered constrained damping wheel and the rigid wheel is the largest.

[0026] S3: Obtain the modal strain energy nephogram and shear strain distribution nephogram at point f of the layered constrained damping wheel, analyze the modal strain energy nephogram and shear strain distribution nephogram, and use the points with maximum modal strain energy and maximum shear strain as the contact points between the annular protrusion on the inner constrained layer and the spoke.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The inner constraint layer is provided with an annular protrusion at the spoke plate, which increases the thickness of the elastic damping layer at this location to form a ridge rib, thereby enhancing the effect of the elastic damping layer in converting vibration mechanical energy into heat energy and dissipating the system vibration energy, thereby reducing the vibration noise generated by the wheel.

[0029] (2) Through the annular protrusions of the inner constraint layer and the ridges of the elastic damping layer, a cavity is formed between the entire constraint damping layer and the spoke, which provides more sufficient space for the shear deformation of the ridges and reduces the constraints on the elastic damping layer, making it easier for the elastic damping layer to produce shear deformation, thereby enhancing the effect of the elastic damping layer in converting vibration mechanical energy into heat energy and dissipating the vibration energy of the system, thereby reducing the vibration noise generated by the wheel.

[0030] (3) A cavity is formed between the annular protrusion and the outer edge of the inner constraining layer, and a cavity is formed between the annular protrusion and the inner edge of the inner constraining layer. The cross-section of the cavity is approximately triangular, completely covering the spoke plate, blocking the radiation of wheel noise to the surrounding space from the propagation path.

[0031] (4) The inner constraint layer, outer constraint layer and elastic damping layer are added only on the basis of the wheel, which does not affect the main shape of the wheel. In addition, the bridge-type damping ridge rib constraint damping layer is light in weight and has little effect on the increase of the unsprung mass of the vehicle, which is easy to promote.

[0032] (5) By analyzing the noise reduction effect of the existing layered constrained damping wheel, the position of the annular protrusion on the inner constrained layer is set at the maximum strain energy of the wheel modal vibration shape where the layered constrained damping noise reduction effect is not obvious, which has a better noise reduction effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the explosion of the bridge-type damping ridge-rib layered constrained damping wheel;

[0034] Figure 2 It is a front view of the outer side of the wheel;

[0035] Figure 3 Schematic diagram of the structure of the ridge ribs on the elastic damping layer;

[0036] Figure 4 The cross-section of the bridge-type damping ridge-rib layered constrained damping wheel;

[0037] Figure 5 is a cross-sectional view of the inner constraining layer, elastic damping layer, and outer constraining layer;

[0038] Figure 6 is the vibration velocity admittance diagram of the rigid wheel and the layered constrained damping wheel;

[0039] Figure 7 The modal strain energy cloud diagram of the layered constrained damping wheel at 2360Hz;

[0040] Figure 8 The shear strain distribution cloud diagram of the layered constrained damping wheel at 2360Hz;

[0041] Figure 9 1 is a comparison diagram of the vibration velocity admittance of the bridge-type damping ridge layered constrained damping wheel and the layered constrained damping wheel in the embodiment;

[0042] Figure numerals: 1. wheel, 11. rim, 12. spoke, 13. hub, 14. inner annular groove, 15. outer annular groove, 2. inner constraint layer, 3. elastic damping layer, 4. outer constraint layer, 5. cavity, 6. ridge rib. DETAILED DESCRIPTION

[0043] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0044] In the drawings, components with identical structures are denoted by the same reference numerals, and components with similar structures or functions are denoted by similar reference numerals. The size and thickness of each component shown in the drawings are arbitrary and are not limited by the present invention. For clarity, some components in the drawings are exaggerated.

[0045] Example 1:

[0046] A bridge-type damping ridge layered constrained damping wheel comprises a wheel 1 and a constrained damping layer tightly fitted to the outer side of the wheel 1, such as Figure 1 As shown, wheel 1 is a spoke-plate wheel, such as a straight-spoke plate wheel or a curved-spoke plate wheel. In this embodiment, wheel 1 is a straight-spoke plate wheel with a diameter of 840 mm. The constrained damping layer includes an inner constraining layer 2, an elastic damping layer 3, and an outer constraining layer 4. The overall shape of the inner constraining layer 2, the elastic damping layer 3, and the outer constraining layer 4 is cut according to the shape of the spoke-plate wheel, so that the constrained damping layer can conform to the wheel 1. The inner constraining layer 2 conforms to the side of the wheel 1, the elastic damping layer 3 is closely bonded to the inner constraining layer 2, and the outer constraining layer 4 is closely bonded to the elastic damping layer 3.

[0047] This application only adds an inner constraint layer 2, an outer constraint layer 4 and an elastic damping layer 3 on the basis of the wheel 1, without affecting the main shape of the wheel 1. In addition, the bridge-type damping ridge rib constraint damping layer is light in weight and has little effect on the increase in the unsprung mass of the vehicle, making it easy to promote.

[0048] like Figure 2 As shown, the wheel 1 includes a rim 11, a spoke 12 and a hub 13 in sequence from the edge to the center of the wheel 1. An outer annular groove 15 is provided at the connection between the spoke 12 and the rim 11, and an inner annular groove 14 is provided at the connection between the spoke 12 and the hub 13. Accordingly, the main part of the damping constraint layer is in contact with the spoke 12, and grooves are provided at both ends to match the inner annular groove 14 and the outer annular groove 15, and are tightly fitted together with the rim 11 and the hub 13 respectively.

[0049] Specifically, in the half wheel from the rim 11 to the hub 13, the cross section of the bridge damping ridge layered constraint damping wheel is as follows: Figure 4As shown, in the three-layer structure of the constrained damping layer, the outer edge of the inner constrained layer 2 is tightly fitted with the rim 11 of the wheel 1, and the inner edge of the inner constrained layer 2 is tightly fitted with the hub 13 of the wheel 1. The inner constrained layer 2 is provided with an annular protrusion facing the spoke plate 12 and coaxial with the wheel 1. From the annular protrusion to the outer edge or inner edge of the inner constrained layer 2, a cavity 5 is formed between the inner constrained layer 2 and the spoke plate 12; the annular protrusion on the inner constrained layer 2 is a groove in the direction of the elastic damping layer 3, and the elastic damping layer 3 is provided with a ridge 6, which is an annular protrusion coaxial with the wheel 1, and the annular protrusion is tightly fitted with the groove.

[0050] In the half wheel from the rim 11 to the hub 13, the cross-sections of the inner constraint layer, the elastic damping layer and the outer constraint layer are as follows: Figure 5 As shown in the figure, the annular protrusion, groove, and ridge 6 are all very small, leaving a slight gap between the spoke 12 and the constrained damping layer at the location of the ridge 6. This creates two cavities 5: one between the annular protrusion and the outer edge of the inner constraining layer 2, and one between the annular protrusion and the inner edge of the inner constraining layer 2. These cavities 5 have a roughly triangular cross-section, completely covering the spoke 12 and blocking the radiation of wheel noise into the surrounding space. Between the rim 11 and the hub 13, the constrained damping layer has a roughly bridge-shaped cross-section.

[0051] The inner constrained layer 2 is glued to the side of the wheel 1, the elastic damping layer 3 is glued to the inner constrained layer 2, and the outer constrained layer 4 is glued to the elastic damping layer 3. In this embodiment, the wheel 1 and the constrained damping layer, as well as the inner constrained layer 2, elastic damping layer 3, and outer constrained layer 4 in the constrained damping layer, are glued together using 801 adhesive.

[0052] The inner constraining layer 2 and the outer constraining layer 4 are constraining layers made of aluminum, steel, or carbon fiber. The thickness of the inner constraining layer 2 is in the range of 0.5 to 5 mm, and the thickness of the outer constraining layer 4 is in the range of 0.5 to 5 mm. In this embodiment, the thickness of the inner constraining layer 2 and the outer constraining layer 4 are the same, both 1 mm.

[0053] The elastic damping layer 3 is made of a high-damping viscoelastic material with a material loss factor greater than 0.3. The thickness of the elastic damping layer 3 ranges from 0.5 to 10 mm. Except for the ridges 6, the thickness of the elastic damping layer 3 is uniform throughout. In this embodiment, the elastic damping layer 3 is made of a high-damping viscoelastic material with a material loss factor of 0.5 and has a thickness of 1.5 mm.

[0054] Through the annular protrusion of the inner constrained layer 2 and the ridge 6 of the elastic damping layer 3, a cavity is formed between the entire constrained damping layer and the spoke 12, providing more sufficient space for the shear deformation of the ridge 6, and reducing the constraints on the elastic damping layer 3, making it easier for the elastic damping layer 3 to produce shear deformation, thereby enhancing the effect of the elastic damping layer 3 in converting vibration mechanical energy into heat energy and dissipating the system vibration energy, thereby reducing the vibration noise generated by the wheel 1.

[0055] like Figure 3 As shown, the cross-section of the ridge 6 is rectangular with dimensions a*b, where side a is parallel to the spoke 12 and side b is perpendicular to the spoke 12. The length of a ranges from 2 to 20 mm, and the length of b ranges from 1 to 15 mm. In this embodiment, the ridge 6 is a rectangle with cross-section dimensions of 12*5 mm, and the 12 mm long side of the ridge 6 is parallel to the spoke 12 and the constrained damping layer.

[0056] The thickness of the elastic damping layer 3 is increased to form a ridge 6. Firstly, the cross-sectional area of ​​the elastic damping layer 3 at the position where the wheel 1 is more deformed is increased, thereby increasing the vibration absorption capacity of the elastic damping layer 3. Secondly, by suspending both sides of the ridge 6, a cavity 5 is formed between the damping layer and the spoke 12. On the one hand, the constraint on the elastic damping layer 3 is reduced, thereby increasing its deformation and thus the vibration absorption capacity. On the other hand, the cavity 5 isolates the noise of the spoke 12 of the wheel 1.

[0057] Regarding the setting position of the annular protrusion on the inner constraint layer 2, or the setting position of the ridge 6, the contact point between the annular protrusion on the inner constraint layer 2 and the spoke 12 is recorded as P, the distance between P and the inner annular groove 14 is greater than L×1 / 5, and the distance between P and the outer annular groove 15 is greater than L×1 / 5, where L represents the radial length of the spoke 12, that is, the length of the spoke 12 from the outer annular groove 15 where the spoke 12 contacts the rim 11 to the inner annular groove 14 where the spoke 12 contacts the hub 13 is L.

[0058] The distances between the annular protrusion and the inner annular groove 14 and the outer annular groove 15 are determined according to the following steps:

[0059] S1: The steady-state responses of a rigid wheel and a layered constrained damping wheel under periodic simple harmonic load excitation are calculated through harmonic response analysis, and the velocity admittance diagrams of the rigid wheel and the layered constrained damping wheel are obtained. The layered constrained damping wheel is obtained by applying the layered constrained damping in the prior art to the rigid wheel.

[0060] S2: Analyze the velocity admittance diagram to find the frequency point set when the velocity admittance of the layered constrained damping wheel is greater than that of the rigid wheel, and then find the frequency f when the difference between the velocity admittances of the layered constrained damping wheel and the rigid wheel is the largest from the frequency point set; Figure 6As shown in the figure, adding layered constrained damping to an ordinary rigid wheel can reduce the vibration at most of the natural frequencies of the wheel, but the vibration velocity at 2360 Hz increases.

[0061] S3: Obtain the modal strain energy cloud map and shear strain distribution cloud map at point f of the layered constrained damping wheel, analyze the modal strain energy cloud map and shear strain distribution cloud map, and use the maximum modal strain energy and maximum shear strain as the contact point between the annular protrusion on the inner constrained layer 2 and the spoke 12.

[0062] The modal strain energy cloud diagram and shear strain distribution cloud diagram corresponding to the layered constrained damping wheel at 2360Hz are as follows: Figure 7 and Figure 8 As shown, according to the modal strain energy cloud diagram and the shear strain distribution cloud diagram, the ridge 6 is arranged at the maximum modal strain energy of the mode, and the contact point P between the annular protrusion on the inner constraint layer 2 and the spoke 12 is arranged at the 1 / 3 position of the spoke 12. The distance between P and the inner annular groove 14 is L×1 / 3, which can reduce the vibration at a frequency of 2360 Hz.

[0063] The inner constraint layer 2 is provided with an annular protrusion at the spoke 12, which increases the thickness of the elastic damping layer 3 at this location to form a ridge 6, thereby enhancing the effect of the elastic damping layer 3 in converting vibration mechanical energy into heat energy and dissipating the system vibration energy, thereby reducing the vibration noise generated by the wheel 1. At the same time, the position of the annular protrusion is set at the maximum strain energy of the wheel modal vibration shape where the layered constraint damping noise reduction effect is not obvious, thereby achieving a better noise reduction effect.

[0064] The ridge rib 6 is a 12*5mm rectangle and is arranged at 1 / 3 of the web 12. The bridge-type damping ridge rib layered constrained damping wheel is compared with the layered constrained damping wheel in the prior art. Figure 9 As shown, it can be seen that the noise reduction effect of this application is better.

[0065] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A bridge-type damping ridge rib layered constrained damping wheel, comprising a wheel (1) and a constrained damping layer tightly fitted to the side of the wheel (1), wherein the wheel (1) is a spoke wheel, characterized in that: The constrained damping layer comprises an inner constrained layer (2), an elastic damping layer (3) and an outer constrained layer (4); the inner constrained layer (2) is in contact with the side of the wheel (1); the elastic damping layer (3) is in close contact with the inner constrained layer (2); and the outer constrained layer (4) is in close contact with the elastic damping layer (3); The outer edge of the inner constraint layer (2) is in close contact with the rim (11) of the wheel (1), and the inner edge of the inner constraint layer (2) is in close contact with the hub (13) of the wheel (1). The inner constraint layer (2) is provided with an annular protrusion facing the spoke plate (12) and coaxial with the wheel (1). A cavity (5) is formed between the inner constraint layer (2) and the spoke plate (12) from the annular protrusion to the outer edge or inner edge of the inner constraint layer (2); The annular protrusion on the inner constraint layer (2) is a groove in the direction of the elastic damping layer (3); the elastic damping layer (3) is provided with a ridge (6); the ridge (6) is an annular convex block coaxial with the wheel (1); the annular convex block is tightly fitted with the groove; The inner constraint layer (2) is glued to the side of the wheel (1), the elastic damping layer (3) is glued to the inner constraint layer (2), and the outer constraint layer (4) is glued to the elastic damping layer (3); An outer annular groove (15) is provided at the connection between the spoke plate (12) and the rim (11), and an inner annular groove (14) is provided at the connection between the spoke plate (12) and the hub (13); The distances between the annular protrusion and the inner annular groove (14) and the outer annular groove (15) are determined according to the following steps: S1: The steady-state responses of the rigid wheel and the layered constrained damping wheel under periodic simple harmonic load excitation are calculated by harmonic response analysis, and the velocity admittance diagrams of the rigid wheel and the layered constrained damping wheel are obtained; S2: Analyze the velocity admittance diagram to find the frequency point set when the velocity admittance of the layered constrained damping wheel is greater than that of the rigid wheel. Then, find the frequency f from the frequency point set when the difference in velocity admittance between the layered constrained damping wheel and the rigid wheel is the largest. S3: Obtain the modal strain energy cloud map and the shear strain distribution cloud map at position f of the layered constrained damping wheel, analyze the modal strain energy cloud map and the shear strain distribution cloud map, and use the maximum modal strain energy and the maximum shear strain as the contact point between the annular protrusion on the inner constrained layer (2) and the spoke (12).

2. The bridge-type damping ridge rib layered constrained damping wheel according to claim 1, characterized in that: The inner constraint layer (2) and the outer constraint layer (4) are constraint layers made of aluminum, steel or carbon fiber materials.

3. The bridge-type damping ridge rib layered constrained damping wheel according to claim 1, characterized in that: The elastic damping layer (3) is a damping layer made of a high-damping viscoelastic material with a material loss factor greater than 0.

3.

4. The bridge-type damping ridge rib layered constrained damping wheel according to claim 1, characterized in that: The thickness of the inner constraint layer (2) is in the range of 0.5 to 5 mm, and the thickness of the outer constraint layer (4) is in the range of 0.5 to 5 mm.

5. The bridge-type damping ridge rib layered constrained damping wheel according to claim 4, characterized in that: The inner constraining layer (2) and the outer constraining layer (4) have the same thickness.

6. The bridge-type damping ridge rib layered constrained damping wheel according to claim 1, characterized in that: The thickness of the elastic damping layer (3) ranges from 0.5 to 10 mm.

7. The bridge-type damping ridge rib layered constrained damping wheel according to claim 1, characterized in that: The cross section of the ridge rib (6) is rectangular, the size of the rectangle is a*b, the side a is parallel to the spoke plate (12), the side b is perpendicular to the spoke plate (12), the length range of a is 2-20 mm, and the length range of b is 1-15 mm.

8. The bridge-type damping ridge-rib layered constrained damping wheel according to claim 1, characterized in that: The contact point between the annular protrusion on the inner constraint layer (2) and the spoke (12) is marked as P, the distance between P and the inner annular groove (14) is greater than L×1 / 5, and the distance between P and the outer annular groove (15) is greater than L×1 / 5, where L represents the radial length of the spoke (12).

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