WO2009042460A2

WO2009042460A2 - Elastic shear band with helical coils

Info

Publication number: WO2009042460A2
Application number: PCT/US2008/076616
Authority: WO
Inventors: Ronald Hobart Thompson; Jaret B. Matthews; Thomas Corey Campbell; John Patrick Gregory; Tenzin Khedrup; Brent Robert Nelson; John Linton Siverd; Anthony Peter Zangoglia
Original assignee: Societe De Technologie Michelin; Michelin Recherche Et Technique S.A.; California Institute Of Technology
Priority date: 2007-09-27
Filing date: 2008-09-17
Publication date: 2009-04-02
Also published as: WO2009042460A3

Abstract

A shear band that may be used as part of a structurally supported wheel is provided. More particularly, a shear band constructed from at least two helical coils attached between inextensible members is described. In certain embodiments, the shear band may be constructed entirely or substantially without elastomeric or polymer-based materials. Multiple embodiments are available including various arrangements of the at least two helical coils between the members as well as varying constructions for the each coil.

Description

PCT PATENT APPLICATION

TITLE

ELASTIC SHEAR BAND WITH HELICAL COILS

TECHNICAL FIELD OF THE INVENTION

[0001] The present invention relates to a shear band that may be used as part of a structurally supported wheel. More particularly, a shear band constructed from helical coils attached between circumferential members is provided. In certain embodiments, the shear band may be constructed entirely or substantially without elastomeric or polymer-based materials, which allows for application in extreme environments.

BACKGROUND OF THE INVENTION

[0002] The use of structural elements to provide load support in a tire without the necessity of air pressure has been previously described. For example, U.S. Patent No. 6,769,465 provides a resilient tire that supports a load without internal air pressure. This tire includes a ground contacting tread portion, a reinforced annular member, and sidewall portions that extend radially inward from the tread portion. By way of further example, U.S. Patent No. 7,201,194 provides a structurally supported non-pneumatic tire that includes a ground contacting tread portion, a reinforced annular element disposed radially inward of the tread portion, and a plurality of web spokes extending transversely across and radially inward from the reinforced annular element and anchored in a wheel or hub. For each of these references, the constructions described are particularly amenable to the use of elastomeric materials including rubber and other polymeric materials. The use of such materials has certain limitations, however. For example, extreme temperatures levels and large temperature fluctuations can make such elastomeric materials unsuitable for certain applications. Accordingly, constructions that can be created in whole or in part with non-elastomeric materials would be advantageous. Also, constructions from materials such as carbon-based elements may also result in reduced weight and lower materials costs. These and other advantages are provided by certain exemplary embodiments of the present invention. THE SUMMARY OF THE INVENTION

[0003] Objects and advantages of the invention will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the invention.

[0004] In one exemplary embodiment of the invention, a shear band is provided that defines axial, radial, and circumferential directions. The shear band includes an outer member extending along the circumferential direction, an inner member extending along the circumferential direction, and at least two helical coils contacting the outer and inner members and located between the members. The helical coils are located adjacent to one another along the axial direction and each extend in a spiral manner about the circumferential direction of the shear band. The helical coils may spiral in the same manner along the circumferential direction of the shear band or may be constructed in an opposing manner. The helical coils may be fastened to the inner and/or outer members, may be at least partially embedded in the outer and inner members, or may otherwise be attached to the outer and inner members. The helical coils may be constructed from a variety of materials. For example, metal wires wound into the coiled shapes may be used. In some embodiments, the outer and inner members may comprise metal members encircled along the circumferential direction. The shear band may be constructed to have a shear efficiency of at least about 50 percent in some embodiments or even higher in others.

[0005] In another exemplary embodiment of the present invention, a wheel is provided defining axial, radial, and circumferential directions. The wheel includes a hub, a shear band, and support elements. The shear band includes an inextensible, outer circumferential member extending along the circumferential direction at a radial position R2; and an inextensible, inner circumferential member extending along the circumferential direction at a radial position Rl. The ratio of Rl to R2 is about 0.8 < (Rl / R2) < 1. The shear band also includes at least two helical coils contacting the outer and inner members and located between the members. The helical coils are located adjacent to one another along the axial direction and each extends in a spiral manner about the circumferential direction of the shear band. The support elements connect the hub and the inner circumferential member of the shear band.

[0006] These and other features, aspects and advantages of the present invention will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:

[0008] Fig. 1 is an exemplary embodiment of the present invention that includes a non- pneumatic wheel incorporating an embodiment of a shear band.

[0009] Fig. 2 is a perspective and partial cross-section view of the exemplary shear band of Fig. 1 taken at the location so identified in Fig. 1.

[0010] Fig. 3 is a cross-sectional view taken along lines 3-3 of the exemplary embodiment of Fig. 1.

[0011] Fig. 4 is a portion of a helical coil used for modeling an exemplary embodiment of a shear band as described below.

[0012] Figs. 5 though 7 provide graphical representations of certain modeling and analysis results as described below.

DETAILED DESCRIPTION

[0013] Objects and advantages of the invention will be set forth in the following description, or may be apparent from the description, or may be learned through practice of the invention. Repeat use of reference characters throughout the present specification and appended drawings is intended to represent same or analogous features or elements of the invention.

[0014] Referring now to Figs. 1 through 3, an exemplary embodiment of a wheel 110 according to the present invention is shown therein. Wheel 110 defines radial directions R, circumferential directions C (Fig. 1) and axial directions A (Figs. 2 and 3). Wheel 110 includes a hub 120 connected to a shear band 140 by multiple support elements 130. Hub 120 provides for the connection of wheel 110 to a vehicle and may include a variety of configurations for connection as desired. For example, hub 120 may be provided with connecting lugs, holes, or other structure for attachment to a vehicle axle and is not limited to the particular configuration shown in Fig. 1. Support elements 130 connect hub 120 to shear band 140 and thereby transmit the load applied to hub 120. As with hub 120, support elements 130 may take on a variety of configurations and are not limited to the particular geometries and structure shown in Fig. IA. In addition, using the teachings disclosed herein, one of skill in the art will understand that tread or other features may be readily added to the outer circumferential surface 155.

[0015] Shear band 140 includes four helical coils 152 that are spaced apart from one another in an adjacent fashion along the axial direction A as shown in Figs. 2 and 3. As seen in Fig. 1, each coil 152 extends in a helical manner about circumferential direction C. As used herein, the word "helical" applies to any spiral form, but is not limited to a particular spiral geometry. Helical coils 152 are positioned between an outer member 150 and an inner member 160, each of which are constructed from relatively inextensible materials. In one embodiment, for example, members 150 and 160 may be constructed from a metal element encircled as shown in Fig. 1. By way of further examples, steel as might be used in the construction of springs, or carbon based filaments may also be utilized for the fabrication of members 150 and 160. While elastomeric materials can also be used, the utilization of non- elastomeric materials for members 150 and 160 provides for extreme temperature applications such as a polar or lunar environment where elastomeric materials may become too rigid or brittle. For example, shear bands (including wheels incorporating such members) capable of functioning at temperatures as low as 100 degrees Kelvin should be achievable where elastomeric constructions are avoided.

[0016] For this particular exemplary embodiment, helical coils 152 are each constructed from a wire rope wrapped into a coil and clamped every 180 degrees to the outer and inner members 150 and 160. More specifically, a pair of fasteners 170 and a bar 180 are used to attach coils 152 in an alternating manner between the outer member 150 and the inner member 160. Numerous other configurations of helical coils 152 and connection to members 150 and 160 may be used. By way of example only, shear band 140 may be constructed with a varying number of helical coils 152 located adjacent to one another about the circumferential direction C. Varying thicknesses and different materials other than wire may be used for a helical coil 152 and, in fact, such may be advantageous for tuning the physical performance of wheel 110 depending upon the application. The height of coils 152 along radial direction R may be varied as well as the density or pitch of the coils about circumferential direction C. While Fig. 2 shows helical coils 152 both spiraling in the same direction circumferentially, the spiraling may varied. For example, helical coils 152 may be arranged such that the direction of spiraling along the circumferential direction alternates between the different coils 152. The helical coils 152 may have a substantially circular cross section shape or other non-circular cross-section shapes. Additionally, numerous other techniques for fastening coils 152 to the outer and inner members 150 and 160 may be used such as, for example, welding, gluing, and embedding. Using the teachings disclosed herein, one of skill in the art will understand that numerous other variations are within the spirit and scope of the present invention.

[0017] Although not limited thereto, the shear band of the present invention has particular application in the construction of wheels including, but not limited to, non-pneumatic tires and other wheels that do not require pneumatic pressure for structural support. For example, in a pneumatic tire, the ground contact pressure and stiffness are a direct result of the inflation pressure and are interrelated. However, a shear band of the present invention may be used to construct a wheel or tire that has stiffness properties and a ground contact pressure that are based on their structural components and, advantageously, may be specified independent of one another. Wheel 110 provides an example of such a construction. In addition, and advantageously, because the present invention includes structures and geometries for a shear band construction that are not limited to elastomeric (e.g. rubber) or polymer-based materials, the present invention provides for the construction of a wheel that may be used in extreme temperature environments. As used herein, extreme temperature environments includes not only environments experiencing temperatures that would be unacceptable for elastomeric or polymer-based materials but also includes environments where large temperature fluctuations may occur.

[0018] Returning to Fig. 1, for example, it will be understood from the figures and description provided above that outer member 150 is longer circumferentially than the inner member 160 and both are relatively inextensible. Accordingly, in operation under an applied load to wheel 110, the shearing of helical coils 152 between the members 150 and 160 allows the shear band 140 to deform and provide a greater contact area with the travel surface (e.g. ground).

[0019] More specifically, helical coils 152 collectively act as a shear layer having an effective shear modulus G_eff. The relationship between this effective shear modulus G_eff and the effective longitudinal tensile modulus E_im of the outer and inner members 150 and 160 controls the deformation of the shear band 140 under an applied load. When the ratio of E_im /Ge_ff is relatively low, deformation of the shear band under load approximates that of the homogeneous member and produces a non-uniform contact pressure with the travel surface. However, when the ratio E_im / G_eff is sufficiently high, deformation of the annular shear band 140 under load is essentially by shear deformation of the shear layer (i.e., helical coils 152) with little longitudinal extension or compression of the inextensible members 150 and 160. Perfectly inextensible members 150 and 160 would provide the most efficient structure and maximize the shear displacement in the shear layer. However, perfect inextensibility is only theoretical: As the extensibility of members 150 and 160 is increased, shear displacement will be reduced as will now be explained in conceptual terms below.

[0020] In the contact region, the inner member 160, located at a radius Rl, is subjected to a tensile force. The outer member 150, located at a radius R2, is subjected to an equal but opposite compressive force. For the simple case where the outer and inner members 150 and 160 have equivalent circumferential stiffness, the outer member 150 will become longer by some strain, e, and the inner member 160 will become shorter by the some strain, -e. For a shear layer having a thickness h, this leads to a relationship for the Shear Efficiency of the bands, defined as:

(1)

Shear Efficiency = (1 TZ )

It can be seen that for the perfectly inextensible members, the strain e will be zero and the Shear Efficiency will be 100%.

[0021] The value of the strain e can be approximated from the design variables by the equation below:

(2)

e =

8 R2 E t

For example, assume we have a proposed design with the following values: h = 10 mm (radial distance between bands 150 and 160)

Ge_ff = 4 N/mm2 (effective shear stiffness between the bands)

L = 100 mm (contact patch length necessary for design load)

R2 = 200 mm (radial distance to outer member)

Rl = 190 mm (radial distance to inner member) E = 20,000 N/mm2 (tensile modulus for both members 150 and 160) t = 0.5 mm (thickness for both members 150 and 160)

Calculating for e using E:

(10) (10O)² e = = 0.0025

8 (200)(20,000)(0.5)

The shear efficiency can then be calculated as:

(3)

0.0025 (190 + 200)

Shear efficiency = 1 = 0.9025

10

Thus, the efficiency in this case is approximately 90%.

[0022] The above analysis assumes that outer and inner members 150 and 160 have identical constructions. However, the thickness and/or the modulus of members 150 and 160 need not be the same. Using the principles disclosed herein, one skilled in the art can readily calculate the strains in members 150 and 160 and then calculate the shear efficiency, using the above approach. A Shear Efficiency of at least 50% should be maintained to avoid significant degradation of the contact pressure with the travel surface. Preferably, a Shear

Efficiency of at least 75% should be maintained.

[0023] Accordingly, as sufficient Shear Efficiency is achieved, contact pressure with the travel surface becomes substantially uniform. In such case, an advantageous relationship is created allowing one to specify the values of shear modulus G_eff and the shear layer thickness h for a given application:

(4)

* h

Where:

P_eff = predetermined ground contact pressure

Ge_ff = effective shear modulus of helical coils 152 within members 150 and 160 h = thickness of the shear layer - i.e. radial height of helical coils 152 R2 = radial position of the outer member 150 As one of skill in the art will appreciate using the teachings disclosed herein, the above relationship is useful in the design context because frequently P_eff and R2 are known - leaving the designer to optimize G_eff and h for a given application.

[0024] The behavior of shear layer 140 and, more specifically, the effective shear modulus Ge_ff may be modeled using an approach as will now be described. Assuming that inextensible member 150, inextensible member 160, and helical coils 152 are each uniform in physical properties along the axial directions A and that helical coils 152 deform predominantly in shear along circumferential directions C, wheel 110 can be modeled as a three-dimensional structure defined by wire-based features (i.e., beam and truss elements). Once such modeling technique includes five distinct parts: (1) an outer membrane 150 defined by Timoshenko beam quadratic finite elements with a rectangular cross-section of width along the axial direction that is equal to the diameter of a helical coil 152; (2) an inner membrane 160 defined by Timoshenko beam quadratic finite elements with a rectangular cross-section of depth equal to the diameter of a helical coil 152; (3) a helical cable (coil 152) modeled with discrete half circular hoops defined by Timoshenko beam quadratic finite elements with circular cross-section; (4) support elements 130 each defined by one linear truss element with no compression, and (5) a ground defined as an analytical rigid surface. [0025] As boundary conditions, the radially inner end of each support element 130 is constrained in displacement. The interaction between the ground and the outer membrane 150 is defined as a frictionless contact in a direction tangential to the membrane 150 and as a hard contact in a vertical direction. During the simulation, the ground is gradually moved vertically upward a predefined distance.

[0026] Using the assumption that the annular band behaves as a shear band, the analogy between the annular band and an isotropic shear band with an equivalent shear modulus is justified. The effective shear modulus G_eff is determined using a model of a single revolution of the helical coil 152 shown in Fig. 4 with appropriate boundary conditions. The material of coil 152 is assumed to be homogeneous and its nonlinear behavior is neglected. The y- direction corresponds to circumferential direction C of wheel 110 and also to the pitch of the coil 152. The x direction corresponds to the radial direction R, and the z direction corresponds to the axial direction A. The two ends of the coil (assumed to be attached to outer membrane 150) are fixed in the six degrees of freedom. A predefined force is applied in the y-direction at the opposite section (assumed to be attached to inner membrane 160). The displacement of this section is constrained in the x- and z-directions. The model of the single coil consists of linear hexahedrons (8 nodes) finite elements. Nonlinear geometry is considered in all analysis although the force is selected such that the displacement is not excessive.

[0027] The computed displacement due to the applied predefined force is used to determine the effective shear modulus G_efr as follows.

(5)

Where:

G_eff = effective shear modulus, in N/mm², τ = shear stress, in N/mm², γ = shear angle, in radians.

The shear stress, τ, is calculated as follows:

(6)

T = FI A

Where:

F = predefined force applied to the single cable coil, in N, A = tributary area defined by:

The tributary area A is calculated as follows:

(V)

A = p * h

Where: p = pitch of helical coil, in mm, h = diameter of helical coil or radial distance between inner and outer membranes, in mm.

The shear angle is determined in terms of the computed displacement as follows:

(8) γ = tan^"1 (δ Ih)

Where: δ = computed displacement due to the applied predefined force, in mm. Combining Equations 5 to 8, the effective shear modulus G_eff is given by:

(9)

Geff = F /(p * h * tan^"1 {δ I h))

Note that the displacement, δ, depends on the material properties of the helical coil 152 (i.e., Young's modulus, E, cross-sectional moment of inertia, I), the diameter h of the helical coil 152, and the pitch p of the helical coil 152. Thus, the designer of the metallic annular band can choose design variables E, δ, h, p, selects a force, F, and computes the displacement, δ, by finite element analysis of a single revolution of the coil in order to obtain the desired effective shear modulus G_eff.

[0028] Using this approach, modeling of a three dimensional wheel 110 having a construction similar to Fig. 1 but with a single helical coil was undertaken. During simulation, the ground was moved upward gradually by a predetermined distance. As will be understood by one of skill in the art using the teachings disclosed herein, commercial software sold under the name Abaqus / CAE (Version 6.6-1) was used to conduct the finite element analysis. The results are provided graphically in Figs. 4, 5, 6, and 7. Unless otherwise noted, all models and analysis assumed the stiffness properties of steel having a Young's modulus E of about 210,000 MPa.

[0029] Fig. 5 is a plot of the effective shear modulus G_eff versus the pitch p of helical coil 152. Data line 500 (squares) represent a radius r of 0.5 mm, where r is the radius of the wire or material from which coil 152 is constructed. Data line 510 (diamonds) represents a radius r of 1.0 mm. As suggested by Fig. 5, effective shear modulus G_eff was relatively constant relative to pitch p at the smaller radius r of 0.5 mm. The effective shear modulus G_eff increased with a larger radius r and was somewhat more sensitive to pitch at the larger radius r of 1.0 mm.

[0030] Fig. 6 is a plot (using logarithmic scales for both the x and y axis) the effective shear modulus Ge_ff versus the product of Young's Modulus E for helical coil 152 and the Area Moment of Inertia I for helical coil 152. Line 600 (diamonds) represents a diameter h for the helical coil 152 of 20 mm. Line 610 (squares) represents a diameter h for the helical coil 152 of 30 mm. Line 620 (triangles) represents a diameter h for the helical coil 152 of 40 mm. As suggested by Fig. 6, the effective shear modulus G_eff increases almost proportionately (on this scale) to increases in Young's modulus E but remains relatively constant with changes in radius r.

[0031] Fig. 7 is a plot of the effective shear modulus G_eff versus the diameter h of helical coil 152. Data line 700 (squares) represent a pitch p of 20 mm per revolution. Data line 710 (diamonds) represent a pitch p of 10 mm per revolution. Data line 720 (triangles) represent a pitch p of 5 mm per revolution. As suggested by Fig. 7, effective shear modulus G_eff decreases with increasing diameter h of helical coil 152. For a constant diameter h, the effective shear modulus G_eff increases with decreasing pitch p.

[0032] Finally, it should be noted that advantages of the present invention are principally obtained where the relative radial distance between the inner and outer members fall within a certain range. More specifically, preferably the following relationship is constructed: (10)

0.8 < (Rl / R2) < 1 where:

R2 = radial position of the outer member (e.g. the distance to the outer member 150 from the axis of rotation or focus of the radius defined by such member) (see Fig. 1)

Rl = radial position of the inner member 160 (e.g. the distance to the inner member from the axis of rotation or focus of the radius defined by such member) (see Fig. 1) [0033] While the present subject matter has been described in detail with respect to specific embodiments thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, the scope of the present disclosure is by way of example rather than by way of limitation, and the subject disclosure does not preclude inclusion of such modifications, variations and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.

Claims

WHAT IS CLAIMED IS:

1. A shear band defining axial, radial, and circumferential directions, the shear band comprising: an outer member extending along the circumferential direction; an inner member extending along the circumferential direction; and at least two helical coils contacting said outer and inner members and located between said members, said at least two helical coils located adjacent to one another along the axial direction and each extending in a spiral manner about the circumferential direction of the shear band.

2. A shear band as in claim 1, wherein said at least two helical coils spiral in the same manner along the circumferential direction of the shear band.

3. A shear band as in claim 1, wherein said at least two helical coils are fastened to said inner and outer members.

4. A shear band as in claim 1, wherein said at least two helical coils are at least partially embedded in said outer and inner members.

5. A shear band as in claim 1, wherein said outer and said inner members comprise metal members encircled along the circumferential direction.

6. A shear band as in claim 1, further comprising means for connecting said at least two helical coils to said outer member.

7. A shear band as in claim 6, further comprising means for connecting said at least two helical coils to said inner member.

8. A shear band as in claim 1, wherein said shear band has a shear efficiency of at least about 50 percent.

9. A shear band as in claim 1, wherein said at least two helical coils comprise metal wires wound to form the coils.

10. A wheel comprising the shear band of claim 1.

11. A wheel defining axial, radial, and circumferential directions, the wheel comprising: a hub; a shear band comprising an inextensible, outer circumferential member extending along the circumferential direction at a radial position R2; an inextensible, inner circumferential member extending along the circumferential direction at a radial position Rl, wherein a ratio of Rl to R2 is about 0.8 < (Rl / R2) < 1; at least two helical coils contacting said outer and inner members and located between said members, said at least two helical coils located adjacent to one another along the axial direction and each extending in a spiral manner about the circumferential direction of the shear band; and a plurality of support elements connecting said hub and said inner circumferential member of said shear band.

12. A wheel as in claim 11, wherein said at least two helical coils spiral in the same manner along the circumferential direction of the shear band.

13. A wheel as in claim 11, wherein said at least two helical coils are fastened to said outer and inner circumferential members.

14. A wheel as in claim 11, wherein said at least two helical coils are at least partially embedded in said outer and inner circumferential members.

15. A wheel as in claim 11, wherein said outer and said inner circumferential members comprise metal members encircled along the circumferential direction.

16. A wheel as in claim 11, further comprising means for connecting said at least two helical coils to said outer circumferential member.

17. A wheel as in claim 16, further comprising means for connecting said at least two helical coils to said inner circumferential member.

18. A wheel as in claim 11, wherein said shear band has a shear efficiency of at least about 50 percent.

19. A wheel as in claim 11, wherein said at least two helical coils comprise metal wires wound to form the coils.