WO2007073306A1

WO2007073306A1 - A wheel arrangement and a vehicle comprising such wheel arrangement

Info

Publication number: WO2007073306A1
Application number: PCT/SE2006/001471
Authority: WO
Inventors: Johnny Pettersson
Original assignee: Maxmove Industrier Ab
Priority date: 2005-12-23
Filing date: 2006-12-21
Publication date: 2007-06-28
Also published as: SE528852C2; SE0502895L; WO2007073307A1

Abstract

A wheel arrangement comprises an essentially vertical driving shaft (120), an essentially circular wheel (111) fixedly provided on a wheel shaft (110), which is rotatable about the vertical driving shaft. A gear (114, 124) interconnects the wheel shaft and the driving shaft. The essentially vertical driving shaft and the wheel shaft form an angle of between 0 and 90 degrees. The wheel has a contact point with the underlying surface forming a virtual circle as the wheel shaft rotates about the driving shaft with a radius from the vertical driving shaft. The gear has a gear ratio based on a modified radius for the virtual circle taking into account factors affecting the shape of the wheel. This provides for a wheel arrangement wherein the turning of the wheel can be performed with a minimum of force and with an improved control.

Description

A WHEEL ARRANGEMENT AND A VEHICLE COMPRISING SUCH WHEEL ARRANGEMENT

FIELD OF INVENTION The present invention relates generally to wheel arrangements and more particularly to a wheel arrangement adapted for carrying out unlimited movement patterns in a horizontal plane with essentially no friction between the wheel and the underlying surface during turning of the wheel. The invention also relates to a vehicle comprising such wheel arrangements.

BACKGROUND

Wheel arrangements are used on most kinds of vehicles, such as cars, lorries, and vehicles adapted for carrying different kinds of loads . The requirements on the wheel arrangements as regards stability, steering capability etc. varies with the vehicle on which the wheels are mounted.

One kind of wheel arrangement adapted for carrying out unlimited movement patterns in a horizontal plane is disclosed in the international publication WO 99/54190. A rectangular chassis with a wheel in each corner as disclosed in this document is shown in Fig. 1. Two diagonally positioned driving wheel arrangements 1 have a special design, are driven and can be turned or swi- veled, and therefore these two drive wheel arrangements are arranged for the driving and controlling or steering function. The remaining two, diagonally positioned non- driving wheels 2 are essentially uniform and are com- posed of conventional caster wheels. A driving wheel arrangement 1 of Fig. 1 will now be described in detail. A wheel 11, see Fig. 2, is rotat- able about a first axis x co-aligned with a wheel shaft 10, which forms an angle α with an essentially vertical axis z which is greater than 0 degrees but less than 90 degrees, usually 45-60 degrees. The wheel can roll about this essentially vertical axis z, which is co-aligned with a vertical driving shaft 20, without the chassis moving itself. This ability leads to varying motion patterns of the chassis in a number of directions on a surface and makes possible for the chassis to be able to be operated out from and into narrow places .

The driving wheel arrangement is driven by electric motors (not shown) with associated mechanics and elec- tronics, wherein a first motor effects the turning of the wheel about the vertical shaft 20 and a second motor rotates the vertical shaft itself. This means that each driving wheel arrangement can be separately controlled, i.e., steered. The positions of the wheel about the vertical shaft and the rotational position of the vertical shaft itself are monitored by means of a respective transducer 13, 23. The motors, transducers etc. are connected to a central unit (not shown) consisting of a microprocessor and associated electronics.

The wheel shaft 10 is provided with a first toothed wheel 14 provided with a number of m teeth. The vertical shaft 20 is provided with a second toothed wheel 24 with a number of n teeth. The first and second toothed wheels together form a gear, wherein the ratio m:n determines the gear ratio between the wheel shaft 10 and the vertical drive shaft 20. In the above mentioned publication, it is assumed that the wheel has a defined contact area with the underlying surface in the form of a rolling point P, wherein this rolling point P has negligible width. When the wheel rolls about the vertical axis z, its contact area with the surface forms a virtual circle on the surface with a radius R, see Figs. 2 and 3, wherein the radius R is determined by the angle α which the wheel shaft forms with the vertical axis z, the diameter D of the wheel, and the configuration of the tread surface of the wheel. Thus the total length of the circle is 2πR.

It is appreciated that the circumference of the wheel is equal to πD.

A feature of the wheel arrangement shown in WO95/54190 is that it can be rotated about the vertical shaft essentially without any friction between the underlying surface and the wheel, also when the vertical drive shaft is fixed. With a correct gear ratio between the wheel shaft 10 and the vertical shaft 20, the wheel can turn without any lateral movement or rotation of the vertical drive shaft 20. This feature will be explained in the following, also with reference to Figs. 2 and 3.

Assuming that the vertical drive shaft 20 is fixed against rotation, the following condition must be met in order to achieve rolling of the wheel about the vertical axis z with a minimum of forces :

πD m:n = 2πR,

wherein m:n is the above mentioned gear ratio. However, these prior art calculations have proven to be inaccurate in real application, leading to degraded performance of vehicles using the above described wheel arrangement, such as lateral movement of the vertical drive shaft 20 during turning of the wheel.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a wheel arrangement of the kind initially mentioned, wherein the drawbacks of prior art are avoided or at least miti- gated. More particularly, an object is to provide a wheel arrangement wherein the forces between the wheel and the underlying surface are minimized when the wheel rolls about the vertical drive shaft.

The invention is based on the realization that the material constituting the tread surface of the wheel is deformed by the pressure from above. This in turn affects the virtual circle created by contact area between the rolling wheel and the surface, requiring adjustment of the gear ratio between the wheel shaft and the vertical drive shaft.

According to the invention there is provided a wheel arrangement as defined in appended claim 1.

By providing an essentially circular wheel with a contact point with the underlying surface forming a virtual circle as the wheel shaft rotates about the driving shaft, wherein the virtual circle has a radius from the vertical driving shaft, and providing a gear with a gear ratio based on a modified radius for the virtual circle taking into account factors affecting the shape of the wheel providing a contact area between the tread surface and the underlying surface, wherein the radius is determined so that the integrated product of the distance from the vertical driving shaft and the contact area inside the radius is essentially equal to the integrated product of the distance from the vertical driving shaft and the contact area outside the radius, the turning of the wheel can be performed with a minimum of force and with an improved control .

In a preferred embodiment, the wheel arrangement comprises a second wheel in order to be able to take up large loads .

Further preferred embodiments are defined by the dependent claims .

BRIEF DESCRIPTION OF DRAWINGS

The invention is now described, by way of example, with reference to the accompanying drawings, in which:

Fig. 1 shows a top view of a rectangular chassis with a wheel in each corner;

Fig. 2 is an overall view of a prior art wheel arrangement ;

Fig. 3 shows a virtual circle followed by the wheel of the wheel arrangement of Fig. 1;

Fig. 4 is a detailed view of a wheel arrangement according to the invention showing the contact area between the tread surface and the underlying surface; Fig. 5 shows a virtual circle followed by the wheel of the wheel arrangement of Fig. 4;

Fig. 6 shows an enlarged view of the wheel footprint shown in Fig. 5;

Fig. 7 is a perspective view of a second embodiment of a wheel arrangement according to the invention;

Fig. 8 is a partially cut away view of the wheel arrangement of Fig. 7;

Fig. 9 is an exploded view of the wheel arrangement of Fig. 7;

Fig. 10 is a sectional view of the wheel arrangement of Fig. 7; and

Fig. 11 shows a virtual circle followed by the wheel of the wheel arrangement shown in Figs. 7-10.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In the following a detailed description of preferred embodiments of the present invention will be given.

Figs. 1-3 have been described in the background section and will not be dealt with further in detail.

In Fig. 4 there is shown a detailed view of a wheel arrangement according to the invention. This wheel arrangement is identical to the prior art wheel arrangement of Fig. 1 with the exception that the gear ratio between the wheel shaft and the driving shaft has been modified as will be explained in the following. In Fig. 4 there is seen that the previously described rolling point P in practice has a horizontal extension in a direction transverse to the rolling direction, marked Sl in the figures. This extension is also shown in Fig. 5, wherein a "footprint" W of the wheel, i.e., the contact area between the tread surface of the wheel 11 and the underlying surface, is shown in a top view. This footprint is created due to the fact that the wheel is provided with a resilient tread surface made up of e.g. a rubber material, such as polyurethane . The rubber material is designated 11a in the figures.

The resiliency of the tread surface not only affects the rolling point; it also modifies the effective diameter D of the wheel.

The calculation of the resulting deformation of the wheel due to the resiliency of the tread surface will not be dealt with in detail in this text. However, the deformation depends on the following factors, among others: the load on the wheel arrangement, i.e., how heavy the vehicle is, Young's module for the tread surface material, the diameter and the width of the wheel, the thickness and geometry of the tread surface etc.

As can be seen in Fig. 5 not only the horizontal extension of the rolling point is affected. The foot print also has an extension S2 in the rolling direction of the wheel.

A detailed view of the wheel footprint of Fig. 5 is shown in Fig. 6. The footprint is divided into two portions labeled Wl and W2, wherein Wl is the footprint portion inside the virtual circle C and W2 is the footprint portion outside of the virtual circle. The following theories and calculations are applied in order to derive the rolling radius R giving optimal forces.

If it is assumed that the tread surface directly on top of the virtual circle C moves essentially without any mutual horizontal movement between the tread surface of the wheel and the underlying surface, that the tread surface of the inner portion Wl of the wheel advances slightly in relation to the underlying surface while the tread surface of the outer portion W2 of the wheel lags slightly behind in relation to the underlying surface. This creates vertical forces labeled Fl and F2, respectively .

In order to optimize the above mentioned gear ratio m:n, the roll radius R is calculated in the following way in order to get a minimum turning torque around the vertical shaft. R is calculated for the condition that the integrated product of the distance from the vertical axis z and the footprint area for the inner portion Wl is equal to or essentially equal to the integrated product of the distance from the vertical axis z and the footprint area for the outer portion W2. This calculation can be done in two ways. In a first way, R is calculated by trial and error, i.e., by assigning a value to the radius R in an iterative process and calculating the integrated results until the integrated result for Wl equals or almost equals that for W2. In a second way, R is calculated by setting up a differential equation. Optionally, a varying friction coefficient between the tread surface and the underlying surface due to the geometrical configuration of the wheel can be taken into account when calculating the radius R. In other words, areas with higher friction count more when integrating over the wheel footprint.

A second embodiment of a wheel arrangement according to the invention will now be described with reference to Figs. 7-11. This wheel arrangement operates in accord- ance with the same principles as the above described one. Nevertheless, there are some differences between the previously described embodiment and the second one shown in Figs. 7-11. The second embodiment comprises two wheels 111 and 112 arranged on a common wheel shaft 110 forming an angle of 90 degrees with a vertical drive shaft 120. The wheels have a rubber portion Ilia and 112a, respectively. Of the two wheels, only the first one 111 is driven by the wheel shaft. The second wheel rotates freely about the wheel shaft, only functioning to make the wheel arrangement taking up larger loads. The wheels 111, 112 are provided on the common wheel shaft 110 at the same distance from the vertical axis z co-axial with the vertical driving shaft 120 in order to get an even load distribution between the two wheels .

The common wheel shaft 110 is provided with a first toothed wheel 114 provided with a number of m teeth. The vertical driving shaft 120 is provided with a second toothed wheel 124 with a number of n teeth. The first and second toothed wheels together form a gear, wherein the ratio m:n determines the gear ratio between the wheel shaft 110 and the vertical drive shaft 120. The virtual circle for this wheel arrangement is calculated in the same way as for the first embodiment. However, the shape of the footprint left of these wheels have a slightly different shape, being relatively broad- er in a direction transversely to the rolling direction. This fact does not alter the basic calculations.

In the following, an example of the calculations for a wheel arrangement according to the second embodiment will be given. The following values are assumed:

D — the wheel diameter including a resilient poly- urethane material forming the tread surface: 450 mm

d — the wheel diameter excluding the resilient poly- urethane material forming the tread surface: 400 mm

Sl - the width of each wheel: 200 mm

W — the load on the wheel arrangement: 11718 kg

E — Young's module for polyurethane : 52.9

With the above values, the length of the wheel footprint, labeled S2, can be calculated to 56.2 mm. The adjustment of the diameter D of the wheel is calculated to 3.52 mm, resulting in an effective wheel diameter D' of 446.5 mm. This effective wheel diameter gives an effective wheel circumference of πD'= 1403 mm.

The values given above, when used for calculating the effective virtual radius, gives a virtual radius R of 181.5 mm. The circumference of the virtual circle is thus 2πR = 1145 mm. These calculations result in a desired gear ratio of 1403/1145 = 1.23

One possible way of achieving this gear ratio with off the shelf components is to use a toothed wheel 114 having 25 teeth for the wheel shaft 110 and a toothed wheel 124 having 19 teeth for the vertical drive shaft 120, resulting in an effective gear ratio of 25/19 = 1.32, being relatively close to the desired value of 1.23. Other options for the number of teeth are of course also feasible.

Preferred embodiments of a wheel arrangement according to the invention have been described. A person skilled in the art realizes that these could be varied within the scope of the appended claims.

Claims

1. A wheel arrangement comprising:

- an essentially vertical driving shaft (20; 120),

- an essentially circular wheel (11; 111) fixedly provided on a wheel shaft (10; 110) and having a tread surface (Ha; Ilia), said wheel shaft being rotatable about the vertical driving shaft, and

- a gear (14, 24; 114, 124) interconnecting the wheel shaft and the driving shaft,

characterized in that

- the essentially circular wheel has a contact point with the underlying surface forming a virtual circle (C) as the wheel shaft rotates about the driving shaft, wherein the virtual circle has a radius (R) from the vertical driving shaft, and

- in that the gear has a gear ratio based on a modified radius for the virtual circle taking into account factors affecting the shape of the wheel providing a contact area between the tread surface and the underlying surface, wherein the radius (R) is determined so that the integrated product of the distance from the vertical driving shaft and the contact area (Wl) inside the radius (R) is essentially equal to the integrated product of the distance from the vertical driving shaft and the contact area (W2) outside the radius (R) .

2. The wheel arrangement according to claim 1, wherein the factors affecting the shape of the wheel comprises: the load on the wheel arrangement, Young's module for the tread surface material, the diameter and the width of the wheel, and the thickness and geometry of the tread surface.

3. The wheel arrangement according to claim 1, wherein the gear ratio takes into account a varying friction coefficient between the tread surface and the underlying surface due to the geometrical configuration of the wheel.

4. The wheel arrangement according to any of claims 1-3, wherein the essentially vertical driving shaft and the wheel shaft form an angle of between 0 and 90 degrees .

5. The wheel arrangement according to any of claims 1-4, wherein the essentially vertical driving shaft (120) and the wheel shaft (110) form an angle of 90 degrees , and

- wherein the wheel arrangement comprises a second wheel (112) mounted to the wheel shaft, wherein the second wheel has a tread surface (112a) and is freely rotatable about the wheel shaft.

6. The wheel arrangement according to claim 5, wherein the wheel (111) and the second wheel (112) are provided at the same distance from the essentially vertical driving shaft (120).

7. The wheel arrangement according to any of claims 1-6, wherein the tread surface material is resilient.

8. The wheel arrangement according to claim 7, wherein the tread surface comprises a rubber material, such as polyurethane .

9. The wheel arrangement according to any of claims 1-8, wherein the radius (R) has been calculated by a differential equation.

10. A vehicle comprising a wheel arrangement according to claim 1.