NL2029427B1

NL2029427B1 - Method for determining a position of the center of gravity (cog) of an elongated body

Info

Publication number: NL2029427B1
Application number: NL2029427A
Authority: NL
Inventors: Van Liempt Frank; Nieuwenhuize Jarno; Grozeva Anna; Lobee Koos
Original assignee: Kok & Van Engelen Composite Structures B V
Priority date: 2021-10-15
Filing date: 2021-10-15
Publication date: 2023-05-16
Also published as: WO2023063816A1

Abstract

A method for determining an offset of the center of gravity (COG) of an elongated body With respect to a geometrical center in a plane of the elongated body is described. The method comprises providing a first rotation axis and a second rotation axis at a distance to the first rotation axis and both perpendicular to the plane and at offset positions to the geometrical center of the elongated body. A subsequent step involves balancing the elongated body on the first rotation axis into an equilibrated first balanced position and subsequently balancing the elongated body on the second rotation axis into an equilibrated second balanced position. A first and a second rotation angle in the plane of the elongated body in the equilibrated first and second balanced positions respectively is then measured. The offset of the COG in the plane is then determined by geometrical triangulation using the measured rotation angles.

Description

METHOD FOR DETERMINING A POSITION OF THE CENTER OF

GRAVITY (COG) OF AN ELONGATED BODY

TECHNICAL FIELD OF THE INVENTION

The invention relates to a method for determining an offset of the center of gravity (CoG) of an elongated body with respect to a geometrical center in a plane of the elongated body. The invention in particular relates to a method for determining an offset of the center of gravity (CoG) of an elongated body made of fiber reinforced composites with respect to a geometrical center in a plane of the elongated body. The invention further relates to a method for determining an offset of the center of gravity (CoG) of a rotor or propeller blade with respect to a geometrical center in a plane of the rotor of propeller blade.

BACKGROUND OF THE INVENTION

In many applications, it is important to be able to accurately determine the position of a center of gravity of the body after manufacture. Any manufacturing method may entail some unbalances in the body and knowing the extent of the unbalance may be seen as an important quality control measure. The above is true for bodies made by more traditional materials, such as wood or metal for instance. The introduction of fiber reinforced composites in modern bodies has led to more flexibility in design shapes and a decrease in body mass, but manufacturing of composite bodies may also entail unbalances that need to be verified. This is particularly of concern for bodies or parts thereof that are moved or rotated in use at relatively large speeds. An exemplary body involves a rotor blade or propeller blade, or a rotor comprising at least two of such rotor blades or propeller blades.

A known method for determining an offset of the center of gravity (CoG) of an elongated body with respect to a geometrical center in a plane of the elongated body is disclosed in ‘A Body for Accurately Determining the Mass and

Center of Gravity of Rigid Bodies’, Meibao Wang, Xiaolin Zhang*, Wenyan Tang and

Jun Wang, Appl. Sci. 2019, 9, 2532; doi:10.3390/app9122532. The known method involves measuring the mass and the CoG of rigid bodies with a multi-point weighing method. Traditional methods usually include two parts with a certain location, i.e, a fixed platform and a mobile platform. One of the problems of the known method is that its accuracy is not sufficient.

SUMMARY OF THE INVENTION

It is an aim of the present invention to provide an improved method for determining an offset of the center of gravity (CoG) of an elongated body with respect to a geometrical center in a plane of the elongated body. The invention in particular aims at providing a method for determining an offset of the CoG of an elongated body made of fiber reinforced composites with respect to a geometrical center in a plane of the elongated body. The invention further aims at providing a method for determining an offset of the

CoG of a rotor or propeller blade with respect to a geometrical center in a plane of a rotor blade, or propeller blade, or a rotor that comprises at least two of such rotor blades or propeller blades.

According to the invention, this and other aims are fulfilled by a method in accordance with claim 1. The method is used for determining an offset of the center of gravity (CoQ) of an elongated body with respect to a geometrical center in a plane of the elongated body, and comprises the following steps of: - providing a first rotation axis and a second rotation axis at a distance to the first rotation axis and both perpendicular to the plane and at offset positions to the geometrical center of the elongated body; - balancing the elongated body on the first rotation axis into an equilibrated first balanced position and subsequently balancing the elongated body on the second rotation axis into an equilibrated second balanced position; - measuring a first and second rotation angle in the plane of the elongated body in the equilibrated first and second balanced positions respectively; and - determining the offset of the CoG in the plane by geometrical triangulation using the measured rotation angles.

DETAILED DESCRIPTION OF THE INVENTION

It has turned out that the method of the invention provides a reliable and reproducible method for determining the position of the CoG of an elongated body. The inventors have found that the method is able to measure an unbalance defined by the product of the mass of the elongated body and the offset of the CoG with respect to the geometrical center of the elongated body (M*E) as low as 50 g*mm, more preferably as low as 40 g*mm, even more preferably as low as 30 g*mm, and most preferably as low as 20 g*mm. This means that the accuracy of the method allows measuring deviations in the unbalance of less than 5 g*mm, more preferably of less than 4 g*mm, even more preferably of less than 3 g*mm, and most preferably of less than 2 g*mm. Such accuracies are difficult if not impossible to reach with the known method.

The method may in principle be used on any elongated body. Such a body has a length to largest width ratio of at least 1.5, more preferably of at least 2.0, even more preferably of at least 2.5 and most preferably of at least 3.0.

An embodiment of the invention provides a method wherein the distance between the first and second rotation axes is A, the first rotation angle is al, the second rotation angle is 02, and the geometrical triangulation results in the following formula:

E =|tan(02)}/{tan (al) + tan (02))] * A - A/2 wherein E is the offset of the CoG with respect to the geometrical center. The offset may be defined in any direction but will preferably be defined in a direction that is parallel to the direction of a line that connects the positions of the first and second rotation axes.

The elongated body may not show any axis or plane of symmetry, or may have a plane of symmetry. For instance, a rotor or propeller blade may have a middle plane that provides a plane of symmetry between an underside of the blade and an upper side. The middle plane runs through a leading edge of the rotor or propeller blade.

Another preferred embodiment provides a method wherein the plane of the elongated body is a plane of symmetry of the elongated body.

In another embodiment, a method is provided wherein providing the first rotation axis and/or the second rotation axis is carried out by inserting a rod in a hole of the elongated body, the hole being provided at at least one of the offset positions. The at least one rod then extends perpendicular to the plane of the elongated body.

In one suitable embodiment, the first rotation axis and the second rotation axis are both provided by inserting a rod in a hole of the elongated body, the hole being provided at the offset positions.

In an embodiment, the insertion of the rod in the hole of the elongated body is a rigid insertion and the suspension of the rod in the support comprises a bearing, preferably an air bearing. This arrangement effectively reduces friction between the balanced elongated body and the support. This means that the bearing is also provided at an offset position to the geometrical center of the elongated body. In order to increase accuracy, an embodiment provides the rod in a bearing in provided on the first rotation axis and on the second rotation axis. Another embodiment provides the bearing on the first (or on the second) rotation axis and uses a counterweight to balance the elongated body such that the center of gravity is located in a middle position of the bearing.

In yet another embodiment, a rod is used as suspension where the rod has a smaller diameter than the hole of the elongated body in which it is inserted. The rod may be supported at both sides of the elongated body by a suitable support, such as one horizontal support at each side of the elongated body. In the suspended state, the elongated body will automatically seek an equilibrium position. This embodiment is advantageous in that friction is virtually non-existent, thereby substantially eliminating any measuring mistakes. The set-up is substantially friction-free since the elongated body is allowed to ‘walk’ onto the rod.

Measuring the angle of equilibrium may be carried out by measuring the horizontal distance between both tips of the elongated body in the equilibrium position. A practical method involves providing two plumb lines that may be translated in a horizontal direction until they are both in line with the tips of the elongated body. The angle may then be determined by calculating arccos (horizontal distance/diameter) where diameter is the tip-to-tip distance along the elongated body. 5 This embodiment is very accurate and robust.

The method according to a practical embodiment of the invention comprises providing the first rotation axis and the second rotation axis by a mounting hole of the elongated body. Such mounting holes are used for mounting the elongated body to a another part of a complete body to which it is connected in use. For instance, in case of a rotor, the mounting holes are used to connect the rotor to a hub of a helicopter. The mounting holes are usually positioned at t distance of each other in order to accommodate force moments that occur because of rotation of the rotor around the hub.

In another embodiment, the method is characterized in that the elongated body is substantially made of a fiber-reinforced composite. The composite material may be based on a thermosetting and/or a thermoplastic matrix material, and may use any type of reinforcing fiber used in the art today.

The method according to another embodiment may be used advantageously for determining the position of the CoG of a rotor blade or a propeller blade, or of a rotor comprising at least two of the rotor blades or propeller blades.

The embodiments of the invention described in this patent application can be combined in any possible combination of these embodiments, and each embodiment can individually form the subject-matter of a divisional patent application.

BRIEF DESCRIPTION OF THE FIGURES

The invention will now be elucidated with reference to the following figures, without however being limited thereto. In the figures:

Figure 1 schematically shows a front view of method steps according to an embodiment of the invention:

Figure 2 schematically shows a front view of mounting holes of a rotor and important parameters used in determining the position of the CoG of the rotor in accordance with an embodiment of the invention;

Figure 3A schematically shows a perspective view of a suspension of a rotor using an air bearing in accordance with an embodiment of the invention; and

Figure 3B schematically shows a front view of a dial plate used in accordance with an embodiment of the invention.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Referring to figure 1, a front view of two method steps according to an embodiment of the invention is shown. The embodiment shown aims at determining an offset E of the center of gravity (CoG) of an elongated body which is a rotor 1, comprising two rotor blades (11, 12) that are connected to a centrally disposed mounting plate 10. As shown in more detail in figure 2, the offset E of the center of gravity (CoG) is determined with respect to a geometrical center 13 in a plane 14 of the rotor 1. The plane 14 is defined as a middle plane of the rotor 1(which corresponds to the plane of the figure), and represents a plane of symmetry of the rotor 1. Each rotor blade (11, 12) has a leading edge (11a, 12a) and a trailing edged (11b, 12b). The geometrical center 13 of the rotor is located in the center of a central hole 15, which is used for attachment to a rotating shaft (not shown) of a helicopter for instance. The mounting plate 10 is thereto provided with a number of holes (10a,..., 10d) through which a screw connection may be provided for attachment to a corresponding mounting plate of the helicopter.

The embodiment of the method uses the holes (10a, ..., 10d) in providing a first rotation axis and a second rotation axis for a free-hanging rotor 1. Indeed, a first step of the method involves providing a first rotation axis by inserting a rod 16 (see figure 3A) in one of the holes (10a, ..., 10d) of the mounting plates, for instance hole 10a, and balancing the rotor 1 on the first rotation axis into an equilibrated first balanced position, as shown on the left of figure 1. A first rotation angle al with respect to a vertical direction is then measured in the plane 14 of the rotor 1 in the equilibrated first position. In a second step of the method, a second rotation axis is provided by inserting the rod (or another rod) in another one of the holes (104, ..., 10d) of the mounting plates, for instance hole 10b, and balancing the rotor 1 on the second rotation axis into an equilibrated second balanced position, as shown on the right of figure 1. A second rotation angle a2 is then measured in the plane 14 of the rotor 1 in the equilibrated second position.

It should be noted that the first and second rotation axes (in the example defined around the holes 10a and 10b respectively) are provided at a distance A to each other and also both perpendicular to the plane 14. The first and second rotation axes (around holes 10a and 10b in the example) are provided at offset positions to the geometrical center 13 of the rotor 1.

The rod 16 may be suspended on a support plate 17 for instance to hold the rotor 1. A useful embodiment comprises inserting the rod 16, for instance a machined shaft, in one of the mounting holes (10a, ..., 10d) and suspend the rod 16 in the support plate 17 using an air bearing 18. Once the air bearing 18 is supplied with sufficient pressured gas, the rotor 1 may easily find its equilibrated balance. One skilled in the art is able to correctly adjust the pressure of the gas of the bearing by routine experimentation. Due to the nature of the setup according to this embodiment, friction or hysteresis is eliminated from the measurement, such that the exact location of the CoG may be measured even more accurately. It should be noted that the use of other bearings is also possible. Also, the suspension of the rod 16 in the support 17 may be a rigid suspension and the insertion of the rod 16 in one of the holes (10a, ..., 10d) of the rotor 1 may comprise a bearing, preferably an air bearing. It is also possible to carry out the method such that the insertion of the rod 16 in one of the holes (10a, ..., 10d) of the rotor 1 comprises a bearing, preferably an air bearing, and the suspension of the rod 16 in the support 17 also comprises a bearing, preferably the air bearing 18.

The angles of rotation (al, a2) of the rotor 1 may be measured accurately from a dial plate or compass rose 19 that is hung vertically behind the rotor 1. The vertical direction corresponds to an angle of rotation (al, a2) of zero. The angular markings on the dial plate 19 may for instance be provided every 0.1°, in particular in the expected rotation angle ranges (19a, 19b), but other accuracy readings also possible.

Alternatively, the angles of rotation (al, a2) of the rotor 1 may be measured by measuring a horizontal distance between the two tips of the rotor 1, for instance by using plumb lines at each tip.

The position of the CoG may be determined by using trigonometry, i.e. by geometrical triangulation using the measured rotation angles (al, a2). It can easily be shown (see figure 2) that the offset E of the CoG with respect to the geometrical center 15 of the rotor | may be calculated as follows:

E = [tan{02)/(tan (al) + tan (a2))] * A - A/2 wherein the distance between the first and second rotation axes is A, the measured first rotation angle is al, and the measured second rotation angle is a2. The rotation angles (al, a2) are both positive numbers, i.e. the absolute value of the measured rotation angles (al, 02) is used in the formula.

According to the invention, the center of gravity (CoG) of an elongated body may be determined by using two off-center hinge points and finding the two angles on which the elongated body will balance itself. When the elongated body finds a natural balance, the CoG will be located directly below the hinge point. In this balanced situation the elongated body will be suspended at an angle ((a1, 02) with the vertical direction 20.

The invention is not limited to the above given examples and variations thereto may be envisaged within the scope of the appended claims.

Claims

CONCLUSIONS

L. Method for determining an offset of the center of gravity (CoG) of an elongate body from a geometric center in a plane of the elongate body, the method comprising: providing a first axis of rotation and a second rotation axis at a distance from the first axis of rotation and both perpendicular to the plane and at positions offset from the geometric center of the elongate body; - balancing the elongate body on the first axis of rotation until a first equilibrium position is reached and then balancing the elongate body on the second axis of rotation until a second equilibrium position is reached; - measuring a first and second angle of rotation in the plane of the elongate body in the first and second equilibrium positions respectively; and - determining the in-plane offset of the CoG by geometric triangulation using the measured rotation angles.

The method of claim 1, wherein the distance between the first and second axes of rotation is λ, the first angle of rotation is α1, the second angle of rotation α2 is 1s. and the geometric triangulation yields the following formula: E = [tan(c2)/(tan (a1) + tan (a2))] * A - A/2 where E is the offset of the CoG from the geometric center .

A method according to claim 1 or 2, wherein the plane of the elongate body is a plane of symmetry.

A method according to any one of the preceding claims, wherein the provision of the first axis of rotation and/or the second axis of rotation is performed by inserting a rod into a hole of the elongate body, the hole being provided in at least one of the offset positions.

The method of claim 4, wherein the first axis of rotation and the second axis of rotation are both provided by inserting a bar into a hole of the elongate body, the hole being provided at the offset positions

A method according to claim 4 or 5, wherein the at least one bar is suspended in a support.

A method according to claim 6, wherein the insertion of the rod into the hole of the elongate body is a rigid insert and the suspension of the rod in the support comprises a bearing, preferably an air bearing.

A method according to any one of the preceding claims, wherein the first axis of rotation and the second axis of rotation are provided through a suspension hole of the elongate body.

A method according to any one of the preceding claims, wherein the elongate body is substantially made of a fiber-reinforced composite.

A method according to any one of the preceding claims. wherein the elongate body comprises a rotor blade or a propeller blade, or a rotor comprising at least two of the rotor blades or the propeller blades.