Method for determining a torsional moment

Abstract

A method for determining a torsional moment of a wheel set shaft of a rail vehicle during the operation of the rail vehicle is used for a wheel set shaft having two wheels secured to ends of the shaft for rolling on two rails. A model is used to calculate a torsional moment which acts on the wheel set shaft, and the model is based on a torsional vibration of the wheel set shaft at a specified slip action point. The torsional moment acting on the wheel set shaft is ascertained based on the energy of the torsional vibration of the wheel set shaft at the slip action point and based on a damping energy which acts on the torsional vibration of the wheel set shaft.

Claims

1. A method for determining a torsional moment of a wheel set shaft of a rail vehicle during operation of the rail vehicle, the method comprising the following steps: providing a wheel set shaft having two ends and two wheels each being secured to a respective one of the ends of the shaft for rolling on a respective one of two rails; using a model to calculate a torsional moment acting on the wheel set shaft; basing the model on a torsional vibration of the wheel set shaft at a specified slip action point; ascertaining the torsional moment acting on the wheel set shaft based on an energy of the torsional vibration of the wheel set shaft at a slip action point and based on a damping energy acting on the wheel set shaft during the torsional vibration; using a model for the energy of the torsional vibration of the wheel set shaft at the slip action point and using a model for the damping energy, both models depending on an amplitude of a vibration angle of the torsional vibration; starting from a starting value for both models, increasing the amplitude of the vibration angle until both models exhibit an equal value for energy at an intersection point; calculating, with a computer, a torsional moment acting on the wheel set shaft based on the amplitude of the torsional vibration at the intersection point and as a function of a specified torsional rigidity of the shaft; and displaying, on a display connected to the computer, at least one of: the calculated torsional moment; dimensions for a newly designed wheel set shaft that will bear the calculated torsional moment without damage; or whether a specified wheel set shaft can bear the calculated torsional moment without damage.

2. The method according to claim 1, which further comprises determining the torsional moment for at least one of a positive or negative acceleration of the rail vehicle, and using the specified slip action point for at least one of the positive or negative acceleration as an operating state.

3. The method according to claim 1, which further comprises subdividing the model for the energy of the torsional vibration into at least three ranges having different characteristics of a friction coefficient between the wheel and the rail.

4. The method according to claim 3, wherein the friction coefficients depend on a slip of the wheels.

5. The method according to claim 3, which further comprises calculating the energy of the torsional vibration during a torsional vibration at the slip action point for each of the at least three ranges, and adding three energy components together to give an energy of the torsional vibration.

6. The method according to claim 1, which further comprises calculating the energy of the torsional vibration as a function of a specified travelling speed range of the rail vehicle.

7. The method according to claim 6, which further comprises using a maximum energy of the torsional vibration for ascertaining a maximum torsional moment of rotation of the wheel set shaft for an intersection point.

8. The method according to claim 1, which further comprises calculating the energy of the torsional vibration as a function of a specified angular velocity range.

9. The method according to claim 8, which further comprises using a maximum energy for ascertaining a maximum torsional moment of rotation of the wheel set shaft.

10. The method according to claim 1, which further comprises using a sine wave to ascertain a vibration angle of a torsion of the wheel set shaft.

11. The method according to claim 1, which further comprises taking a slip during a torsional vibration into consideration as a function of an angular velocity of the torsional vibration.

12. The method according to claim 1, which further comprises using a respective mechanical connecting structure to connect each wheel to the shaft, and dimensioning at least one of the shaft or the connecting structure so that the wheel set shaft bears the calculated torsional moment without damage.

13. The method according to claim 1, which further comprises using a respective mechanical connecting structure to connect each wheel to the shaft, capturing at least one of a thickness of the shaft or a strength parameter of the connecting structure to check the wheel set shaft, and performing a check with reference to at least one of the thickness of the shaft or the strength parameter to determine whether the wheel set shaft is suitable for bearing the calculated torsional moment without damage.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

(1) The properties, features and advantages of the invention as described above, and the manner in which these are achieved, become clearer and easier to understand in the context of the following description of the exemplary embodiments, these being explained in greater detail with reference to the drawings, in which:

(2) FIG. 1 shows a schematic illustration of a model for an single mass vibrator,

(3) FIG. 2 shows a schematic illustration of a diagram for a friction coefficient as a function of the slip or the rotational wheel speed,

(4) FIG. 3 shows a diagram containing a schematic illustration of a torsional vibration at a slip action point,

(5) FIG. 4 shows a diagram containing a schematic illustration of a temporal profile of a vibration angle and a vibration angular velocity during a torsional vibration of a wheel set shaft at the slip action point,

(6) FIG. 5 shows a schematic illustration of a profile of a vibration energy and an absorption energy according to a numerical calculation,

(7) FIG. 6 shows a schematic illustration of a program sequence for performing the method, and

(8) FIG. 7 shows a device for performing the method.

DESCRIPTION OF THE INVENTION

(9) In the context of a design process for dimensioning wheel set shafts or in the context of a checking method for checking wheel set shafts, it important to be able to realistically estimate a magnitude of possible dynamic shaft torsional moments, i.e. torsional moments acting on a wheel set shaft of a rail vehicle, caused by drive train vibrations. In the case of rail vehicles, self-excited torsional vibrations in the wheel set shaft can occur during a driving movement, i.e. when accelerating or braking under unfavorable frictional connection conditions between wheels of the wheel set shaft and rails on which the wheels run. In this case, a form of vibration occurs in which the two wheels vibrate in opposite phase to each other in the torsional resonance frequency of the drive train. As a result of the slight damping in the wheel set shaft, high torsional moments can occur in this way.

(10) This vibration is also referred to as chatter vibration or rolling vibration. Damping equalization of the torsional vibration is produced by the negative increase of the frictional connection characteristic in the macro slip range between the wheel and the rail. The degree of the damping depends on the steepness of the negative increase of the frictional connection characteristic at the slip action point. With sufficient damping equalization, the torsional vibration becomes unstable. A limit cycle appears in the frictional connection diagram. In addition to the damping energy, a maximum amplitude for small slips is limited by a stable branch of the frictional connection characteristic, and a maximum amplitude for large slips is also or exclusively limited by a frictional connection characteristic which becomes flatter. The maximum amplitude of the torsional vibration of the limit cycle is determined from an energy balance over the limit cycle.

(11) The analytical description of the dynamic torsional moment is derived from the kinematic relationship between the slip amplitude and the opposite-phase vibration of the wheels.

(12) The analytical description of the dynamic torsional moment can be derived from the kinematic relationship between the slip amplitude and the opposite-phase vibration of the wheel disks, the straight line: the slip action point gives v.sub.chatter=s.Math.v the SIN vibration at frequency f and v.sub.chatter give a maximum torsional angle .sub.chatter .sub.chatter=v.sub.chatter/(2r.sub.0f) since wheel set shaft damping is low, the maximum torsional M.sub.t=c .sub.wheel,max moment is given as c torsional rigidity of the shaft or the analytical connection (straight line) as M.sub.t=c v.sub.chatter/(2r.sub.0f).

(13) The relationship defined by the straight line is usually used to estimate dynamic torsional moments in the design process.

(14) The proposed analytical method for ascertaining the dynamic torsional moment in wheelBset shafts applies the hypothesis that the dynamic torsional moment can be derived from a limit cycle at the respective slip or slide speed action point. The maximum amplitude of the limit cycle is determined from the energy balance over a limit cycle.

(15) Accordingly, for any frictional connection characteristics, the analytical method calculates the balance over a vibration of the elastic energy in the wheel set shaft and the energy which is produced by the force and the running speed in the wheel/rail contact. The following steps are required for this purpose:

(16) FIG. 1 shows a schematic illustration of a model for a vibration system of the wheel set shaft, wherein J designates the moment of inertia of the wheels, C.sub.w the torsional rigidity of the shaft, and d.sub.w the torsional damping of the wheel set shaft. The moment of inertia, the torsional rigidity and the torsional damping are specified or derived from mechanical parameters including a slip control parameter of the rail vehicle. The slip controller of the rail vehicle is designed such that during acceleration or braking of the rail vehicle, the running speed of the wheels is controlled at a specified slip action point. The slip action point s.sub.0 is determined in this way.

(17) The vibration angle and the vibration angular velocity {dot over ()} of the wheel set can be represented by sine and cosine functions:
=A.Math.sin(t),{dot over ()}=A.Math.Q cos(t),(1)
where =2f, f being the chatter frequency, and A is the amplitude of the vibration angle .

(18) The chatter frequency f and therefore the angular frequency are calculated theoretically or ascertained experimentally.

(19) FIG. 2 shows a diagram in which the friction coefficient is plotted over the slip s and the rotational wheel speed w. For simpler illustration, the characteristic of the friction coefficient illustrated in FIG. 2 is subdivided into three ranges I, II, III. Depending on the model used, it is also possible to define a plurality of straight lines for more than three ranges or fewer than three ranges for the approximation of the friction coefficient characteristic.

(20) In a first range I between 0 and s.sub.m, the friction coefficient has a positive first rate of increase k.sub.1 (d/ds=k.sub.1). In a second range II between s.sub.m and s.sub.1, the friction coefficient has a negative second rate of increase k.sub.2. In the range where the slip is greater than s.sub.1, the friction coefficient has a negative third rate of increase d/ds=k.sub.3.

(21) In formulaic format, the diagram is as follows:

(22) $\begin{array}{cc}\left(s\right)=\{\begin{array}{cc}{}_0+k_1.Math.\left(s-s_m\right)+k_2.Math.\left(s_m-s_0\right),& 0s<s_m\\ {}_0+k_2.Math.\left(s-s_0\right),& s_{m}s<s_1\\ u_0+k_3.Math.\left(s-s_1\right)+k_2.Math.\left(s_1-s_0\right),& s_{1}s<\end{array}& \left(2\right)\end{array}$
Where s.sub.0 is the slip action point (reference slip of the slip controller) and .sub.0 is the friction coefficient at s.sub.0.

(23) Using slip definition,

(24) $s=\frac{{}_R.Math.R-v_0}{v_0}$
the rotational wheel speeds can be converted at all vertices in the Illustration 3.2:

(25) $\begin{array}{cc}{}_m=\frac{\left(s_m+1\right)v_0}{R};{}_0=\frac{\left(s_0+1\right)v_0}{R};{}_1=\frac{\left(s_1+1\right)v_0}{R}& \left(3\right)\end{array}$

(26) In (3), v.sub.0 is the travelling speed, R is the radius of the wheel and is the rotational wheel speed.

(27) The dynamic slip and the rotation moment at the wheel can be described as a function of the (clatter) vibration speed.

(28) If a wheel set clatters, the (dynamic) slip vibrates at the action point s.sub.0. The dynamic slip vibration s can be represented as a function of the vibration speed {dot over ()}:

(29) $\begin{array}{cc}s\left(\stackrel{.}{}\right)=\frac{\left({}_0+\stackrel{.}{}\right).Math.R-v_0}{v_0}=s_0+\frac{\stackrel{.}{}.Math.R}{v_0}& \left(4\right)\end{array}$

(30) If only the clatter vibration is examined, the dynamic rotation moment at the wheel MRS, as generated by tangential force Fx (=.Math.Q with the wheel contact force Q), is derived from the equation (2):

(31) $\begin{array}{cc}{M}_{\mathrm{RS}}\left(s\right)=Q.Math.R.Math.\{\begin{array}{cc}{k}_1.Math.\left(s-s_m\right)+k_2.Math.\left(s_m-s_0\right),& 0s<s_m\\ k_2.Math.\left(s-s_0\right),& s_{m}s<s_1\\ k_3.Math.\left(s-s_1\right)+k_2.Math.\left(s_1-s_0\right),& s_{1}s<\end{array}& \left(5\right)\end{array}$

(32) If the equation (4) is inserted into the equation (5), the dynamic rotation moment at the wheel can likewise be expressed as a function of the vibration speed {dot over ()}:

(33) $\begin{array}{cc}{M}_{\mathrm{RS}}\left(s,\stackrel{.}{}\right)=Q.Math.R.Math.\{\begin{array}{cc}{k}_1.Math.\frac{R.Math.\stackrel{.}{}}{v_0}+\left(s_0-s_m\right).Math.\left(k_1-k_2\right),& 0s<s_m\\ k_2.Math.\frac{R.Math.\stackrel{.}{}}{v_0},& s_{m}s<s_1\\ k_3.Math.\frac{R.Math.\stackrel{.}{\stackrel{.}{}}}{v_0}+\left(s_1-s_0\right).Math.\left(k_2-k_3\right),& s_{1}s<\end{array}& \left(6\right)\end{array}$

(34) Operational signs and time points of the vibration speed can be described as a function of the frictional connection profile.

(35) By reformatting the equation (4), the vibration speed {dot over ()} can be represented as a function of the slip s:

(36) $\begin{array}{cc}\stackrel{.}{}=\frac{\left(s-s_0\right).Math.v_0}{R}& \left(7\right)\end{array}$

(37) The equation (7) can be used to ascertain the operational sign of the vibration speed in all slip ranges of the frictional connection profile.

(38) Starting from the slip action point s.sub.0, the time points at which the slip vibration respectively enters or leaves the first, second and third range are illustrated by means of FIG. 3. FIG. 3 shows a schematic illustration of the profile of the friction coefficient over the slip s and a torsional vibration in a limit cycle as a closed curve represented by a broken line. At the zeroth time point to, the wheel set shaft is situated at the slip action point s.sub.0. Starting from the zeroth time point t0, the slip varies in the direction of smaller values during the torsional vibration, reaching the value s.sub.m at the first time point t1. After this, the slip initially becomes even smaller until it reaches a minimum value, and then increases again. At a second time point t2, the slip reaches the value s.sub.m again. Starting from the second time point t2, the slip increases further, reaching the value s.sub.1 at a third time point t3. During the further course of the vibration, the slip increases further until it reaches a maximum value, after which it decreases again. At a subsequent fourth time point t4, the slip reaches the value s.sub.1 again. The slip action point s.sub.0 is finally reached again at a fifth time point t5.

(39) The value range of the angular velocity 4 is negative in the first range I, changes in the second range II from a negative value to a positive value, and has a positive value in the third range III.

(40) TABLE-US-00001 In the In the range I In the range II range III Value range of $\frac{-s_0{v}_0}{R}\stackrel{.}{}<{}_m-{}_0$ .sub.m .sub.0 {dot over ()} < .sub.1 .sub.0 .sub.1 .sub.0 {dot over ()} < the {dot over ()} Opera- Negative From negative Positive tional sign to positive of the {dot over ()}

(41) FIG. 4 shows a schematic illustration of the vibration angle and the vibration angular velocity {dot over ()} for a vibration at the slip action point s.sub.0. The vibration angle can be assumed as a sine wave with the amplitude A and the angular frequency . The vibration angular velocity {dot over ()} can be assumed with the amplitude A multiplied by the angular frequency multiplied by a cosine with the angular frequency .

(42) On the basis of the assumptions for the vibration angle and the vibration angular velocity, the time points can be calculated for the zeroth time point t0, the first time point t1, the second time point t2, the third time point t3, the fourth time point t4 and the fifth time point t5 according to the following table:

(43) Temporal profile of the vibration speed in a chatter vibration cycle

(44) TABLE-US-00002 Time point t0 t1 t2 t3 t4 t5 Time 0 $\frac{1}{}{\sin }^{-1}\left(\frac{{}_0-{}_m}{A}\right)$ 0$\frac{}{}-t1$ $\frac{}{}+\frac{1}{}{\sin }^{-1}\left(\frac{{}_0-{}_m}{A}\right)$ $\frac{3}{}-t3$ $\frac{2}{}$

(45) On the basis of the model used with the three ranges for the friction coefficient , the energy balance for a torsional vibration (clatter vibration) of the wheel set shaft for a vibration cycle can be calculated according to the following formulas:

(46) Energy Balance of the Clatter Vibration in a Vibration Cycle

(47) The vibration energy of the slip vibration E.sub. in a vibration cycle can be calculated in all three ranges of the frictional connection profile.

(48) a) In the range I

(49) $\begin{array}{cc}\begin{array}{c}{E}_1=Q.Math.R.Math.{}_{t1}^{t2}\left(k_1.Math.\frac{R.Math.\stackrel{.}{}}{v0}+c_1\right).Math.\stackrel{.}{}.Math.\mathrm{dt}\\ =A.Math..Math.c_1.Math.Q.Math.R.Math.{[\sin \left(t\right].Math.}_{t1}^{t2}+\\ {\frac{Q.Math.R^2.Math.k_1}{v_0}{A}^2.Math.{}^2\left(\frac{t}{2}+\frac{1}{4}\sin \left(2t\right)\right).Math.}_{t_1}^{t_2}\end{array}& \left(8\right)\\ \mathrm{where}{c}_1=\left(s_0-s_m\right).Math.\left(k_1-k_2\right)& \end{array}$
b) In the range II

(50) $\begin{array}{cc}\begin{array}{c}{E}_2=Q.Math.R.Math.{}_{t0,t2,t4}^{t1,t3,t5}\left(k_2.Math.\frac{R.Math.\stackrel{.}{}}{v0}\right).Math.\stackrel{.}{}.Math.\mathrm{dt}\\ {=\frac{Q.Math.R^2.Math.k_2}{v_0}{A}^2.Math.{}^2\left(\frac{t}{2}+\frac{1}{4}\sin \left(2t\right)\right).Math.}_{t0,t2,t4}^{t1,t3,t5}\end{array}& \left(9\right)\end{array}$
c) In the range III

(51) $\begin{array}{cc}\begin{array}{c}{E}_3=Q.Math.R.Math.{}_{t3}^{t4}\left(k_3.Math.\frac{R.Math.\stackrel{.}{}}{v0}+d_1\right).Math.\stackrel{.}{}.Math.\mathrm{dt}\\ =A.Math..Math.d_1.Math.Q.Math.R.Math.{[\sin \left(t\right].Math.}_{t3}^{t4}+\frac{Q.Math.R^2.Math.k_3}{v_0}{A}^2.Math.\\ {{}^2\left(\frac{t}{2}+\frac{1}{4}\sin \left(2t\right)\right).Math.}_{t_3}^{t_4}\end{array}& \left(10\right)\\ \mathrm{where}{d}_1=\left(s_1-s_0\right).Math.\left(k_2-k_3\right)& \end{array}$

(52) The total vibration energy is then derived from the slip vibration
E.sub.=E.sub.1+E.sub.2+E.sub.3(11)

(53) The absorbed vibration energy due to the resulting damping can be calculated easily:
E.sub.RS=d.sub.w.Math.A.sup.2.Math..Math.(12)

(54) Finally, the energy component E.sub. and E.sub.RS as a function of the amplitude of the vibration angle can be calculated using the equations (8) to (12).

(55) Using a numerical method, it is possible to calculate a maximum value for the torsional moment during a clatter vibration at the slip action point S.sub.0 by equating the formula (11) and the formula (12). By progressively increasing the amplitude A, for example, it is possible to increase the total vibration energy and the absorbed vibration energy until the total vibration energy according to formula (11) and the absorbed energy according to formula (12) have equal values.

(56) FIG. 5 shows an example of a corresponding numerical calculation. In this case, starting from an amplitude A of the vibration angle having the value 0 for the angular vibration at the slip action point during a clatter vibration, the value of the amplitude A of the vibration angle was progressively numerically increased for both the total vibration energy E.sub. and the absorbed damping energy E.sub.RS until, at an amplitude A of 1.95 for the vibration angle, the total vibration energy and the absorbed damping energy are both equal. The amplitude A of the vibration angle can start at an angle of 0.5 rad, for example, and the value of the amplitude A can be increased in steps of 0.1 rad.

(57) A correspondence of the total vibration energy and the absorbed vibration energy can also be recognized if the total vibration energy and the absorbed vibration energy differ by less than 5%, in particular by less than 2%.

(58) The value of the maximum vibration angle is therefore situated at this intersection point.

(59) A maximum torsional moment M.sub.max for the clatter vibration at the slip action point can be calculated as a function of the maximum vibration angle and the maximum amplitude A.sub.max of the vibration angle according to the following formula:
M.sub.max=A.sub.max.Math.c.sub.w,
where A.sub.max designates the maximum amplitude at the intersection point and c.sub.w designates the torsional rigidity of the wheel set shaft.

(60) FIG. 6 shows a schematic illustration of a program sequence for performing the described method. At a program start point 100, the computing unit reads in the chatter frequency f, the torsional rigidity c.sub.w, the torsional damping d.sub.w, the values of the friction coefficient for at least one and in particular three different ranges as a function of the slip s or the rotational wheel speed , the radius R of a wheel of the wheel set shaft, the travelling speed v0, and a starting value for the amplitude A of the vibration angle from a memory.

(61) At a program point 110 following thereupon, the formulas 8-11 described above are used to calculate the sum of the slip vibration energy E.sub.=E.sub.1+E.sub.2+E.sub.3 for a starting value of an amplitude A of the vibration angle. At a program point 120, the absorbed vibration energy due to the resulting damping is then calculated according to the formula (12): E.sub.RS=d.sub.WA.sup.2.Math..Math.. The starting value for the amplitude A of the vibration angle is likewise used in this case.

(62) At program point 130, the value of the total vibration energy E.sub. and the value of the absorbed damping energy E.sub.RS are then compared with each other. If the total vibration energy and the absorbed damping energy are equal, the program branches to program point 140.

(63) If the result of the comparison at program point 130 indicates that the sum of the slip vibration energy E.sub. is greater than the absorbed damping energy E.sub.RS, the program branches to program point 150. At program point 150, the value for the amplitude A of the vibration angle is increased by a specified value. The program then branches back to program point 110.

(64) The program steps 110, 120, 130 and 150 are performed until the total vibration energy and the absorbed damping energy are equal and, on the basis of the existing maximum amplitude A.sub.max of the vibration angle, a maximum clatter moment M.sub.max is calculated in program step 140 using the following formula:
M.sub.max=A.sub.max.Math.c.sub.w.
A.sub.max corresponds to the amplitude of the vibration angle at which the total vibration energy and the absorbed vibration energy are equal.

(65) Depending on the embodiment variant, it is then possible to branch to the end at program point 180.

(66) In a further embodiment variant, a further program point 160 can optionally be performed after program point 140. At the program point 160, on the basis of the maximum clatter moment calculated at program point 140, a newly designed wheel set shaft is so dimensioned that the shaft and/or the connecting structure between the shaft and the wheel are made in such a way that the wheel set shaft bears the calculated maximum clatter moment without any damage. Depending on the embodiment variant, it is then possible to branch to the end at program point 180.

(67) In a further embodiment, instead of or in addition to the program point 160, a further program point 170 can optionally be performed. The further program point 170 consists in checking with reference to specified values for a wheel set shaft, e.g. the thickness of the shaft, the material of the shaft, the type of connecting structure and in particular at least a strength parameter of the connecting structure, whether a specified wheel set shaft bears the calculated maximum torsional moment without being damaged. Corresponding limit values are defined for this purpose. For example, it is assumed that the wheel set shaft bears the calculated maximum torsional moment without damage if the wheel set shaft is so dimensioned as to withstand at least 120% of the maximum torsional moment without damage.

(68) Those values for the wheel set shaft which are required for the purpose of checking are either captured with reference to a specified wheel set shaft or checked with reference to stored values. In this case, a check is performed in respect of e.g. the thickness of the shaft, the material of the shaft, or a strength parameter of a connecting structure between the shaft and the wheel, in order to determine whether the wheel set shaft is suitable for bearing the calculated torsional moment without damage. Corresponding limit values are defined for this purpose. For example, it is assumed that the wheel set shaft bears the calculated maximum torsional moment without damage if the wheel set shaft is so dimensioned as to withstand at least 120% of the maximum torsional moment without damage.

(69) FIG. 7 shows a schematic illustration of a device for performing the method in which the energy of the torsional vibration is calculated as a function of a specified travelling speed range of the rail vehicle, and wherein in particular a maximum energy of the torsional vibration is used for the purpose of ascertaining a maximum torsional moment of rotation of the wheel set shaft for an intersection point. The device has a computing unit 200 which is connected to a memory 210. The computing unit 200 can also have a sensor unit 220 by means of which it is possible to capture the thickness of a shaft 1 of a wheel set shaft 2 and/or a strength parameter of a connecting structure between the shaft 1 and a wheel 4 of the wheel set shaft 2 of a rail vehicle 5. The wheel set shaft 2 rolls with one wheel 4 on each rail 6. The computing unit 200 can also have an output unit 230 by means of which a result of the method steps of the program points 140, 160 or 170 are displayed. Furthermore, the display 230 can be designed to show a diagram as per FIG. 5, in which the profile of the total vibration energy E and the profile of the absorbed vibration energy ERS are displayed in accordance with the program points 110 and 120.

(70) Although the invention is illustrated and described in detail with reference to the preferred exemplary embodiment, the invention is not restricted by the examples disclosed herein, and other variations may be derived therefrom by a person skilled in the art without thereby departing from the scope of the invention.