FIELD OF THE INVENTION

The present invention relates to a bearing arrangement, a wind energy converter, a method for manufacturing a wind energy converter and an apparatus for accomplishing the method.

BACKGROUND ART

Wind energy converters (hereinafter "WECs") convert kinetic energy from wind into mechanical energy. Fig. 1 shows, in a section view, an example of a WEC known in the art.

The WEC 100 comprises a rotor 102 having a number of blades 104 connected to a hub 106. The rotor 102 is connected via a hollow shaft 108 to a generator 110 to produce electrical power. The hollow shaft 108 is supported inside a bearing housing 112 using a bearing arrangement 113. The bearing arrangement 113 comprises two taper roller bearings 116 and 118. The generator 110 is arranged inside a nacelle 120 and comprises a stator 122 and a rotor 124. The stator 122 is fixedly connected to the nacelle 120 and the rotor 124 is connected to the hollow shaft 108.

An air gap 126 is formed between the rotor 124 and the stator 122. The size of the air gap 126 is largely determined by the bending of the hollow shaft 108 during operation of the WEC 100. This bending depends on a number of factors, like the weight of the rotors 102 and 124 and the length of the shaft 108. Fig. 1 shows, in an exaggerated manner, the rotor 124 arranged askew with respect to the stator 120 as a result of the bending of the hollow shaft 108. Thus, the air gap 126 needs to be sized to prevent collision of the rotor 124 and stator 122.

To a large extent, the air gap 126 determines the efficiency of the EC 100: the smaller the air gap 126, the more efficient the WEC 100. Thus, it is desirable to make the air gap 126 small.

SUMMARY OF THE INVENTION

The present invention provides a bearing arrangement comprising: a first bearing having a first outer and inner ring, wherein a plurality of tapered rollers rides between an inner surface of the first outer ring and an outer surface of the first inner ring ; and a second bearing having a second outer and inner ring, wherein a plurality of tapered rollers rides between an inner surface of the second outer ring and an outer surface of the second inner ring; wherein the first and second bearing are arranged coaxially on a centerline; and wherein a first pressure line normal to the inner surface of the first outer ring intersects a line normal to the centerline at a first angle and a second pressure line normal to the inner surface of the second outer ring intersects a line normal to the centerline at a second angle different from the first angle .

Further, the present invention provides a wind energy converter comprising the bearing arrangement as described above.

Even further, the present invention provides a method for manufacturing a wind energy converter comprising: a rotor; a generator or a gearbox; a shaft; and a bearing housing;

wherein the rotor and the generator or gearbox are connected to the shaft and the bearing arrangement supports the shaft inside the bearing housing between the rotor and the generator or gearbox, the method comprising the steps of: providing a desired air gap inside the generator or gear clearance inside the gearbox; adjusting, in a simulation tool, the difference between the first and the second angle to a value unequal to 0 degrees; using the simulation tool for simulating the resulting air gap in the generator or gear clearance inside the gearbox; repeat the steps of adjusting and simulating until the desired air gap is obtained; machining the first outer ring with the first angle and the second outer ring with the second angle.

Even further, the present invention provides an apparatus for accomplishing the method described above, said apparatus comprising: an input device for providing a desired air gap inside the generator or gear clearance inside the gearbox; a simulation tool being configured such that the difference between the first and the second angle is adjusted to a value unequal to 0 degrees, wherein the resulting air gap in the generator or gear clearance inside the gearbox can be simulated; and a machine tool for machining the first outer ring with the first angle and the second outer ring with the second angle .

By making the first and second angle different, a number of factors, e. g. the bending of the shaft of the WEC, is influenced so as to minimize the air gap inside the generator or optimize the gear clearance inside the gearbox, thus increasing efficiency and reliability. Another factor being influenced is a radial and axial offset of the shaft. When the axis of a respective tapered roller of the first or second bearing is almost aligned parallel with the centerline of said bearings, the radial stiffness of said bearing is high and thus the radial offset of the shaft supported by said bearing is small. Also, when the axis of a respective tapered roller of the first or second bearing is almost normal parallel to the centerline of said bearings, the axial stiffness of said bearing is high and thus an axial offset of the shaft supported by the bearing is small. However, the axial offset moves the tapered rollers with respect to the inner and outer ring of said bearing, thus again influencing the radial offset.

The dependent claims describe advantageous embodiments of the present invention.

Presently, "axial" and "radial" always refer to the centerline of the first and second bearings.

The "inner surface" of the first and second outer ring refers to a surface facing inwards, i.e. towards the centerline.

Likewise, the "outer surface" of the first and second inner ring refers to a surface facing outwards, i.e. away from the centerline .

According to an embodiment of the bearing arrangement of the present invention the difference between the first and second angle is between 0.1 and 30 degrees, preferably between 2 and 15 degrees.

According to an embodiment of the bearing arrangement of the present invention the first and second outer ring or the first and second inner ring are made of a single piece. This embodiment minimizes space requirements of the first and second bearing in the axial direction.

According to an embodiment of the bearing arrangement of the present invention the first and second outer ring and the first and second inner ring are spaced apart from each other, respectively. This embodiment allows the shaft to be supported at two locations being spaced a far distance apart, thus reducing bending of the shaft in many instances.

According to an embodiment of the wind energy converter of the present invention the wind energy converter further comprises: a rotor; a generator or a gearbox; a shaft; and a housing;

wherein the rotor and the generator or gearbox are connected to the shaft and the bearing arrangement supports the shaft inside the housing between the rotor and the generator or gearbox .

According to an embodiment of the wind energy converter of the present invention the difference between the first and second angle is adjusted to a value between 0.1 and 25 degrees, preferably between 2 and 10 degrees. This embodiment has been found to be specifically suitable for high axial and low radial loads acting on the shaft.

According to an embodiment of the wind energy converter of the present invention the first bearing is arranged far from and the second bearing is arranged close to the generator or gearbox and the first angle lies between 15 and 40 degrees and the second angle between 25 and 45 degrees. This embodiment has been found to be specifically suitable for low axial and high radial loads acting on the shaft, "far from" and "close to" is to be understood such that the first bearing is arranged further away from the generator or gearbox than the second bearing .

According to an embodiment of the wind energy converter of the present invention the first bearing is arranged far from and the second bearing is arranged close to the generator or gear- box and an intersection of the second pressure line with an axis of the shaft lies inside the generator or gearbox. This embodiment has been found to provide a particularly small air gap.

According to an embodiment of the method of the present invention the difference between the first and second angle is adjusted to a value between 0.1 and 30 degrees, preferably between 2 and 15 degrees. The inventors discovered that this choice of the difference between the first and the second angle is particularly useful.

According to an embodiment of the method of the present invention, the difference between the first and second angle is determined as a function of an axial load, radial load, axial elastic deformation of the first and/or second bearing, radial elastic deformation of the first and/or second bearing and/or a bending deflection. The axial and radial "elastic deformation" of the bearing correspond to the axial and radial offset of the shaft mentioned above.

According to an embodiment of the method of the present invention, the difference between the first and second angle is determined so as to provide for a) the least radial elastic deformation in the second bearing, wherein the first bearing is arranged far from and the second bearing is arranged close to the generator or gearbox, b) the least radial load in the second bearing, wherein the first bearing is arranged far from and the second bearing is arranged close to the generator or gearbox, or c) the least bending deflection in the shaft in order to achieve the desired air gap. The criteria a), b) and c) have proven to be particularly useful when trying to obtain a small air gap. BRIEF DESCRIPTION OF THE DRAWINGS

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

Fig. 1 shows a section view of a wind energy converter known in the art;

Fig. 2 shows a section view of a wind energy converter according to a first embodiment;

Fig. 3 shows a section view of a wind energy converter according to a further embodiment;

Fig. 4 shows a section view of a bearing arrangement in a wind energy converter according to a further embodiment ;

Fig. 5 shows a section view of a bearing arrangement in a wind energy converter according to a further embodiment ;

Fig. 6 shows a section view of a bearing arrangement in a wind energy converter according to a further embodiment ;

Fig. 7 shows a section view of a bearing arrangement in a wind energy converter according to a further embodiment of the present invention, which was used to obtain the data shown in Fig. 8 to 12;

Fig. 8 shows a diagram illustrating the deflection of the shaft of the wind energy converter of Fig. 7 as a function of the length of the shaft for different first and second angles of the first and second bearing;

Fig. 9 is an enlarged view I from Fig. 8; Fig. 10 shows a diagram illustrating the rated life of the first bearing in the bearing arrangement of Fig. 7 for different first and second angles of the first and second bearing;

Fig. 11 shows a diagram illustrating the rated life of the second bearing in the bearing arrangement of Fig. 7 for different first and second angles of the first and second bearing;

Fig. 12 shows a diagram illustrating, in relation to each

other, the deflection of the shaft and the housing of the wind energy converter of Fig. 7 as a function of the length of the shaft and the housing for different first and second angles of the first and second bearing;

Fig. 13 shows schematically an apparatus; and Fig. 14 illustrates a method.

In the figures, the same reference numbers refer to the same or functionally equivalent components unless stated otherwise.

DETAILED DESCRIPTION OF THE DRAWINGS

Fig. 2 shows a section view of a wind energy converter 100 (hereinafter "WEC") according to a first embodiment. The WEC according to Fig. 2 differs from the WEC of Fig. 1 in at least the following aspects.

The first taper roller bearing 116 comprises an outer ring 200 and an inner ring 202. A plurality of tapered rollers 204

(each roller 204 having a roller axis 208) rides between an inner surface 201 of the outer ring 200 and an outer surface 203 of the inner ring 202. A first pressure line 206 normal to the inner surface 201 of the outer ring 200 intersects a line 210 normal to the centerline 212 of the shaft 108 at a first angle a.

The second taper roller bearing 118 comprises an outer ring 220 and an inner ring 222. A plurality of tapered rollers 224 (each roller 224 having a roller axis 228) rides between an inner surface 221 of the outer ring 220 and an outer surface 223 of the inner ring 222. A second pressure line 226 normal to the inner surface 221 intersects a line 230 normal to the centerline 212 of the shaft 108 at a second angle β.

The first angle a is different from the second angle β. The difference between the first angle a and the second angle β is preferably between 0.1 to 30 degrees, more preferably between 2 and 15 degrees. By choosing the difference between the first and second angle α, β such, the air gap 126 inside the generator 110 is minimized. Of course, the exact choice of the first and second angle , β depends on the loading conditions, i.e. expected wind loads, weight of the rotors 102, 126, weight of the shaft 108, size of the shaft 108 etc.

For example, the first angle a may lie between 25° and 45° and the second angle between 0 and 35° in cases of high axial and low radial loads acting on the shaft 108. On the other hand, the first angle a may lie between 15° and 40° and the second angle β between 25° and 45° in cases of high radial loads and low axial loads acting on the shaft 108.

In connection with Fig. 13 and 14 an apparatus and a method for obtaining the angles a and β will be explained. The first bearing 116 is arranged further from the generator 110 (or gearbox 300, see Fig. 3), i.e. closer to the rotor 102, than the second bearing 118.

The bearing housing 112 is flanged to the nacelle 120 or otherwise supported at the top of a tower 121.

Fig. 3 shows a section view of a WEC 100 according to a further embodiment. The WEC according to Fig. 3 differs from the WEC of Fig. 2 in at least the following aspects.

Fig. 2 shows a WEC 100 that is based on the so-called direct drive principle, i.e. the shaft 108 is directly connected to the rotor 124 of the generator 110. The WEC 100 of Fig. 3 on the other hand has a gearbox 300 interposed between the shaft 108 and the generator 110. The shaft 108 drives a first gear 302 of the gearbox. The first gear 302 meshes with a second gear 304 driving the rotor 124 of the generator 110 directly or indirectly. The first and second gear 302, 304 form a gear clearance 306 therebetween. The gear clearance 306 determines, to a significant extent, the efficiency and reliability of the gearbox 300 and thus the overall efficiency of the WEC 100. The gear clearance 306 depends on, for example, the bearings (not shown) supporting the gears 302, 304 inside the gear box 300. However, the gear clearance 306 also depends on the deflection of the shaft 108, the radial offset of the shaft 108, etc..

Again, by having different first and second angles , β the gear clearance 306 may be easily set to the desired value, and thus the efficiency and reliability of the WEC 100 is improved. As already explained in connection with the WEC 100 of Fig. 2, the difference between the first angle a and the second angle β in the WEC 100 of Fig. 3 is also preferably be- tween 0.1 and 30 degrees, more preferably between 2 and 15 degrees. Of course, the exact choice of the first and second angle α, β depends on the loading conditions, i.e. expected wind loads, weight of the rotors 102, 126, size of the shaft 108 etc.. In connection with Fig. 13 and 14 an apparatus and a method for obtaining the angles a and β will be explained.

Fig. 4 shows a section view of a bearing arrangement 113 in a EC 100 according to a further embodiment.

For example, in the WEC 100 of Fig. 2 the shaft 108 tapers down from the first bearing 116 towards the second bearing 118, i.e. from the rotor 102 towards the generator 110. Thus, the outer and inner ring 200, 202 of the first bearing 116 have a larger diameter than the outer and inner ring 220, 222 of the second bearing.

On the other hand, the bearing arrangement 113 of Fig. 4 is arranged on a shaft 108 of a WEC (only shown partially) , the shaft 108 having a substantially constant diameter. Thus, the outer and inner ring 200, 202 of the first bearing 116 have substantially the same diameter as the outer and inner ring 220, 222 of the second bearing.

According to another example, the point of intersection 400 of the line 226 normal to the inner surface 221 of the outer ring 220 and the centerline 212 of the shaft 108 lies inside the generator 110.

Fig. 5 shows a section view of a bearing arrangement 113 in a WEC 100 according to a further embodiment.

For example, in the WEC of Fig. 4 the first and second bearing 116, 118 are spaced apart. On the other hand, in the WEC of Fig. 5 the first and second bearing 116, 118 are arranged adjacent to each other. For example, the outer rings 200, 220 of the first and second bearing 116, 118 may be connected to each other (as shown) or form as a single piece. Herein, "single piece" means that the corresponding elements, in this case the outer rings 200, 220, are formed integrally and from the same material .

According to another embodiment the inner rings 202, 222 of the first and second bearing 116, 118 are connected to each other or form a single piece.

Fig. 6 shows a section view of another bearing arrangement 113 in a EC 100.

The shaft 108 in the WEC of Fig. 6 is formed with a collar 600, which folds over backwards. The collar 600 may be formed with the shaft 108 as a single piece as shown in Fig. 6.

Alternatively, the collar 600 is formed as a separate piece connected to the shaft. Fig. 6 shows a corresponding parting line 602.

The collar 600 surrounds the bearing housing 112 at its perimeter. The collar 600 comprises a radial portion 604 extending radially with respect to the shaft 108 and an axial portion 606 extending axially along the shaft 108 and connecting to the radial portion 604 at its one end. The axial portion 606 carries a front portion of the rotor 124 of the generator 110. In the embodiment of Fig. 6, the bearing 118 is moved far more to the right when compared to the embodiment of Fig. 2. Thus, the point of intersection 400 of the line 226 normal to the inner surface 221 of the outer ring 220 and the centerline 212 of the shaft 108 lies inside the generator 110, more specifically, inside the rotor 124.

The collar 600 may alternatively be formed on the other side of the bearings 116, 118, as partially shown with a dashed line in Fig. 6.

Fig. 7 shows a section view of a bearing arrangement 113 in a WEC 100 according to an even further embodiment, which was used to obtain the data shown in Fig. 8 to 12. Herein, "load" means force unless otherwise indicated.

The WEC 100 substantially corresponds to the configuration shown in Fig. 4. Further, Fig. 7 shows various loads applied to the WEC 100 during operation. First, there is an axial load 700 exerted on the shaft 108 that results from wind loads acting on the rotor 102. Second, there is a radial load 702 acting on the shaft 108 at its far end from the generator 110. The radial load 702 results from the weight of the rotor. The radial load 702 usually comprises, in addition to the force acting transversally on the shaft, a bending moment. Third, there is a radial load 704 acting on the shaft 108 at its end close to the generator. The radial load 704 results from the weight of the rotor 124 of the generator 110 and eccentric wind loads. Fourth, a radial load 706 acting on the bearing housing is shown. The radial load 706 is a reaction load resulting from the nacelle 120 supporting the bearing housing 112 at the indicated position.

Fig. 7 also shows various dimensions, wherein reference sign 720 indicates a distance between the radial load 702 and the radial load 706, reference sign 722 indicates a distance between the radial load 706 and the radial load 704, reference sign 724 indicates a distance between the radial load 702 and the bearing 116, reference sign 726 indicates a distance between the bearings 116, 118, reference sign 728 indicates a distance between the bearing 118 and the radial load 704, reference sign 730 indicates the outer diameter of the shaft 108, reference sign 732 indicates the inner diameter of the shaft 108, reference sign 734 indicates the outer diameter of the bearing housing 112 and reference sign 736 indicates the inner diameter of the bearing housing 112.

According to one example, the loads and dimensions were chosen as shown in table below, wherein "T" means metric tons, "m" meters and "MW" Megawatts.

Parameter Value

axial load 1,3 T

700

radial load 74, 5 T

702 (force)

4971 kNm

(bending moment )

radial load 40 T

704

dimension 3,3 m

720

dimension 2,7 m

722

dimension 1,5 m

724

dimension 2,3 m

726

dimension 2,2 m

728

dimension 1,7 m 730

dimension 1,4 m

732

dimension 2,5 m

734

dimension 2,1 m

736

rated elec3 MW

tric power

of the EC

100

The shaft 108 and the bearing housing 112 are made of ductile cast iron, also known as "spheroidal graphite iron", in this instance. However, other materials may also be used.

Fig. 8 shows a diagram illustrating the deflection δ, see Fig. 7, of the shaft 108 of the wind energy converter 100 of Fig. 7 as a function of the length X of the shaft 108 for different first and second angles α, β of the first and second bearings 116, 118. Fig. 9 shows an enlarged view I from Fig. 8.

Different first and second angles α, β were tested. The table below shows the angles and the corresponding air gap 126 obtained inside the generator 110, i.e. at a position of X equals 7,5 m. The air gap 126 is given as a dimensionless number, wherein a equals 35° and β equals 45° was used as a basis .

Test a β air

No. gap

126 1 45° 45° > 6

2 35° 45° 1

3 20° 35° < 1

The asymmetric configuration, i.e. a unequal to β, provides the lowest deflection values, the air gap 126 obtained with the symmetric configuration (a = 45°, β = 45°) being at least 6 times larger than the air gap 126 obtained with the asymmetric configurations. Thus, the corresponding air gap 126 can be designed small using the asymmetric configuration.

Fig. 10 shows a diagram illustrating the rated life of the first bearing 116 in the bearing arrangement 113 of Fig. 7 for different first and second angles α, β of the first and second bearing 116, 118. The rated life is shown as a percentage of the rated life obtained, when using a and β equal to 45°. The values for the first and second angle a, β that were used are shown in the table above (Tests No. 1 to 3) . The rated life was determined according to the different standards "Lnh", "Lnmh" and "Lnmrh" defined in ISO Standard 281.

Clearly, the asymmetric configuration, i.e. a unequal to β, provides the best results. The rated life obtained, in one example, may be as high as 180% of the rated life obtained using the symmetric configuration, i.e. a equal to β.

Fig. 11 shows a diagram illustrating the rated life of the second bearing 118 in the bearing arrangement 113 of Fig. 7 for different first and second angles α, β of the first and second bearing 116, 118. The rated life is shown as a percentage of the rated life obtained, when using a and β equal to 45°. The values for the first and second angle α, β that were used are shown in the table above (Tests No. 1 to 3) . Again, the rated life was determined according to the different standards "Lnh", "Lnmh" and "Lnmrh" defined in ISO Standard 281.

Clearly, the asymmetric configuration, i.e. a unequal to β, provides the best results. The rated life obtained, in one example, may be as high as 425% of the rated life obtained using the symmetric configuration, i.e. a equal to β.

The tests performed and results obtained herein were based on a numeric simulation tool.

Fig. 12 shows a diagram illustrating, in relation to each other, the deflection δ of the shaft 108 and the housing 112 of the wind energy converter 100 of Fig. 7 as a function of the length X of the shaft 108 and the housing 112 for different first and second angles α, β of the first and second bearing 116, 118.

Different first and second angles α, β were tested.

Fig. 12 shows that for the asymmetric configuration, i.e. a unequal to β, the deflection δ of the housing 112 corresponds to the deflection δ of the shaft 108. Thus, collision of the shaft 108 and the housing 112 is not an issue.

On the other hand, for the symmetric configuration, i.e. a equal to β, the deflection δ of the housing 112 deviated substantially from the deflection δ of the shaft 108. Thus, col- lision of the shaft 108 and the housing 112 can be an issue in this design.

Fig. 13 shows schematically an apparatus 1300 according an embodiment of the present invention.

The apparatus 1300 comprises an input device 1302 for providing a desired air gap 126 inside the generator 110 or gear clearance 306 inside the gearbox 300. The input device 1302 is a keyboard or touchpad, for example. Further, the apparatus 1300 comprises a simulation tool 1304, which may be a set of instructions encoded on a computer-readable medium. The simulation tool 1304 is executed on a computer. The simulation tool 1304 receives input data from the input device 1302. The apparatus 1300 has a machine tool 1306 receiving a design specification for the first and second bearing 116, 118 from the simulation tool 1304. The machine tool 1306 machines the first and second bearing 116, 118, in particular the first outer and inner ring 200, 202 as well as the second outer and inner ring 220, 222, in accordance with the design specification .

A method according to an embodiment of the present invention will now be explained with reference to Fig. 14. The method is preferably carried out with the apparatus 1300 of Fig. 13.

First, a desired air gap 126 inside the generator 110 or gear clearance 306 inside the gearbox 300 is provided by a user, for example. For the sake of brevity it will only be referred to the air gap 126 inside the generator 110 hereinafter. The following explanations equally apply to the gear clearance 306 inside the gearbox 300. The desired air gap 126 is entered into the input device 1302 in step 1400.

Hereafter, the simulation tool 1304 adjusts the difference between the first and the second angle α, β to a value unequal to 0 degrees (1402) . The simulation tool 1304 may for example start out from a. equal to 45° and increment or decrement this value by 0,1° each time. The same process may be used for β. The difference between the first and second angle , β may be adjusted to a value between 0.1 to 30 degrees, preferably between 2 and 15 degrees, for example.

For each value of a and β the simulation tool simulates the resulting air gap in the generator 110 taking into account specified dimensions, forces and materials of the EC to be designed (step 1404). The dimensions, forces and materials (as well as other properties) may, with regard to their type (i.e. length, width, diameter) and not necessarily with regard to their specific value (i.e. 100 t) , in one example correspond to the dimensions and forces used in the embodiment of Fig. 7. Said properties may comprise an axial load, radial load, axial elastic deformation of the first and/or second bearing 116, 118, radial elastic deformation of the first and/or second bearing 116, 118 and/or a bending deflection δ. The dimensions, forces and materials (as well as other properties) may also be entered by means of the input device 1302 and sent to the simulation tool 1304 in step 1400.

In step 1406, the resulting air gap is compared to the desired air gap 126 and, if they are not equal, steps 1402 and 1404 are repeated, wherein the values of a and β are adjusted as explained above, for example. Once the resulting air gap equals the desired air gap 126, the simulation tool 1304 forwards the corresponding values of a and β to the machine tool 1306.

In step 1408, the machine tool 1306 machines the first outer and inner ring 200, 202 in accordance with the first angle a and the second outer and inner ring 220, 222 in accordance with the second angle β.

At the same time, while trying to achieve the desired air gap 126, the difference between the first and second angle , β may be determined (in step 1402) so as to provide for the least radial elastic deformation in the second bearing 118, the least radial load in the second bearing 118, and/or the least deflection δ in the shaft 108.

Although the present invention has been described in accordance with preferred embodiments, it is obvious for a person skilled in the art that modifications are possible in all embodiments without departing from the scope of the claims. In particular, the values provided for dimensions, forces and angles herein only serve an improved understanding of the present invention and are not to limit the scope of the invention .

LIST OF REFERENCE SIGNS

100 wind energy converter (WEC)

102 rotor

104 blade

106 hub

108 shaft

110 generator

112 bearing housing

113 bearing arrangement

116 first bearing

118 second bearing

120 nacelle

122 stator

124 rotor

126 air gap

200 outer ring

201 inner surface

202 inner ring

203 outer surface

204 tapered roller

206 pressure line

208 roller axis

210 line

212 centerline

220 outer ring

221 inner surface

222 inner ring

223 outer surface

224 tapered roller

226 pressure line

228 roller axis

230 line

300 gearbox 302 gear 304 gear

306 gear clearance 400 intersection 600 collar

602 parting line 604 radial portion 606 axial portion 700 axial force 702 radial force 704 radial force 706 radial force 720 dimension

722 dimension

724 dimension

726 dimension

728 dimension

730 dimension

732 dimension

734 dimension

736 dimension

1300 apparatus

1302 input device 1304 simulation tool 1306 machine tool 1400 method step 1402 method step 1404 method step 1406 method step 1408 method step