Shaft Calculation Base

edition of October 2008 draft.

The proof of the bearing ability for shafts an axes is produced by defining a calculated safety. This safety is divided in the safety against fatigue fracture and the residual deformation (and flaw or forced break).

When calculating the avoidance of fatigue fracture, constant stress amplitudes being equivalent to damaging loads are taken as a basis. These ones are resulting from the predetermined loads. When proving against the residual deformation or forced break, designated as a safety against yielding, only the maximum occurring load is determinant. This one is resulting from the predetermined loads, too.

The calculation of safeties is related only to the point of a clear notch effect. For it, 9 calculable notches are at your disposal due to the graphical selection, principally.

The scope is limited to steels. Welded members should be calculated separately. But the utilized standard or the present program is ineffective for this purpose!

The calculation base for the module Shaft Calculation is provided by DIN 743, edition of October 2008 draft, part 1-4 “Tragfähigkeitsberechnung von Wellen and Achsen” (“Calculation of bearing capacity of shafts and axes”).

Input data:

Shaft calculation in accordance with DIN 743 - standard version

Geometry scheme General shaft

geometry

Calculation process Dynamic and static

strength proof

Type of loading: tension-pressure Dynamically pure cyclic

Type of loading: bending Dynamically pure cyclic

Type of loading: torsion Dynamically pure cyclic

Factor for maximum loading (tension-pressure) 1

Factor for maximum loading (bending) 1

Factor for maximum loading (torsion) 1

Specifications about the material

Strength values according to MDESIGN database

(DIN 743)

Material designation 18MoCrS4

Material number 1.7323

Gage diameter dB = 11 mm

For the gage diameter

Tensile strength B (Rm) = 1100 N/mm

²

Yield stress S (Re) = 775 N/mm

²

Cyclic fatigue strength under bending stress bW = 550 N/mm

²

Cyclic tension and pressure fatigue strength zdW = 440 N/mm

²

Cyclic torsional fatigue strength tW = 330 N/mm

²

Shear modulus G = 83000 N/mm ²

Density  = 7850 kg/m³

Apply surface hardening to Total shaft

Material group Cemented steels

Heat treatment trial hardened

Surface hardening no Shaft geometry Shaft geometry Nr. Da l mm Di lmm Da rmm Di rmm Lmm Rzµm rmm d:mm mmt: zd:b: t: nzd: nb: nt: dBK:zd BK:bd K:dB dBK: 1 60 0 60 0 24.7 5 1.6 1 59.4 0 0 0 0 0 0 0 0 0 0 0 2 70 0 70 0 6 6.3 2 0 0 0 0 0 0 0 0 0 0 0 0 3 90 0 90 0 105 3.2 2 0 0 0 0 0 0 0 0 0 0 0 0 4 85 0 85 0 5 6.3 1 0 0 0 0 0 0 0 0 0 0 0 0 5 75 0 75 0 81 1.6 1 0 0 0 0 0 0 0 0 0 0 0 0 6 70 0 70 0 30 1.6 0 0 0 0 0 0 0 0 0 0 0 0 0

Predetermine the diameter determinant for the heat treatment ? no

Calculation of the deflection for point x = 0 mm

Shaft speed n : 222.22 1/min

Consideration of dead weight no

Bearing

Nr. Type = Position x =

mm

1 Location bearing -> 22

2 Location bearing <- 229.75

Specifications about loadings Axial forces Fax

Nr. Position x =

mm Amount =N Radius =mm Angle °  =

1 83.25 -3047.13 50 90

2 181.25 3364.37 142.125 0

Nr. Position x = mm Amount =N Angle °  = 1 83.25 15676.16 180 2 181.25 -3373.016 0 3 83.25 4858.45 90 4 181.25 -5744.76 270 Torsion Nr. Position x =

mm Torsion moments Mt:N*mm Power P:kW Transition part =

1 83.25 783808 0 drive

2 181.25 783808 0 takeoff

Specifications about the load/loadings

Loading case Constant mean stress

(loading case 1)

Change the limit number of loading cycles ? no

Minimum safety against fatigue fracture SDmin = 1.2

Minimum safety against residual deformation SFmin = 1.2

Minimum safety against incipient crack with hard surface SGmin = 1.2 Results:

Calculation process: Dynamic and static strength proof

Total shaft length L = 251.750 mm

Total shaft mass m = 9.912 kg

Mass moment of inertia of the shaft J = 0.00840 kg*m² Geometrical moment of inertia of the shaft I = 1032.952 cm4 Position of the centre of gravity in the X-axis xs = 121.350 mm Angle of torsion  = 0.012 °

Additional shaft data: Shaft fillet number l

mm cm4Ip cm³Wt kgm kg*m²J cm4I cm³Wb 1 24.8 127.235 42.412 0.549 0.0002 63.617 21.206 2 6.0 235.718 67.348 0.181 0.0001 117.859 33.674 3 105.0 644.125 143.139 5.244 0.0053 322.062 71.569 4 5.0 512.478 120.583 0.223 0.0002 256.239 60.292 5 81.0 310.631 82.835 2.809 0.0020 155.316 41.417

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Supporting forces:

No. Type Position x mm Radial force in the Y-axis Ry N Radial force in the Z-axis Rz N Result. radial force R N Axial force in the X-axis Rax N 1 Location bearing -> 22.000 9540.253 -4033.826 10358.001 3047.130 2 Location bearing <- 229.750 9508.923 -6569.384 11557.527 -3364.370

Resulting maximum bending moment:

Position x = 83.250 mm

Amount Mbmax = 707.811 N*m

Resulting maximum torsional moment:

Position x = 83.250 mm

Amount Mtmax = 783.808 N*m

Resulting maximum tension-pressure-force:

Position x = 181.250 mm

Amount Fzdmax = -3364.370 N

Resulting maximum tension-pressure-stress:

Position x = 24.750 mm

Amount zdmax = -1.078 N/mm²

Resulting maximum bending stress:

Position x = 181.250 mm

Amount bmax = 13.534 N/mm²

Resulting maximum torsional stress:

Position x = 181.250 mm

Amount tmax = 9.462 N/mm²

Resulting maximum deflection:

Position x = 133.787 mm

Amount ymax = 0.004535 mm

Angle of the maximum deflection:

Position x = 248.873 mm

Amount  = 0.004828 °

Minimum safety against yielding:

Position x = 181.250 mm

Amount SF = 26.635

Minimum safety against fatigue fracture:

Position x = 140.750 mm

Amount SD = 7.815

Minimum safety against incipient crack with hard surface:

Position x = 140.750 mm

Amount SG = 61.088

Material parameter for def = 90.000 mm

Material designation 18MoCrS4

Material number 1.7323

Tensile strength B = 688.305 N/mm²

Yield stress S = 484.942 N/mm²

Cyclic tension and pressure fatigue zdW = 275.322 N/mm²

stress

Cyclic torsional fatigue strength tW = 206.491 N/mm² Technological dimension factor (tensile strength) K1Bdeff = 0.626 Technological dimension factor (yield stress) K1Sdeff = 0.626 Parameter of cross-sections:

Tension-pressure force Fzd and tension/pressure stress zd No. Type Positio

n x mm Result. Fzdx N Amplitud e Fzda N Mean Fzdm N Maximu m Fzdmax N Amplitud e zda N/mm² Mean zdm N/mm² Maximu m zdmax N/mm² 1 Fillet with recess 24.8 -3047.13

0 -3047.130 0.000 -3047.130 -1.100 0.000 -1.100 2 Shaft fillet 30.8 -3047.13 0 -3047.130 0.000 -3047.130 -0.792 0.000 -0.792 3 Shaft fillet 135.8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4 Shaft fillet 140.8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 5 Shaft fillet 221.8 -3364.37 0 -3364.370 0.000 -3364.370 -0.874 0.000 -0.874 6 Calculation results for point x 0.0 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Bending moment Mb and bending stress b No. Type Positio

n x mm Result. Mbx N*m Amplitud e Mba N*m Mean Mbm N*m Maximu m Mbmax N*m Amplitud e ba N/mm² Mean bm N/mm² Maximu m bmax N/mm² 1 Fillet with recess 24.8 28.485 28.485 0.000 28.485 1.384 0.000 1.384 2 Shaft fillet 30.8 90.633 90.633 0.000 90.633 2.691 0.000 2.691 3 Shaft fillet 135.8 442.249 442.249 0.000 442.249 7.335 0.000 7.335 4 Shaft fillet 140.8 421.328 421.328 0.000 421.328 10.173 0.000 10.173 5 Shaft fillet 221.8 92.460 92.460 0.000 92.460 2.746 0.000 2.746 6 Calculation results for point x 0.0 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Torsional moment Mt und Torsional stress t No. Type Positio

n x mm Result. Mtx N*m Amplitud e Mta N*m Mean Mtm N*m Maximu m Mtmax N*m Amplitud e ta N/mm² Mean tm N/mm² Maximu m tmax N/mm² 1 Fillet with recess 24.8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2 Shaft fillet 30.8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3 Shaft fillet 135.8 783.808 783.808 0.000 783.808 6.500 0.000 6.500 4 Shaft fillet 140.8 783.808 783.808 0.000 783.808 9.462 0.000 9.462 5 Shaft fillet 221.8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6 Calculation results for point x 0.0 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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Calculation results for point x = 0.000 mm Trend of curve of the transverse force Qx = 0.000 N

deflection yx = 0.001502 mm

Angle of deflection  = 0.003912 °

Strength proof:

K2(d) - Geometrical dimension factor KF - Influence factor of surface roughness

,  - Form factors

No. Type Position x mm Tension-pressur e K2(d) Bending and torsion K2(d) Tension-pressure, bending KF Torsion KF Tension-pressur e zd Bending b Torsion 

1 Fillet with recess 24.8 1.00 0.86 0.98 0.99 3.03 2.75 1.86 2 Shaft fillet 30.8 1.00 0.85 0.91 0.95 2.70 2.42 1.72 3 Shaft fillet 135.8 1.00 0.84 0.91 0.95 2.22 2.06 1.48 4 Shaft fillet 140.8 1.00 0.85 0.98 0.99 3.12 2.86 1.89 5 Shaft fillet 221.8 1.00 0.85 0.98 0.99 2.68 2.52 1.69 6 Calculation results for point x 0.0 1.00 0.86 0.98 0.99 - - - G - Relative stress drop

n,  - Bearing factor

No. Type Position x mm Tension-pressure Gzd 1/mm Bending Gb 1/mm Torsion Gt 1/mm Tension-pressure nzd Bending nb Torsion n

1 Fillet with recess 24.8 2.51 2.51 1.15 1.15 1.15 1.10 2 Shaft fillet 30.8 1.26 1.26 0.57 1.11 1.11 1.07 3 Shaft fillet 135.8 1.33 1.33 0.57 1.11 1.11 1.07 4 Shaft fillet 140.8 2.51 2.51 1.15 1.15 1.15 1.10 5 Shaft fillet 221.8 2.58 2.58 1.15 1.16 1.16 1.10 6 Calculation results for point x 0.0 - - - -

zddBK, bdBK, dBK - Stress concentration factor at dBK

zd, b,  - Stress concentration factors Kv - Influence factor of surface hardening

No. Type Positio n x mm Tensio n-pressu re zddB K Bendi ng bdB K Torsio n dBK Tensio n-pressu re zd Bendin g b Torsion  Tensio n-pressu re Kvzd Bendin g Kvb Torsion Kv 1 Fillet with recess 24.8 - - - 2.62 2.38 1.68 1.00 1.00 1.00 2 Shaft fillet 30.8 - - - 2.43 2.18 1.60 1.00 1.00 1.00 3 Shaft fillet 135.8 - - - 1.99 1.85 1.38 1.00 1.00 1.00 4 Shaft fillet 140.8 - - - 2.70 2.48 1.72 1.00 1.00 1.00

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results for point x

K, K - Total influence factor

zdWK, bWK, tWK - Cyclic fatigue strength of the notched part K2F - Static bearing effect

No. Type Positio n x mm Tensio n-pressu re K Bendin g K Torsion K Tensio n-pressu re zdWK N/mm² Bendin g bWK N/mm² Torsion s tWK N/mm² Tensio n-pressu re K2Fzd Bendin g K2Fb Torsion K2Ft 1 Fillet with recess 24.8 2.65 2.79 1.97 103.94 123.42 104.98 1.00 1.20 1.20 2 Shaft fillet 30.8 2.54 2.67 1.94 108.60 128.95 106.40 1.00 1.20 1.20 3 Shaft fillet 135.8 2.10 2.31 1.70 131.34 148.78 121.16 1.00 1.20 1.20 4 Shaft fillet 140.8 2.73 2.95 2.04 100.93 116.50 101.17 1.00 1.20 1.20 5 Shaft fillet 221.8 2.34 2.58 1.82 117.50 133.32 113.76 1.00 1.20 1.20 6 Calculation results for point x 0.0 1.02 1.19 1.18 268.69 290.20 175.70 1.00 1.20 1.20

F - Yield point rise

zdFK, bFK, tFK - Yield point of the part No. Type Position

x mm Tension-pressure Fzd Bending Fb Torsion Ft Tension-pressure zdFK N/mm² Bending bFK N/mm² Torsion tFK N/mm² 1 Fillet with recess 24.8 1.15 1.10 1.00 557.68 640.12 335.98 2 Shaft fillet 30.8 1.10 1.10 1.00 533.44 640.12 335.98 3 Shaft fillet 135.8 1.10 1.10 1.00 533.44 640.12 335.98 4 Shaft fillet 140.8 1.15 1.10 1.00 557.68 640.12 335.98 5 Shaft fillet 221.8 1.10 1.10 1.00 533.44 640.12 335.98 6 Calculation results for point x 0.0 1.00 1.00 1.00 484.94 581.93 335.98 Static safety

No. Type Position

x mm SF In Point1 SF1 in Point2 SF2 1 Fillet with recess 24.8 241.88 - -

2 Shaft fillet 30.8 175.78 - - 3 Shaft fillet 135.8 44.47 - - 4 Shaft fillet 140.8 30.92 - - 5 Shaft fillet 221.8 168.68 - - 6 Calculation results for point x 0.0 10000.00 - -

 - Influence factor of the mean stress sensitivitz

mv, mv - Comparative mean stress No. Type Positio

n x Tension -pressur Bendin g bK Torsion K N/mm²mv N/mm²mv N/mm²mv1 N/mm²mv1 N/mm²mv2 N/mm²mv2

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1 Fillet with recess 24.8 0.08 0.10 - 0.00 0.00 - - - - 2 Shaft fillet 30.8 0.09 0.10 - 0.00 0.00 - - - - 3 Shaft fillet 135.8 - 0.12 0.10 0.00 0.00 - - - - 4 Shaft fillet 140.8 - 0.09 0.08 0.00 0.00 - - - - 5 Shaft fillet 221.8 0.09 0.11 - 0.00 0.00 - - - - 6 Calculation results for point x 0.0 - - - 0.00 0.00 - - - -

Alternating fatigue strength of the part (rated fatigue limit) No. Type Positio

n x mm Tension -pressur e zdAD K N/mm² Bendin g bADK N/mm² Torsion tADK N/mm² Tension -pressur e in Point1 zdAD K1 N/mm² Bendin g in Point1 bADK 1 N/mm² Torsio n in Point1 tADK 1 N/mm² Tension -pressur e in Point2 zdAD K2 N/mm² Bendin g in Point2 bADK 2 N/mm² Torsio n in Point2 tADK 2 N/mm² 1 Fillet with recess 24.8 103.94 123.42 - - - - 2 Shaft fillet 30.8 108.60 128.95 - - - - 3 Shaft fillet 135.8 - 148.78 121.16 - - - - 4 Shaft fillet 140.8 - 116.50 101.17 - - - - 5 Shaft fillet 221.8 117.50 133.32 - - - - 6 Calculation results for point x 0.0 - - - - Dynamic safety

No. Type Position

x mm SD in Point1 SD1 in Point2 SD2 1 Fillet with recess 24.8 45.88 - -

2 Shaft fillet 30.8 35.51 - - 3 Shaft fillet 135.8 13.72 - - 4 Shaft fillet 140.8 7.82 - - 5 Shaft fillet 221.8 35.67 - - 6 Calculation results for point x 0.0 10000.00 - - Safety against incipient crack

with hard surface

No. Type Position

x mm SG In Point1 SG1 in Point2 SG2 1 Fillet with recess 24.8 4838.12 - -

2 Shaft fillet 30.8 525.16 - - 3 Shaft fillet 135.8 116.22 - - 4 Shaft fillet 140.8 61.09 - - 5 Shaft fillet 221.8 503.99 - - 6 Calculation results for point x 0.0 10000.00 - -

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Material = 18MoCrS4 Number = 1.7323

N/mm2

N/mm2

Unnotched (part dimension) for point x



B(deff)

= 688

N/mm²

zdF

= 485

N/mm²

bF

= 582

N/mm²

tF

= 336

N/mm²

zdW

= 275

N/mm²

bW

= 344

N/mm²

tW

= 206

N/mm²

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Material = 18MoCrS4 Number = 1.7323

N/mm2

N/mm2

Notched (part dimension) for point x



B(deff)

= 688

N/mm²

zdFK

= 485

N/mm²

bFK

= 582

N/mm²

tFK

= 336

N/mm²

zdWK

= 269

N/mm²

bWK

= 290

N/mm²

tWK

= 176

N/mm²

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0 50 100 150 200 250

Trend of curve of the transverse force in the Y-X-plane

L, mm

Qy, N

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0 50 100 150 200 250

Trend of curve of the transverse force in the Z-X-plane

L, mm

Qz, N

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0 50 100 150 200 250

Trend of curve of the transverse force (combined characteristic)

L, mm

Q, N

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0 50 100 150 200 250

Bending moment in the Y-X-plane

L, mm

Mby, Nm

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0 50 100 150 200 250

Trend of curve of the bending moment curve in the Z-X plane

L, mm

Mbz, Nm

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0 50 100 150 200 250

Trend of curve of the bending moment (combined characteristic)

L, mm

Mb, Nm

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0 50 100 150 200 250

Trend of curve of the torsional moment

L, mm

Mt, Nm

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0 50 100 150 200 250

Trend of curve of the tension-pressure forces

L, mm

Fzd, N

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0 50 100 150 200 250

Deflection and angle of deflection in the Y-X-plane

L, mm y, mm -9.04e-3 -6.03e-3 -3.01e-3 0.00 3.01e-3 6.03e-3 9.04e-3  -3.22e-3 -2.14e-3 -1.07e-3 0.00 1.07e-3 2.14e-3 3.22e-3 Deflection Angle

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0 50 100 150 200 250

Deflection and angle of deflection in the Z-X-plane

L, mm y, mm -1.04e-2 -6.91e-3 -3.45e-3 0.00 3.45e-3 6.91e-3 1.04e-2  -3.60e-3 -2.40e-3 -1.20e-3 0.00 1.20e-3 2.40e-3 3.60e-3 Deflection Angle

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0 50 100 150 200 250

Deflection and angle of deflection (combined characteristic)

L, mm y, mm -1.36e-2 -9.07e-3 -4.54e-3 0.00 4.54e-3 9.07e-3 1.36e-2  -4.83e-3 -3.22e-3 -1.61e-3 0.00 1.61e-3 3.22e-3 4.83e-3 Deflection Angle

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0 50 100 150 200 250

Comparative mean stress (normal stress)

L, mm



mv, N

N/mm²

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0 50 100 150 200 250

Comparative mean stress (shear stress)

L, mm



mv, N

N/mm²

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0 50 100 150 200 250

Safety factor against yielding

L, mm

SF

(Cross-section: SF=5*SFmin)

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0 50 100 150 200 250

Safety against fatigue fracture

L, mm

SF

(Cross-section: SD=5*SDmin)

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0 50 100 150 200 250

Safety against incipient crack with hard surface

L, mm

SG

(Cross-section: SG=5*SGmin)

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0 50 100 150 200 250

Maximum value of the tension-pressure stress (combined characteristic)

L, mm



max, N

N/mm²

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0 50 100 150 200 250

Maximum value of the bending stress (combined characteristic)

L, mm



max, N

N/mm²

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0 50 100 150 200 250

Maximum value of the torsional stress (combined characteristic)

L, mm



max, N

N/mm²

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0 50 100 150 200 250

Amplitude value of the tension-pressure stress (combined characteristic)

L, mm



zda, N

N/mm²

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0 50 100 150 200 250

Amplitude value of the bending stress (combined characteristic)

L, mm



ba, N/mm²

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0 50 100 150 200 250

Amplitude value of the torsional stress (combined characteristic)

L, mm



ta, N/mm²

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0 50 100 150 200 250

Mean value of the tension-pressure stress (combined characteristic)

L, mm



zdm, N

N/mm²

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0 50 100 150 200 250

Mean value of the bending stress (combined characteristic)

L, mm



bm, N

N/mm²

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0 50 100 150 200 250

Mean value of the torsional stress (combined characteristic)

L, mm



tm, N/mm²

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Safety factor against yielding

> 1.20

L1

L2

Safety against fatigue fracture

> 1.20

L1

L2

Safety against incipient crack with hard surface

> 1.20

L1

L2

0 41.958 83.917 125.875 167.833 209.792 251.75

x, mm

y

Resultant graphic Y-X-plane

0 25.175 50.35 75.525 100.7 125.875 151.05 176.225 201.4 226.575 251.75

x, mm

z

Resultant graphic Z-X-plane