1 Girder Kinematics Modeling - PowerPoint Presentation

Slide1

1

Girder Kinematics ModelingBy Arsalan Jamialahmadi

Aim of the Study

To provide a model to study:Static deformation of the Micro-Control girder for the Main Beam of the CLIC two-beam prototype module. Maximum possible displacement of the beam axis on the maximum master movement(s).

The parametric actuation of the conceptual design.

2

Maximum vertical and lateral static deformation of 10

μm Maximum girder weight of 240 kgMaximum girder length is almost 2 m

Maximum sustainable dead weight of 400 kg/m

Maximum cross section of 320 mm × 150 mm

Maximum master actuation of ±0.3 mm

Maximum slave travel of ±3 mm

Modelling

3

Figure 1 – Master-Slave movement

Micro-Control Technical Requirements:

Modelling

Girders and V-supports are integrated parts which are glued to each other and to the cradles. Cradles and actuators have multiple parts glued to each other.Actuators, flexural joints and supportsDummy load as accelerating structure

Z-direction movement at the end cradles suppressed

Roller

compensated by frictionless contact

4

Figure

2

– Two-Girder system

Modelling

Material/ComponentYoung’s Module (GPa)

Density

(kg/m

3

)

Poisson RatioYield’s Strength (

MPa

)

SiC

250

3215

0.163440

Structural Steel 200

78500.3

250

Dummy Acc.

Stru

. (Cu properties)

100

39706

0.34

69

5

Table 1 – Material Properties

Modelling

Cylindrical joint for actuatorSupporting the structureFlexural joints bear stressFrictionless contact simulates rotation

6

Figure

3

– Actuator modelling

Figure

4

– Compensation of rotation by frictionless contact

Modelling

7

Analysis Type

Assemblies

Purpose

Static deflection

– no actuation

1

-Girder

To control

the static deflection for comparison with the real model

2-Girder

3-Girder

Static

deflection

– maximum actuation

1-Girder with spring

To extract the extreme cases of deflection

2-Girder with spring

3-Girder

with spring

Modal Analysis

2-Girder fixed

To

find the resonance frequencies

2-Girder with

spring

Parametric Study

1-Girder with spring

To give a tool for alignment

2-Girder with

spring

Table 2 – Performed studies

System

1-Girder

2-Girder

3-Girder

Number of Elements

36350

74446

98888

Table 3 – Number of Elements for different configurations

Note: Girder with spring points out the girder system in which spring serves as the master-slave movement provider for actuators.

Results

8

System

Maximum Stress

(

MPa

)

Maximum Deflection

(

μ

m)

1-Girder

37.427.38

2-Girder

68.630.6

3-Girder

68.6

32.4

Table 4 – Static deflection results

Figure

5

– Static deflection with no actuation

Static deflection – no actuation

Note: The load/actuator

and the Z-direction

movement suppression

are the contributors

to the increase of deflection and stress

. The values of deflection are lower compared to the values given by Micro-Control without pre-stress.

Results

9

Static deflection – maximum actuation

Applied abbreviations:

a,b,c

Actuator position on cradle

1,2,3 Cradle number

p,n

Positive or negative

F,R Front and rear

Figure

6

– Displacement b1p-c1n

Results

10

Static deflection – maximum actuation

a1

b1

c1

a2

b2

c2

f1x

f1y

f1z

r1x

r1y

r1z

teta

-x(

Rad

)

teta

-y(

Rad

)

c1n

-9.7091

9.20725

-300

-0.26954

2.35335

-20.156

-323.15

-9.2261

-4.2624

-16.4815

-7.2197

-3.7117

0.0063

0.0824

c1p

4.633

-6.348

300

2.59505

0.22516

21.3565

314.29

-9.8721

-3.8705

16.098

-6.8258

-3.32065

-0.0029

-0.0743

a1n

-300.06

-17.3605

-147.19

-15.5442

-2.1398

-111.695

384.88-

-170.92

39.201

-117.785

-13.691

39.7665

0.0185

0.1299

a1p

299.93

20.6405

145.44518.11554.77395114.5377.97154.55-48.002119.166-0.014-47.4585-0.0153-0.1229b1n-21.179-300.06152.5-2.3065-15.1778106.395385.1-172.940.004110.3115-13.52740.565-0.0449-0.0539b1p15.7695299.93-156.534.5507517.588-104.5-395.86152.1-47.616-109.872-0.362-47.08150.04790.0628a1n-c1n-300.065-300.065-299.995-16.0752-1.5493-120.995-544.44-168.7538.564-124.718-13.703539.13050.02070.1679a1n-c1p-300.065-300.065300-13.9893-3.86843-84.461582.062-177.2741.064-97.497-13.650541.6250.01210.0167a1p-c1n299.93299.93-30016.5696.49787.3845-87.153160.87-49.86498.9535-0.075-49.328-0.0090-0.0101a1p-c1p299.93299.9330018.6524.17575123.92539.35152.35-47.355126.16350.008-46.812-0.0175-0.1614b1n-c1n-32.8685-300.065-300-4.63109-14.199678.842-86.66-178.8541.43889.776-14.099542.013-0.03970.0637b1n-c1p-17.3672-300.06300-1.54855-15.4971115.38538.88-170.9639.537116.994-13.33940.098-0.0466-0.0921b1p-c1n12.06232299.935-3003.8125517.898-113.24-545.44150.22-47.16-116.3585-0.536-46.6220.04960.0999b1p-c1p27.5622299.9353006.897616.603-76.694580.1158.1-49.068-89.15750.195-48.52750.0426-0.0558a1n-b1n-300.065-300.0657.162-17.8015-17.4295-5.36666.399-315.1778.072-6.7429-19.65378.651-0.02640.0679a1n-b1p-300.065299.93-321.3-13.035615.0024-231.095-824.91-9.0255-4.3466-242.44-6.7325-3.79810.06880.1984a1p-b1n299.935-300.065320.7315.5177-12.6092235.1822.04-9.107-3.7446245.07-6.202-3.19255-0.0662-0.1922a1p-b1p299.935299.935-7.752220.356519.89559.4197-9.3043297.06-86.4749.446055.61285-85.94150.0291-0.0614a1n-b1n-c1n-300.065-300.065-300-18.9545-16.692-21.101-307.29-315.1677.962-17.5005-19.863578.5455-0.02340.1445a1n-b1n-c1p-300.065-300.065300-16.702-18.1339.6356305.46-315.1878.1783.5112-19.449578.7505-0.0293-0.0059a1n-b1p-c1n-300.065299.935-300-12.955714.9514-230.005-803.16-9.0264-4.339-241.695-6.718-3.790250.06860.1932a1n-b1p-c1p-300.065299.935300-10.702113.51045-199.255-190.42-9.0517-4.1236-220.72-6.303-3.57670.06260.0443a1p-b1n-c1n299.925-300.06-30013.1884-11.1177203.325188.12-9.0808-3.9691223.355-6.6375-3.40495-0.0601-0.0380a1p-b1n-c1p299.93-300.0630015.43985-12.5593234.065800.86-9.1061-3.752244.37-6.2165-3.19985-0.0660-0.1872a1p-b1p-c1n299.935299.935-30019.259520.597-5.5497-307.76297.07-86.579-0.78445.41225-86.0540.03200.0122a1p-b1p-c1p299.935299.93530021.51219.155525.194304.99297.05-86.36320.1895.8263-85.8320.0260-0.1382

Table 5 – Deflection values for One-Girder system with spring

Note: Displacements are in micrometer

Results

11

Static deflection – maximum actuation

Table 5 gives the following information:

Slave movement of actuators with respect to maximum actuation of the master movement(s).

Beam axis movement with respect to maximum actuation of the master movement(s).

Angle of rotation of beam axis with respect to its initial position.

Figure

7

– Two-Girder system maximum actuation a2p-b2p-c2p

Results

12

Modal Analysis

Mode Number

Frequency (Hz)

with spring

with fixed actuators

1

58.2

45.5

2

60.8

47.7

3

69.5

55.4

4

92.5

60.3

5

99.0

103.0

Table 6 – Resonance frequencies for Two-Girder system

Note: The resonance values of the system with spring might be used for comparison

only

For this system, the first resonance frequency estimate from Micro-Control analysis is 49.8 Hz.

Results

13

Modal Analysis

Frequency 45.5 Hz, Max

1.83 mm

In-phase bending

b) Frequency 47.7 Hz,

Max 1.85 mm

Anti-phase bending

c) Frequency 55.4 Hz, Max 1.55 mm

First girder shear

d)Frequency 60.4 Hz, Max 1.58 mm

Second girder shear

Figure

8

– First 4 resonance frequencies and mode shapes of the Two-Girder system with fixed actuators

Results

14

Parametric Study

Overview:

Number of input variables: 3

Number of output variables: 9 (1-Girder) or 18 (2-Girder)

The range for input variables are ±0.3 mm.

The 3 input variables are the two vertical and one horizontal actuator movements of one cradle.

Output variables give the changes in x, y and z coordinates of the beam axis ends for each girder.

Results (outputs) are shown as variation diagrams of two input variables while the third input variable remains constant.

Results

15

Parametric Study

Figure

9

– Parametric study of One-Girder system. F1x is a function of three variables a1,b1 and c1. Here c1=0

Two vertical actuators of the first cradle are moving while the horizontal actuator is set to be fixed at zero. By having the same amount of actuation for the vertical actuators, front point of the beam axis will not have any displacement component in x-direction.

Results

16

Parametric Study

Figure

10

– Parametric study of One-Girder system. Ry1 is a function of three variables a1, b1 and c1. Here a1=0.156

The second vertical (b1) and the horizontal actuator (c1) from the first cradle are moving while the first vertical actuator (a1) is set to be fixed at 0.156 mm displacement. By having the b1 constant, rear point of the beam axis will not have any displacement component in y-direction.

Conclusions

17

Static deformation values

are relative values as the pre-stress

option was

not possible with ANSYS

. If pre-stress is considered, then only static deflection values are to be changed.

Worst case deflection is not passing the ±3 mm limits.

Lowest resonance frequency is 45.5 Hz.

Parametric study is a suitable tool to locate the beam axis

Further Work

18

The mechanism of master-slave movement needs to be studied more thoroughly. The snake system kinematics is governing.

Modal analysis can be done again with accelerating structure for comparison purpose.

The more the number of girders, the more precise results but heavier model at the same time!

Number of input variables of the parametric study can be increased to consider 6 actuator movements for

alignment study.

A thorough report of this work will be written for through description of the results.

19

Thank You!