Hanyu Yao Dynamic Balancing Design

Simulation for Certain Type of

Satellite antenna

Aerospace Systems Design II

Content

I. Introduction

II. Establishment of the finite element model

III. Analysis of Initial static and static unbalance

IV. Dynamic Balancing Design

V. Analysis of the effect of wind load

VI. Error analysis of gravity and centrifugal force

Introduction

Establish the finite model

Analysis of Initial unbalance

Dynamic Balancing Design

Analysis of

wind load

Error analysis

Gravity Centrifugal force

The best balancing scheme

1. Establishment of the finite element model

Main components of the model：

① the main reflector

② the sub-reflector

③ the feedhore

④ The HF caseShell element

Beam element

2. Analysis of Initial unbalance

The calculation formula of unbalance：

results

static unbalance 2.38E+04 (kg·mm)

dynamic unbalance 1.55e+07(kg·mm2)

2.Amount of dynamic unbalance：

= 𝑀𝑋 2 + 𝑀𝑌 2

=

𝒊=𝟏

𝒏

𝒎𝒊 𝒙𝒊𝒛𝒊

𝟐

+

𝒊=𝟏

𝒏

𝒎𝒊 𝒚𝒊𝒛𝒊

𝟐

1.Amount of static unbalance：

= 𝑀 ∗ 𝑋 2 + 𝑌 2

=

𝒊=𝟏

𝒏

𝒎𝒊 𝒙𝒊

𝟐

+

𝒊=𝟏

𝒏

𝒎𝒊 𝒚𝒊

𝟐

The initial unbalance value

3. Dynamic Balancing Design

3.1 The double planes balance method

Plane Ⅰ Plane ⅡF1

F21

F11

F2

FA

F12

F22

FB（F1 and F2 are two unbalanced forces on the rotor ,

Plane Ⅰ and Ⅱ are two optional plane ）

（1）F1 and F2 can be decomposed onto two balancing planes

（2）Combining the forces in Planes Ⅰ and Ⅱ to obtain equivalent forces FA and FB

（3） In Planes Ⅰ and Ⅱ, the balance masses with the same value and opposite directions as FA

and FB can be added to eliminate the unbalance force

3. Dynamic Balancing Design

The 1st position：Balancing position ：Top of the sub-reflectorCoordinates of the mass :[-2215.76 , -98.76 , 1088.42]Balancing mass：7.34kg

The 2st position：Balancing position: Bottom of the HF caseCoordinates of the mass：[662.76, 397.90, 85.50]Balancing mass：4.39kg

（1）The 1st position of counter weight

（2）The 2st position of counter weight

Results after balancing

static unbalance 16.00(kg·mm)dynamic unbalance 2692.75(kg·mm2)

3.2 The best balancing scheme

4. Analysis of the effect of wind load

Working

conditionPart Main vector（N） Position of the vector（mm）

sea-level

pressure environm

ent

1 （4.52，-0.06，0） （15.64,1180.55,5181.45）

2 （1.28，0.06，0） （-70.48,1589.51,3882.41）

3 （-1.40，0.06，0） （-72.27,-1593.03,3757.50）

4 （-4.55，-0.04，0） （10.40,-1175.90,2546.80）

lower

pressure tank

1 （0.052,-0.001,0） （22.85,1129.41,5085.97）

2 （0.011,0.001,0） （-85.80,1552.99,3906.38）

3 （-0.012,0.001,0） （-87.87,-1560.49,3750.65）

4 （-0.053,-0.001,0） （19.06,-1123.69,2711.36）

Combined with CFD fluid simulation and MATLAB simulation, wind loads of the main reflector at working speed were calculated under two working condition.

4.1 The wind load analysis

4. Analysis of the effect of wind load

(1) Obtain the resultant force and moment

The forces at four points can be translated to the point A on the central axis to obtain the resultant force 𝐹𝐴0 and the resultant moment 𝑀0

the resultant force and moment

4.2 Analysis of the effect of wind

load on dynamic balance

4. Analysis of the effect of wind load

(2) Decompose the moment into the 𝑭𝑨𝟏 and 𝑭𝑩𝟏

According to the formula 𝑀 = 𝐹 × 𝐿, the moment 𝑀0𝑥 , 𝑀0𝑦 were equivalent to two forces 𝐹𝐴1 and 𝐹𝐵1in equal magnitude and opposite direction.

4.2 Analysis of the effect of wind

load on dynamic balance

4. Analysis of the effect of wind load

(3)The effect of wind load was converted into the form of mass

The resultant forces 𝐹𝐴 and 𝐹𝐵 were calculated. Then according to the formula 𝐹𝑁 = 𝑚𝜔2𝑅, 𝐹𝐴 and 𝐹𝐵 is equivalent to the centrifugal force generated by the mass weights 𝑚𝑃 and 𝑚𝑄 .

4.2 Analysis of the effect of wind

load on dynamic balance

4. Analysis of the effect of wind load

Based on the wind load data, the equivalent mass of both working condition is added to the satellite antenna model, and the effect of the wind load on the balancing result is calculated.

4.3 The influence of wind load on Balance Value

Without wind load

With wind load under sea-level

pressure

With wind load in low-pressure

tank

Static balance 16.00 18.68 15.56Dynamic balance 2692.75 1.56e+06 19247.13

The influence of wind load on Balance Value

5. Error analysis of gravity and centrifugal force

The gravity load is applied. The deformation of each element of the model is obtained by the analysis of static force. And the amount of dynamic and static unbalance is reanalysed.

5.1 Effect of gravity on dynamic balance

Gravity unapplied Gravity applied

Dynamic unbalance

2692.75 8.03e+04

Static unbalance

16.00 30.48

The influence of gravity on Balance Value

5. Error analysis of gravity and centrifugal force

The centrifugal force load is applied. The deformation of each element of the model is obtained by the analysis of static force. And the amount of dynamic and static unbalance is reanalysed.

5.2 Effect of centrifugal force on dynamic balance

centrifugal force unapplied

centrifugal force applied

Dynamic unbalance

2692.75 154770.77

Static unbalance 16.00 29.53

The influence of centrifugal force on Balance Value

5. Error analysis of gravity and centrifugal force

The re-balancing scheme after considering centrifugal force.

5.2 Effect of centrifugal force on dynamic balance

SchemeBalancing position /mm Balancing

mass/kg

dynamic unbalance/

kg·mm2

Static unbalance

/kg·mmx y z

Without centrifugal

force

614.09 368.68 45.50 4.542692.75 16.00

-2181.85 -88.89 1088.42 7.40

With centrifugal

force

-2120.79 -94.55 647.82 4.701012.34 5.17

-2181.92 -88.47 1088.42 7.74

With that small weight at specific position, the effects of centrifugal force on thestatic and dynamic unbalance can be almost completely eliminated.

5. Summary

In this paper, the simulation and tests of the dynamic balancing design for the satellite antenna are carried out:

a) An accurate finite element model was created from the PROE model;b) By making use of the double planes dynamical balance method, the static

and dynamic unbalance of the satellite antenna reach the design index;c) The effect of wind load on the main reflector was also studied. which

gathering valuable experience for the subsequent ground balancing test of those kind of cable-net antenna；

d) The effects of gravity and centrifugal force on the dynamic balancing of the antenna were analyzed, obtaining the measures to eliminate those effects

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