1. Optimization design of the vibration isolation of AC magnet girder
Zhang Junsong ,Yu Jiebing, Wang Guangyuan, Kang Ling

2. Contents: 1.The vibration measurment of CSNS/RCS AC magnets.
2.The theory study of vibration isolation system for RCS dipole magnets.
3.The design of vibration isolator structure for RCS AC magnets，which must work in the radiation environment.
4.The vibration response test for AC magnet girder system with vibration isolation, and interpretation of result.

3. 1. The vibration measurment
The dipole magnets of RCS/CSNS worked with 1100A DC and 880A AC supply. The frequency of AC suppy is 25Hz. By mean of eddy current effect and alternate force, the iron core and loop make large vibration. Following shown the vibration performance test of dipole magnets woking on rated power supply.
AC supply
Z direction
X direction
Y direction
0.06
0.05
0.27
200
0.32
0.44
12.15
400
0.68
0.83
18.88
600
0.89
1.16
25.66
880
1.58
1.26
37.38
The frenquency is 25Hz. For the dipole magnets, the major vibration direction is vertical.

4. The dipole magnet vibration
For dipole magnets, the planeness of iron core junction surface have effect on the magnet vibration. According to much vibration response test of dipole mangets, the worse planeness made a larger vibration.

5. The quadrupole magnet vibration
With AC power supply，the quadrupole magnet had the same vibration characteristic with the dipole magnet, the vibration frequency is 25Hz.
The vibration response is micrometer, and larger gap between the magnet iron core makes larger vibration.

6. 2.The theory study of vibration isolation system
According the vibration response test, In CSNS/RCS, the AC dipole magnets have vertical vibration in working order. In view of  the vertical vibration, the dipole girder system can be simplified the following model. M
stiff girder F1 F2 K C
M is the dipole magnet mass, the K and C is the isolator stiffness and damping. F1 is the magnets vibration force, and F2 is the force on the girder.

7. The dipole magnet vibration model
stiff girder F1 F2 K C
1.When the frequency ratio is more than , the transfer rate is less than 1, the isolator have effects；
2.When the frequency ratio is more than 3, the transfer rate is close to constant. The large frequency rate makes a soft supply.
3.When the frequency ratio is close to 1, the system is in the resonance frequency. In this situation, increasing more damping will decrease vibration.

8. The dipole magnet vibration modelFr K1 M1 C1 K2 M2 C2 Fd
The dipole magnets girder is not a real stiff girder. According the ANSYS analysis and model testing, the stiffness of girder can be imputed. The magnets girder can be simplified to the two degrees of freedom system.
When designed the isolator of the dipole magnets girder，the TR was designed near 0.9.

9. The dipole magnet vibration model
ANSYS analog simulation ：
Following is the model parameter:
material
elastic modulus(Pa)
Poisson ratio
density (Kg/.m3)
steel
2.09E11
0.269
7890
stalloy
1.97E11
0.26
7650
The beam loss distribution on the primary collimator is estimated by using ORBIT .The corresponding average power density distribution can be expressed as this expression. The total power deposition is about 15 W.
According to the characteristic of the energy deposition, steady-state heat transfer analysis is performed to determine the temperature distribution. Convective heat transfer boundary condition is used in the calculation. The FEM model of one scraper is shown in Fig. Free air cooling condition has been considered in the thermal analysis.

10. Modal analysis ASNYS：without vibration isolator
Modal order
Modal frequency
Model shape 1
6.657 Hz
Y vertical 2 Hz
X horizontal 3 Hz
Whirling around Z 4
23.77 Hz 5
28.45 Hz 6
36.33 Hz
Whirling around X
The beam loss distribution on the primary collimator is estimated by using ORBIT .The corresponding average power density distribution can be expressed as this expression. The total power deposition is about 15 W.
According to the characteristic of the energy deposition, steady-state heat transfer analysis is performed to determine the temperature distribution. Convective heat transfer boundary condition is used in the calculation. The FEM model of one scraper is shown in Fig. Free air cooling condition has been considered in the thermal analysis. 1 2 3 4 5 6

11. Modal analysis ASNYS：with vibration isolator：
Vibration isolator is comprised of spring and damping. Owing to optimization design, the stiffness K= 21000N/mm，damping C=71440N.m/s2
spring
Combin40 damping
Modal analysis outcome:
The beam loss distribution on the primary collimator is estimated by using ORBIT .The corresponding average power density distribution can be expressed as this expression. The total power deposition is about 15 W.
According to the characteristic of the energy deposition, steady-state heat transfer analysis is performed to determine the temperature distribution. Convective heat transfer boundary condition is used in the calculation. The FEM model of one scraper is shown in Fig. Free air cooling condition has been considered in the thermal analysis.
Modal order
Modal frequency
Model shape 1
5.984 Hz
Y vertical 2
10.289Hz
X horizontal 3 Hz
Whirling around Z 4
16.789Hz 5 Hz 6 Hz
Whirling around X

12. Modal analysis ASNYS：with vibration isolator1阶 2阶 3阶 4阶 5阶 6阶

13. Modal analysis with and without isolator:
1.There are the same vibration shape between with and without isolator.
2. When the system fix with isolator, the natural frequency is less than that without isolator.
3. The vibration direction of the No.4 Modal order is vertical. When the system fixed vibration isolator, the natural frequency decrease to Hz, which less than 23.77Hz.

14. Frequency extraction test of dipole girder system
Three steps:
1. Setting up model system, fixing the sensor and calibration system
2. Adopt hammering method to stimulate the girder system. Measuring the system vibration response and the time history. Counting the frequency response function.
3. Analyze the model parameter and vibration space.
sensor
Force point
The beam loss distribution on the primary collimator is estimated by using ORBIT .The corresponding average power density distribution can be expressed as this expression. The total power deposition is about 15 W.
According to the characteristic of the energy deposition, steady-state heat transfer analysis is performed to determine the temperature distribution. Convective heat transfer boundary condition is used in the calculation. The FEM model of one scraper is shown in Fig. Free air cooling condition has been considered in the thermal analysis. Y Z X

15. model test
Adopt the soft exciting hammer. It can inspire the system vibration frequency from 1 to 70Hz. This frequency range meets the frequency extraction test.
3 times pulse excitation

16. Natural frenquency /Hz
The result of Frequency extraction test
Girder system without the vibration isolator
Model order 1 2 3 4 5 6
Natural frequency /Hz
8.664
11.093
15.328
23.205
28.436
36.215
Damping /%
1.772
2.602
2.647
5.519
2.786
3.922
Girder system with the vibration isolator
Model order 1 2 3 4 5 6
Natural frenquency /Hz
7.25
10.47
15.48
16.81
22.34
26.38
Damping /%
1.727
2.101
2.196
9.293
3.264
2.845
The result of frequency extraction test is same as the ANSYS analysis. The No.4 model space is vertical direction vibration, and the frequency is close to 25Hz, when the girder without the vibration isolator.

17. 1—Disc spring，6—metal-rubber（down），7—metal-rubber（up）
3.The design of vibration isolator structure
The difficult problem in vibration isolator design:
anti-fatigue performance; radiation-proof property; height limited
Following is the structure of vibration isolator: Disc spring and metal-rubber
1—Disc spring，6—metal-rubber（down），7—metal-rubber（up）
The merit of disc spring:
large bearing capacity; small height space; better anti-fatigue performance
The merit of metal-rubber:
It is made up with stainless steel material. It can working in the radiation environment.

18. The elastic and damping spare parts
There is a quality assurance, which made by product company, for that the spring have a less creep deformation.(less than 0.05mm in one year)
The metal-rubber was made up by stainless steel wire. The fatigue experiment was been done during the product.

19. 隔振器上
The isolator vibration response test was been done. Vibrating motor generated the 25Hz vibration. The vibration isolator load 6 Ton mass.
According to the test, in 25Hz, the vibration isolation force decrease to 19.8% from without to with isolator
隔振器下

20. 4.The vibration response test
The vibration response test included the girder with and without vibration isolator. The dipole magnet working in the rated power supply. DC 1100A and AC 880A. The center height of the magnet is 1200 mm。
test point 2
test point 1
test point 3
test point 2 Y Z X
test point 5
test point 4
test point 6
test point 5

21. test point
X direction
Ydirection
Zdirection
acceleration(m/s2)
amplitude(μm)
test point1
without
0.033
0.921
0.118
4.1666
0.034
1.087
with
0.3298
2.136
0.8939
decrement/%
test point2
0.0866
2.185
0.1382
3.851
0.0525
1.205
0.9451
0.0661
1.3205
56.746
test point3
0.053
1.976
0.1193
4.423
0.0237
0.63
0.0882
1.8011
0.6489
test point（girder）
Ydirection
acceleration(m/s2)
amplitude(μm)
test point4
without
0.1206
3.272
0.0433
2.8429
with
decrement%
64.096
13.12
test point5
0.1063
3.223
0.0511
1.8526
51.93
42.52
test point6
0.1181
3.555
0.0472
2.1153
60.034
40.49
The table is the result of response test. The maximun isolation decrement is 65.7% in vertical direction. Because of fixing the damping part, the decrement is lower than the design decrement, and the magnets amplitude is more small.

22. 5.The quadrupole magnet vibration problem solution
The quadrupole magnets in RCS makes vibration by the gaps between the each two iron corns. The larger gaps, the larger vibration. The direction of the vibration is the normal direction of iron corn junction surface.
Owing to the quadrupole magnets have a larger height, there was no a space to fixing vibration isolators. In CSNS, the way of decreasing vibration on quadrupole magnets is to improve the magnets corn precision.

23. Sextupole magnets vibration in AC magnetic force
QB272 quadrupole magnets in working makes the 25Hz AC magnetic field. The two sextupole magnets ,which are close to the quadrupole magnet, makes very large vibration by the AC magnetic force. The vibration amplitude is from micrometer. By long time working in this situation, the sextupole magnets will be broken.

24. Sextupole magnets vibration in AC magnetic force
For lower the vibration on sextupole magnets, a structure was designed and fixed on the top of sextupole magnets and quadrupole magnets. According to response test, the vibration force decrease to 25%.

25. RCS vibration monitoring system
For the safely and reliably working in CSNS/RCS, the vibration monitoring system was designed and produced. In RCS, every dipole magnets, quadrupole magnets, sextupole magnets and corrector magnets were fixed the vibrating sensor. When the vibration response is large 20 micrometer (experience value), the system will make the warning, and the magnets will stop working.

26. summary
For CSNS/RCS，the precision of the magnets iron core is the most important factor to the vibration problem.
The isolator between girder and magnets can prevent structure damage which may make more vibration.
The vibration monitoring system is another important way to make the device safety.

27. Thank you for attention