Hydroforming of elliptical cavities

Activities of the past several years in developing the technique of forming seamless (weldless) cavity cells by hydroforming are summarized. An overview of the technique developed at DESY for the fabrication of single cells and multicells of the TESLA cavity shape is given and the major rf results are presented. The forming is performed by expanding a seamless tube with internal water pressure while simultaneously swaging it axially. Prior to the expansion the tube is necked at the iris area and at the ends. Tube radii and axial displacements are computer controlled during the forming process in accordance with results of finite element method simulations for necking and expansion using the experimentally obtained strain-stress relationship of tube material. In cooperation with industry different methods of niobium seamless tube production have been explored. The most appropriate and successful method is a combination of spinning or deep drawing with flow forming. Several single-cell niobium cavities of the 1.3 GHz TESLA shape were produced by hydroforming. They reached accelerating gradients $E_{\text{acc}}$ up to $35\mathrm{MV}/\mathrm{m}$ after buffered chemical polishing (BCP) and up to $42\mathrm{MV}/\mathrm{m}$ after electropolishing (EP). More recent work concentrated on fabrication and testing of multicell and nine-cell cavities. Several seamless two- and three-cell units were explored. Accelerating gradients $E_{\text{acc}}$ of $30–35\mathrm{MV}/\mathrm{m}$ were measured after BCP and $E_{\text{acc}}$ up to $40\mathrm{MV}/\mathrm{m}$ were reached after EP. Nine-cell niobium cavities combining three three-cell units were completed at the company E. Zanon. These cavities reached accelerating gradients of $E_{\text{acc}}=30–35\mathrm{MV}/\mathrm{m}$. One cavity is successfully integrated in an XFEL cryomodule and is used in the operation of the FLASH linear accelerator at DESY. Additionally the fabrication of bimetallic single-cell and multicell NbCu cavities by hydroforming was successfully developed. Several NbCu clad single-cell and double-cell cavities of the TESLA shape have been fabricated. The clad seamless tubes were produced using hot bonding or explosive bonding and subsequent flow forming. The thicknesses of Nb and Cu layers in the tube wall are about 1 and 3 mm respectively. The rf performance of the best NbCu clad cavities is similar to that of bulk Nb cavities. The highest accelerating gradient achieved was $40\mathrm{MV}/\mathrm{m}$. The advantages and disadvantages of hydroformed cavities are discussed in this paper.

Figure 1

Elongation at break vs temperature for high purity niobium.

Figure 2

Comparison of the tensile test result in continuos and pulsed (stepwise) stress regime.

Figure 3

Scheme of the bulge test device.

Figure 4

(a) Comparison of FEM simulated wall thicknesses $T$ after necking with experimental data (Tubes 8–9,11,13). (b) Calculated stress distribution after necking.

Figure 5

(a) Simulation of radius growth during hydroforming in comparison with experiment (Tube 13). (b) Calculated stress distribution after hydroforming.

Figure 6

(a) and (b) FEM simulations of the iris reduction vs axial displacement (upper image) and of internal pressure vs axial displacement (lower image).

Figure 7

(a) Principle of the necking at the iris. (b) Principle of the necking at the tube end.

Figure 8

(a) Principle of profile ring movement during the end cell necking. (b) Principle of the profile ring movement during iris necking.

Figure 9

Central part of DESY necking device.

Figure 10

Example of the Nb three-cell units after necking.

Figure 11

Setup of the hydroforming machine at DESY.

Figure 12

The hydroforming machine.

Figure 13

(a) Conical anomaly of intermediate tube shape. (b) Anomalous tube shape for circumferential variation of yield strength.

Figure 14

Typical pressure vs axial displacement and radius vs axial displacement curves.

Figure 15

Shape of the intermediate constraint.

Figure 16

Pressure and radius growth vs axial displacement on the first stage of the expansion.

Figure 17

Shape of the molds for final forming.

Figure 18

Pressure and radius growth vs the axial displacement on the second stage of the expansion.

Figure 19

Schema of high pressure calibration device.

Figure 20

DESY calibration device for hydroformed cavities.

Figure 21

Vickers hardness HV along the cell contour—starting from the iris. Cells are hydroformed from tubes of $\mathrm{ID}=130\mathrm{mm}$ and $\mathrm{ID}=150\mathrm{mm}$. Straight line represents the HV of the original tube.

Figure 22

Microstructure of the electron beam weld of high purity niobium. The grain size scope is $50–2000\mu \mathrm{m}$.

Figure 23

Microstructure of the back extruded niobium tube with RRR300.

Figure 24

(a) Spinning process. (b) Spun Nb tubes.

Figure 25

(a) Flow forming process. (b) Subsequently flow formed spun Nb tubes.

Figure 26

Orientation Imaging microscope figures of the Nb tube produced by combination of spinning and flow forming.

Figure 27

Three- and two-cell units, hydroformed from BL-WC tubing.

Figure 28

Maximal accelerating gradients of BCP treated single-cell hydroformed cavities.

Figure 29

$Q_{\mathrm{o}}$ vs $E_{\text{acc}}$ at 2K for cavity 1K2 produced from deep drawn tube after BCP and final EP. RRR100, post purified at $1400°\mathrm{C}$. BCP and rf tests done at JLab. EP done at KEK [35].

Figure 30

Hydroforming of cells can be done by three cells simultaneously as well as cell by cell.

Figure 31

Two- and three-cell cavities hydroformed at DESY.

Figure 32

$Q_{\mathrm{o}}$ (Eacc) performance of the two-cell hydroformed cavity 2H3. Vertical EP done at Cornell University by A. Crawford.

Figure 33

$Q_{\mathrm{o}}$ ($E_{\text{acc}}$) of three-cell hydroformed cavities after post purification at $1250°\mathrm{C}$. The total material removal is ca. $250\mu \mathrm{m}$ by BCP.

Figure 34

Hydroformed nine-cell TESLA cavities Z145, Z163 and Z164 from left to the right.

Figure 35

Radial tuning of the cavity Z163.

Figure 36

Radio-frequency performance of nine-cell hydroformed cavities Z145, Z163 and Z164.

Figure 37

NbCu clad cavities from explosive bonded tubes welded for preparation at DESY and JLab.

Figure 38

Examples of rf results achieved in single-cell explosively bonded NbCu cavities. 1NC2 at 2K: Preparation and rf tests done at JLab: $180\mu \mathrm{m}$ BCP, annealing at $800°\mathrm{C}$, baking at $140°\mathrm{C}$ for 30 hours, HPR. 1NC5 at 1.8K: Preparation and rf tests done at KEK: CBP $50\mu \mathrm{m}$, BCP $110\mu \mathrm{m}$, HT $750°\mathrm{C}$, EP $50\mu \mathrm{m}$, baking at $130°\mathrm{C}$.

Figure 39

$Q_{\mathrm{o}}$ ($E_{\text{acc}}$) curve of the NSC-3 cavity at 2K: CBP $50\mu \mathrm{m}$, BCP $10\mu \mathrm{m}$, annealing $750°\mathrm{C}$ 3h, EP $70\mu \mathrm{m}$ (K. Saito) [44].

Figure 40

Microstructure of Cu0.15%Zr after annealing at $800°\mathrm{C}$ for 2 hours.

Figure 41

Additional surface resistance after quenches in the cavity 1NC2 at ca $40\mathrm{MV}/\mathrm{m}$.

Figure 42

Radio-frequency performance of TESLA shape single-cell cavity produced at company Butting by hydroforming. RRR250, radio-frequency tests done at JLab, EP done at KEK.