Pipe forming method based on real-time calculation and control of coil set energization zone

Abstract

This invention relates to a tube forming method based on real-time calculation and control of the energized area of ​​a coil group. Each turn of the driving coil group is connected to the power supply via an individual switch. During tube forming, the conduction state of each turn of the driving coil group is individually controlled according to the real-time tube forming position, i.e., the energized area of ​​the driving coil group is adjusted in real time, ensuring that the electromagnetic field direction at the tube is parallel to the tube surface, and the electromagnetic force on the tube is always perpendicular to the tube surface. This invention improves the flatness of the metal tube surface, thus improving the forming quality of the metal tube, enhances the heat dissipation effect of the coil, and increases the convenience of inspection and maintenance of each turn of the driving coil group.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic forming control of metal workpieces, and specifically relates to a tube forming method based on real-time calculation and control of the energized area of ​​a coil group. Background Technology

[0002] Research indicates that lightweighting is a crucial technological approach in the aerospace and automotive industries. Lightweighting encompasses two aspects: structure and materials. Achieving lightweighting through structure involves optimizing the structure to reduce material usage and thus workpiece weight while ensuring sufficient workpiece strength. Achieving lightweighting through materials involves selecting high-strength, lightweight materials, such as low-density alloys like magnesium, aluminum, and titanium, to significantly reduce workpiece mass while still meeting structural strength requirements through alloying. However, lightweight alloys are characterized by their light weight and thinness, resulting in poor plasticity and low forming limits at room temperature. Therefore, traditional machining methods often lead to problems like workpiece breakage and surface springback, limiting the industrial application of lightweight, high-strength materials. Electromagnetic forming offers a new technological means for lightweight metal processing.

[0003] Electromagnetic forming (EMF) is a high-speed forming method that uses magnetic field force to deform metal blanks. It utilizes the interaction between a pulsed strong magnetic field generated by a coil and the eddy currents induced in the workpiece by the current to generate electromagnetic force, driving the workpiece deformation. During EMF, a capacitor typically discharges a pulsed strong current to the drive coil. Simultaneously, the changing magnetic field generated by this pulsed current induces eddy currents in the metal workpiece near the drive coil. Under the influence of the pulsed electromagnetic force between the coil current and the workpiece eddy currents, the metal workpiece accelerates and deforms, achieving the forming process. Compared to traditional forming methods, EMF has the following advantages: First, it improves the forming limit, as it is a high strain rate forming process, which increases the material's strain rate sensitivity and strain hardening rate; second, it applies force non-contactly, which improves stress concentration during the forming process, resulting in high surface quality of the formed workpiece.

[0004] Existing electromagnetic forming related patents mainly focus on using magnet collectors and changing the position of the drive coil to change the positive pressure provided by the drive coil, thereby improving the forming performance of the workpiece. In 2023, Shao Zihao's paper "Electromagnetic Force and Formability Analysis of Tubes Based on Convex Magnet Collectors [1]" proposed using magnet collectors to improve the forming performance. The basic principle is to use magnet collectors to change the magnetic flux distribution, thereby strengthening the axial electromagnetic force. This method solves the problems of uneven forming and thinning of wall thickness of magnetic tubes, but it cannot achieve efficient utilization of electromagnetic force. At the same time, the cost of magnet collectors is higher and the energy conversion rate is reduced. The Chinese invention "An Electromagnetic Forming Device and Method" with publication number CN108080483B discloses an electromagnetic forming device, in which the main device is a forming coil and a pressing coil. The forming coil provides the workpiece expansion force; according to the forming state, the position of the drive coil is changed to realize the progressive forming of the workpiece. This invention solves the problem of unidirectional electromagnetic force in traditional electromagnetic forming methods. However, during the movement of the forming coil, a superior control device is required for position control, placing very high demands on the response time and accuracy of the control device. Furthermore, progressive forming leads to material hardening, which can easily cause wrinkling. In summary, existing technologies lack superior methods and devices for improving the electromagnetic forming performance of pipe fittings.

[0005] References:

[0006] [1] Shao Zihao, Wu Weiye, Wang Chenxin, et al. Electromagnetic force and formability analysis of pipe fittings based on convex magnet collectors [J]. Journal of Plasticity Engineering, 2023, 30(11):36-44. Summary of the Invention

[0007] The purpose of this invention is to provide a tube forming method based on real-time calculation and control of the energized area of ​​a coil group, aiming to solve the problem of uneven stress on the tube surface and its impact on tube quality caused by existing metal workpiece forming methods such as tube bulging. By using a coil group composed of single-turn coils controlled by an independent power supply to replace the traditional integral coil group, the problems of large size, difficulty in winding, and poor heat dissipation of integral coils are solved. Each turn of the coil is driven by a different switch to control the conduction of the driving coil group. By controlling the energized area of ​​the driving coil group in real time, the metal tube is subjected to an electromagnetic force perpendicular to the tube surface, improving the flatness of the metal tube surface and thus improving the forming quality of the metal tube.

[0008] The technical solution of this invention is a tube forming method based on real-time calculation and control of the coil group energization zone, comprising the following steps:

[0009] Step 1: Secure the pipe fitting using the edge clamping device;

[0010] Step 2: Based on the material and forming specifications of the tube to be formed, determine the parameters of the drive coil group, including the number of coil layers and the coil spacing, and model the drive coil using the finite element analysis software Comsol Ansys.

[0011] Step 3: Each coil of the drive coil group is powered independently. Each coil is connected to the power supply via a switch. At time t0, the coil switch is controlled to energize each coil. The tube begins to deform under the electromagnetic field of the drive coil group. t0 represents the initial time of tube forming.

[0012] Step 4: During the forming process of the pipe fitting, the maximum deformation in the horizontal direction of the pipe fitting at time t is detected by a displacement detection device, and the angle between the pipe fitting and the vertical plane at time t, i.e., the inclination angle, is calculated.

[0013] Step 5: Draw a first boundary surface parallel to the first bulging part of the tube and a second boundary surface parallel to the second bulging part of the tube through the outer center line of the drive coil group. Draw a third boundary surface and a fourth boundary surface parallel to the first bulging part and the second bulging part of the tube, respectively, through the center points of both ends of the drive coil group. The area enclosed by the first boundary surface, the second boundary surface, the third boundary surface, the fourth boundary surface and the end faces of both ends of the drive coil group is taken as the energized area of ​​the drive coil group. Construct the energized area at time t in the finite element analysis software Comsol Ansys.

[0014] Step 6: Calculate the current carrying coefficient of each coil based on the volume of each coil in the energized area, determine whether a single coil is conducting based on the current carrying coefficient, and control the coil switch based on the determination result of each coil.

[0015] Step 7: Let t = t + Δt, that is, add a time step to time t, where Δt represents the time step, and determine if t ≤ t end Is the condition true? If the result is yes, proceed to step 4; otherwise, end the process. end Indicates the forming deadline.

[0016] Furthermore, the first and second boundary surfaces are both frustum-shaped boundary surfaces, while the third and fourth boundary surfaces are both conical boundary surfaces.

[0017] Preferably, in step 6, the current carrying coefficient C i,j The value of is coil X i,j The area within the cross-section of the energized region and the coil X i,j The ratio of the cross-sectional areas, C i,jLet i = 1, 2…M and j = 1, 2…N represent the energizing coefficient of the j-th turn of the i-th layer. The driving coil group is numbered sequentially from top to bottom, and sequentially from outside to inside, with M being the number of coil layers in the driving coil group and N being the number of turns in each layer. It is worth noting that if the tube forming presents a horizontal centerline axially symmetrical distribution, then the number of coil layers in the driving coil group should be even, i.e., M should be even.

[0018] Preferably, a threshold T for the current conduction coefficient is set, if

[0019] C i,j ≥T

[0020] Then control coil X i,j The switch causes coil X to... i,j power ups.

[0021] Furthermore, the threshold T is determined based on the value of the coil spacing L.

[0022] Preferably,

[0023] When 0mm ≤ L < 5mm, T = 1 / 2

[0024] When 5mm≤L≤10mm, T=2 / 3.

[0025] Preferably, the time step Δt ranges from 0 to 1000 μs.

[0026] Preferably, a capacitor power supply is used to power each turn of the drive coil group, and the discharge voltage of the capacitor power supply is 1-100kV.

[0027] Preferably, the capacitance of the capacitor power supply is 2-200μF.

[0028] An electromagnetic forming apparatus includes a drive coil assembly, a capacitor power supply, a pressing device, a displacement detection device, and a computer. The drive coil assembly includes multi-turn coils arranged in layers, with each coil connected to the capacitor power supply via a separate air switch. The displacement detection device is communicatively connected to the computer and is used to detect the deformation of the pipe fitting.

[0029] Preferably, the displacement detection device is a laser displacement meter.

[0030] Preferably, the number of coil layers in the drive coil group is even.

[0031] Under the action of pulsed current, the drive coil group generates a pulsed magnetic field. Eddy currents are generated in the pipe under the pulsed magnetic field, and the interaction between the eddy currents and the magnetic field generates an electromagnetic force, thus providing conditions for the deformation of the pipe. The coils provided by this invention are represented in the form of an array in a spatial cross-sectional view. After the pipe is deformed to a certain extent, the energized area of ​​the drive coil group will change according to the deformation of the pipe. Different energized areas generate different directions of pulsed magnetic fields. Under the interaction between the eddy currents and the magnetic field, only an electromagnetic force perpendicular to the surface of the pipe wall at the current moment is generated.

[0032] Compared with the prior art, the beneficial effects of the present invention include:

[0033] 1) The present invention uses a drive coil group composed of discrete coils. Each turn of the drive coil group is connected to the power supply via a separate switch. By controlling the energized area of ​​the drive coil group in real time, the metal pipe is only subjected to electromagnetic force in the direction perpendicular to the surface of the pipe, thereby improving the flatness of the surface of the metal pipe and thus improving the forming quality of the metal pipe.

[0034] 2) This invention uses a coil group composed of discrete, individually energized single-turn coils to replace the traditional integral coil group, which facilitates precise control of the energizing time, energizing duration, and current magnitude of each coil, and also improves the heat dissipation effect of each coil. In addition, it also increases the convenience of inspection and maintenance of each coil in the drive coil group. Attached Figure Description

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] Figure 1 This is a flowchart illustrating a tube forming method based on real-time calculation and control of the coil group energized zone.

[0037] Figure 2 The equivalent circuit diagram of each turn of the drive coil group in the embodiment is connected to the power supply.

[0038] Figure 3 This is a schematic diagram of the force direction of the pipe fitting and the drive coil in the initial state of Example 1.

[0039] Figure 4 This is a schematic diagram of the force direction of the pipe fitting and the driving coil when the pipe fitting tilt angle is 11.6° in Example 1.

[0040] Figure 5 This is a schematic diagram of the force direction of the pipe fitting and the driving coil when the pipe fitting tilt angle is 18.4° in Example 1.

[0041] Figure 6 This is a schematic diagram of the force direction of the pipe fitting and the drive coil in the initial state of Example 2.

[0042] Figure 7This is a schematic diagram of the force direction of the pipe fitting and the driving coil when the pipe fitting tilt angle is 10.8° in Example 2.

[0043] Figure 8 This is a schematic diagram of the force direction of the pipe fitting and the driving coil when the pipe fitting tilt angle is 30.7° in Example 2.

[0044] Explanation of reference numerals in the attached drawings: 1. Pipe fitting; 1.1. First bulging part; 1.2. Second bulging part; 2. Pressing device; 3. Drive coil assembly. Detailed Implementation

[0045] Example 1

[0046] An electromagnetic forming apparatus for pipe forming includes a drive coil group 3, a capacitor power supply, a pressing device 2, a displacement detection device, and a computer. The drive coil group 3 comprises multi-turn coils arranged in layers, each coil connected to the capacitor power supply via a separate air switch. The displacement detection device is communicatively connected to the computer. The displacement detection device detects the deformation of the pipe and calculates the angle (inclination angle) between the pipe wall and the vertical line at time t. In this embodiment, the displacement detection device is a laser displacement gauge. The drive coil group uses a circular ring coil.

[0047] like Figure 1 As shown, the tube forming method based on real-time calculation and control of the coil group energized area includes:

[0048] Step 1: Fix the pipe fitting 1 using the edge clamping device 2.

[0049] Step 2: Based on the material and forming specifications of the tube to be formed, determine the parameters of the drive coil group, including the number of coil layers and the coil spacing, and model the drive coil group using the finite element analysis software Comsol Ansys.

[0050] Step 3: Power each turn of the drive coil group independently, with each turn connected to the power supply via a switch, such as... Figure 2 As shown. At time t0, the control coil switch energizes each turn of the coil, and the tube begins to deform under the electromagnetic field of the drive coil group. t0 represents the initial time of tube forming.

[0051] In this embodiment, the discharge voltage of the capacitor power supply is 30kV, and the capacitance of the capacitor power supply is 20μF.

[0052] Step 4: During the forming process of the pipe fitting, the displacement detection device is used to detect the maximum deformation of the pipe fitting in the horizontal direction at time t, and the angle between the pipe fitting and the vertical plane at time t is calculated, i.e., the inclination angle.

[0053] Step 5: Draw a first boundary surface parallel to the first bulging part 1.1 of the tube and a second boundary surface parallel to the second bulging part 1.2 of the tube through the outer center line of the drive coil group. Draw a third boundary surface and a fourth boundary surface parallel to the first bulging part and the second bulging part of the tube through the center points of both ends of the drive coil group. The area enclosed by the first boundary surface, the second boundary surface, the third boundary surface, the fourth boundary surface and the end faces of both ends of the drive coil group is the energized area of ​​the drive coil group.

[0054] The first and second boundary surfaces are both frustum-shaped boundary surfaces, while the third and fourth boundary surfaces are both conical boundary surfaces.

[0055] Construct the energized region at time t in the finite element analysis software Comsol Ansys.

[0056] Step 6: Calculate the current carrying coefficient of each coil based on the area of ​​each coil in the energized region, determine whether a single coil is conducting based on the current carrying coefficient, and control the coil switch based on the determination result of each coil.

[0057] Current carrying coefficient C i,j The value of is coil X i,j The area within the cross-section of the energized region and the coil X i,j The ratio of the cross-sectional areas, C i,j Let i = 1, 2…M and j = 1, 2…N represent the energizing coefficient of the j-th turn of the i-th layer. The driving coil group is numbered sequentially from top to bottom, and sequentially from outside to inside, with M being the number of coil layers in the driving coil group and N being the number of turns in each layer. It is worth noting that if the tube forming presents a centerline axially symmetrical distribution, then the number of coil layers in the driving coil group should be even, i.e., M is even.

[0058] In the embodiment, M=6, N=6, meaning the drive coil group has 6 layers, and each layer has 6 turns of coil, such as... Figure 3 As shown.

[0059] Set a threshold T for the current carrying capacity.

[0060] If C i,j ≥T,

[0061] Then control coil X i,j The switch causes coil X to... i,j power ups.

[0062] In this embodiment, the coil spacing L is 0 mm and the threshold T = 1 / 2.

[0063] Step 7: Let t = t + Δt, that is, add a time step to time t, where Δt represents the time step, and determine if t ≤ t end Is the condition true? If the result is yes, proceed to step 4; otherwise, end the process.end Indicates the forming deadline.

[0064] In this embodiment, Δt is set to 10 μs.

[0065] Figure 4 The diagram shows a schematic of the first bulge section 1.1 of the pipe fitting, with an angle of 11.6° between the pipe wall and the vertical line. The computer calculates the inclination angle of the pipe wall based on the real-time horizontal displacement detected by a laser displacement gauge. The energized area of ​​the drive coil is determined in the drive coil group model established in the finite element analysis software Comsol Ansys. Based on the area of ​​each coil turn within the energized area, the energizing coefficient of each coil turn is calculated, and it is determined whether the energizing coefficient is greater than or equal to 1 / 2. If the energizing coefficient is not less than 1 / 2, the switch of that coil turn is controlled to conduct; otherwise, the switch of that coil turn is turned off. Specifically, the judgment result is: First layer coil X... 1,1 X 1,2 X 1,3 X 1,4 X 1,5 X 1,6 When energized, the second layer coil X 2,2 X 2,3 X 2,4 X 2,5 X 2,6 When energized, the third layer coil X 3,1 X 3,2 X 3,3 X 3,4 X 3,5 Power on, fourth layer coil X 4,1 X 4,2 X 4,3 X 4,4 X 4,5 Power on, fifth layer coil X 5,1 X 5,2 X 5,3 X 5,4 X 5,5 X 5,6 Power on, sixth layer coil X 6,1 X 6,2 X 6,3 X 6,4 X 6,5 X 6,6 When energized, the electromagnetic field generated by the coil and the eddy current induced on the pipe work together to produce an electromagnetic force F perpendicular to the surface of the pipe.

[0066] When the angle between the pipe wall of the first bulge portion 1.1 of the pipe fitting and the vertical line is 18.4°, if... Figure 5As shown, the computer calculates the inclination angle of the pipe wall based on the real-time horizontal displacement detected by the laser displacement gauge. Then, in the finite element analysis software Comsol Ansys, it determines the energized area of ​​the drive coil and calculates the energization coefficient of each turn. This coefficient is then compared with a threshold of 1 / 2 to determine whether the turn is energized. Specifically, the result is: First layer coil X... 1,2 X 1,3 X 1,4 X 1,5 X 1,6 When energized, the second layer coil X 2,1 X 2,2 X 2,3 X 2,4 X 2,5 X 2,6 When energized, the third layer coil X 3,1 X 3,2 X 3,3 X 3,4 X 3,5 Power on, fourth layer coil X 4,1 X 4,2 X 4,3 X 4,4 X 4,5 Power on, fifth layer coil X 5,1 X 5,2 X 5,3 X 5,4 X 5,5 X 5,6 Power on, sixth layer coil X 6,2 X 6,3 X 6,4 X 6,5 X 6,6 When energized, the magnetic field generated by the energized coil interacts with the eddy currents induced on the pipe to produce an electromagnetic force perpendicular to the surface of the pipe.

[0067] Example 2

[0068] The tube forming method in Example 2 is the same as in Example 1. The difference between the electromagnetic forming device in Example 2 and Example 1 is that the drive coil group includes 8 layers of coils, each layer having 3 turns, i.e., M=8, N=3, as shown below. Figure 6 As shown.

[0069] In this embodiment, the coil spacing L is 6mm and the threshold T = 2 / 3.

[0070] The time step Δt is 10us.

[0071] When the angle between the pipe wall of the first bulge portion 1.1 of the pipe fitting and the vertical line is 10.8°, such as Figure 7As shown. The computer calculates the inclination angle of the pipe wall based on the real-time horizontal displacement detected by the laser displacement gauge. In the finite element analysis software Comsol Ansys, the energized area of ​​the drive coil is determined. Based on the area of ​​each coil within the energized area, the energizing coefficient of each coil is calculated, and it is determined whether the energizing coefficient is greater than or equal to 2 / 3. If the energizing coefficient is not less than 2 / 3, the switch of that coil is controlled to make it conduct; otherwise, the switch of that coil is turned off. Specifically, the judgment result is: First layer coil X... 1,2 X 1,3 When energized, the second layer coil X 2,2 X 2,3 When energized, the third layer coil X 3,1 X 3,2 Power on, fourth layer coil X 4,1 X 4,2 Power on, fifth layer coil X 5,1 X 5,2 Power on, sixth layer coil X 6,1 X 6,2 Power on, seventh layer coil X 7,2 X 7,3 Power on, eighth layer coil X 8,2 X 8,3 When energized, the electromagnetic field generated by the coil and the eddy current induced on the pipe work together to produce an electromagnetic force F perpendicular to the surface of the pipe.

[0072] When the angle between the pipe wall of the first bulge portion 1.1 of the pipe fitting and the vertical line is 30.7°, if... Figure 8 As shown, the computer uses a laser displacement gauge to detect and calculate the inclination angle of the pipe fitting. In the finite element analysis software Comsol Ansys, it determines the energized area of ​​the drive coil in the drive coil group model and calculates the energization coefficient of each turn. This coefficient is then compared with a threshold of 2 / 3 to determine whether the turn is energized. Specifically, the result is: First layer coil X... 1,3 When energized, the second layer coil X 2,2 When energized, the third layer coil X 3,2 Power on, fourth layer X 4,1 When the coil is energized, the fifth layer coil X 5,1 Power on, sixth layer coil X 6,2 Power on, seventh layer coil X 7,2 Power on, eighth layer coil X 8,3 When energized, the magnetic field generated by the energized coil interacts with the eddy current induced on the pipe to produce an electromagnetic force F perpendicular to the surface of the pipe.

Claims

1. A method for forming tubular components based on real-time calculation and control of the energized zone of a coil group, characterized in that, Each coil of the drive coil group is connected to the power supply via a separate switch. During the tube forming process, the conduction state of each coil of the drive coil group is individually controlled according to the real-time tube forming position, that is, the energized area of ​​the drive coil group is adjusted in real time, so that the direction of the electromagnetic field at the tube is parallel to the tube surface, and the electromagnetic force on the tube is always perpendicular to the tube surface, thereby improving the tube forming effect and quality. The tube forming method includes the following steps: Step 1: Secure the pipe fitting using the edge clamping device; Step 2: Based on the material and forming specifications of the tube to be formed, determine the parameters of the drive coil group, including the number of coil layers and the coil spacing, and model the drive coil using the finite element analysis software Comsol Ansys. Step 3: Each coil of the drive coil group is powered independently. Each coil is connected to the power supply via a switch. At time t0, the coil switch is controlled to energize each coil. The tube begins to deform under the electromagnetic field of the drive coil group. t0 represents the initial time of tube forming. Step 4: During the forming process of the pipe fitting, the maximum deformation in the horizontal direction of the pipe fitting at time t is detected by a displacement detection device, and the angle between the pipe fitting and the vertical plane at time t, i.e., the inclination angle, is calculated. Step 5: Draw a first boundary surface parallel to the first bulging part of the tube and a second boundary surface parallel to the second bulging part of the tube through the outer center line of the drive coil group. Draw a third boundary surface and a fourth boundary surface parallel to the first bulging part and the second bulging part of the tube through the center points of both ends of the drive coil group. The area enclosed by the first boundary surface, the second boundary surface, the third boundary surface, the fourth boundary surface and the end faces of both ends of the drive coil group is the energized area of ​​the drive coil group. The first and second boundary surfaces are both frustum-shaped boundary surfaces, while the third and fourth boundary surfaces are both conical boundary surfaces. Construct the energized region at time t in the finite element analysis software Comsol Ansys; Step 6: Calculate the current carrying coefficient of each coil based on the volume of each coil in the energized area, determine whether a single coil is conducting based on the current carrying coefficient, and control the coil switch based on the determination result of each coil. Step 7: Let t = t + Δt, that is, add a time step to time t, where Δt represents the time step, and determine if t ≤ t end Is the condition true? If the result is yes, proceed to step 4; otherwise, end the process. end Indicates the forming deadline.

2. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 1, characterized in that, In step 6, the current carrying coefficient C i,j The value of is coil X i,j The area within the cross-section of the energized region and the coil X i,j The ratio of the cross-sectional areas, C i,j Let i = 1, 2…M and j = 1, 2…N represent the energizing coefficient of the j-th turn of the i-th layer. The driving coil group is numbered sequentially from top to bottom, and sequentially from outside to inside, with M being the number of coil layers in the driving coil group and N being the number of turns in each layer.

3. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 2, characterized in that, The number of coil layers M is an even number.

4. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 3, characterized in that, Set a threshold T for the current carrying capacity. like C i,j ≥T Then control coil X i,j The switch causes coil X to... i,j power ups.

5. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 4, characterized in that, The threshold T is determined based on the value of the coil spacing L. When 0mm ≤ L < 5mm, T = 1 / 2 When 5mm≤L≤10mm, T=2 / 3.

6. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 5, characterized in that, A capacitor power supply is used to power each turn of the drive coil group, and the discharge voltage of the capacitor power supply is 1-100kV.

7. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 6, characterized in that, The capacitance of the capacitor power supply is 2-200μF.

8. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 2, 3, 4, 5, 6, or 7, characterized in that, The time step Δt ranges from 0 to 1000 μs.

9. The tube forming method based on real-time calculation and control of the coil group energized area according to claim 8, characterized in that, The displacement detection device is a laser displacement meter.

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