Design method of brake disc assembly for airplane

Abstract

The invention discloses a design method of a brake disc assembly for an airplane, and belongs to the field of airplane brakes. In order to solve the problem of 10-20 Hz vibration caused by a high impact load of 750 kN or above when an aircraft lands, a triple vibration suppression technical scheme is provided, Y-shaped damping holes are formed in a static disc, nodes are located in a reference circle, and the static disc is filled with a nano aerogel porous material; a lotus leaf-shaped damping hole is formed in the movable disc, an obtuse angle node is matched with a reference circle, and the movable disc is filled with a nano aerogel porous material; a carbon fiber damping sleeve (movable disc) and a U-shaped damping net (static disc) are additionally arranged on a key groove boss. The friction pair even number, the reference circle and the braking force acting point are limited; the graphitization degree of the carbon brake material is controlled to be 55-65%, and the temperature uniformity of the heat treatment furnace is less than or equal to + / -20 DEG C. The vibration amplitude of the brake disc assembly designed through the method is reduced by 84%, the convergence time is shortened by 75%, and the reliability requirement of extreme working conditions is met.

Description

Technical Field

[0001] The invention belongs to the field of aircraft brakes, and in particular relates to a design method for an aircraft brake disc assembly. Background Art

[0002] An aircraft's takeoff and landing performance is directly related to flight safety and stability. This is especially true for aircraft that experience radial impact loads exceeding 750kN during single-wheel landing and need to brake within a distance of 100 meters. This places stringent demands on the braking system: Extreme working conditions: The superposition of arresting braking load and impact load causes the brake disc assembly to vibrate widely in the 10–20 Hz frequency range; Dynamic coupling effect: The braking process is a typical thermal-mechanical coupling process. The friction coefficient changes nonlinearly with the instantaneous speed, resulting in dynamic fluctuations in the braking torque, which further stimulates system resonance. Space constraints: The landing gear must meet comprehensive requirements such as impact resistance, strong vibration resistance, and short-distance braking within a limited space.

[0003] Current brake disc designs primarily focus on static dimensional constraints. For example, the design is based on the internal and external dimensions of the brake cavity, with the inner and outer diameters of the brake disc as the primary design points. This design fails to address the large impact loads (single-wheel landing radial impact load limit exceeding 750kN) encountered during landing braking. Wide load fluctuations cause the brake disc to vibrate in the 10Hz to 20Hz range, making it difficult to meet the landing brake requirements for aircraft with high impact loads. Specific drawbacks are as follows: Lack of vibration suppression design: The product has not been dynamically optimized for broadband vibration (10–20 Hz) under high impact loads, resulting in resonance in extreme operating conditions, posing a safety threat. Lack of damping mechanism: No correlation model between friction coefficient, velocity change rate and system damping has been established, making it impossible to improve dynamic stability through structural design; Rough material processing: The speed sensitivity of the friction coefficient is not precisely controlled by the degree of graphitization, resulting in fluctuations in the braking torque and increased vibration.

[0004] To solve this problem, the present invention proposes a design method for an aircraft brake disc assembly. Summary of the Invention

[0005] Technical issues to be solved: To overcome the shortcomings of existing technologies, this invention provides a design method for aircraft brake disc assemblies. This upgrades cavity vibration suppression to a composite material-aerogel-air triple energy dissipation configuration, overcoming the technical bottleneck of effectively implementing damping in brake discs under high-temperature / high-load conditions. This invention addresses the vibration divergence caused by the coupling of high impact loads and frictional excitation, meeting the reliability requirements of high-impact aircraft brake systems.

[0006] The technical solution of the present invention is: a design method for an aircraft brake disc assembly, wherein the brake disc assembly includes a pressure disc, a static disc, a pressure disc and a dynamic disc; the specific steps are as follows: Step 1: Design the Y-shaped damping hole structure of the stator disc, and open a Y-shaped damping hole with a diameter of φC = φ2mm ~ φ5mm in the middle layer of the stator disc in the thickness direction; N 内 -1 group of Y-shaped damping holes are arranged radially along the circumference of the stator, N 内 is the number of keyways on the inner edge of the stator disc. The nodes of each Y-shaped damping hole are located at the action point of the brake piston actuator or on the pitch circle of the brake disc assembly. The Y-shaped damping hole is filled with nano-aerogel porous material and sealed with a carbon fiber cylindrical plug. Step 2: Design the lotus leaf-shaped damping hole structure of the moving disk, and open a lotus leaf-shaped damping hole with a diameter of φD = φ3mm ~ φ7mm in the middle layer of the moving disk in the thickness direction; N 外 The lotus leaf-shaped damping holes are evenly distributed along the circumference of the moving disk, N 外 is the number of keyways on the outer edge of the rotor disc, and the bending nodes of each lotus-shaped damping hole are located in the action area of ​​the brake actuator or on the pitch circle of the brake disc assembly; the lotus-shaped damping hole is filled with nano-aerogel porous material and sealed with a carbon fiber cylindrical plug; Step 3: Add a carbon fiber damping sleeve inside the boss protection shell between the key slots of the dynamic plate, and add a U-shaped carbon fiber damping net inside the boss protection shell between the key slots of the static plate; Step 4: Control the friction pair number n≤5 and be an odd number, the static plate thickness ≥15mm, and the dynamic plate thickness ≥20mm; Step 5: Calculate the pitch circle diameter of the brake disc assembly using the following formula: D f =0.274×D lw -twenty two Among them, D f D is the pitch circle diameter of the brake disc assembly; lw is the tire assembly diameter; Step 6: Set the number of braking force application points to be greater than or equal to 6, and the application area of ​​each application point to 1800mm 2 ~3500mm 2 ; Step 7: The moving plate and the static plate are both made of carbon brake material, and their graphitization degree is controlled to be 55% to 65%. The furnace temperature uniformity of the graphitization heat treatment is ≤±20°C. A further technical solution of the present invention is: in step 1, the Y-shaped damping hole radially penetrates the boss and the outer peripheral surface between the key grooves on the inner edge of the stator, with the single hole end facing the boss side and the double hole end facing the outer peripheral surface side, and the acute angle between the double hole ends is 50° to 60°; wherein, The diameter of the Y-shaped damping hole φC is 20% of the thickness of the static disk. When the thickness of the static disk is greater than 25mm, φC=φ5mm. The size of the carbon fiber cylindrical plug is (φC+0.05mm)×6mm. A further technical solution of the present invention is: in step 2, the lotus leaf-shaped damping hole radially penetrates the inner annular surface and the outer edge keyway of the movable plate, and includes two symmetrical groups of bent holes, and the two groups of bent holes form an acute angle of 60° at the outer edge keyway, and the bending part of each group of bent holes is an obtuse angle of 120°; wherein, The diameter of the lotus leaf damping hole φD is 20% of the thickness of the moving plate. When the thickness of the moving plate is greater than 35mm, φD=φ7mm. The size of the carbon fiber cylindrical plug is (φD+0.05mm)×6mm.

[0007] A further technical solution of the present invention is: in step 3: The carbon fiber damping sleeve is a box structure with one end open, covering the entire outer wall of the boss between the keyways on the outer edge of the moving plate; The carbon fiber damping net is a U-shaped structure, covering the circumferential outer wall of the boss between the keyways on the inner edge of the stator.

[0008] A further technical solution of the present invention is: in step 4: the number of friction pairs is preferably n=3 or 5. A further technical solution of the present invention is: in step 6: The angular spacing of the circular distribution of the braking force application points is less than 60°, and the radius of a single application area is 24mm to 34mm.

[0009] A further technical solution of the present invention is: said step 7 comprises: Graphitization heat treatment system: heating to 1500℃ within 3 minutes, then heating to 2000±70℃ within 2 minutes, and then keeping at 2000±70℃ under argon protection for 27 minutes; When the graphitization degree of the moving plate and the static plate does not meet the standard, the graphitization heat treatment is repeated until it meets the standard. A brake disc assembly for an aircraft comprises a stationary disc with a Y-shaped damping hole and a dynamic disc with a lotus leaf-shaped damping hole; a carbon fiber damping sleeve is provided on the periphery of the keyway boss of the dynamic disc, and a carbon fiber damping mesh is provided on the periphery of the keyway boss of the stationary disc; The stator disc is provided with a Y-shaped damping hole running through the radial direction. The Y-shaped damping hole is composed of three branch holes intersecting at a node. The node is located at the action point of the brake piston actuator or on the pitch circle of the brake disc assembly. The hole diameter φC = φ2mm to φ5mm. The Y-shaped damping hole is filled with nano-aerogel porous material, and the hole opening is closed by a carbon fiber cylindrical plug. The movable disc is provided with a radially extending lotus-shaped damping hole, which is composed of two symmetrically arranged groups of four branch holes, with the bends forming an obtuse angle. The nodes are located in the active area of ​​the brake actuator or on the pitch circle of the brake disc assembly, and the hole diameter is φD = φ3mm to φ7mm. The lotus-shaped damping hole is filled with nano-aerogel porous material, and the hole opening is sealed by a carbon fiber cylindrical plug. The bosses between the keyways on the outer edge of the movable plate are covered with a carbon fiber damping sleeve, which is a box structure with one end open; The bosses between the keyways on the inner edge of the static disk are covered with a U-shaped carbon fiber damping net.

[0010] A method for verifying vibration suppression of an aircraft brake disc assembly comprises the following steps: Step 1: Obtain key parameters of the brake disc assembly to be tested: Obtain the number of friction pairs n and the friction radius r of the friction pairs; Calculate the normal force acting on the brake disc assembly based on the brake pressure and the pressure acting area ; Get the actual structural damping C1; Step 2: Calculate the vibration stability criterion threshold, the expression is as follows:

[0011] Where C2 is the structural damping threshold, is the coefficient of variation of the instantaneous kinetic friction coefficient relative to the instantaneous velocity; Step 3: Verify the effectiveness of the vibration suppression structure: Condition judgment: If , go to step 4; if , the vibration suppression design is judged to be unqualified; Step 4: Vibration table test verification: Simulating impact conditions, brake tests were performed under a single-wheel radial load of 750kN: Convergence verification: Detect the vibration acceleration time domain signal in the 10-20 Hz frequency band, requiring the amplitude curve to be monotonically decreasing and the convergence time to be ≤0.5 seconds; Amplitude verification: When the vibration duration is less than 0.5 seconds, the acceleration of 5-20Hz is ≤4g, and the acceleration of 150-1000Hz is ≤50g; When the vibration duration is greater than 0.5 seconds, the acceleration of 5-20Hz is ≤2g, and the acceleration of 150-1000Hz is ≤25g; Beneficial effects The beneficial effects of the present invention are: the present invention improves the vibration energy absorption efficiency by more than 3 times through the triple energy dissipation configuration of Y-shaped damping hole + lotus leaf-shaped damping hole, and the time domain signal shows that the maximum amplitude is reduced by 84% compared with the traditional design (see attached Figure 12 and 13 ), the vibration frequency domain is in a convergent state; among them, the Y-shaped damping hole node is located at the action point of the brake piston actuator or on the pitch circle of the brake disc assembly, and the obtuse-angle node of the lotus-shaped damping hole is located in the action area of ​​the brake actuator or on the pitch circle of the brake disc assembly, forcibly changing the vibration transmission path and discretizing the excitation frequency. The 10-20Hz frequency domain vibration changes from divergence to convergence; The carbon fiber damping net / sleeve (resistant to 2000℃ / 750kN impact) of the keyway boss of the present invention increases the energy absorption rate of key vibration transmission nodes by 70%, solving the problem of uncontrolled vibration transmission under high-load conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is a flow chart of a method for designing a brake disc assembly for an aircraft according to an embodiment of the present invention; Figure 2 Schematic diagram of the internal structure of a stator disk with a Y-shaped damping hole in an embodiment of the present invention; Figure 3 Schematic diagram of the external structure of a stator plate with a Y-shaped damping hole in an embodiment of the present invention; Figure 4 Schematic diagram of the internal structure of the moving plate with lotus-shaped damping holes in an embodiment of the present invention; Figure 5 Schematic diagram of the external structure of the moving plate with lotus-shaped damping holes in an embodiment of the present invention; Figure 6 Schematic diagram of the damping structure of the moving disk in an embodiment of the present invention; Figure 7 Schematic diagram of the structure of the carbon fiber damping sleeve of the dynamic disk in an embodiment of the present invention; Figure 8 Schematic diagram of the static disk damping structure in an embodiment of the present invention; Figure 9 Schematic diagram of the structure of the carbon fiber damping net of the static disk in an embodiment of the present invention; Figure 10 Schematic diagram of the overall structure of an aircraft brake disc assembly according to an embodiment of the present invention; Figure 11 This is a flow chart of controlling the graphitization degree of a carbon brake disc in an embodiment of the present invention; Figure 12 This is a time domain signal diagram of a conventional brake disc (the horizontal axis is time, the vertical axis is acceleration amplitude); Figure 13This is a time domain signal diagram after improvement using the design method of the present invention (the horizontal axis is time, and the vertical axis is acceleration amplitude).

[0013] Explanation of the accompanying reference numerals: 1. moving disc, 2. moving disc protective shell, 3. moving disc carbon fiber damping sleeve, 4. stator disc, 5. stator disc protective shell, 6. stator disc carbon fiber damping net. DETAILED DESCRIPTION

[0014] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0015] The aircraft braking process is a typical dynamic process, one involving frictional heat generation and transfer. Given the structure and materials of the brake main wheel, the dynamic characteristics of each component, such as mass / moment of inertia, stiffness, and damping, are also determined. Typically, as braking time increases, the brake disc temperature continues to rise and the disc speed continues to decrease. The brake disc friction coefficient is typically a variable affected by multiple factors. The changing frictional braking torque applied to the brake main wheel via the brake disc causes a dynamic response in the brake main wheel structure, resulting in reduced speed and increased temperature. These effects, in turn, influence the state of the brake disc friction surface (including temperature, pressure, and speed), thus affecting the change in the dynamic friction coefficient. Therefore, the aircraft braking process is a complex, time-varying thermodynamic coupling process.

[0016] The main brake wheel is installed on an aircraft's landing gear, primarily for parking, taxiing, landing, and energy absorption. It consists of a brake mechanism and a wheel assembly, which are mounted together on the main landing gear axle. The wheel assembly primarily includes components such as the hub, rim, and bearings. The brake mechanism consists of a cylinder seat, piston assembly, brake housing, and brake disc assembly. When the aircraft taxis, the main brake wheel rolls on the ground. The rotor disc on the brake mechanism rotates synchronously with the rotor, while the pressure disc, static disc, and pressure disc mounted on the brake housing remain stationary and do not rotate. The rotor disc rotates relative to the single-sided static disc. When the aircraft brakes, high-pressure brake fluid enters the piston assembly. The piston, under the influence of brake pressure, moves forward, pressing the stationary pressure disc, static disc, and pressure disc against the rotating rotor disc. This generates frictional torque between the brake discs, which is transmitted to the wheel assembly through the keyway in the dynamic disc, braking the wheel. Simultaneously, the piston moves forward, compressing the return spring. When the brake is released, the brake pressure is released, the piston retreats under the action of the return spring, the dynamic and single-sided static discs release, and the main wheel brake is released. The above-mentioned pressure disc, static disc, pressure disc, and dynamic disc are collectively referred to as the brake disc assembly, and both the static disc and the dynamic disc are considered brake discs.

[0017] In response to the high-impact load mechanical environment faced by aircraft brake systems, this invention clarifies the design process for aircraft brake discs and proposes a structural design method for aircraft high-vibration-resistant discs to meet aircraft operating requirements. The specific process of this invention is as follows: The vibration excitation (vibration energy source) of aircraft brake discs primarily comes from two sources: the high-frequency, high-amplitude load excitation during landing, and the inherent friction excitation between the brake pairs during braking. Since the aircraft's landing configuration cannot be changed, the high-load excitation during landing is essentially unadjustable and unchangeable. Therefore, the only approach is to reduce the excitation generated by the brake disc through vibration suppression design, or to minimize the transmission and impact of the brake disc excitation to avoid system resonance. Braking is a dynamic process involving multiple coupled systems, and the key to suppressing brake vibration lies in increasing damping and weakening the transmission and impact of the vibration excitation. Current research indicates that the friction coefficient of the brake disc is the primary parameter causing system vibration. Mathematical modeling based on the instantaneous kinetic friction coefficient of braking can analyze key parameters, guide specialized brake disc structural design, and address vibration issues.

[0018] Establish a mathematical model for aircraft brake disc vibration suppression based on the instantaneous dynamic friction coefficient: S1: Based on the material properties of the brake disc used in aircraft brake systems, the instantaneous dynamic friction characteristics of the brake disc are simplified into the following formula:

[0019] Where, is the instantaneous kinetic friction coefficient, is the coefficient of variation of the instantaneous kinetic friction coefficient relative to the instantaneous velocity, is the instantaneous linear velocity, is the static friction coefficient; S2: The relative friction between the moving plate and the static plate generates an instantaneous braking torque of:

[0020] Where, is the instantaneous braking torque, is the friction pair number, a static disk and a moving disk rubbing against each other is a friction pair, is the friction radius of the friction pair, is the normal force acting on the brake disc assembly, where:

[0021] Where, is the normal pressure acting on the brake disc assembly, i.e. the brake pressure, is the pressure action area of ​​the piston assembly; S3: Establish the vibration characteristic equation of the moving disk assembly:

[0022] Where, is the stiffness of the moving plate assembly, is the structural damping, is the moment of inertia, is the rotation angle; Combine steps S1, S2, and S3 into similar items:

[0023]

[0024] but:

[0025] It can be seen from the formula that to ensure the convergence of system vibration, the structural damping must be positive, then:

[0026] From the above analysis, it can be seen that the damping characteristics of the brake disc of the brake device and the rate of change of the brake pressure are the key factors affecting the stability of the brake device. The rate of change of the dynamic friction coefficient with speed and the damping matching of the brake device are the main factors affecting the vibration of the brake device. According to the above steps, the vibration characteristic equations of the pressure plate, static plate and pressure plate can be derived in the same way. Here, the present invention refers to the dynamic plate as the dynamic subsystem, and the pressure plate, static plate and pressure plate are combined and referred to as the stator system. It can be seen from the above derivation formula that the damping of the stator system and the rotor system increases, and the friction pair number n, the friction radius of the friction pair r and the normal force of the brake disc assembly are reduced. , and reduce the coefficient of change of the instantaneous kinetic friction coefficient relative to the instantaneous velocity , which can effectively improve the motion stability of the stator and rotor systems and avoid vibration divergence. During the design of the brake disc assembly of the brake device, the mutual friction between the rotor and stator systems generates a braking torque, which stops the aircraft.

[0027] According to the above derivation, increasing the damping of the brake disc assembly, reducing the number of brake disc friction pairs, reducing the friction radius of the friction pairs, reducing the normal force of the brake disc assembly, and reducing the coefficient of change of the instantaneous kinetic friction coefficient relative to the instantaneous velocity are effective solutions to reduce the damping of the system. Figure 1 As shown, the present invention proposes a damping structure, a number of friction pairs, a friction radius of the friction pairs, a normal force acting on the brake disc assembly, and a brake disc torque control method suitable for aircraft brake discs. The specific steps are as follows: Step 1 Design of high damping structure of aircraft brake disc assembly: Vibration excitation is generated during braking. Increasing vibration damping is mainly achieved by blocking and slowing down the conduction of excitation, thereby reducing the possibility of system resonance. Therefore, damping structures are added to the dynamic and static discs in the brake disc assembly.

[0028] Step 1.1 Reference Figure 2 and 3 As shown, a damper is provided on the stator disk; Vibration excitation during braking is primarily generated by the rotor and stator discs. Therefore, a damping structure is required on the stator disc to mitigate and absorb vibration energy, thereby reducing system vibration amplitude and suppressing vibration transmission. This invention requires the creation of Y-shaped damping holes (φC = φ2mm to φ5mm) in the middle layer of the stator disc through its thickness. (If the stator disc is 15mm thick, a φ3mm hole is used, using a 20% thickness coefficient. Aircraft stator discs are typically no thicker than 15mm. If the brake disc is thicker than 25mm, a φ5mm hole is still used. This is because a larger hole diameter can cause severe delamination of the carbon brake composite material, reducing its shear resistance and susceptibility to delamination and damage.) The damping holes are Y-shaped and arranged radially along the radius of the stator disc. The nodes of the Y-shaped damping holes are located at the application point of the brake piston actuator or on the pitch circle of the brake disc assembly. The initial Y-shaped damping holes are oriented outward along the outer circumference normal of the brake disc. The triangular structure provides stability, allowing vibration to be transmitted through the holes into the air. The damping effect of the air and the nano-aerogel porous material is used to delay the release of vibration energy. The Y-shaped acute angle is recommended to be 50°~60°. The reason is that this angle can ensure that the brake disc area damaged by the Y-shaped damping hole is as small as possible below 50% of the total sector, avoiding structural strength problems. The number of Y-shaped damping holes is determined by the number of keyways on the inner edge of the static disc. If the number of keyways on the inner edge is N 内 , then the number of groups of Y-shaped damping holes is N 内 -1. After completing the drilling, fill the Y-shaped damping hole with nano-aerogel porous material, and use a carbon fiber cylindrical plug with a length of 6 mm to bond and seal the hole mouth. If the hole size calculation formula is φC+0.05, that is, a φ3mm hole is sealed with a φ3.05mm×6mm carbon fiber cylindrical plug.

[0029] The stator disc with Y-shaped damping holes has the following advantages: 1. The total length of the Y-shaped damping hole is 40% to 50% longer than that of the straight hole in the existing technology; 2. Opening Y-shaped damping holes can avoid holes in the same direction being too long and too close together, minimizing damage to the structural integrity of the brake disc assembly. 3. The stator disc is a non-rotating brake disc. The Y-shaped damping holes can be arranged in combination with the piston distribution. After product assembly, there are two situations: the piston is basically near the node where the three Y-shaped damping holes intersect, or between two Y-shaped damping holes. When the piston near the node brakes, the vibration excitation can be evenly transmitted into the three vibration suppression holes, and the excitation frequency changes. The piston between the two Y-shaped damping holes will be surrounded by four vibration suppression holes when braking. The transmission of the vibration excitation will be absorbed and weakened. The stator disc adopts Y-shaped damping holes. When the piston is in different areas, its output vibration excitation frequency will change, avoiding system resonance. 4. The stator disc with Y-shaped damping holes proposed in this invention contains heat-resistant nano-aerogel porous material. Together with the stator disc, it forms a triple hybrid vibration suppression structure of brake composite material, air, and nano-aerogel porous material. Compared with traditional cavity air vibration suppression, it is more effective. 5. The static disc with Y-shaped damping hole has better resistance to brake shear and impact than round or flat box type cavity brake disc.

[0030] Step 1.2 Reference Figure 4 and 5 As shown, a damper is provided on the moving plate; The vibration excitation during braking is mainly generated by the moving disc and the static disc. Therefore, a damping structure needs to be designed on the moving disc to slow down / absorb the vibration energy, thereby reducing the vibration amplitude of the system and suppressing vibration transmission. The present invention requires that a φD lotus-shaped damping hole be opened in the middle layer in the thickness direction of the rotor disc, where φD = φ3mm to φ7mm. At the same time, φD should not be the same as φC, so as to achieve a structural non-similar design and improve the vibration suppression effect. (If the thickness of the rotor disc is 20mm, a φ4mm hole is taken according to a thickness coefficient of 20%. The thickness of the aircraft rotor disc is generally not less than 20mm. If the thickness of the rotor disc is greater than 35mm, a φ7mm hole is still opened. The reason is that an excessively large hole diameter will cause serious delamination of the carbon brake composite material, reduce its shear resistance, and easily cause delamination damage.) The contour shape of the damping hole is lotus-shaped, and the lotus-shaped shape is composed of four holes, wherein the acute angle is 60° and the obtuse angle is 120°. The obtuse angle node is located in the action area of ​​the brake actuator or on the pitch circle of the brake disc assembly, wherein the blade tip is outward along the normal line of the outer circumference of the brake disc. The number of lotus-shaped damping hole groups is equal to the number N of keyways on the outer edge of the rotor disc. 外 The reason for this is that the holes primarily penetrate the inner and outer edges of the rotor disc. A lotus leaf-shaped hole on the outer edge of the rotor disc can only be machined through the keyway. Holes drilled elsewhere would damage structures like rivet holes. Therefore, the number of lotus leaf-shaped damping holes in the rotor disc is limited by the number of keyways. After drilling, the damping holes are filled with a porous nanoaerogel material. The openings are sealed with a 6mm-long carbon fiber cylindrical plug. If the hole size is calculated as φD + 0.05, a φ4mm hole can be sealed with a φ4.05mm × 6mm carbon fiber cylindrical plug.

[0031] The moving disc with lotus-shaped damping holes has the following advantages: 1. The total opening length of the lotus leaf damping hole is 80% to 90% longer than that of the straight hole in the existing technology. The reason is that the impact and shear force of the dynamic plate are very large. Generally, except for the rivet holes for installing the protective clip / protective shell, drilling holes that damage the base material are not allowed on the boss between the outer edge keyways. 2. Compared with round or flat box cavities, the lotus leaf-shaped damping hole has less damage to the structural strength of the moving plate. At the same time, it can avoid the use of a split structure for the moving plate, making it easier to ensure structural strength. 3. The dynamic disc is a rotating brake disc. The lotus-shaped damping holes can achieve uniform distribution and the maximum number of damping holes (double the number of long hole solutions) while ensuring the basic strength of the brake disc. 4. The proposed rotor disc with lotus-shaped damping holes contains heat-resistant nano-aerogel porous material. Together with the rotor disc, this creates a triple hybrid vibration damping structure of brake composite material, air, and nano-aerogel porous material. This provides superior vibration damping performance compared to the cavity-air structure of traditional brake discs. 5. The dynamic disc with lotus-shaped damping holes has better resistance to brake shear and impact than round or flat box-type cavity brake discs.

[0032] Step 1.3 Reference Figure 6 and Figure 7 As shown, a damping sleeve is added between the moving plate steel clamp and the moving plate: The moving disc is matched with the convex key of the wheel hub through the outer circular keyway. During the braking process, the vibration is transmitted through the matching part between the wheel hub and the brake disc assembly. Therefore, a carbon fiber damping sleeve is added to the protective shell on the boss between the outer circular keyways of the moving disc to slow down the vibration transmission. The carbon fiber damping sleeve is a box structure with one end open. The inner cavity of the box is used to cover the boss between the keyways on the outer edge of the moving disc. Holes are opened on both sides to avoid hindering the installation of the fixing rivets of the moving disc protective shell. The number of carbon fiber damping sleeves is the same as the number of keyways on the outer edge of the moving disc N 外 Equal, that is, the boss between every two keyways needs to be installed.

[0033] Step 1.4 Reference Figure 8 and Figure 9 As shown, a damping net is added between the static disc steel clamp and the static disc; The stator disc is matched with the convex key of the brake housing through the inner edge keyway. During the braking process, the vibration is transmitted between the brake housing and the brake disc assembly through the matching part. Therefore, a carbon fiber damping net is added to the protective shell on the boss between the inner edge keyways of the stator disc to slow down the vibration transmission. The damping net is a U-shaped structure, which is used to cover the boss between the inner edge keyways of the stator disc. The number of U-shaped carbon fiber damping nets is the same as the number of keyways on the inner edge of the stator disc N. 内 Equal, that is, the boss between every two keyways needs to be installed.

[0034] The invention is the first to propose a device suitable for aircraft, comprising a static disc with a U-shaped carbon fiber damping net and a dynamic disc with a carbon fiber damping sleeve, which acts as a buffer at the braking impact transmission node and reduces vibration transmission. In existing technologies, damping structures are used to suppress vibrations. However, due to the stringent temperature and impact load requirements of carbon brake discs, their use is extremely limited, and there has been no previous application of them on static brake discs. Static discs with carbon fiber damping pads have the following advantages: 1. The carbon fiber damping mesh is made of micron-grade carbon fiber filaments and has a porous mesh structure with good vibration absorption effect.

[0035] 2. Unlike the high-temperature resistant vibration suppression materials filled in the cavity, the vibration suppression damping pad not only needs to be resistant to high temperatures, but also needs to meet the impact strength requirements. Otherwise, under the action of impact loads, the structure of the carbon fiber damping mesh is prone to damage and rapid feathering. The carbon fiber damping mesh made of micron-grade carbon fiber precursor can meet the requirements of structural strength and high-temperature resistance at the same time.

[0036] 3. Unlike other brake disc vibration suppression solutions, the stator disc with a carbon fiber damping mesh proposed in this solution uses a carbon fiber damping mesh structure in the keyway mating area of ​​the brake disc, reducing the size and weight of the damping structure. This makes it possible to add a carbon fiber damping mesh to an integral stator disc, resulting in a significant weight advantage.

[0037] In existing technologies, damping structures are used to suppress vibrations. However, due to the stringent temperature and impact load requirements of carbon brake discs, their use is extremely limited, and there has been no previous application of them on dynamic brake discs. Dynamic discs with carbon fiber damping sleeves have the following advantages: 1. The carbon fiber damping sleeve is made of micron-grade carbon fiber filaments. The carbon fiber damping sleeve has a porous mesh structure and has a good vibration absorption effect.

[0038] 2. Unlike the high-temperature resistant vibration suppression materials filled in the cavity, the vibration suppression damping sleeve not only needs to be resistant to high temperatures, but also needs to meet the impact strength requirements. Otherwise, under the action of impact loads, the carbon fiber damping sleeve structure is prone to damage and rapid feathering. The carbon fiber damping sleeve made of micron-grade carbon fiber precursor can meet the requirements of structural strength and high-temperature resistance at the same time.

[0039] 3. Unlike other brake disc vibration suppression solutions, the dynamic disc with a carbon fiber damping sleeve proposed in this solution adopts a damping structure in the keyway matching area of ​​the brake disc, which is the first time to realize the installation of a damping structure in the area where the impact load of the dynamic disc directly acts.

[0040] Step 2 Reference Figure 10 As shown, the aircraft brake disc friction dual design: The moving disc and the static disc rub against each other to form a pair. On the one hand, during the braking process, the piston assembly in the brake device extends axially under the action of the hydraulic oil, and applies the brake pressure to the brake disc assembly. The hydraulic pressure acts on the brake disc assembly. The more friction pairs the brake disc assembly has, the higher the frequency domain width and amplitude of the brake vibration excitation, which easily leads to resonance. According to the vibration dynamics simulation of the present invention, the friction pair number of the brake disc assembly for aircraft should be ≤5, preferably an odd-to-even number. If the product uses a single-sided static disc, the transmission of resonance will be magnified. Therefore, a damping layer needs to be provided between the single-sided static discs to suppress vibration. Since insufficient thickness of the brake disc will also cause the vibration amplitude to increase, the thickness of the brake disc in the friction pair is specified as follows: for the static disc, its thickness is not less than 15mm, and for the moving disc, its thickness is not less than 20mm.

[0041] The present invention proposes friction pair design requirements for aircraft brake disc assemblies and provides specific design parameter requirements for aircraft brake disc assemblies. The brake disc assembly includes a pressure disc, a static disc, a pressure disc, and a dynamic disc. Both the static disc and the dynamic disc are called brake discs, and adjacent static discs and dynamic discs form a pair of brake discs. The number of friction pairs is the number of brake disc pairs. According to the calculation method of aircraft brake disc vibration dynamics, reducing the friction pair number n is beneficial to increasing structural damping. Therefore, the design requires that the friction pair number of brake discs should be as small as possible. However, there is an obvious contradiction in the design. The aircraft braking energy is large and the deceleration and braking performance requirements are high. It is basically impossible for one pair of brake discs or two pairs of brake discs to meet the performance requirements. Therefore, at least three pairs of brake discs are required. According to the calculation formula for the number of brake discs, the number of brake discs = 2×number of brake disc pairs + 1. Three pairs of brake discs contain 7 brake discs. The number of brake discs increases proportionally with the increase in the number of brake disc pairs. For the heat storage, the total thickness of the heat storage is basically determined under the condition of certain energy. The more brake discs there are, the smaller the thickness of a single dynamic disc or static disc, and the more likely it is to vibrate. Therefore, the pair number cannot exceed 5. Considering that an even number does not conform to the odd number vibration suppression principle, the aircraft brake disc adopts a 3 or 5-pair brake disc structure.

[0042] Step 3 Design of the pitch circle (brake force action circle) of the aircraft brake disc assembly: Brake disc assembly pitch circle D f Determines the braking performance requirements, and also determines the structural size requirements of the brake disc assembly. In order to ensure that the amplitude of the braking vibration of the aircraft is at a low level, the pitch circle size of the brake disc assembly should be at a relatively low level. lw , gives the brake disc assembly pitch circle D f Calculation method: D f =0.274×D lw -twenty two The present invention proposes a method for calculating the pitch circle of an aircraft brake disc assembly and clarifies the structural dimension design requirements; The advantages of the brake disc assembly pitch circle calculation method proposed in the present invention are: It can perform formulaic calculations based on the tire assembly diameter, avoiding the defects of previous products designed according to experience. It can quickly carry out brake disc structural size evaluation and brake performance evaluation based on the tire assembly diameter, making the initial demonstration design more efficient and scientific.

[0043] Step 4 Design of normal force of aircraft brake disc: The normal force acting on the brake disc assembly is the product of the brake pressure and the pressure acting area of ​​the piston assembly (according to the formula ), the force on the brake disc assembly is determined by the number of force points and the area of ​​a single force position. In addition, the position line of the force pitch circle must also be designed to match the damping structure of the aircraft.

[0044] Step 4.1 Design the distribution of braking force application points and the application area requirements for each single application position; , at hydraulic pressure P S When the area A is larger, the force N z The bigger.

[0045] A=am, where a is the area of ​​a single piston and m is the number. The braking force application points of an aircraft brake disc should be at a relatively large number of levels. The present invention requires no less than 6 application points, and an odd number of application points should be evenly distributed as much as possible to ensure a stable braking force and avoid a surge in instantaneous amplitude.

[0046] The area of ​​a single action position of the aircraft brake disc is at a reasonable level. The present invention requires that the area of ​​a single action position should be 1800mm 2 ~3500mm 2 (The radius corresponding to the single-action position is between 24mm and 34mm) to ensure the stability of the braking force and avoid instantaneous amplitude surges.

[0047] Step 4.2 Requirements for the pitch circle of the intersection of the vibration suppression structure hole; The pitch circle requirement of the intersection of the vibration suppression structure hole should match the damper design of the dynamic and static discs. The pitch circle radius R l One half of the pitch circle diameter of the brake disc assembly: R l =D f / 2 The present invention proposes design requirements related to the brake disc force and structure, clarifies the number of action points and the action area requirements at corresponding positions, and realizes the quantification of design requirements; The requirements for brake disc force and structural design proposed in this invention are based on the mutual determination of brake pressure, brake force application area, and the number of application areas. Based on the principle of force application, the number and area of ​​application locations determine the force per unit area. Considering the uniformity of brake force application (hydraulic oscillations and instability occur during hydraulic application, and the fewer brake pressure application points, the greater the force fluctuations during hydraulic oscillations), the number of hydraulic pressure application points should be as large as possible. Force stability is achieved when the angular spacing of the application points is less than 60°, distributed across a 360° circumference. The area of ​​the brake disc assembly's brake force application locations is influenced by two factors: larger areas provide more structural space and a greater weight impact. Smaller areas increase the force applied, even with a given number of application points, affecting the force per unit area. Therefore, a range of application point areas is provided. The clamping mechanism at the application points is generally designed to be circular, so a radius of 24mm to 34mm is recommended.

[0048] Step 5 Reference Figure 11 As shown, the graphitization degree is regulated to reduce the rate of change of friction coefficient with instantaneous speed: High-temperature heat treatment (above 2000°C) can adjust the graphitization degree of carbon brake materials. A higher degree of graphitization results in a softer carbon brake material matrix and a lower rate of change in the friction coefficient with instantaneous velocity. To control the rate of change in the friction coefficient of a brake, a clear brake disc heat treatment process is first established. Following the traditional heat treatment of carbon brake discs, a graphitization heat treatment is then added, followed by a post-furnace graphitization inspection. This invention requires that the graphitization degree of aircraft brake discs be controlled between 55% and 65%. If the graphitization degree does not meet the requirements, reheat treatment is required to increase the graphitization degree to meet the minimum requirement. Furthermore, during the high-temperature heat treatment of carbon brake material within the same furnace, the smaller the temperature difference between different zones within the furnace, the less consistent the graphitization degree of the carbon brake material within the furnace. Therefore, this invention requires that the temperature difference between different temperature zones during the aircraft brake disc production process be ≤±20°C.

[0049] The present invention proposes a method for adjusting the heat treatment process of a brake disc by controlling the graphitization degree as the core, thereby improving the temperature requirement of the heat treatment process area, thereby achieving the regulation of the instantaneous rate of change of the friction coefficient.

[0050] The present invention proposes a friction coefficient control method, the core of which is: Propose requirements for graphitization degree, temperature difference consistency, and heat treatment system requirements that can meet graphitization requirements.

[0051] Graphitization heat treatment system: During the insulation stage of brake disc preparation, the furnace temperature is required to rise from room temperature to 1500°C within 3 minutes, then rise from 1500°C to 2000±70°C within 2 minutes, and be kept at 2000±70°C for 27 minutes, using high-purity argon protection.

[0052] After completing this stage, the temperature is lowered and the graphitization degree is tested. If the graphitization degree does not meet the requirements, the graphitization heat treatment is repeated until the requirements are met.

[0053] Reference Figure 12 and Figure 13 As shown, after the present invention adopts the above comprehensive measures, the maximum vibration amplitude of the brake disc and aircraft using the existing technology is reduced by 84%, and the vibration frequency domain curve shows a convergence state.

[0054] The following is a further analysis of the above technical solution with reference to examples: In one embodiment, taking a 35MPa pressure-resistant high-pressure cylinder seat of an aircraft wheel as an example, the brake disc assembly is Figure 10 As shown, the design method is as follows: Step 1: Vibration suppression structure design: 1.1 Install a damper on the stator; The thickness of the static disc is 21.7mm, and the diameter of the Y-shaped damping hole is φ4.34mm. The shape of the damping hole is Y-shaped, and it is arranged radially along the radius of the brake disc. The acute angle of the Y-shape is selected to be 55°, and it is connected to the long side. The position of the long hole opening is the midline of the angle between the two keyways. The outer diameter of the friction surface of the static disc described in this embodiment is φ400mm, and the number of inner edge keyways is 11, so the number of Y-shaped damping holes is 10 groups. After the drilling is completed, the Y-shaped damping hole is filled with nano-aerogel porous material, and the orifice of the Y-shaped damping hole is sealed with a carbon fiber cylindrical plug with a length of 6mm, and sealed with a φ4.39mm×6mm carbon fiber cylindrical plug.

[0055] The Y-shaped damping hole node is forced to match the piston action point, so that the vibration energy is discretized along the three-way branch conduction.

[0056] 1.2 Install a damper on the moving plate; The rotor disc is 23.9mm thick, and the lotus-shaped damping holes have a diameter of φ4.78mm. The lotus-shaped damping holes consist of four rows of holes, with acute angles of 60° and obtuse angles of 120°. The obtuse-angle nodes are located in the brake actuator's active area or on the brake disc assembly's pitch circle, with the blade tips pointing outward along the outer circumference normal of the brake disc. The rotor disc has nine keyways on its outer edge, and nine lotus-shaped damping hole groups. After drilling, the lotus-shaped damping holes are filled with a porous nanoaerogel material. The orifice is sealed with a 6mm-long carbon fiber cylindrical plug for bonding, and then sealed with a φ4.83mm x 6mm carbon fiber cylindrical plug.

[0057] The obtuse-angle node of the lotus-shaped damping hole cuts off the impact load transmission path, and the four-branch configuration increases the opening length by 87%.

[0058] 1.3 Add a carbon fiber damping sleeve between the moving plate steel clamp and the moving plate: A carbon fiber damping sleeve is added to the protective shell on the boss between the keyways on the outer edge of the moving plate. The carbon fiber damping sleeve is a square box structure. ， The thickness is 1mm, with three rivet holes on both sides. The opening width is 18mm, the length is 100mm, the outer diameter is φ440mm, and the inner diameter is φ420mm. The damping sleeve material is carbon fiber and there are 9 of them.

[0059] 1.4 Add a carbon fiber damping net between the stator plate steel clamp and the stator plate; The carbon fiber damping mesh is a U-shaped structure with an overall thickness of 1mm, a height of 9mm on both sides, an inner diameter of φ350mm, and a chord length of 46mm. The carbon fiber damping mesh is made of carbon fiber and has 11 pieces.

[0060] Step 2: System parameter collaborative design: The friction pair number of the brake disc assembly of this embodiment is 3, the thickness of the static disc is 21.7 mm, and the thickness of the dynamic disc is 23.9 mm.

[0061] This embodiment uses a tire with an outer diameter of φ1144mm, so the brake disc assembly pitch circle is: D f =0.274×D lw -22=313.5mm The number of action points is determined to be 7, and the pressure area of ​​a single position is 1800mm 2 , corresponding to an area radius of 24mm.

[0062] The pitch circle of the intersection of the vibration suppression structure holes is determined by the pitch circle of the brake disc assembly: R l =D f / 2=313.5 / 2=156.75mm Step 3: Key processes of graphitization heat treatment: The graphitization degree of the brake disc should be controlled to 60%. If the graphitization degree does not meet the requirements, it needs to be reheated to increase the graphitization degree to meet the minimum requirements. In addition, during the high-temperature heat treatment process of the same batch of carbon brake material, the smaller the temperature difference between different areas in the furnace, the smaller the temperature difference will be, which will affect the consistency of the graphitization degree of the carbon brake material in the same batch. The present invention requires that the temperature difference between different temperature zones during the preparation of aircraft brake discs should be ≤±20°C.

[0063] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for designing a brake disc assembly for an aircraft, wherein the brake disc assembly comprises a pressure disc, a static disc, a pressure disc and a dynamic disc; The specific steps are as follows: Step 1: Design the Y-shaped damping hole structure of the stator disc, and open a Y-shaped damping hole with a diameter of φC = φ2mm ~ φ5mm in the middle layer of the stator disc in the thickness direction; N 内 -1 group of Y-shaped damping holes are arranged radially along the circumference of the stator, N 内 is the number of keyways on the inner edge of the stator disc. The nodes of each Y-shaped damping hole are located at the action point of the brake piston actuator or on the pitch circle of the brake disc assembly. The Y-shaped damping hole is filled with nano-aerogel porous material and sealed with a carbon fiber cylindrical plug. Step 2: Design the lotus leaf-shaped damping hole structure of the moving disk, and open a lotus leaf-shaped damping hole with a diameter of φD = φ3mm ~ φ7mm in the middle layer of the moving disk in the thickness direction; N 外 The lotus leaf-shaped damping holes are evenly distributed along the circumference of the moving disk, N 外 is the number of keyways on the outer edge of the rotor disc, and the bending nodes of each lotus-shaped damping hole are located in the action area of ​​the brake actuator or on the pitch circle of the brake disc assembly; the lotus-shaped damping hole is filled with nano-aerogel porous material and sealed with a carbon fiber cylindrical plug; Step 3: Add a carbon fiber damping sleeve inside the boss protection shell between the key slots of the dynamic plate, and add a U-shaped carbon fiber damping net inside the boss protection shell between the key slots of the static plate; Step 4: Control the friction pair number n≤5 and be an odd number, the static plate thickness ≥15mm, and the dynamic plate thickness ≥20mm; Step 5: Calculate the pitch circle diameter of the brake disc assembly using the following formula: Among them, D f D is the pitch circle diameter of the brake disc assembly; lw is the tire assembly diameter; Step 6: Set the number of braking force application points to be greater than or equal to 6, and the application area of ​​each application point to 1800mm 2 ~3500mm 2 ; Step 7: The moving plate and the static plate are both made of carbon brake material, and their graphitization degree is controlled to be 55% to 65%. The furnace temperature uniformity of the graphitization heat treatment is ≤±20°C.

2. The design method of an aircraft brake disc assembly according to claim 1, characterized in that: In step 1, the Y-shaped damping hole radially penetrates the boss and the outer peripheral surface between the key grooves on the inner edge of the stator, with the single hole end facing the boss side and the double hole end facing the outer peripheral surface side, and the acute angle between the double hole ends is 50° to 60°; wherein, The diameter of the Y-shaped damping hole φC is 20% of the thickness of the static disk. When the thickness of the static disk is greater than 25mm, φC=φ5mm. The size of the carbon fiber cylindrical plug is (φC+0.05mm)×6mm.

3. The design method of an aircraft brake disc assembly according to claim 1, characterized in that: In step 2, the lotus leaf-shaped damping hole radially penetrates the inner annular surface and the outer edge keyway of the movable plate, and includes two symmetrical groups of bent holes, and the two groups of bent holes form an acute angle of 60° at the outer edge keyway, and the bending part of each group of bent holes is an obtuse angle of 120°; wherein, The diameter of the lotus leaf damping hole φD is 20% of the thickness of the moving plate. When the thickness of the moving plate is greater than 35mm, φD=φ7mm. The size of the carbon fiber cylindrical plug is (φD+0.05mm)×6mm.

4. The method for designing an aircraft brake disc assembly according to claim 1, wherein: In step 3: The carbon fiber damping sleeve is a box structure with one end open, covering the entire outer wall of the boss between the keyways on the outer edge of the moving plate; The carbon fiber damping net is a U-shaped structure, covering the circumferential outer wall of the boss between the keyways on the inner edge of the stator.

5. The method for designing an aircraft brake disc assembly according to claim 1, characterized in that: In step 4: the number of friction pairs is preferably n=3 or 5.

6. The method for designing an aircraft brake disc assembly according to claim 1, characterized in that: In step 6, the circumferential distribution angle spacing of the braking force application points is less than 60°, and the radius of a single application area is 24 mm to 34 mm.

7. The method for designing an aircraft brake disc assembly according to claim 1, wherein: The step 7 comprises: Graphitization heat treatment system: heating to 1500℃ within 3 minutes, then heating to 2000±70℃ within 2 minutes, and then keeping at 2000±70℃ under argon protection for 27 minutes; When the graphitization degree of the moving plate and the static plate does not meet the standard, the graphitization heat treatment is repeated until it meets the standard.

8. An aircraft brake disc assembly, obtained by the design method for an aircraft brake disc assembly according to any one of claims 1 to 7; characterized in that: It includes a static plate with a Y-shaped damping hole and a dynamic plate with a lotus leaf-shaped damping hole; a carbon fiber damping sleeve is provided on the periphery of the keyway boss of the dynamic plate, and a carbon fiber damping net is provided on the periphery of the keyway boss of the static plate; The stator disc is provided with a Y-shaped damping hole running through the radial direction. The Y-shaped damping hole is composed of three branch holes intersecting at a node. The node is located at the action point of the brake piston actuator or on the pitch circle of the brake disc assembly. The hole diameter φC = φ2mm to φ5mm. The Y-shaped damping hole is filled with nano-aerogel porous material, and the hole opening is closed by a carbon fiber cylindrical plug. The movable disc is provided with a radially extending lotus-shaped damping hole, which is composed of two symmetrically arranged groups of bent holes formed by four branch holes. The bends are obtuse-angled, and the nodes are located in the active area of ​​the brake actuator or on the pitch circle of the brake disc assembly. The hole diameter φD = φ3mm to φ7mm; the lotus-shaped damping hole is filled with nano-aerogel porous material, and the hole opening is closed by a carbon fiber cylindrical plug; the boss between the keyways on the outer edge of the movable disc is covered with a carbon fiber damping sleeve, which is a box structure with one end open; The bosses between the keyways on the inner edge of the static disk are covered with a U-shaped carbon fiber damping net.

9. A vibration suppression verification method for an aircraft brake disc assembly according to claim 8, characterized in that: The following steps are involved: Step 1: Obtain key parameters of the brake disc assembly to be tested: Obtain the number of friction pairs n and the friction radius r of the friction pairs; Calculate the normal force acting on the brake disc assembly based on the brake pressure and the pressure acting area ; Get the actual structural damping C1; Step 2: Calculate the vibration stability criterion threshold, the expression is as follows: Where C2 is the structural damping threshold, is the coefficient of variation of the instantaneous kinetic friction coefficient relative to the instantaneous velocity; Step 3: Verify the effectiveness of the vibration suppression structure: Condition judgment: If , go to step 4; if , the vibration suppression design is judged to be unqualified; Step 4: Vibration table test verification: Simulating impact conditions, brake tests were performed under a single-wheel radial load of 750kN: Convergence verification: Detect the vibration acceleration time domain signal in the 10-20 Hz frequency band, requiring the amplitude curve to be monotonically decreasing and the convergence time to be ≤0.5 seconds; Amplitude verification: When the vibration duration is less than 0.5 seconds, the acceleration of 5-20Hz is ≤4g, and the acceleration of 150-1000Hz is ≤50g; When the vibration duration is greater than 0.5 seconds, the acceleration of 5-20Hz is ≤2g, and the acceleration of 150-1000Hz is ≤25g.

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