Helicopter moving ring fatigue test device and test method
By designing a helicopter ring fatigue test device and applying test load using components such as the actuator and variable distance pull rod load joint, the problem of lack of helicopter ring fatigue test methods and devices in China is solved, and the fatigue test of helicopter ring is realized Accurate simulation and efficient assessment.
Patent Information
- Application Number
- CN202411434229.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-15
- Publication Date
- 2025-02-14
- Estimated Expiration
- 2044-10-15
AI Technical Summary
There has not been a helicopter ring fatigue test method and related devices that can be referenced and referenced in China. It is urgent to design a helicopter ring fatigue test loading device and formulate corresponding fatigue test methods to guide the helicopter ring fatigue test.
A helicopter ring fatigue test device was designed, including a fixed ring counter, a moving cylinder, a variable distance pull rod loading joint, a torsion arm loading fork ear assembly, etc. The test load was applied through these components to simulate the real installation of the helicopter ring machine. Boundary conditions and loading characteristics.
The device can accurately simulate the loading process of the helicopter ring in flight, provide a real and accurate helicopter ring fatigue test and assessment environment, realize coordinated loading of each support arm of the helicopter ring and fatigue loading of the ear piece connecting the dynamic ring and the torque arm. , the load feedback data and the command data have a high degree of overlap, and the total test error can be controlled within 3%.
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Figure CN119437673A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of helicopter fatigue testing, and in particular relates to a helicopter dynamic ring fatigue testing device and a testing method. Background Art
[0002] With the rapid development of my country's economy, supported by a strong economic scale, the development of domestic helicopter models has shown a blowout development, and many new models and new configurations have emerged, which indirectly promoted the further development of helicopter-related fatigue test technology. The helicopter dynamic ring is a key dynamic component structure in the helicopter main rotor system. When it rotates with the main rotor, it mainly bears the alternating loads from the pitch rod and the torque arm. Therefore, the helicopter dynamic ring is prone to fatigue damage and causes the failure of the main rotor system, which directly affects the flight safety of the helicopter. For this reason, it is crucial to conduct fatigue tests on the helicopter dynamic ring during the helicopter development stage to simulate the stress state of the helicopter dynamic ring during flight and determine the fatigue performance and weak points of the helicopter dynamic ring. In view of the fact that there is no reference and reference to the helicopter dynamic ring fatigue test method and related devices in China, it is urgent to design a helicopter dynamic ring fatigue test loading device and formulate corresponding fatigue test methods to guide the helicopter dynamic ring fatigue test. Summary of the invention
[0003] Purpose of the invention: The present invention designs a helicopter dynamic ring fatigue loading test device and provides a helicopter dynamic ring fatigue method. By designing a special loading test device and adopting a scientific and feasible test method, the test load is applied by an actuator to simulate the actual installation boundary conditions and load characteristics of the helicopter dynamic ring installation, and a real and accurate helicopter dynamic ring fatigue test assessment environment is provided, so that accurate fatigue hazardous parts and failure modes of the helicopter dynamic ring can be obtained, providing a test basis for determining its service life.
[0004] The present invention relates to a helicopter dynamic ring fatigue test method and loading device, including a helicopter dynamic ring support arm fatigue test and a helicopter dynamic ring and torque arm connection ear fatigue test. The design scheme and test method capable of realizing the helicopter dynamic ring support arm fatigue test loading and the helicopter dynamic ring and torque arm connection ear fatigue test loading provide a reference for the current helicopter dynamic ring structure design and improvement, as well as life evaluation.
[0005] Technical Solution
[0006] A helicopter dynamic ring fatigue test device, comprising: a stationary ring dummy, a stationary ring dummy mounting support, a fixed platform, an actuator base, a variable pitch pull rod loading joint, a torque arm loading fork ear assembly, an anti-twist fork ear assembly, an anti-twist rod assembly and a torque arm loading support;
[0007] The bottom surface of the fixed ring dummy mounting support is mounted on a fixed platform, and the fixed ring dummy is mounted on the top of the fixed ring dummy mounting support;
[0008] The outer cylindrical surface of the fixed ring dummy and the inner cylindrical surface of the helicopter moving ring large bearing are installed through interference fit;
[0009] The actuator base is installed on a fixed platform and evenly distributed around the fixed ring dummy mounting bracket. The fixed end of the actuator is connected to the actuator base, and the loading end of the actuator is connected to the torque rod loading joint. The other end of the torque rod loading joint is fixed to the helicopter dynamic ring support arm.
[0010] The torque arm loading fork ear assembly is connected to the helicopter dynamic ring 2# torque arm, one end of the anti-torsion fork ear assembly is connected to the helicopter dynamic ring 1# torque arm, and the other end is connected to the anti-torsion rod assembly;
[0011] The torque arm loading fork ear assembly and the anti-torsion bar assembly are fixed to the ground rail through the torque arm loading support.
[0012] Furthermore, a force sensor is installed between the variable pitch tie rod loading joint and the loading end of the actuator cylinder.
[0013] Furthermore, both ends of the anti-twist bar assembly are reverse-threaded for adjusting the length.
[0014] Furthermore, the torque arm loading fork ear assembly and the anti-torsion fork ear assembly are symmetrically installed about the center of the dynamic ring.
[0015] A method for fatigue testing of a helicopter dynamic ring, the method is implemented based on the device, and comprises the following steps:
[0016] Step 1: Debug the test device;
[0017] Step 2: Determine the initial dynamic ring arm load F 1i , i = 1, n, n is the number of east ring arms, and the initial dynamic ring torque arm load F2;
[0018] Step 3: Load according to the determined test load;
[0019] Step 4: Regularly check and record the test load, test cycle number and test damage during the loading process;
[0020] Step 5: When detectable cracks appear in the helicopter dynamic ring or the set number of cycles is reached, the test is terminated. Otherwise, the load is increased based on the initial dynamic ring support arm load and the initial dynamic ring torque arm load, and the test returns to step 3.
[0021] Furthermore, the initial dynamic ring arm load calculation formula is as follows:
[0022] F 1i =Fs1+F d1*cos[wt-2π / 5(i-1)]
[0023] Among them, F s1 is the static load of the arm, F d1 is the dynamic load of the arm, w is the angular velocity, t is the time, and i is the arm number.
[0024] Furthermore, the calculation formula of the initial dynamic ring torque arm load F2 is as follows:
[0025] F2=F s2 +F d2 *cos(wt)
[0026] Among them, F s2 is the static load of the torque arm, F d2 is the dynamic load of the torque arm, w is the angular velocity, and t is the time.
[0027] Further, in step 1, the debugging process of the test device is as follows:
[0028] Start the test device, preheat for 1 minute, check the communication status, and ensure that the test device works normally;
[0029] Adjust the polarity of the force sensor, define the pulling direction as positive and the pressing direction as negative, and the positive direction of the load F actually applied by the actuator is the same as the test load F. 1i Or the positive direction defined by F2 is consistent;
[0030] Generally, 10%, 40%, 60%, 90% and 100% F are applied in 5 levels. 1i Or F2 load, adjust the proportional, integral and differential parameters of the control channel to ensure that the feedback signal can quickly follow the command signal and eliminate hysteresis as much as possible;
[0031] At the same time, set upper and lower limit protection and load error protection.
[0032] Further, in step 5, the second level load F is increased B Compared with the first load F before the increase A With the following relationship:
[0033] F B / F A =[F s1 +(1+20%)*F d1 *cos(wt)] / [F s1 +F d1 *cos(wt)] or F B / F A =[F s2 +(1+20%)
[0034] *F d2*cos(wt)] / [F s2 +F d2 *cos(wt)].
[0035] In summary, the beneficial effects of the present invention are as follows:
[0036] The helicopter dynamic ring fatigue loading test device designed by the present invention can simultaneously meet the coordinated loading of each arm of the dynamic ring and the fatigue loading of the connection between the dynamic ring and the torque arm, and can truly and accurately simulate the boundary conditions and load characteristics of the helicopter dynamic ring installation, effectively solving the problem of the domestic helicopter dynamic ring fatigue test device field from scratch, filling the domestic helicopter fatigue strength test technology blank field, and further improving the strength test level of helicopters in my country. The helicopter dynamic ring fatigue test method involved in the present invention is reasonable and correct, and can accurately reproduce the loading process of the helicopter dynamic ring in flight. It is proved by experiments that the loading device and the test method can accurately simulate the boundary conditions and load characteristics of the helicopter dynamic ring installation in the helicopter dynamic ring fatigue test, provide a real and accurate assessment environment for the helicopter dynamic ring, realize the coordinated loading of each arm of the helicopter dynamic ring and the fatigue loading of the ear piece connecting the dynamic ring and the torque arm, and the load feedback data has a high overlap with the command data. The total error of the test can be controlled within 3% when the helicopter dynamic ring fatigue test is carried out by using the test device. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1 This is a schematic diagram of the load on the helicopter's dynamic ring;
[0038] Figure 2 This is a schematic diagram of the structure of a helicopter dynamic ring fatigue test device;
[0039] Figure 3 The figure is a flow chart of a helicopter dynamic ring fatigue test method. DETAILED DESCRIPTION
[0040] For the fatigue test of helicopter dynamic ring, a test device is provided that can simultaneously meet the coordinated loading of each arm of the dynamic ring and the fatigue loading of the ear piece connecting the dynamic ring and the torque arm. The structural design, size and fitting tolerance of the device simulate the installation boundary conditions of the helicopter dynamic ring. At the same time, variable pitch pull rod force and torque arm load are applied to the helicopter dynamic ring through tooling dummy parts, which simulates the stress state of the helicopter dynamic ring on the helicopter and can accurately reproduce the loading process of the helicopter dynamic ring in flight.
[0041] The technical solution of the present invention: The helicopter dynamic ring fatigue loading device is composed of a stationary ring dummy 1, a stationary ring dummy mounting support 2, a fixed platform 3, an actuator base 4, a variable pitch pull rod loading joint 5, a torque arm loading fork ear assembly 6, an anti-torsion fork ear assembly 7, an anti-torsion rod assembly 8 and a torque arm loading support 9.
[0042] The outer cylindrical surface of the stationary ring dummy 1 and the inner cylindrical surface of the helicopter dynamic ring large bearing are installed and fixed by interference fit. The stationary ring dummy 1 together with the helicopter dynamic ring is installed on the installation plane of the stationary ring dummy mounting support 2 through the bolt holes on the stationary ring dummy 1 and fixed. The lower bottom surface of the stationary ring dummy mounting support 2 is surface-to-surface with the upper plane of the fixed platform 3 and fixed with standard bolts; the actuator base 4 is evenly distributed and fixed on the upper plane of the fixed platform 3, and the fixed end of the actuator is connected to the actuator base. The loading end of the actuator is connected to the embedded threaded hole of the variable pitch rod loading joint 5, and the other end of the variable pitch rod loading joint 5 is fixed on the helicopter dynamic ring support arm to realize the loading of the variable pitch rod force of the helicopter dynamic ring; the torque arm loading fork ear assembly 6 is installed at the connection of the helicopter dynamic ring 2# torque arm, and the anti-torsion fork ear assembly 7 is installed at the connection of the helicopter dynamic ring 1# torque arm and connected to the anti-torsion bar assembly 8. Finally, the torque arm loading fork ear assembly 6 and the anti-torsion bar assembly 8 are fixed to the ground rail through the torque arm loading support 9.
[0043] (1) Test device: The device of the invention is designed with a stationary ring dummy, a stationary ring dummy mounting bracket, a fixed platform, an actuator base, a variable pitch pull rod loading joint, a torque arm loading fork ear assembly, a torque arm loading bracket, an anti-torsion fork ear assembly and an anti-torsion rod assembly, and an actuator is used to apply the test load. The device can realize phase-coordinated loading of the loads of each arm of the helicopter dynamic ring, that is, each arm can be loaded in the same phase or out of phase, meeting the assessment requirements of the helicopter dynamic ring under different working conditions. At the same time, by designing tooling such as a stationary ring dummy, the actual boundary conditions and loading conditions of the helicopter dynamic ring installation are simulated, providing a real and accurate helicopter dynamic ring fatigue test assessment environment, so that accurate fatigue hazardous locations and failure modes of the helicopter dynamic ring can be obtained, providing a test basis for determining its service life. The main features of the device are as follows: (1) The variable pitch tie rod load loading device (consisting of the variable pitch tie rod loading joint, force sensor, actuator and actuator base) is designed to be in the same direction as the load, so that the loading is stable in the tensile direction; at the same time, each set of variable pitch tie rod load loading devices is independent of each other, which can realize phase coordinated loading on the one hand, and facilitate the adjustment and calibration of the installation angle on the other hand. (2) The anti-twist bar assembly adopts a reverse thread design at both ends, which can adjust the length of the anti-twist bar without disassembly, thereby realizing the adjustment of the torque arm loading angle, reducing the disassembly time and labor cost. (3) The torque arm loading device (consisting of the torque arm loading fork ear assembly, force sensor, actuator and torque arm loading support) and the anti-twist device (consisting of the anti-twist fork ear assembly, anti-twist bar assembly, force sensor and torque arm loading support) are designed to be centrally symmetrical. The torque generated during loading is transmitted to the fixed platform through the fixed ring dummy mounting support, realizing the internal force balance of the system, improving the stability of the test bench, and reducing the fluctuation of the test load, thereby improving the test efficiency.
[0044] In summary, the test device can accurately simulate the boundary conditions and load conditions of the helicopter dynamic ring during flight, and at the same time meet the requirements of the fatigue test of the helicopter dynamic ring support arm and the fatigue test of the ear piece connecting the dynamic ring and the torque arm. It has a clever structural design, stable and reliable working performance, good adjustability, and is easy to install and disassemble. The total test error can be controlled within 3%, which can fully verify the fatigue performance of the helicopter dynamic ring, thereby providing a basis for determining the service life and weak points of the helicopter dynamic ring.
[0045] (II) Test methods:
[0046] The helicopter dynamic ring is subjected to complex fatigue loads under different flight conditions such as takeoff, landing and hovering. Once fatigue damage occurs, the helicopter rotor system control will fail and cause the helicopter to crash. For flight safety, fatigue tests need to be carried out on the helicopter dynamic ring on the ground to simulate the fatigue loads on the helicopter dynamic ring under flight conditions, so as to determine the fatigue performance and weak points of the helicopter dynamic ring and provide a basis for determining its service life. In view of the current lack of fatigue life test methods for helicopter dynamic rings, the present invention provides a helicopter dynamic ring fatigue method, which mainly includes: test installation and fixing methods, test load determination, test implementation steps and test installation, loading and inspection requirements, etc. The basic test process is shown in Figure 3 The helicopter dynamic ring fatigue method comprises two parts: dynamic ring support arm fatigue test loading and torque arm connection ear fatigue test loading.
[0047] (1) In the fatigue test of helicopter dynamic ring, the fatigue test of the dynamic ring support arm is generally carried out first, and then the fatigue test of the torque arm connecting ear is carried out.
[0048] (2) Installation and fixing method of helicopter dynamic ring fatigue test Figure 2 shown.
[0049] (3) Fatigue test load of helicopter dynamic ring. The fatigue test load of helicopter dynamic ring is usually given in the test task book. The fatigue test load given in the test task book is calculated based on the load-stress relationship determined by the finite element analysis of the helicopter dynamic ring and the average SN curve of the material.
[0050] The load direction of the helicopter dynamic ring arm is perpendicular to the dynamic ring rotation surface. The load is transmitted by the pitch rod end joint bearing and acts on the dynamic ring arm through the connecting bolts. The corresponding pitch rod is pulled positively. The loads on each arm of the helicopter dynamic ring have a phase relationship. The specific phase needs to be determined according to the structural distribution of the helicopter dynamic ring. Generally, the load form of the helicopter dynamic ring with 5 arms is as follows: F 1i =Fs1+F d1 *cos[wt-2π / 5(i-1)],F s1 is the static load, F d1is the dynamic load, w is the angular velocity, t is the time, and i is the arm number.
[0051] The torque arm connecting ear of the helicopter dynamic ring bears the torque arm load, which is tangent to the rotating surface of the dynamic ring. The load is transmitted by the torque arm and acts on the dynamic ring ear through the connecting bolts. The positive direction of the load is opposite to the rotation direction of the helicopter main rotor. The load form of the torque arm connecting ear of the helicopter dynamic ring is as follows: F2 = F s2 +F d2 *cos(wt), F s2 is the static load, F d2 is the dynamic load, w is the angular velocity, and t is the time.
[0052] (4) Test implementation steps:
[0053] a) Test installation, according to Figure 2 The test installation is completed as shown;
[0054] b) Test debugging: Start the coordinated loading control system, preheat for 1 minute, check the software communication, and ensure that the test equipment works normally; adjust the polarity of the force sensor, define the pulling direction as positive and the compressive direction as negative, and ensure that the positive direction of the load F actually applied by the actuator is consistent with the test load F 1i Or the positive direction defined by F2; generally, 10%, 40%, 60%, 90% and 100% of F are applied in 5 levels respectively. 1i Or F2 load, adjust the proportional, integral and differential parameters of the control channel to ensure that the feedback signal can quickly follow the command signal and eliminate the hysteresis phenomenon as much as possible; after the previous step is completed, load 100% test load F 1i Or F2 for testing, and set upper and lower limit protection at the same time to prevent the load F applied by the actuator from abnormally exceeding the bearing range of the helicopter dynamic ring and causing abnormal damage; set load error protection to ensure that the actual loading load F is consistent with the test load F 1i Or the ratio of F2 does not exceed 2.5%, that is, the loading error does not exceed 2.5%, which involves error allocation. The error allocation scheme of this test method is set as follows: during the test, the error of the load measurement sensor is controlled within 0.5%, and the error of the control system is controlled within 0.5%, that is, the error of the load measurement sensor and the control system selected for this test does not exceed 0.5%; the loading error is controlled within 2.5%, and the total test error is calculated according to the root mean square of each error to ensure that the total test error does not exceed 3%.
[0055] c) Conduct the test: The test is started after debugging without any problems. In the fatigue test of the helicopter dynamic ring, the test load is applied to the helicopter dynamic ring through the telescopic movement of the actuator. When conducting the fatigue test of the helicopter dynamic ring arm, the load is transmitted to each arm of the helicopter dynamic ring through the variable pitch pull rod loading joint. The load direction is perpendicular to the rotation surface of the helicopter dynamic ring. At the same time, the torque arm is used to load the anti-twist assembly at the connection of the helicopter dynamic ring 1# torque arm to constrain the circumferential displacement of the helicopter dynamic ring and measure the constraint force. When conducting the fatigue test of the connection between the dynamic ring and the torque arm, the test load is applied to the connection of the helicopter dynamic ring 2# torque arm through the torque arm loading assembly. At the same time, the torque arm is used to load the anti-twist assembly at the connection of the helicopter dynamic ring 1# torque arm to constrain the circumferential displacement of the helicopter dynamic ring and measure the constraint force. The arms of the helicopter dynamic ring are in an unconstrained state.
[0056] (5) Test installation, loading and inspection requirements
[0057] a. The installation of the helicopter dynamic ring shall be carried out according to the requirements of the test device drawing, and the required tightening torque shall be applied to the helicopter dynamic ring connecting bolts;
[0058] b. Loads should be monitored during the helicopter dynamic ring fatigue test, including but not limited to setting load errors and limit protection;
[0059] c Helicopter dynamic ring fatigue test load upgrade adjustment, the dynamic load F can be adjusted step by step during the test d1 or F d2 Generally, the adjustment ratio is 20% of the first level dynamic load, that is, the second level load F B / First level load F A For: F B / F A =[F s1 +(1+20%)*F d1 *cos(wt)] / [F s1 +F d1 *cos(wt)] or F B / F A =[F s2 +(1+20%)*F d2 *cos(wt)] / [F s2 +F d2 *cos(wt)], generally, if the helicopter dynamic ring is not damaged after 300,000 to 500,000 test load cycles, the fatigue test dynamic load can be increased until it is damaged or the assessment purpose is achieved. The first-level test load of the latter piece can be adjusted according to the test results of the previous piece;
[0060] d. During the fatigue test of helicopter dynamic ring, it is necessary to check and record the test load, test cycle number, test damage, etc. regularly (generally no more than 100,000 cycles);
[0061] e. Test termination conditions: the test can be terminated if one of the following conditions occurs: visually detectable cracks appear on the helicopter dynamic ring (the crack length is generally greater than 2mm) or the test purpose is achieved;
[0062] f Principles for determining test validity: After the test, visually inspect the dynamic ring. If there is no crack, the number of completed test cycles is valid. If visually visible cracks appear on the dynamic ring, review the relevant test data. If there is a significant change in load, the number of cycles when the load changes significantly is taken as the valid number of test cycles.
Claims
1. A helicopter dynamic ring fatigue test device, characterized in that: The device includes: Immovable ring dummy, immovable ring dummy mounting support, fixed platform, actuator base, variable pitch tie rod loading joint, torque arm loading fork ear assembly, anti-twist fork ear assembly, anti-twist bar assembly and torque arm loading support; The bottom surface of the fixed ring dummy mounting support is mounted on a fixed platform, and the fixed ring dummy is mounted on the top of the fixed ring dummy mounting support; The outer cylindrical surface of the fixed ring dummy and the inner cylindrical surface of the helicopter moving ring large bearing are installed through interference fit; The actuator base is installed on a fixed platform and evenly distributed around the fixed ring dummy mounting bracket. The fixed end of the actuator is connected to the actuator base, and the loading end of the actuator is connected to the torque rod loading joint. The other end of the torque rod loading joint is fixed to the helicopter dynamic ring support arm. The torque arm loading fork ear assembly is connected to the helicopter dynamic ring 2# torque arm, one end of the anti-torsion fork ear assembly is connected to the helicopter dynamic ring 1# torque arm, and the other end is connected to the anti-torsion rod assembly; The torque arm loading fork ear assembly and the anti-torsion bar assembly are fixed to the ground rail through the torque arm loading support.
2. The device according to claim 1, characterized in that: A force sensor is installed between the variable pitch tie rod loading joint and the loading end of the actuator.
3. The device according to claim 2, characterized in that: The anti-twist bar assembly is reverse threaded at both ends for adjusting the length.
4. The device according to claim 3, characterized in that: The torque arm loading fork ear assembly and the anti-twist fork ear assembly are symmetrically installed about the center of the dynamic ring.
5. A method for fatigue testing of helicopter dynamic rings, the method being implemented based on the device described in any one of the above, characterized in that: The following steps are involved: Step 1: Debug the test device; Step 2: Determine the initial dynamic ring arm load F 1i , i = 1, n, n is the number of east ring arms, and the initial dynamic ring torque arm load F2; Step 3: Load according to the determined test load; Step 4: Regularly check and record the test load, test cycle number and test damage during the loading process; Step 5: When detectable cracks appear in the helicopter dynamic ring or the set number of cycles is reached, the test is terminated. Otherwise, the load is increased based on the initial dynamic ring support arm load and the initial dynamic ring torque arm load, and the test returns to step 3.
6. The method according to claim 5, characterized in that: The calculation formula of the initial dynamic ring arm load is as follows: F 1i =Fs1+F d1 *cos[wt-2π / 5(i-1)] Among them, F s1 is the static load of the arm, F d1 is the dynamic load of the arm, w is the angular velocity, t is the time, and i is the arm number.
7. The method according to claim 6, characterized in that: The calculation formula of the initial dynamic ring torque arm load F2 is as follows: F2=F s2 +F d2 *cos(wt) Among them, F s2 is the static load of the torque arm, F d2 is the dynamic load of the torque arm, w is the angular velocity, and t is the time.
8. The method according to claim 7, characterized in that: In step 1, the test device debugging process is as follows: Start the test device, preheat for 1 minute, check the communication status, and ensure that the test device works normally; Adjust the polarity of the force sensor, define the pulling direction as positive and the pressing direction as negative, and the positive direction of the load F actually applied by the actuator is the same as the test load F. 1i Or the positive direction defined by F2 is consistent; Generally, 10%, 40%, 60%, 90% and 100% F are applied in 5 levels. 1i Or F2 load, adjust the proportional, integral and differential parameters of the control channel to ensure that the feedback signal can quickly follow the command signal and eliminate hysteresis as much as possible; At the same time, set upper and lower limit protection and load error protection.
9. The method according to claim 8, characterized in that: In step 5, the second level load F is increased B Compared with the first load F before the increase A With the following relationship: F B / F A =[F s1 +(1 + 20%)*F d1 *cos(wt)] / [F s1 +F d1 *cos(wt)] or F B / F A =[F s2 +(1 + 20%)*F d2 *cos(wt)] / [F s2 +F d2 *cos(wt)].
Citation Information
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