CN109543249B - Two-stage plane four-bar mechanism and parameter design method - Google Patents

Two-stage plane four-bar mechanism and parameter design method Download PDF

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CN109543249B
CN109543249B CN201811303393.8A CN201811303393A CN109543249B CN 109543249 B CN109543249 B CN 109543249B CN 201811303393 A CN201811303393 A CN 201811303393A CN 109543249 B CN109543249 B CN 109543249B
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bar mechanism
stage plane
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CN109543249A (en
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张涛
郭爱民
周晓丽
贾磊
刘维玮
吴迪
苏玲
崔占东
姚纳新
孔文秦
彭波
石小亮
张庆利
徐喆
彭扬
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China Academy of Launch Vehicle Technology CALT
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Abstract

A two-stage plane four-bar mechanism and a parameter design method are disclosed, wherein a motion equation, a velocity equation and a generalized transmission ratio of the two-stage plane four-bar mechanism in a polynomial form are established, and the velocity equation is used as the motion input of an ADAMS model of the mechanism; establishing an ADAMS (adaptive dynamic mechanical system) parameterized model of a two-stage plane four-bar mechanism, and obtaining actuator thrust, stroke and part load of a steering engine by using the model, wherein the actuator thrust and the stroke are used as the basis of the design requirement of the steering engine, and the part load is used as the input condition for strength check; and establishing a two-stage plane four-bar mechanism part finite element model by using finite element software ANSYS to obtain the strength and the rigidity of the part. The strength of the part is used as the basis for strength check, and the rigidity of the part is used as the input of the system rigidity; an ADAMS model for calculating the rigidity of the two-stage plane four-bar mechanism system is established, and a solving method for the linear rigidity and the torsional rigidity of the system is provided and used as a basis for rigidity checking. The invention realizes the efficient parameterization design of the two-stage plane four-bar mechanism.

Description

Two-stage plane four-bar mechanism and parameter design method
Technical Field
The invention relates to a two-stage plane four-bar mechanism and a parameter design method, and belongs to the field of mechanism design.
Background
The two-stage plane four-bar mechanism is one of the mechanism configurations commonly used for aircraft control surface transmission mechanisms. The swing guide rod and flat four-bar mechanism is a typical two-stage plane four-bar mechanism, the first stage of the mechanism is a swing guide rod mechanism, the telescopic motion of a steering engine actuator (a swing guide rod) is converted into the rotary motion of an auxiliary rocker arm, and the second stage of the mechanism is a flat four-bar mechanism, and the rotary motion of the auxiliary rocker arm drives a control surface through a connecting rod to enable the control surface to swing. With the requirements of light weight, high rigidity and long-term work of a control surface transmission mechanism system provided by a novel aircraft, the traditional design method is more difficult to adapt to task requirements. The main body is as follows: (1) The mechanism analysis has no mature parameterized modeling method, so that the modeling efficiency is low; (2) The deviation between the strength analysis result and the rigidity analysis result and the test result is large, and the design requirement is difficult to meet. The design of the parameters of the mechanism is the first step of the design of the mechanism system, and the parameters to a certain extent directly determine the weight and the performance of the system. Guo Aimin, peng Bo (publication No. CN 105184005B) a control surface transmission mechanism overall parameter optimization method, peng Bo, guo Aimin and other patent (publication No. CN106844838 a) an aircraft air rudder performance evaluation method describe in detail the parameter design and performance evaluation method of the swing guide rod type control surface transmission mechanism, which is a useful attempt for the mechanism parameter design method. At present, the introduction of a public parameter design method for a domestic and foreign two-stage planar four-bar mechanism is not seen.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, provides a two-stage plane four-bar mechanism and a parameter design method, establishes a motion equation of the two-stage plane four-bar mechanism, a motion equation in a polynomial form, a velocity equation and a generalized transmission ratio, and takes the velocity equation as the motion input of an ADAMS model of the mechanism; establishing an ADAMS (automatic dynamic analysis of mechanical systems) parameterized model of a two-stage plane four-bar mechanism, and obtaining actuator thrust, stroke and part load of a steering engine by using the model, wherein the actuator thrust and the stroke are used as the basis of the design requirement of the steering engine, and the part load is used as the input condition for strength check; and establishing a finite element model of the two-stage plane four-bar mechanism part by using finite element software ANSYS to obtain the strength and the rigidity of the part. The strength of the part is used as the basis for strength check, and the rigidity of the part is used as the input of the system rigidity; an ADAMS model for calculating the rigidity of the two-stage plane four-bar mechanism system is established, and a solving method for the linear rigidity and the torsional rigidity of the system is provided and used as a basis for rigidity checking. The invention realizes the high-efficiency parameterization design of the two-stage plane four-bar mechanism and is convenient for engineering technicians to use.
The purpose of the invention is realized by the following technical scheme:
a two-stage plane four-bar mechanism parameter design method is provided, the two-stage plane four-bar mechanism parameters at least include steering engine actuator thrust, actuator stroke, part strength, and linear stiffness and torsional stiffness of the two-stage plane four-bar mechanism, and the method comprises the following steps:
step one, establishing a polynomial form motion equation of the two-stage plane four-bar mechanism, and obtaining a speed equation of the two-stage plane four-bar mechanism and a generalized transmission ratio of the two-stage plane four-bar mechanism;
step two, establishing a parameterized model of the two-stage plane four-bar mechanism, and taking the velocity equation in the step one as a motion input parameter of the two-stage plane four-bar mechanism model to obtain actuator thrust, actuator stroke and part load of the two-stage plane four-bar mechanism model;
step three, establishing a finite element model of the two-stage plane four-bar mechanism, and taking the part load in the step two as an input parameter for strength check to obtain the part strength and the part rigidity;
and step four, establishing a rigidity model of the two-stage plane four-bar mechanism, taking the part rigidity in the step three as an input parameter of the rigidity of the two-stage plane four-bar mechanism, and obtaining the linear rigidity of the two-stage plane four-bar mechanism and the torsional rigidity of the two-stage plane four-bar mechanism by utilizing the generalized transmission ratio in the step one.
In the above two-stage planar four-bar mechanism parameter design method, the polynomial form equation of motion of the two-stage planar four-bar mechanism is:
Figure BDA0001852950940000021
in the formula (I), the compound is shown in the specification,
Figure BDA0001852950940000022
for the elongation of the actuator obtained by a polynomial fitting formula, b 1 、b 2 And b 3 Are all coefficients of a polynomial form motion equation, and delta is a rudder deflection angle.
In the above two-stage planar four-bar mechanism parameter design method, the velocity equation of the two-stage planar four-bar mechanism is as follows:
Figure BDA0001852950940000031
in the formula, v l Is the linear velocity of the actuator, b 1 、b 2 And b 3 Are all coefficients of a polynomial form motion equation, delta is a rudder deflection angle,
Figure BDA0001852950940000032
the rudder angle speed (derivative of rudder angle).
In the parameter design method of the two-stage planar four-bar mechanism, the generalized transmission ratio of the two-stage planar four-bar mechanism is as follows:
i lo1 ＝b 1 +2b 2 δ+3b 3 δ 2
in the formula i lo1 Generalized transmission ratio of two-stage planar four-bar mechanism, b 1 、b 2 And b 3 Are all coefficients of a polynomial form motion equation, and delta is a rudder deflection angle.
In the above two-stage planar four-bar mechanism parameter design method, the parts of the two-stage planar four-bar mechanism include a connecting rod, and the calculation method of the rigidity of the connecting rod is as follows:
Figure BDA0001852950940000033
in the formula, k t_gan Is the tensile stiffness, x, of the connecting rod t_nax_gan Maximum axial displacement of the surface of the ear hole in the axial direction of the connecting rod, x, per unit tensile load t_nin_gan Minimum axial displacement of the earhole surface acting for a unit tensile load along the axial direction of the connecting rod;
Figure BDA0001852950940000034
in the formula, k c_gan Is the compression stiffness, x, of the connecting rod c_nax_gan Maximum axial displacement of the surface of the ear hole in the axial direction of the connecting rod, x, for unit pressure load c_nin_gan Is the minimum axial displacement of the surface of the ear hole acting per unit of compression load in the axial direction of the connecting rod.
In the above two-stage planar four-bar mechanism parameter design method, the parts of the two-stage planar four-bar mechanism include an auxiliary rocker arm, and the calculation method of the rigidity of the auxiliary rocker arm is as follows:
Figure BDA0001852950940000035
in the formula, k t_fy To assist the tensile stiffness of the rocker arm, x t_nax_fy The maximum displacement of the surface of the ear hole under the action of unit tensile load along the direction of the line connecting the circle centers of the two ear holes, x t_nin_fy The surface of the ear hole under the action of unit tensile load is least displaced along the direction of the connection line of the circle centers of the two ear holes;
Figure BDA0001852950940000041
in the formula, k c_fy To assist the compressive stiffness of the rocker arm, x c_nax_fy The maximum displacement of the surface of the ear hole under the action of unit tensile load along the direction of the line connecting the circle centers of the two ear holes, x c_nin_fy The surface of the ear hole under the action of unit tensile load is minimum displacement along the direction of the connecting line of the circle centers of the two ear holes.
In the above two-stage planar four-bar mechanism parameter design method, the two-stage planar four-bar mechanism comprises a support, and the calculation method of the rigidity of the support is as follows:
Figure BDA0001852950940000042
in the formula, k zh For the stiffness of the support, x nax_zh Displacement of the ear hole surface in the loading direction per unit tensile load.
According to the parameter design method of the two-stage plane four-bar mechanism, the part stiffness in the step three is used as an input parameter of the two-stage plane four-bar mechanism stiffness, the two-stage plane four-bar mechanism stiffness is obtained, and then the linear stiffness of the two-stage plane four-bar mechanism is calculated;
the calculation method of the rigidity of the two-stage plane four-bar mechanism comprises the following steps:
Figure BDA0001852950940000043
in the formula, k r_t_s For the pull stiffness of a two-stage planar four-bar mechanism, M eq For the unit force acting on the centre of pressure to be equivalent to the torque on the rudder shaft, Δδ t The difference between the measured rudder deflection angle and the target rudder deflection angle when the connecting rod and the auxiliary rocker arm are pulled;
Figure BDA0001852950940000044
in the formula, k r_p_s Is the compression stiffness, delta, of a two-stage planar four-bar mechanism p The difference between the measured rudder deflection angle and the target rudder deflection angle when the connecting rod and the auxiliary rocker arm are pressed is obtained.
In the two-stage planar four-bar mechanism parameter design method, the calculation method of the linear stiffness of the two-stage planar four-bar mechanism comprises the following steps:
Figure BDA0001852950940000051
in the formula, k l_t_s Stiffness of the tensile line for a two-stage planar four-bar linkage, i lo1 A generalized transmission ratio;
Figure BDA0001852950940000052
in the formula, k l_p_s The compression line stiffness of the two-stage plane four-bar mechanism is shown.
A design method of a two-stage plane four-bar mechanism comprises the following steps:
step one, establishing a polynomial form motion equation of the two-stage plane four-bar mechanism according to the geometric configuration size of the two-stage plane four-bar mechanism, and obtaining a speed equation of the two-stage plane four-bar mechanism and a generalized transmission ratio of the two-stage plane four-bar mechanism;
establishing a parameterized model of the two-stage plane four-bar mechanism, and taking the velocity equation in the step one as a motion input parameter of the two-stage plane four-bar mechanism model to obtain actuator thrust, actuator stroke and part load of the two-stage plane four-bar mechanism model; judging whether the design of the steering engine meets the preset requirements or not, and if the design of the steering engine meets the preset requirements, turning to the third step; otherwise, adjusting the geometric configuration size of the two-stage plane four-bar mechanism, and turning to the step I;
step three, establishing a finite element model of the two-stage plane four-bar mechanism, and taking the part load in the step two as an input parameter for strength check to obtain the strength and the rigidity of the part;
step four, judging whether the strength of the part in the step three meets the preset strength, and if the strength of the part meets the preset strength, turning to step five; otherwise, adjusting the design size of the part and turning to the third step;
step five, establishing a rigidity model of the two-stage plane four-bar mechanism, taking the part rigidity in the step three as an input parameter of the rigidity of the two-stage plane four-bar mechanism, and obtaining the linear rigidity of the two-stage plane four-bar mechanism and the torsional rigidity of the two-stage plane four-bar mechanism by utilizing the generalized transmission ratio in the step one; and judging whether the linear stiffness of the two-stage plane four-bar mechanism and the torsional stiffness of the two-stage plane four-bar mechanism meet the preset stiffness requirement, if so, finishing the design of the two-stage plane four-bar mechanism, and otherwise, turning to the third step.
Compared with the prior art, the invention has the following beneficial effects:
(1) The invention establishes a motion equation of a two-stage plane four-bar mechanism, a motion equation in a polynomial form, a speed equation and a generalized transmission ratio, improves the precision of motion analysis and lays a theoretical foundation for mechanism design;
(2) The ADAMS parameterized model of the two-stage plane four-bar mechanism is established, and the modeling and part load calculation efficiency is improved;
(3) A finite element model of the two-stage plane four-bar mechanism part is established by using finite element software ANSYS, and a basis is provided for accurately evaluating the strength of the part;
(4) An ADAMS model for calculating the rigidity of the two-stage plane four-bar mechanism system is established, and a solving method for the linear rigidity and the torsional rigidity of the system is provided. Compared with the traditional method, the rigidity calculation method has obviously improved precision, is put forward for the first time in the field, and fills the blank at home and abroad.
Drawings
FIG. 1 is a flow chart of the steps of parameter design according to the present invention;
FIG. 2 is a schematic diagram of a two-stage planar four-bar mechanism of the present invention;
FIG. 3 is a schematic diagram of an ADAMS parameterization model of a two-stage planar four-bar mechanism according to the invention;
FIG. 4 is a schematic view of a finite element model loading of a part of the two-stage planar four-bar mechanism of the present invention;
FIG. 5 is a schematic view of a finite element model loading for calculating the stiffness of an auxiliary rocker arm of the two-stage planar four-bar mechanism according to the present invention;
FIG. 6 is a schematic diagram of a system rigidity ADAMS model of a two-stage planar four-bar mechanism according to the invention;
fig. 7 is an overall flow chart of the mechanism design of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The flow of a two-stage plane four-bar mechanism parameter design method is shown in figure 1, and comprises the following steps;
(1) A schematic diagram of a two-stage planar four-bar mechanism is shown in fig. 2. The invention establishes a motion equation of a two-stage plane four-bar mechanism, a motion equation in a polynomial form, a speed equation and a generalized transmission ratio.
(1a) The motion equation of the two-stage plane four-bar mechanism is as follows:
Figure BDA0001852950940000071
in the formula, theta 0 Is the initial value of the angle between the rocker arm and the left fixed rod, theta 1 To assist the angle between the left rocker of the rocker arm and the y-axis, theta 2 To assist the angle between the right rocker of the rocker and the y-axis, theta 4 Is an included angle between the left fixed rod and the right fixed rod, and the zero position length of the steering engine actuator is l 0 ，l 1 Is the length of the rocker arm, /) 2 Is the length of the connecting rod l 3 To assist the length of the left rocker arm of the rocker arm,/ 4 To assist inLength of right rocker arm of rocker arm l 5 Is the length of the left fixed rod, /) 6 The right fixation rod length. Alpha is alpha 11 、α 12 、α 1 And alpha 2 Is an intermediate variable of angle,/ AB Is the length intermediate variable. Theta is the included angle of the rocker arm and the left fixed rod, delta is the rudder deflection angle, l is the total length of the actuator of the steering engine, and delta l is the elongation of the actuator.
(1b) Polynomial form of the equation of motion of a two-stage planar four-bar mechanism:
Figure BDA0001852950940000072
in the formula (I), the compound is shown in the specification,
Figure BDA0001852950940000073
for the elongation of the actuator obtained by a polynomial equation, δ is the rudder deflection angle, b 1 、b 2 And b 3 All coefficients of a polynomial form motion equation are determined by the following method: firstly, outputting 20-100 actuator elongation-rudder deflection angle data by equation (1) in equal step length, then determining polynomial coefficients by a polynomial fitting method, and specifically realizing the polynomial coefficients by Origin equal numerical processing software.
(1c) And (3) obtaining a polynomial form of the velocity equation of the two-stage plane four-bar mechanism by derivation of the polynomial form of the motion equation of the two-stage plane four-bar mechanism:
Figure BDA0001852950940000081
in the formula, v l Is the linear velocity of the actuator or actuators,
Figure BDA0001852950940000082
the rudder angle speed (derivative of the rudder angle).
(1d) Obtaining a polynomial form of the generalized transmission ratio of the two-stage planar four-bar mechanism according to the polynomial form of the speed equation of the two-stage planar four-bar mechanism:
i lo1 ＝b 1 +2b 2 δ+3b 3 δ 2 (4)
(2) An ADAMS parameterized model of a two-stage planar four-bar mechanism was established, as shown in fig. 3. The velocity equation obtained in the step (1) is used as the motion input of a model, and the thrust, the stroke and the part load of an actuator are obtained by using the model, wherein the thrust and the stroke of the actuator are used as the basis of the design requirement of the steering engine;
(2a) The initial values of the basic geometric variables are realized by Design variables (Design variables). The basic geometric variables comprise an initial value theta of an included angle between the rocker arm and the left fixed rod 0 Angle theta between left rocker of auxiliary rocker arm and y axis 1 The included angle theta between the right rocker of the auxiliary rocker arm and the y axis 2 An included angle theta between the left fixing rod and the right fixing rod 4 Zero position length l of actuator 0 Length l of rocker arm 1 Length of connecting rod l 2 Length l of left rocker of auxiliary rocker arm 3 Length l of right rocker of auxiliary rocker arm 4 Length l of left fixing rod 5 And right fixation rod length l 6 。
(2b) Point1, point2, point3, point4, point5 and Point6 are defined within the XY plane. Wherein Point1 represents the position of the rudder shaft and is positioned at the origin of coordinates; point2 represents the connecting position of the rocker and the connecting rod; point3 represents the connecting position of the auxiliary rocker arm and the support; point4 represents the connecting position of the connecting rod and the left rocker of the auxiliary rocker arm; point5 represents the connecting position of the right rocker of the auxiliary rocker arm and the actuator; point6 indicates the actuator and support connection location. The coordinates of Point2 to Point6 can be obtained by using a drawing method in the structural design software such as CATIA according to the input condition of (2 a).
(2c) A shell and an actuating rod of the actuator are built by utilizing the Cylinder, and orientation is realized; defining a moving pair of the actuator, and modifying the z directions of an i moving pair and a j Marker by utilizing the direction of the Cylinder to enable the z directions to be consistent with the moving direction of the actuator;
(2d) Building a rocker arm and a connecting rod by using Link;
(2e) Building an auxiliary rocker arm by using a Plate (Plate);
(2f) Hinges (revolute pairs) are respectively defined between the rocker arm and the group, between the auxiliary rocker arm and the actuating rod, and between the actuator shell and the group;
(2g) Defining the measurement of the stroke of an actuator, the thrust of the actuator, the total length of the actuator, the rudder deflection angle and the like;
(2h) And (3) applying drive (Motion) on the actuator moving pair, defining a displacement expression and setting the linear velocity of the steering engine. For convenience, the linear speed of the steering engine is set to meet the requirement that the rudder swings to a target position from a zero position at a constant speed within a specified time. Then the linear velocity of the steering engine is
Figure BDA0001852950940000091
In the formula, delta o Respectively, the target rudder deflection angle, t is the motion process time, and is generally expressed by time in ADAMS e End time of exercise.
If the motion ending time is 1s, the linear velocity of the steering engine is
v l ＝b 1 δ e +2b 2 δ e 2 t+3b 3 δ e 3 t 2 (6)
(2i) And establishing 1 MAERKER which is coincident with the control surface load reference coordinate system as a projection coordinate system for applying the control surface load. The rudder surface load is usually given in the form of a hinge moment or a six-component force. The load is applied to the rudder shaft position of the rocker arm and an appropriate projection coordinate system is selected.
(2j) Defining 1 Marker parallel to a part coordinate system (a common full aircraft coordinate system) on each part respectively as a reference point for outputting part load;
(2k) According to different working conditions, respectively setting simulation end time to make it and motion end time t e And (5) the consistency is achieved. The simulation steps can be 10-100, and Static force (Static) is selected for the simulation type; and closing the gravity and solving.
(2 l) selecting a format of ANSYS by using a finite element load output function of ADAMS, respectively selecting the Marker defined in (2 j) as a projection coordinate system of the load, and setting the output time as t e And outputting the part load in the text file format.
(3) And (3) establishing a two-stage plane four-bar mechanism part finite element model by using finite element software ANSYS, and obtaining the strength and the rigidity of the part by using the part load obtained in the step (2) as an input condition for strength check as shown in figures 4-5. The strength of the part is used as the basis for strength check.
(3a) Analyzing type static selection;
(3b) Selecting a hexahedron leader by a grid division method, and controlling the precision by 80-100;
(3c) When solving the movable components (comprising auxiliary rocker arms and connecting rods), opening the options of inertial release and weak springs, and when solving the non-movable components (comprising steering engine supports and rudder shaft supports), adopting default settings;
(3d) The movable part does not apply position constraint, and the non-movable part applies displacement constraint according to the actual condition;
(3e) The lug load is divided into 3 types and is applied respectively, and the radial force, the axial force and the bending moment are applied to the surface of the inner hole of the whole lug. Wherein the ear hole radial force is applied to the ear hole inner surface in the form of a bearing load, the ear hole axial force is applied to the ear hole inner surface in the form of a force, and the ear hole bending moment is applied to the ear hole inner surface in the form of a bending moment. Wherein, the axial force of the ear piece and the bending moment of the ear hole are usually small and are usually ignored.
(3f) And (5) checking the equivalent stress as a basis for intensity checking after calculation.
(3g) The rigidity calculation of the connecting rod can be based on the finite element model, the load is changed into the bearing load with equal size and opposite direction along the axial direction, and then the solution is carried out. And extracting the difference between the maximum value and the minimum value of the axial displacement of the surface of the ear hole from the finite element result. The stiffness of the connecting rod is calculated by:
Figure BDA0001852950940000101
in the formula, k t_gan Is the tensile stiffness, x, of the connecting rod t_nax_gan Maximum axial displacement of the surface of the ear hole along the axial direction of the connecting rod, x, for a unit tensile load t_nin_gan Minimum axial position of ear hole surface along axial direction of connecting rod for unit pulling load actionAnd (5) moving.
Figure BDA0001852950940000102
In the formula, k c_gan Is the compression stiffness, x, of the connecting rod c_nax_gan Maximum axial displacement of the surface of the ear hole in the axial direction of the connecting rod, x, for unit pressure load c_nin_gan Is the minimum axial displacement of the ear hole surface acting by unit pressure load along the axial direction of the connecting rod.
(3h) The rigidity calculation of the auxiliary rocker arm can be based on the finite element model of the auxiliary rocker arm, the load is changed into the bearing load with equal size and opposite direction along the connecting line direction of the circle centers of the two upper ear holes, the force of the support connecting the ear holes is deleted, and the solution is carried out. And extracting the difference between the maximum value and the minimum value of the displacement of the surfaces of the ear holes along the direction of the connecting line of the circle centers of the two ear holes from the finite element result. The stiffness of the auxiliary rocker arm is calculated using the following equation:
Figure BDA0001852950940000111
in the formula, k t_fy To assist the tensile stiffness of the rocker arm, x t_nax_fy The maximum displacement of the surface of the ear hole under the action of unit tensile load along the direction of the line connecting the circle centers of the two ear holes is x t_nin_fy The surface of the ear hole under the action of unit tensile load is minimum displacement along the direction of the connection line of the circle centers of the two ear holes.
Figure BDA0001852950940000112
In the formula, k c_fy To assist the compressive stiffness of the rocker arm, x c_nax_fy The maximum displacement of the surface of the ear hole under the action of unit tensile load along the direction of the line connecting the circle centers of the two ear holes is x c_nin_fy The surface of the ear hole under the action of unit tensile load is minimum displacement along the direction of the connection line of the circle centers of the two ear holes.
(3i) The rigidity calculation of the support can be based on the support finite element model, and the ear hole load is changed into the unit bearing load perpendicular to the symmetrical plane of the support in the mechanism motion flat sheet. The displacement constraint is preserved. And extracting the displacement of the surface of the earhole in the unit load direction from the solving and element limiting results. The stiffness of the mount is calculated using the following equation:
Figure BDA0001852950940000113
in the formula, k zh Is the stiffness of the support, x nax_zh Displacement of the ear hole surface in the loading direction per unit tensile load.
The equivalent torsional rigidity of the support stiffness to the support mounting surface is calculated according to the following formula
k r_zh ＝k zh h zh 2 (12)
In the formula, k r_zh Torsional stiffness equivalent to the mounting surface of the mount, h zh The equivalent height of the support is the distance from the mounting surface of the support to the axis of the ear hole.
(4) And establishing an ADAMS model for calculating the rigidity of the two-stage plane four-bar mechanism system, as shown in FIG. 6. And (4) taking the part rigidity given in the step (3) as the input of the system rigidity, and giving a solving method of the system linear rigidity and the torsional rigidity as the basis of rigidity check.
(4a) The definition of Point7, point8, point9, point10 and Point11 is added in the XY plane. Wherein Point7 represents the control surface center-of-pressure position; point8 represents the position of the mounting surface of the rudder shaft support; point9 represents the installation surface position of the auxiliary rocker arm support; point10 represents the position of the mounting surface of the steering engine support; the coordinates of the points are determined according to the geometric relationship;
(4b) A rudder shaft support, an auxiliary rocker support and a steering engine support are established by a connecting rod (Link); a rotating pair of the support and the ground is defined on the mounting section of the support, and a torsion spring is defined at the position. Because the number of the rudder shaft supports is 2, the rigidity of a torsion spring between the rudder shaft support and the ground is multiplied by 2; the spring stiffness is given by the formulas (11) and (12);
(4c) Deleting the revolute pairs between the rocker arm and the ground and between the actuator and the ground, and defining the revolute pairs between the rocker arm and the rudder shaft support as well as between the actuator and the steering engine support;
(4d) Deleting the connecting rod, defining a spring between the hinge point on the rocker arm and the hinge point on the left rocker arm, wherein the rigidity of the spring is given by formulas (7) and (8);
(4e) Deleting the auxiliary rocker arm, and establishing an independent left rocker arm and an independent right rocker arm by using a connecting rod; respectively defining a left rocker, a connecting rod and a revolute pair of the auxiliary rocker arm support; respectively defining a right rocker, an actuator and a revolute pair of an auxiliary rocker support; the spring is defined at the hinge position on the left rocker and the right rocker, and the rigidity of the spring is given by formulas (7) and (8);
(4f) Deleting the original load of the control surface, and applying unit force vertical to the control surface at the pressure center;
(4g) And (3) calculating the elongation of the actuator according to the target rudder deflection angle and the formula (1), and taking the elongation as the speed input of the actuator motion. Setting the simulation ending time to be 1s, and carrying out simulation;
(4h) Measuring the value of the rudder deflection angle, and calculating the system rigidity by using the following formula:
Figure BDA0001852950940000121
in the formula, k r_t_s For the tensile stiffness of the system, M eq For the unit force acting on the pressure center to be equivalent to the torque on the rudder shaft, Δ δ t The difference between the measured rudder deflection angle and the target rudder deflection angle when the connecting rod and the auxiliary rocker arm are pulled.
Figure BDA0001852950940000122
In the formula, k r_p_s For the compressive stiffness of the system, M eq For the torque equivalent to the rudder shaft of the unit force acting on the pressure center, Δ δ p The difference between the measured rudder deflection angle and the target rudder deflection angle when the connecting rod and the auxiliary rocker arm are pressed is obtained.
The linear stiffness equivalent to the steering gear axis is calculated by the following equation
Figure BDA0001852950940000131
In the formula, k l_t_s For the system tensile line stiffness, i lo1 The value of which is determined by equation (4) for the generalized gear ratio.
Figure BDA0001852950940000132
In the formula, k l_p_s The system compression line stiffness.
A design method of a two-stage plane four-bar mechanism is shown in figure 7 and comprises the following steps:
step one, establishing a polynomial form motion equation of the two-stage plane four-bar mechanism according to the geometric configuration size of the two-stage plane four-bar mechanism, and obtaining a speed equation of the two-stage plane four-bar mechanism and a generalized transmission ratio of the two-stage plane four-bar mechanism;
step two, establishing a parameterized model of the two-stage plane four-bar mechanism, and taking the velocity equation in the step one as a motion input parameter of the two-stage plane four-bar mechanism model to obtain actuator thrust, actuator stroke and part load of the two-stage plane four-bar mechanism model; judging whether the design of the steering engine meets the preset requirements or not, and if the design of the steering engine meets the preset requirements, turning to the third step; otherwise, adjusting the geometric configuration size of the two-stage plane four-bar mechanism, and turning to the first step;
step three, establishing a finite element model of the two-stage plane four-bar mechanism, and taking the part load in the step two as an input parameter for strength check to obtain the part strength and the part rigidity;
step four, judging whether the strength of the part in the step three meets the preset strength, and if the strength of the part meets the preset strength, turning to step five; otherwise, adjusting the design size of the part and turning to the third step;
step five, establishing a rigidity model of the two-stage plane four-bar mechanism, taking the part rigidity in the step three as an input parameter of the rigidity of the two-stage plane four-bar mechanism, and obtaining the linear rigidity of the two-stage plane four-bar mechanism and the torsional rigidity of the two-stage plane four-bar mechanism by utilizing the generalized transmission ratio in the step one; and judging whether the linear stiffness of the two-stage plane four-bar mechanism and the torsional stiffness of the two-stage plane four-bar mechanism meet the preset stiffness requirement, if so, finishing the design of the two-stage plane four-bar mechanism, and otherwise, turning to the third step.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are not particularly limited to the specific examples described herein.

Claims (7)

1. The utility model provides a two-stage plane four-bar linkage parameter design method, two-stage plane four-bar linkage parameter include steering wheel actuator thrust, actuator stroke, part intensity, two-stage plane four-bar linkage's linear rigidity and torsional rigidity at least, its characterized in that: the method comprises the following steps:
step one, establishing a polynomial form motion equation of the two-stage plane four-bar mechanism, and obtaining a speed equation of the two-stage plane four-bar mechanism and a generalized transmission ratio of the two-stage plane four-bar mechanism;
establishing a parameterized model of the two-stage plane four-bar mechanism, and taking the velocity equation in the step one as a motion input parameter of the two-stage plane four-bar mechanism model to obtain actuator thrust, actuator stroke and part load of the two-stage plane four-bar mechanism model;
step three, establishing a finite element model of the two-stage plane four-bar mechanism, and taking the part load in the step two as an input parameter for strength check to obtain the strength and the rigidity of the part;
step four, establishing a rigidity model of the two-stage plane four-bar mechanism, taking the part rigidity in the step three as an input parameter of the rigidity of the two-stage plane four-bar mechanism, and obtaining the linear rigidity of the two-stage plane four-bar mechanism and the torsional rigidity of the two-stage plane four-bar mechanism by utilizing the generalized transmission ratio in the step one;
the polynomial form motion equation of the two-stage plane four-bar mechanism is as follows:
Figure FDA0004056635130000011
in the formula (I), the compound is shown in the specification,
Figure FDA0004056635130000012
for the elongation of the actuator obtained by a polynomial fitting formula, b 1 、b 2 And b 3 Are coefficients of a polynomial form motion equation, and delta is a rudder deflection angle;
the speed equation of the two-stage plane four-bar mechanism is as follows:
Figure FDA0004056635130000013
in the formula, v l In order to be the linear velocity of the actuator,
Figure FDA0004056635130000014
is the rudder deflection angle speed;
the generalized transmission ratio of the two-stage plane four-bar mechanism is as follows:
i lo1 ＝b 1 +2b 2 δ+3b 3 δ 2
in the formula i lo1 The generalized transmission ratio of the two-stage plane four-bar mechanism is provided.
2. The two-stage planar four-bar mechanism parameter design method according to claim 1, wherein: the parts of the two-stage plane four-bar mechanism comprise connecting rods, and the calculation method of the rigidity of the connecting rods comprises the following steps:
Figure FDA0004056635130000021
in the formula, k t_gan Is the tensile stiffness, x, of the connecting rod t_nax_gan Maximum axial displacement of the surface of the ear hole in the axial direction of the connecting rod, x, per unit tensile load t_nin_gan The minimum axial displacement of the surface of the ear hole acting as unit tensile load along the axial direction of the connecting rod;
Figure FDA0004056635130000022
in the formula, k c_gan Is the compression stiffness, x, of the connecting rod c_nax_gan Maximum axial displacement of the surface of the ear hole along the axial direction of the connecting rod, x, for unit pressure load c_nin_gan Is the minimum axial displacement of the ear hole surface acting by unit pressure load along the axial direction of the connecting rod.
3. The two-stage planar four-bar mechanism parameter design method according to claim 1, characterized in that: the parts of the two-stage plane four-bar mechanism comprise an auxiliary rocker arm, and the rigidity of the auxiliary rocker arm is calculated by the following method:
Figure FDA0004056635130000023
in the formula, k t_fy To assist the tensile stiffness of the rocker arm, x t_nax_fy The maximum displacement of the surface of the ear hole under the action of unit tensile load along the direction of the line connecting the circle centers of the two ear holes, x t_nin_fy The surface of the ear hole under the action of unit tensile load is minimum displaced along the direction of the connecting line of the circle centers of the two ear holes;
Figure FDA0004056635130000024
in the formula, k c_fy To assist the compressive stiffness of the rocker arm, x c_nax_fy The maximum displacement of the surface of the ear hole under the action of unit tensile load along the direction of the line connecting the circle centers of the two ear holes is x c_nin_fy The surface of the ear hole under the action of unit tensile load is minimum displacement along the direction of the connection line of the circle centers of the two ear holes.
4. The two-stage planar four-bar mechanism parameter design method according to claim 1, wherein: the parts of the two-stage plane four-bar mechanism comprise a support, and the calculation method of the rigidity of the support comprises the following steps:
Figure FDA0004056635130000031
in the formula, k zh Is the stiffness of the support, x nax_zh Displacement of the ear hole surface in the loading direction per unit tensile load.
5. The two-stage planar four-bar mechanism parameter design method according to claim 1, wherein: taking the part stiffness obtained in the step three as an input parameter of the two-stage plane four-bar mechanism stiffness to obtain the two-stage plane four-bar mechanism stiffness, and then calculating the linear stiffness of the two-stage plane four-bar mechanism;
the calculation method of the rigidity of the two-stage plane four-bar mechanism comprises the following steps:
Figure FDA0004056635130000032
in the formula, k r_t_s For the pull stiffness of a two-stage planar four-bar mechanism, M eq For the torque equivalent to the rudder shaft of the unit force acting on the pressure center, Δ δ t The difference between the measured rudder deflection angle and the target rudder deflection angle when the connecting rod and the auxiliary rocker arm are pulled;
Figure FDA0004056635130000033
in the formula, k r_p_s Is the compression stiffness, delta, of a two-stage planar four-bar mechanism p The difference between the measured rudder deflection angle and the target rudder deflection angle when the connecting rod and the auxiliary rocker arm are pressed is obtained.
6. The two-stage planar four-bar mechanism parameter design method according to claim 5, characterized in that: the calculation method of the linear stiffness of the two-stage plane four-bar mechanism comprises the following steps:
Figure FDA0004056635130000034
in the formula, k l_t_s For the tensile line stiffness of a two-stage planar four-bar mechanism, i lo1 A generalized transmission ratio;
Figure FDA0004056635130000035
in the formula, k l_p_s The compression line stiffness of the two-stage plane four-bar mechanism is shown.
7. A design method of a two-stage plane four-bar mechanism is characterized by comprising the following steps: the method comprises the following steps:
step one, establishing a polynomial form motion equation of the two-stage plane four-bar mechanism according to the geometric configuration size of the two-stage plane four-bar mechanism, and obtaining a speed equation of the two-stage plane four-bar mechanism and a generalized transmission ratio of the two-stage plane four-bar mechanism;
step two, establishing a parameterized model of the two-stage plane four-bar mechanism, and taking the velocity equation in the step one as a motion input parameter of the two-stage plane four-bar mechanism model to obtain actuator thrust, actuator stroke and part load of the two-stage plane four-bar mechanism model; judging whether the design of the steering engine meets the preset requirements or not, and if the design of the steering engine meets the preset requirements, turning to the third step; otherwise, adjusting the geometric configuration size of the two-stage plane four-bar mechanism, and turning to the step I;
step three, establishing a finite element model of the two-stage plane four-bar mechanism, and taking the part load in the step two as an input parameter for strength check to obtain the part strength and the part rigidity;
step four, judging whether the strength of the part in the step three meets the preset strength, and if the strength of the part meets the preset strength, turning to step five; otherwise, adjusting the design size of the part and turning to the third step;
step five, establishing a rigidity model of the two-stage plane four-bar mechanism, taking the part rigidity in the step three as an input parameter of the rigidity of the two-stage plane four-bar mechanism, and obtaining the linear rigidity of the two-stage plane four-bar mechanism and the torsional rigidity of the two-stage plane four-bar mechanism by utilizing the generalized transmission ratio in the step one; judging whether the linear stiffness of the two-stage plane four-bar mechanism and the torsional stiffness of the two-stage plane four-bar mechanism meet the preset stiffness requirement, if the linear stiffness of the two-stage plane four-bar mechanism and the torsional stiffness of the two-stage plane four-bar mechanism meet the preset stiffness requirement, finishing the design of the two-stage plane four-bar mechanism, and if not, turning to the third step;
the polynomial form motion equation of the two-stage plane four-bar mechanism is as follows:
Figure FDA0004056635130000041
in the formula (I), the compound is shown in the specification,
Figure FDA0004056635130000042
for the elongation of the actuator obtained by a polynomial fitting formula, b 1 、b 2 And b 3 Are coefficients of a polynomial form motion equation, and delta is a rudder deflection angle;
the speed equation of the two-stage plane four-bar mechanism is as follows:
Figure FDA0004056635130000043
in the formula, v l In order to be the linear velocity of the actuator,
Figure FDA0004056635130000051
is the rudder deflection angle speed;
the generalized transmission ratio of the two-stage plane four-bar mechanism is as follows:
i lo1 ＝b 1 +2b 2 δ+3b 3 δ 2
in the formula i lo1 The generalized transmission ratio of the two-stage plane four-bar mechanism is provided.
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