Double-crank adjusting mechanism numerical simulation method based on crank connecting rod dynamics

Abstract

The invention discloses a double-crank adjusting mechanism numerical simulation method based on crank connecting rod dynamics. The method comprises the following steps: S1, establishing mechanism coordinates according to a double-crank adjusting mechanism; s2, establishing kinematics and dynamics models of the double-crank adjusting mechanism; s3, calculating kinematics and dynamics parameters of all components in a full time domain according to the model in the step S2; and S4, drawing a motion law curve graph of each component and a driving force change curve graph of the driving component. According to the method, mathematical processing is carried out on the geometric equation of the double-crank-link mechanism system, so that an angle solution can be obtained, and an analytical solution and an accurate solution of the mechanism dynamics control equation are calculated.

Description

Technical Field

[0001] This invention belongs to the field of This invention relates to the technical field of kinematic force analysis of a double-crank connecting rod adjusting mechanism driven by a motor, and particularly relates to a numerical simulation method for a double-crank adjusting mechanism based on crank-connecting rod dynamics. Background Art

[0002] In the field of mechanical control, crank-connecting rods and crank-sliders are the most common and basic forms of adjusting and controlling mechanisms, which can realize the conversion between circular motion and reciprocating linear motion. With the gradual development of electrification and automation, the application of a crank-connecting rod adjusting mechanism driven by a motor to rotate the crank is becoming more and more extensive. At this time, the adjusting mechanism plays a role in converting circular motion into reciprocating swing or circular motion. Analyzing the dynamic characteristics of this form of adjusting mechanism plays an important role in some engineering problems with high control precision, fast response requirements, high reliability requirements, and complex working conditions, and can provide theoretical basis and support for the performance and structural optimization of the entire mechanism. The motion analysis of traditional double-crank mechanisms or four-link crank-rocker mechanisms relies on means such as drawing methods, experience, and tests, lacking accurate solutions and global analysis of the entire motion process, and also lacking means for quickly evaluating and analyzing the instantaneous stress and strain fields of the mechanism during the motion process. Although the dynamic models of crank-connecting rod plus slider mechanisms have been widely used in the theoretical analysis and test applications of various engineering problems, in the double-crank connecting rod mechanism, due to the inability to directly obtain a simple theoretical expression compared with the crank-slider mechanism in solving geometric equations, the full-time domain solution application of its full-mechanism dynamic model is restricted. At present, there is no literature showing research on the full-mechanism full-time domain solution of its dynamic model. Contents of the Invention In view of this, the purpose of this invention is to propose a numerical simulation method for a double-crank adjusting mechanism based on crank-connecting rod dynamics to solve at least one technical problem in the background art. This invention provides a numerical simulation method for a double-crank adjusting mechanism based on crank-connecting rod dynamics, which can realize the solution and analysis of dynamic parameters such as displacement, angle, velocity, acceleration, and mechanism force during the entire motion process of the double-crank connecting rod mechanism, guiding engineering design and tests. It fills the technical gap in the rapid simulation calculation of the dynamic numerical research of double-crank mechanisms.

[0004] To achieve the above purpose, the technical solution of this invention is realized as follows: A numerical simulation method for a double-crank adjusting mechanism based on crank-connecting rod dynamics includes the following steps: S1: Establish the mechanism coordinates according to the double-crank adjusting mechanism; S2: Establish the kinematic and dynamic models of the double-crank adjusting mechanism; S3: Calculate the kinematic and dynamic parameters of each component in the full time domain according to the model in step S2; S4: Plot the curve of the motion law of each component and the curve of the change of the driving force of the driving component.

[0005] Further, in the establishment of the mechanism coordinates in step S1, the fixed end of the driven rotating crank of the double-crank connecting rod adjustment mechanism is point A, the other end of the component connected to the fixed end is point B, the other connection end of the connecting component is point C, point C is the moving end of the driving rotating crank, and the fixed end of the driving rotating crank is point D; Taking point A as the origin, the line AD as the hypotenuse of a right triangle, and the two right sides as the x-axis and y-axis respectively, the positive direction of the x-axis is the horizontal direction from point A to point D, and the positive direction of the y-axis is the vertical direction from point A to point D.

[0006] Further, in the modeling process of step S2, the friction between each kinematic pair is not considered, and it is assumed that the double-crank adjustment mechanism is on a horizontal plane, and the number of moving rods of the double-crank adjustment mechanism is 3. Among them, the driven crank is denoted as 1, the connecting rod is denoted as 2, and the driving crank is denoted as 3; The rod length of each rod is denoted as L i , and the angle between each rod and the x-axis is denoted as ϕ i , where i = 1, 2, 3; The gravitational potential energy of each mechanism is zero, and the geometric equation, kinematic velocity equation, kinematic acceleration equation and dynamic equation of the mechanism are obtained. Among them, the motion time is defined as t and the number of solution steps is n.

[0007] Further, in step S3, calculating the kinematic and dynamic parameters of each component in the full time domain includes giving the initial conditions of each component and the motion law of the driving rotating crank, solving the kinematic and dynamic equations of the mechanism at time t, and obtaining the kinematic and dynamic parameters of each component in the full time domain.

[0008] Further, the dynamic parameters in step S3 include one or more of velocity, acceleration, displacement or nodal force based on the dynamics of the crank connecting rod.

[0009] Further, the calculation of the kinematic and dynamic parameters of each component in the full time domain in step S3 includes the following steps: A1: The position of the driving rotating crank of the mechanism is known and denoted as ϕ3; and the angular velocity ω3(t) of the driving rotating crank is given, and the geometric equation of the motion system, that is, the motion position relationship equation of the mechanism, is established, as shown in equations (1)-(2). The angle ϕ3 of the driving rotating crank at a certain moment t is obtained according to the angular velocity ω3(t), as shown in equation (3); After knowing ϕ3, the equations (1)-(2) can be solved to obtain the values of the position parameters of each moving part at any time t, that is, the values of ϕ1 and ϕ2; (1); (2); (3); X AD is the length of AD in the x-axis direction, with the unit of mm; Y AD is the length of AD in the y-axis direction, with the unit of mm; L3 is the rod length of the driving crank, with the unit of mm; ϕ1 is the angle between the moving crank and the x-axis, with the unit of °; ϕ2 is the angle between the connecting rod and the x-axis, with the unit of °; ϕ3 is the angle between the driving crank and the x-axis, with the unit of °; w3 is the angular velocity of the driving rotating crank, with the unit of °; A2: Define θ = ϕ 1- ϕ2, θ is obtained according to equation (4). Thus, equations (5)-(6) are a system of binary linear equations for sin ϕ1 and cos ϕ1. Solving the system of equations can obtain the values of sin ϕ1 and cos ϕ1, and further finally obtain the values of ϕ1 and ϕ2; (4); (5); (6); L1 is the rod length of the moving crank, with the unit of mm; L2 is the rod length of the connecting rod, with the unit of mm; A3: Based on the geometric equations in step A1, take the derivative with respect to time to obtain the relationship between the angular velocities of the components of the mechanism system and obtain the expression of the angular velocity; Based on the angular velocity expression, take the derivative with respect to time t to obtain the expression of the angular acceleration of each component at time t; Based on the values of the angles of each component at time t obtained in A2 and ω3(t), finally obtain the values of the angular velocity and angular acceleration of each component at time t; A4: Based on the values of the angles of each component at time t calculated in step A1, obtain the position coordinates of nodes B and C at time t, and the centroid coordinates of component BC; According to the centroid coordinates of component BC, the translational velocity and acceleration magnitudes of component BC at time t can be calculated.

[0010] Further, the equation has the matrix form of equation (7) as follows; Based on the calculation in step S3, substitute the result at time t into the system of equations, and perform linear algebra solution on the system of equations to obtain the magnitudes of the nodal forces at each node at time t and the torque M of the actively rotating crank D magnitude; (7).

[0011] Further, step S4 includes obtaining the values of the velocity, angular velocity, acceleration, angular acceleration, and nodal force of each component of the system in the full time domain, and using the MatLab plotting function to obtain the motion law curve graph of each component and the driving force change curve graph of the active component

[0012] Compared with the prior art, the numerical simulation method of the double-crank adjustment mechanism based on crank-slider dynamics of the present invention has the following advantages The present invention is ingeniously conceived, and a mathematical method is proposed to perform mathematical processing on the geometric equations of the double-crank linkage mechanism system, enabling it to obtain the solutions of the angles, thereby calculating the analytical and accurate solutions of the dynamic control equations of the mechanism. Compared with the traditional drawing method and empirical method, the calculation results have high reliability, the analysis method has strong adaptability, is easy to operate, does not rely on the experience of engineering technicians, and can directly use the present invention to perform professional dynamic characteristic analysis on the adjustment mechanism, providing a theoretical basis for engineering design and optimization; compared with finite element commercial software, it does not require prior geometric modeling and mesh generation work, is easy to operate, has a short calculation time and high efficiency, and can greatly improve the analysis efficiency of engineering design BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings Figure 1 is the structural schematic diagram of the double-crank adjustment mechanism described in the embodiment of the present invention Figure 2 is the graph of the rotation angle of the driven crank (component AB) changing with time described in the embodiment of the present invention Figure 3 is the graph of the rotation angular velocity of the driven crank (component AB) changing with time described in the embodiment of the present invention Figure 4 is the graph of the rotation angular acceleration of the driven crank (component AB) changing with time described in the embodiment of the present invention Figure 5 is the graph of the driving torque of the actively rotating crank (component CD) changing with time described in the embodiment of the present invention Figure 6 is the real-time display graph of the motion process and force change process of the double-crank adjustment mechanism described in the embodiment of the present invention Figure 7 This is the numerical simulation flow chart of the double crank adjustment mechanism based on crank - connecting rod dynamics according to the embodiments of the present invention. Detailed implementation manners

[0014] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0015] The present invention will be described in detail below with reference to the drawings and in combination with the embodiments.

[0016] A numerical simulation method for a double crank adjustment mechanism based on crank - connecting rod dynamics, and the steps of the numerical simulation method are as follows: 1) Establish a mechanism coordinate system. The fixed end of the driven rotating crank of the double crank - connecting rod adjustment mechanism is point A, the other end of the component connected to the fixed end is point B, the other connecting end of the connecting component is point C, and point C is the moving end of the driving rotating crank. The fixed end of the driving rotating crank is point D. Taking point A as the origin, the line connecting A and D as the hypotenuse of a right - angled triangle, and the two right - angled sides are the x - axis and y - axis respectively. The positive direction of the x - axis is the horizontal direction from point A to point D, and the positive direction of the y - axis is the vertical direction from point A to point D; 2) Define mechanism parameters, establish the kinematic and dynamic models of the double crank adjustment mechanism. During the modeling process, the friction between each kinematic pair is not considered, and it is assumed that the mechanism is on a horizontal plane. The number of moving rods of the double crank adjustment mechanism is 3. Among them, the driven crank is denoted as 1, the connecting rod is denoted as 2, and the driving crank is denoted as 3. The rod length of each rod is denoted as L i , the angle between each rod and the x - axis is denoted as ϕ i , where i = 1, 2, 3. The gravitational potential energy of each mechanism is zero, and the geometric equation, kinematic velocity equation, kinematic acceleration equation and dynamic equation of the mechanism are obtained. Define the motion time as t and the number of solution steps as n.

[0017] 3) Given the initial conditions of each component and the motion law of the driving rotating crank, solve the kinematic and dynamic equations of the mechanism at time t to obtain the kinematic and dynamic parameters of each component in the full time domain, including velocity, acceleration, displacement and nodal force, and obtain the motion law of the mechanism. The steps of solving the kinematic and dynamic equations of the mechanism in the full time domain are as follows: 3a) The position of the driving rotating crank of the mechanism is input as known, denoted as ϕ3; and the angular velocity ω3(t) of the driving rotating crank is given; establish the geometric equation of the motion system, that is, the motion position relationship equation of the mechanism, as shown in equations (1) - (2); the angle ϕ3 of the driving rotating crank at a certain moment t can be obtained according to the angular velocity ω3(t), as shown in equation (3); after knowing ϕ3, equations (1) - (2) can be solved to obtain the values of the position parameters of each moving part at any moment t, that is, the values of ϕ1 and ϕ2; (1) (2) (3) 3b) There are four unknown trigonometric functions and two unknown angles in equations (1)-(2). Since the sine and cosine of the two angles are in a quadratic relationship, it is difficult to directly solve equations (1)-(2). The numerical method of the present invention realizes the solution of the equations by performing mathematical transformation processing on equations (1)-(2). After squaring and adding equations (1) and (2), the transformed equation (4) can be obtained. Let θ = ϕ1 - ϕ2 and substitute it into equations (1)-(2), then equations (5)-(6) can be obtained, where θ can be obtained from equation (4). Thus, equations (5)-(6) are a system of linear equations of two variables for sin ϕ1 and cos ϕ1. Solving the system of equations can obtain the values of sinϕ1 and cos ϕ1, and further finally obtain the values of ϕ1 and ϕ2; (4) (5) (6) 3c) Based on the geometric equations in 3a), by taking the derivative with respect to time, the relationship between the angular velocities of the components of the mechanism system can be obtained, and the expression of the angular velocity can be obtained; further, based on the expression of the angular velocity, by taking the derivative with respect to time t, the expression of the angular acceleration of each component at time t can be obtained; based on the values of the angles of each component at time t obtained in 3b) and ω3(t), finally the values of the angular velocity and angular acceleration of each component at time t can be obtained; 3d) Based on the values of the angles of each component at time t calculated in 3a), the position coordinates of nodes B and C at time t, and the centroid coordinates of component BC can be obtained; according to the centroid coordinates of component BC, the translational velocity and acceleration magnitudes of component BC at time t can be calculated; 4) Establish the dynamic equation of the double-crank mechanism at any time t, that is, the motion balance equation set, and the equation has the matrix form of equation (7) below. Based on the calculations in step 3), substitute the results at a certain time t into the equation set, and perform linear algebra solution on the equation set to obtain the magnitudes of the node forces of each node at time t, and the torque M D magnitude; (7) 5) Based on steps 3) - 4), solve for different moments \(t\) to obtain the values of the velocity, angular velocity, acceleration, angular acceleration, and nodal force of each component of the system in the full time domain. Using the plotting function of MatLab, obtain the motion law curves of each component and the driving force change curve of the driving component. The results of the key dynamic parameters are output in the form of images and change curves. Based on the output results, the purpose and function of analyzing the dynamic characteristics of the mechanism system are realized.

[0018] When dynamic analysis needs to be carried out for a certain double - crank adjustment mechanism, only the basic dimensions and geometric information of the mechanism need to be provided as initial conditions and input into the simulation calculation program of the present invention, then the solution and analysis of each dynamic parameter in the full motion process of the mechanism can be completed. Through the program calculation results and data output images of the present invention, the change of the crank rotation torque, angular velocity, etc. during the motion process can be intuitively obtained, providing a theoretical basis for engineering design and optimization.

[0019] Example 1: In this example, a double - crank connecting - rod adjustment mechanism is taken as the research object. As Figure 1 shown, establish the coordinate system of the mechanism. Take point A as the coordinate origin. With the line AD as the hypotenuse of a right - triangle, the two right - angled sides are the x - axis and y - axis respectively. The positive direction of the x - axis is the horizontal direction from point A to point D, and the positive direction of the y - axis is the vertical direction from point A to point D; the parameters of each component of the mechanism are shown in Table 1.

[0020] Table 1 Parameters of each component of the double - crank connecting - rod adjustment mechanism Define the mechanism parameters and establish the kinematic and dynamic models of the mechanism system. Set the angular velocity of the active rotating crank (component CD) to be uniform, that is, the angular acceleration is zero. The motion time of the active crank is 1 s, and the rotation angle is 60°. The number of calculation time steps \(n = 100\). The calculation steps are as follows: 1a) Establish the geometric equations and kinematic equations of the mechanism, that is, the displacement relationships of each component of the mechanism and the mutual relationships between velocity, acceleration, and displacement. The equation forms are shown in formulas (1) - (3); 1b) Perform mathematical processing on the equations in 1a) to obtain formulas (4) - (6). Solve formulas (4) - (6) to obtain the values of the kinematic parameters of each component of the mechanism at moment \(t\), that is, the values of the motion velocity, angular velocity, acceleration, and angular acceleration of each component, and further obtain the motion law of the mechanism; 2a) Establish the dynamic equations of the double - crank mechanism at any moment \(t\), that is, the motion balance equations. The equations have the matrix form of formula (7); 2b) The number of calculation time steps is 100 steps. Therefore, the time step \(\Delta t=0.01\ s\). The motion process of the mechanism is divided into 100 steps, and each step moment is \(t\)i = i×Δt, where i = 0, 1, 2…100. Through the principles of linear algebra, for t i the dynamic equation at the moment is solved, and finally the solutions of the mechanism dynamic parameters in the full time domain are obtained, namely the forces at the mechanism nodes and parameters such as the torque of the driving crank; Using the program file written in MatLab, the curve graph of the motion law change of the follower crank (component AB) is obtained, as Figures 2 - 4 shown, the curve graph of the driving torque change of the driving crank (component CD), as Figure 5 shown, and the display graph of the mechanism motion process, as Figure 6 . Since the entire solution process is a direct solution of the dynamic equations, the dynamic parameters at any moment are all accurate solutions of the control equations, with fast solution speed, high efficiency, and accurate results. When calculating and solving in the present invention, the motion change process of the mechanism is output in real time, and the magnitudes and directions of the forces at each node are displayed in the image for researchers to view the motion and force conditions of the mechanism. The mechanism dynamic parameters can be obtained from the result file output by the program for subsequent data processing and analysis by researchers.

[0021] The above are only the preferred embodiments of the present invention, and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A numerical simulation method for a double crank adjustment mechanism based on crank - connecting rod dynamics, characterized in that: It includes the following steps: S1: Establish the mechanism coordinates according to the double-crank adjustment mechanism; S2: Establish the kinematic and dynamic models of the double-crank adjustment mechanism; S3: Calculate the kinematic and dynamic parameters of each component in the full time domain according to the model in step S2; S4: Draw the curve graphs of the motion laws of each component and the curve graph of the change of the driving force of the driving component.

2. The numerical simulation method of the double crank adjustment mechanism based on crank - connecting rod dynamics according to claim 1, wherein: The establishment of the mechanism coordinates in step S1 includes that the fixed end of the driven rotating crank of the double-crank connecting rod adjustment mechanism is point A, the other end of the component connected to the fixed end is point B, the other connecting end of the connecting component is point C, point C is the moving end of the driving rotating crank, and the fixed end of the driving rotating crank is point D; Taking point A as the origin, the connection line AD as the hypotenuse of the right triangle, the two right sides are the x-axis and the y-axis respectively, the horizontal direction from point A to point D is the positive direction of the x-axis, and the vertical direction from point A to point D is the positive direction of the y-axis.

3. The numerical simulation method of the double crank adjusting mechanism based on crank-connecting rod dynamics according to claim 1, wherein: In the modeling process of step S2, the friction between each kinematic pair is not considered, and it is assumed that the double-crank adjustment mechanism is on a horizontal plane, and the number of moving rods of the double-crank adjustment mechanism is 3. Among them, the driven crank is denoted as 1, the connecting rod is denoted as 2, and the driving crank is denoted as 3; The length of each rod is denoted as L i , and the angle between each rod and the x-axis is denoted as ϕ i , where i = 1, 2, 3; The gravitational potential energy of each mechanism is zero, and the geometric equation, kinematic velocity equation, kinematic acceleration equation and dynamic equation of the mechanism are obtained. Among them, the motion time is defined as t and the number of solution steps is n.

4. The numerical simulation method of the double crank adjustment mechanism based on crank - connecting rod dynamics according to claim 1, characterized in that: The calculation of the kinematic and dynamic parameters of each component in the full time domain in step S3 includes giving the initial conditions of each component and the motion law of the driving rotating crank, solving the kinematic and dynamic equations of the mechanism at time t, and obtaining the kinematic and dynamic parameters of each component in the full time domain.

5. The numerical simulation method of the double crank adjustment mechanism based on crank - connecting rod dynamics according to claim 1, characterized in that: The dynamic parameters in step S3 based on the dynamics of the crank connecting rod of the double-crank adjustment mechanism include one or more of velocity, acceleration, displacement or nodal force.

6. The numerical simulation method of the double crank adjustment mechanism based on crank - connecting rod dynamics according to claim 1, characterized in that: The calculation of the kinematic and dynamic parameters of each component in the full time domain in step S3 includes the following steps: A1: The position of the driving rotating crank of the mechanism is input and known, denoted as ϕ3; and the angular velocity ω3(t) of the driving rotating crank is given, and the geometric equation of the motion system is established, that is, the motion position relationship equation of the mechanism, as shown in equations (1)-(2). The angle ϕ3 of the driving rotating crank at a certain time t is obtained according to the angular velocity ω3(t), as shown in equation (3); After knowing ϕ3, equations (1)-(2) can be solved, that is, the values of the position parameters of each moving part at any time t can be obtained, that is, the values of ϕ1 and ϕ2; （1）； （2）； （3）； X AD is the length of AD in the x-axis direction, with the unit of mm; Y AD is the length of AD in the y-axis direction, with the unit of mm; L3 is the rod length of the driving crank, with the unit of mm; ϕ1 is the angle between the driven crank and the x-axis, with the unit of °; ϕ2 is the angle between the connecting rod and the x-axis, with the unit of °; ϕ3 is the angle between the driving crank and the x-axis, with the unit of °; w3 is the angular velocity of the driving rotating crank, with the unit of °; A2: Define θ = ϕ 1- ϕ2, obtained according to Equation (4). Thus, Equations (5)-(6) are a system of linear equations of the first order in sin ϕ1 and cos ϕ1. Solving the system of equations can obtain the values of sin ϕ1 and cos ϕ1, and further finally obtain the values of ϕ1 and ϕ2; （4）； （5）； （6）； L1 is the rod length of the driven crank, with the unit of mm; L2 is the rod length of the connecting rod, with the unit of mm; A3: Based on the geometric equation in step A1, take the derivative with respect to time to obtain the relationship between the angular velocities of each component of the mechanism system and obtain the expression of the angular velocity; Based on the angular velocity expression, take the derivative with respect to time t to obtain the expression of the angular acceleration of each component at time t; Based on the angular values of each component at time t obtained in A2 and ω3(t), the angular velocity and angular acceleration values of each component at time t are finally obtained; A4: Based on the angular values of each component at time t calculated in step A1, the position coordinates of nodes B and C at time t, and the centroid coordinates of component BC are obtained; according to the centroid coordinates of component BC, the translational velocity and acceleration magnitudes of component BC at time t can be calculated.

7. The numerical simulation method of the double crank adjustment mechanism based on crank - connecting rod dynamics according to claim 1, characterized in that: The equation has the matrix form of equation (7) as follows; Based on the calculation in step S3, substitute the result at time t into the system of equations, and perform linear algebra solution on the system of equations to obtain the magnitudes of the nodal forces at each node at time t and the torque M of the actively rotating crank D Magnitude; (7)。 8. The numerical simulation method of the double crank adjustment mechanism based on crank - connecting rod dynamics according to claim 1, characterized in that: Step S4 includes obtaining the values of the velocity, angular velocity, acceleration, angular acceleration, and nodal forces of each component of the system in the full time domain, and using the MatLab plotting function to obtain the motion law curves of each component and the driving force change curve of the driving component.

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