A single-degree-of-freedom cosine rocking platform based on rope-tethered cam drive and design method thereof

Abstract

The present invention provides a single-degree-of-freedom cosine-type swing table and a design method based on a rope-tethered cam drive, and belongs to the technical field of swing tables. The single-degree-of-freedom cosine-type swing table can meet the required swing form, and the structure can control the swing table to swing with a single degree of freedom only by rotating a low-speed motor at a constant speed, and the required different swing forms can be achieved by designing the cam shape. The present invention realizes the swing form with high precision, and cams of various shapes can be designed according to actual needs, which can be combined with the swing platform to achieve various swing forms. The present invention is easy to operate and control the swing table, and the swing can be achieved by controlling the motor to rotate at a constant speed. The present invention is designed according to the space size of the experimental site and the relative position relationship of the device, and can fully adapt to various sizes of experimental sites and meet the needs of different working conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of rocking platforms, and relates to a single-degree-of-freedom cosine rocking platform device, and in particular to a single-degree-of-freedom cosine rocking platform driven by a rope-type cam and a design method thereof. Background Art

[0002] As an excellent spatial motion mechanism, the rocking table is used in aerospace, ship and offshore equipment, automotive industry, military training and other fields. When analyzing the kinematic and dynamic performance of ships and offshore equipment under loads such as waves, the use of a rocking table for testing is the most direct and reliable.

[0003] From the perspective of domestic and foreign research, the parallel six-degree-of-freedom platform proposed by Stewart is currently more popular. However, in many cases, only a few degrees of freedom are required to move or swing in a certain plane. It is difficult for the parallel six-degree-of-freedom platform to achieve swinging motion in a single plane or a few degrees of freedom. In addition, the swing table is similar to a simple pendulum, and it is difficult and complicated to control the swing table to swing. Not only is the mathematical model nonlinear, but the control of the pendulum is also nonlinear.

[0004] Nowadays, most swing tables use complex hydraulic control systems, such as the patent "A servo device for a swing table" (application number: 202120425430.3). The structure of this swing table is not only complex, but also cumbersome to use and operate, and the device itself is costly. Small swing experiments are not suitable for such complex swing tables, but are more suitable for swing tables that are simple, easy to operate, and have low cost, such as the patent "A swing table" (application number: 202022661901.9). For most swing experiments, the required swing form is often in the form of trigonometric functions, and the production of the above-mentioned simple swing table does not mention how to determine the swing form. Therefore, it is very necessary to make a swing table that is simple, easy to operate, low in cost, and can determine the swing form for various small swing experiments.

[0005] In response to the complex control problems of electronic control systems, many scholars have also studied mechanically controlled swing tables. However, most of them also involve electro-hydraulic drive devices such as hydraulic cylinders, and it is also difficult to use these devices to control the movement of the swing table. And because it involves devices such as hydraulic cylinders, the scale of the swing table will be large, which takes up more experimental space and is not suitable for small swing experiments. Most of the swing tables controlled by hydraulic cylinders also have six degrees of freedom, and it is difficult to achieve swing motion in a single plane. There are also some mechanical swing tables that can achieve single-plane motion, but their swing form is relatively single, and it is difficult to provide help for experiments that require different swing forms.

[0006] In addition, under some engineering experimental conditions, in view of the above, the present invention designs a swing table structure suitable for single degree of freedom, convenient for controlling the motion of the swing table and capable of satisfying the required swing form. The structure can control the swing table to swing with a single degree of freedom simply by rotating the low-speed motor at a constant speed, and realizes the required different swing forms by designing the cam shape. Summary of the invention

[0007] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a single-degree-of-freedom cosine-type rocking platform driven by a rope-type cam and a design method thereof.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] The invention discloses a single-degree-of-freedom cosine-type swing platform driven by a rope-type cam. The swing platform is mainly composed of a low-speed motor, a cam, a thin rope and a swing platform.

[0010] The low-speed motor is a device that provides a cam with uniform rotation speed, and can control the rotation speed and can rotate at a uniform and low speed.

[0011] The cam is a convex wheel structure, and the cam plane shape is composed of a curve The closed figure is composed of the cam with a thickness of ; In thickness An inner groove is provided at the position.

[0012] The inner groove is also a convex wheel-shaped structure, and the plane shape of the inner groove of the cam is composed of a curve The closed figure is composed of the thickness of the groove in the cam. ; The curve With curve is a similar relationship, and the size ratio is ,in .curve The inner groove formed mainly serves to fix the thin rope that is wound around the cam as the cam rotates.

[0013] The thin rope is as long as , the diameter is ,in The two ends of the thin rope are fixed, one end of which is fixed in the groove of the cam and is wound along with the uniform rotation of the cam; the other end is fixed on the swing table, and the swing table moves along with the wound end.

[0014] The swing platform is mainly composed of a fixing device, a swing shaft, and a swing platform, wherein the fixing device is fixed to the swing shaft, and the swing platform is fixed to the swing shaft, and can swing freely in one direction. The swing platform is , the width is , thickness is One side of the swing platform is fixedly connected to one end of the thin rope on the platform groove, which is located on the width center line and is 1 / 4 of the platform side. .

[0015] When using, determine the curve according to the specific swing form required and , rope length, cam and rope fixing point, rope and swing platform fixing point, rope length and relative position between swing platform and cam. When swinging, the swinging form of a specified cycle can be obtained by controlling the rotation speed of the low-speed motor. When the cam rotates one circle, the rope pulls the swing platform from the highest point to the lowest point, and the swing platform has achieved half a cycle of swing.

[0016] A design method of a single-degree-of-freedom cosine-type rocking platform based on a rope-tethered cam drive comprises the following steps:

[0017] The first step is to determine the cosine oscillation form required for the experiment: , mainly including amplitude and angular frequency Two parameters.

[0018] The second step is to Determine the inclination angle of the rocking platform at the initial moment , where the absolute value of the tilt angle is the amplitude. Finally, the swing table can achieve The range of swings.

[0019] The third step is to use the angular frequency Determine the rotational speed of the cam and motor, where the angular frequency The angular velocity of the cam and the motor is .

[0020] Step 4: According to the size of the experimental site, you can design the appropriate device size by yourself: including the rope length , rope diameter , length of the swing platform ,width ,thickness , Cam thickness , Cam groove thickness , the distance between the groove of the swing table and one side of the swing table .

[0021] The fifth step is to solve the cam shape parameters of the swing platform. When the swing platform is in a horizontal position, take the cam center as the origin and the length direction of the swing platform as direction, along the thickness direction of the swing table Direction, along the length of the swing table direction. Since the rocking platform only Plane swing, The device parameters of the direction will not affect the entire solution process. For the convenience of solution, the device can be ignored. The coordinates of the direction.

[0022] 5.1: Determine the number of cam shape parameters;

[0023] The cam shape equation selected by the present invention is:

[0024] (1)

[0025] in is the coordinate of the above coordinate system. The cam parameters represented by this equation are 8 in total. , , , , , , , Since there are many parameters, it is difficult to solve the problem later. You can reduce the parameters.

[0026] Select four points of the cam on the coordinate axis , whose coordinates are , , , . Based on the coordinate information of these four points, , , , , , , , Parameters, the formula is:

[0027] [ c 2 c 1 d 2 − d 1 c 2 c 1 d 2 − d 1 a 2 a 1 b 2 − b 1 a 2 a 1 b 2 − b 1 ] * [ A ' B ' C ' D ' E ' F ' G ' H ' ] = 0 (2)

[0028] Therefore, according to formula (2), the 8 The parameters are converted to 4 Parameters, later solution The parameters can be used to obtain the cam shape equation.

[0029] 5.2: Solve the range of the four parameters of the cam;

[0030] 5.2.1: Solution ideas

[0031] It is relatively complicated to directly calculate the cam parameters by knowing the swing form and device parameters. The present invention adopts the inversion method to first arbitrarily give The parameter size is calculated by formula (2): Parameters, substitute into equation (1) and convert it into polar coordinates.

[0032] Then, under the condition of known device parameters, the swing form of the cam and the relative error with the given swing form are calculated. A certain interval range is selected around the parameter value (the larger the relative error, the larger the interval range is selected), and the Monte Carlo method is used to randomly select Select points within the parameter range and calculate the swing form and relative error, record the parameters with relative errors less than 1%, and re-determine the range of the four cam parameters within these parameters. Then, use the heterogeneous comprehensive learning particle swarm optimization (HCLPSO) method to determine the optimal solution for the four parameters.

[0033] 5.2.2: Determine the swing pattern and relative error of the cam based on the given cam parameters.

[0034] When calculating the swing form, it is necessary to know the swing angle of the swing platform at each moment and the position of the connection point between the string and the cam. Since the cam parameters are already given, the position information of the connection point can be regarded as an unknown quantity. Therefore, two equations need to be constructed at each moment to calculate the swing angle and connection point information.

[0035] From a geometric point of view, the connection point between the cam and the string is the tangent point between the string and the cam. A tangent equation can be established at each moment:

[0036] (3)

[0037] Among them, the subscript D represents the tangent point of the cam and the string at time t, and the subscript A represents the connection point between the swing platform and the string at time t. The coordinates of point A are only related to the coordinates of the fixed point of the swing platform. , Length of swing platform And the swing angle of the swing table Due to the length of the swing platform and the coordinates of the fixed points of the swing table is known and does not change, so only the swing angle needs to be known The coordinates of point A can be found, namely:

[0038] (4)

[0039] In addition, when the cam drives the swing table to swing, the thin rope will be partially wrapped around the cam, but the total length of the thin rope will not change. A rope length equation can be established at each moment:

[0040] (5)

[0041] in, is the rope length, is the length of the string wrapped around the cam, is the length of the string from the connection point A to the tangency point D; is the polar angle coordinate of point D on the cam at the initial moment, and point D is the tangent point between the cam and the string at moment t; is the rotation angle of the cam around the rotation center at time t; is the polar angle coordinate of point B on the cam at the initial moment, and point B is the initial moment The tangency point between the cam and the string; is the polar coordinate of the point on the cam, is the derivative of the polar diameter with respect to the polar angle; , is the coordinate of point D in the rectangular coordinate system, , is the coordinate of point A in the rectangular coordinate system.

[0042] Combining equations (3) and (5), it can be seen that there are two equations and two unknown quantities at each moment: the connection point coordinates and the swing angle. Therefore, the connection point position and the swing angle in each time period can be calculated, thereby calculating the relative error between the actual swing angle of the cam and the specified swing angle.

[0043] 5.2.3: Select the range of the four parameters of the cam;

[0044] According to the relative error calculated above, at a given cam A certain interval range is selected around the parameter value (the larger the relative error, the larger the interval range is selected). The Monte Carlo method is used to calculate the swing angle error caused by each set of cam parameters according to 5.2.2, and the parameters with a relative error less than 1% are recorded. Among the four parameter values ​​recorded, the range of each parameter is defined as (minimum value in the record, maximum value in the record).

[0045] 5.2.4: Determine the optimal solution of the four parameters of the cam;

[0046] After obtaining the range of each cam shape parameter in 5.2.3, the four cam parameter values ​​are used as optimization variables, and the swing angle error caused by each set of cam parameters is calculated according to 5.2.2 as the optimization objective function. The heterogeneous comprehensive learning particle swarm optimization (HCLPSO) optimization method is used to determine the four cam parameter values ​​that minimize the swing angle error.

[0047] Step 6: Make a cam according to the cam parameters obtained in step 5, install the cam on the low-speed motor, and connect it to the swing platform with a thin rope. , the inclination angle of the rocking platform is adjusted to When the low-speed transfer is started, the swing table will swing in the designed manner. Perform the swing.

[0048] The present invention has the following beneficial effects:

[0049] (1) The present invention can design a swing that satisfies various cosine swing forms according to the design method of the cam. For some small and medium-sized experiments that require a specific cosine swing form, a single-degree-of-freedom cosine swing table based on a rope-tethered cam drive designed by the present invention can meet the requirements with high precision.

[0050] (2) The single-degree-of-freedom swing table designed by the present invention can swing by simply starting a low-speed motor to rotate at a constant speed according to a specified angular velocity. Compared with the existing electro-hydraulic driven swing table, the swing table designed by the present invention is very easy to operate.

[0051] (3) When designing a single-degree-of-freedom swing table, the present invention designs the size of the device according to the space size of the experimental site. Compared with large swing tables, the swing table designed by the present invention can fully adapt to various sizes of experimental sites and meet the needs of different working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a real picture of an embodiment of the invention; it consists of a low-speed motor, a cam, a thin rope, a fixing device, a swing platform and a swing shaft.

[0053] In the figure: 1 low-speed motor; 2 cam; 3 thin rope; 4 fixing device; 5 swing platform; 6 swing shaft.

[0054] Figure 2 This is a schematic diagram of the initial moment of the rope-connected cam driving the swing platform in the embodiment of the invention; in the figure: the cam is The angular velocity is counterclockwise, is the cam rotation center, is the tangent point between the string and the cam at the initial moment, is the tangent point at the next moment, The location where one end of the string is connected to the swing platform. The center position of the swing platform. is the angle between the swing platform and the horizontal line at the initial moment (at this time, it is the angle between the left end and the horizontal line, set to negative), is the total length of the rocking platform.

[0055] Figure 3 In the embodiment of the invention A schematic diagram of a swing platform driven by a cam with a constant rope; in the figure: the cam is The angular velocity is counterclockwise, is the cam rotation center, for The point of tangency between the string and the cam, is the tangent point at the initial moment or the previous moment, for The position of one end of the string connected to the swing platform at all times, The center position of the swing platform. for The angle between the swing platform and the horizontal line at any moment (in this case, the angle between the right end and the horizontal line, set to positive), is the total length of the rocking platform.

[0056] Figure 4 This is a comparison diagram of the swing form of the embodiment after it is produced and tested with the required form; the swing curve measured in the embodiment in the figure almost coincides with the specified swing curve, which verifies that under actual working conditions, the produced swing table can swing in the specified swing form. DETAILED DESCRIPTION

[0057] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0058] The first step is to determine the cosine oscillation form required for the experiment: , mainly including the amplitude of the angle and angular frequency Two parameters.

[0059] The second step is to Determine the inclination angle of the rocking platform at the initial moment - , where the absolute value of the tilt angle is the amplitude. Finally, the swing table can achieve Angle range swing.

[0060] The third step is to use the angular frequency Determine the rotational speed of the cam and motor, where the angular frequency The angular velocity of the cam and the motor is .

[0061] Step 4: Design the appropriate device size according to the size of the experimental site: including rope length , rope diameter , length of the swing platform ,width ,thickness , Cam thickness , Cam groove thickness , the distance between the groove of the swing table and one side of the swing table .

[0062] The fifth step is to solve the cam shape parameters of the rocking platform. According to the steps of the fifth step of the invention, the shape parameters of the cam can be obtained:

[0063] (6)

[0064] Step 6: Make a cam according to the cam parameters obtained in step 5, install the cam on the low-speed motor, and connect it to the swing platform with a thin rope. , the inclination angle of the rocking platform is adjusted to - When the low-speed transfer is started, the swing table will swing in the designed manner. Perform the swing.

[0065] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A single-degree-of-freedom cosine rocking platform based on a rope-tethered cam drive, characterized in that: The swing platform comprises a low-speed motor, a cam, a thin rope and a swing platform; The low-speed motor is a device that provides a uniform rotation of the cam; The cam is a convex wheel-shaped structure, the plane shape of the cam is a closed figure surrounded by the curve L1, and the thickness of the cam is h1; At the position, there is a groove formed along the curve L1; The groove is also a convex wheel-shaped structure, the plane shape of the cam groove is composed of a closed figure surrounded by the curve L2, and the thickness of the cam groove is h2; The thin rope has a length of l0 and a diameter of d1, where d1≤h2; the two ends of the thin rope are fixed, one end of which is fixed in the groove of the cam and is wound along with the uniform rotation of the cam; the other end is fixed on the swing platform, and the swing platform moves along with the wound end; The swing platform comprises a fixing device, a swing shaft, and a swing platform, wherein the fixing device is fixed to the swing shaft, and the swing platform is fixed to the swing shaft, and can swing freely in one direction; the swing platform is L in length, d2 in width, and h3 in thickness; one side of the swing platform is fixedly connected to one end of the rope on a groove of the platform, and the groove is located on the center line of the width and is d3 away from one side of the platform; When in use, the curves L1 and L2, rope length, fixed points of the cam and the thin rope, fixed points of the thin rope and the swing platform, rope length, and the relative position of the swing platform and the cam are determined according to the specific swing form required; when performing the swing operation, controlling the rotation speed of the low-speed motor can obtain a swing form of a specified period.

2. A single-degree-of-freedom cosine-type rocking platform based on a rope-type cam drive according to claim 1, characterized in that: The curve L2 has the same shape as the curve L1, and the size ratio is L2=n1L1, wherein 0.95<n1<1.

3. A design method for a single-degree-of-freedom cosine-type rocking platform based on a rope-type cam drive according to claim 1 or 2, characterized in that: The following steps are involved: The first step is to determine the cosine swing form required for the experiment: |α0|cos(ωt), which includes two parameters: amplitude |α0| and angular frequency ω; The second step is to determine the inclination angle α0 of the swing platform at the initial moment according to the amplitude |α0|, where the absolute value of the inclination angle is the amplitude; finally, the swing platform can swing in the range of -α0 to α0; The third step is to determine the rotation speed of the cam and the motor according to the angular frequency ω, where the angular frequency ω is the rotation angular speed of the cam and the motor ω; The fourth step is to design the size of the device according to the size of the venue: including the rope length l0, the diameter of the thin rope d1, the length L, width d2, thickness h3 of the swing platform, the thickness h1 of the cam, the thickness h2 of the cam groove, and the distance d3 between the swing platform groove and one side of the swing platform; The fifth step is to solve the cam shape parameters of the swing platform; when the swing platform is in a horizontal position, the cam center is taken as the origin, the length direction of the swing platform is the X direction, the thickness direction of the swing platform is the Y direction, and the length direction of the swing platform is the Z direction; since the swing platform only swings in the XY plane, the device parameters in the Z direction will not affect the entire solution process, and the coordinates of the device in the Z direction are ignored during the solution process; The sixth step is to manufacture a cam according to the cam parameters obtained in the fifth step, install the cam on the low-speed motor, and connect it to the swing platform with a thin rope; adjust the angular velocity of the low-speed motor to ω and the inclination angle of the swing platform to α0; when the low-speed transfer is started, the swing platform will swing according to the designed swing form |α0|cos(ωt).

4. A design method for a single-degree-of-freedom cosine-type rocking platform based on a cable-tethered cam drive according to claim 3, characterized in that: The fifth step is as follows: 5.1: Determine the number of cam shape parameters; Select the cam shape equation as: A'xy 2 +B'yx 2 +C'x 2 +D'y 2 +E'xy+F'x+G'y+H'=0 (1) Among them, x, y are the coordinates of the above coordinate system, and the cam parameters represented are 8 in total, namely A', B', C', D', E', F', G', H'; Select four points a, b, c, d on the coordinate axis of the cam, whose coordinates are (a, 0), (-b, 0), (0, c), (0, -d) respectively; according to the coordinate information of these four points, calculate the parameters A', B', C', D', E', F', G', H', and the formula is: According to formula (2), the eight parameters A', B', C', D', E', F', G', H' are converted into four parameters a, b, c, d. Solving the parameters a, b, c, d can obtain the cam shape equation; 5.2: Solve the range of the four parameters of the cam; 5.2.1: Using the inversion method, first arbitrarily set the values ​​of a, b, c, and d parameters, calculate the parameters A', B', C', D', E', F', G', and H' using formula (2), substitute them into formula (1), and convert them into polar coordinates; Under the condition of known device parameters, the swing form generated by the cam and the relative error with the given swing form are calculated; the interval range of the given a, b, c, d parameter values ​​is selected, and the Monte Carlo method is used to randomly select points in the a, b, c, d parameter range and calculate the swing form and relative error generated, record the parameters with relative errors less than 1%, and re-determine the interval range of the four cam parameters among these parameters; determine the optimal solution of the four parameters through the heterogeneous comprehensive learning particle swarm optimization method; 5.2.2: Determine the swing form and relative error of the cam based on the given cam parameters; When calculating the swing form, two equations need to be constructed at each moment to calculate the swing angle and connection point information; Establish a tangency equation at each time instant: in, Subscript D represents the tangent point between the cam and the string at time t, and subscript A represents the connection point between the swing table and the string at time t; the coordinates of point A are only related to the coordinates of the fixed point of the swing table (x C ,y C ), the length L of the swing table and the swing angle α of the swing table; Since the length L of the swing table and the coordinates of the swing table fixed point (x C ,y C ) is known and will not change, so the coordinates of point A can be calculated by knowing the swing angle α, that is: x A (t)=x C +Lcosα(t),y A (t)=y C +Lsinα(t) (4) In addition, when the cam drives the swing table to swing, a rope length equation is established at each moment: Among them, l0 is the rope length, l s (t) is the length of the string wrapped around the cam, l(t) is the length of the string from the connection point A to the tangent point D; θ D (t0) is the polar angle coordinate of point D on the cam at the initial time, and point D is the tangent point between the cam and the string at time t; β(t) is the rotation angle of the cam around the rotation center at time t; θ B (t0) is the polar angular coordinate of point B on the cam at the initial time, and point B is the tangent point between the cam and the string at the initial time t0; r is the polar radial coordinate of the point on the cam, is the derivative of the polar diameter with respect to the polar angle; x D ,y D is the coordinate of point D in the rectangular coordinate system, x A ,y A is the coordinate of point A in the rectangular coordinate system; Combining equations (3) and (5), it can be seen that by finding the connection point position and swing angle in each time period, the relative error between the actual swing angle of the cam and the specified swing angle can be calculated; 5.2.3: Select the range of the four parameters of the cam; According to the relative error calculated above, select the interval range based on the given cam a, b, c, d parameter values; use the Monte Carlo method to calculate the swing angle error caused by each set of cam parameters according to 5.2.2, and record the parameters with relative errors less than 1%; 5.2.4: Determine the optimal solution of the four parameters of the cam; After obtaining the range of each cam shape parameter in 5.2.3, take the four cam parameter values ​​as optimization variables, and calculate the swing angle error caused by each set of cam parameters according to 5.2.2 as the optimization objective function; use the heterogeneous comprehensive learning particle swarm optimization method to determine the four cam parameter values ​​that minimize the swing angle error.

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