CN110287627B - Envelope-based large-scale series transmission mechanism generation method - Google Patents
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Abstract
The invention discloses an envelope-based large-scale series transmission mechanism generation method, which can automatically solve series transmission mechanisms among all rotary parts aiming at a complex rotary machine consisting of a large number of rotary parts. On the basis of finishing the layout of all rotary parts, constructing motion envelope surfaces of a rod and a fork in the transmission mechanism, analyzing different intersection conditions of the envelope surfaces, and searching for appropriate envelope surface parameters, thereby obtaining feasible rod and fork parameters and forming a transmission mechanism solution. The method can obviously reduce the design difficulty of the series transmission mechanism in the large-scale complex rotary machine, so that a designer can automatically solve and generate a feasible transmission mechanism by the method without professional knowledge of mechanical design, and the motion feasibility of the designed machine is guaranteed.
Description
Technical Field
The invention relates to the field of mechanical design methods, in particular to a large-scale series transmission mechanism generation method based on envelops.
Background
The complex rotary machine composed of large-scale rotary parts, such as large-scale rotary machines, rotary buildings and the like, integrates the beauty of engineering and artistry, provides rich aesthetic experience for art, and has great attraction due to the complex structure and the periodic dynamic effect. However, their design is very difficult, and many existing works are designed by interdisciplinary experts or teams after many trial and error, which is inefficient in design. Where the design of the transmission between the parts is the most difficult part, it is almost impossible, even for technical background engineers, to solve a feasible transmission in a hand-drawn manner. And the use of pure manual calculation requires solving a large number of parameters and a large number of iterations, which is very inefficient. The automatic and parameterized transmission mechanism design method is developed, the transmission structure is automatically solved according to the position relation of the rotary parts, the design efficiency and accuracy can be greatly improved, and designers and even novices can quickly and conveniently design the complex rotary machines.
Disclosure of Invention
In order to solve the problems of low efficiency and poor accuracy of the traditional manual analysis and calculation large-scale series transmission mechanism, the invention aims to provide the envelope-based large-scale series transmission mechanism generation method of the rotary complex rotary machinery, which has high adaptability and reliability and can meet various forms.
The purpose of the invention is realized by the following technical scheme: an envelope-based large-scale series transmission mechanism generation method comprises the following steps:
(1) for every two adjacent rotary parts in the complex rotary machine with finished part layout, according to the space transformation and the size of a shaft sleeve of the rotary parts, an envelope surface for one circle of rotation of the rotary parts and the envelope surface for one circle of rotation of the rotary parts are constructed;
(2) and (3) analyzing the spatial relationship of the axes of the envelope surfaces of the transmission rod and the transmission fork for every two adjacent rotary parts, and directly providing feasible envelope surface parameters if the axes are superposed.
(3) If the axes in the step (2) are parallel, intersected or out-of-plane, iterative search is carried out on the parameters of the envelope surface, and a feasible envelope surface size is searched for so as to ensure that the transmission rod and the transmission fork are always in contact;
(4) if a feasible envelope surface is obtained, generating a three-dimensional model of the transmission rod and the transmission fork according to the size of the envelope surface;
(5) if the envelope surface is not feasible, no feasible transmission mechanism solution exists, highlight display is carried out on the two related adjacent rotary parts at the moment, the highlight display is fed back to a user, and the user is reminded of modifying the shape of the main shaft near the two rotary parts.
(6) And (4) executing the steps (1) to (4) on all the adjacent two rotary parts in the machine to finish the automatic solution and generation of the transmission mechanism.
Further, the step (1) specifically includes the following sub-steps:
(1.1) for every two adjacent rotating parts, calculating a coordinate transformation matrix T from a local coordinate system to a world coordinate system of the two rotating parts 1 ,T 2 ；
And (1.2) reading the shaft sleeve sizes of two adjacent rotary parts in the step (1.1). All rotating parts have the same bushing dimension, set as r 0 ；
(1.3) respectively constructing envelope surfaces F1 and F2 of the transmission rod and the transmission fork which rotate for one circle, wherein the two envelope surfaces are congruent circular truncated cone side surfaces and have the same initialization parameters: the included angle theta between the generatrix of the circular truncated cone and the axis and the height h of the circular truncated cone. The expressions of F1 and F2 in the respective coordinate systems of the rotating parts are:
to F is aligned with 1 The method comprises the following steps:
to F 2 The method comprises the following steps:
wherein: z belongs to [0, h ]]，φ∈[0,2π]. For ease of design and manufacture, the lengths of the drive link and the drive fork tend to be the same, which means h 1 ＝h 2 H, the included angle between the generatrix and the shaft is equal to theta 1 ＝θ 2 ＝θ。
In order to ensure the feasibility of large-scale rotary mechanical motion, the motion rod must be uniformly inserted into the transmission fork groove, and the motion rod and the motion fork need to meet the following requirements:
T 1 (F θ1,h (z 1 ,φ 1 ))＝T 2 (F θ2,h (z 2 ,φ 2 )) (3)
to prevent the design mechanism from being oversized and narrow the solution range, θ ∈ [ π/6, π/3], h ∈ [0.6dz,0.9dz ] are defined.
Further, the step (2) specifically includes the following sub-steps:
(2.1) coordinate transformation matrix T according to the coordinate transformation matrix described in (1.1) 1 ,T 2 Calculating expressions A1 and A2 of the envelope axes of the transmission rod and the transmission fork in world coordinates;
(2.2) the spatial relationship of A1, A2 was analyzed. If a1, a2 coincide, a feasible solution can be obtained directly, i.e. h is 0.6d z ，θ＝π/3。
Further, in the step (3), the iteratively searching for envelope surface parameters to find a feasible envelope surface size includes the sub-steps of:
(3.1) finding a possible solution by taking the initial value of θ ═ 5 °, h ═ 0.1, z ═ 0.1, and Φ ═ 5 °.
(3.2) taking a point in the round table of the transmission rod, F 1 (z 1 ,φ)＝(x 1 ,y 1 ,z 1 ) And calculating the coordinate transformation of the point in the original transmission fork circular table coordinate transformation system, namely (x) 2 ,y 2 ,z 2 )＝T(x 1 ,y 1 ,z 1 ). Will (x) 2 ,y 2 ) Brought to F 2 Is obtained from the expression of 2 ′。
(3.3) calculation of Δ z ＝z 2 -z 2 '. If Δ z >0, replacing the value of theta and returning to the step (3.2); if Δ z <0, replacing the phi value and returning to the step (3.2); if there is a delta for any value of phi z <0, the feasible solution is the current value of θ, h.
(3.4) if no feasible solution exists in the step (3.3), the reason is that the rotary parts are too sparse or the joint angles are too large, the system skips two connected rotary parts to solve and highlights the two connected rotary parts, and a user is reminded to modify the shape of the main shaft near the two rotary parts.
Further, in the step (4), for obtaining a feasible envelope surface, the generating a three-dimensional model of the transmission rod and the transmission fork according to the size of the envelope surface specifically comprises the following sub-steps:
(4.1) the length l of the driving rod and the driving fork is (1+ lambda) h/cos theta. A safety factor lambda is adopted, so that the separation of the transmission rod and the transmission fork at the extreme position is avoided, wherein lambda is 0.1. Depth l of transmission fork groove g ＝0.2l。
(4.2) installation phase of Transmission rod phi 1 ∈[0,2π]Is random, the mounting phase phi of the transmission fork 2 According to the obtained theta, h, phi 1 And solved in equation (3).
And (4.3) solving and generating a transmission device of each rotating part, and then obtaining an integral three-dimensional model design result.
The invention has the beneficial effects that:
1. the transmission mechanism of the large-scale rotary machine can be quickly designed aiming at the large-scale rotary machine rotary parts with different shapes and positions, and the design efficiency is greatly improved.
2. The method is used for calculating the shapes and positions of rotary parts of large-scale rotary machinery and analyzing the feasibility of the design of a transmission mechanism. If the design structure feasibility does not exist according to a certain rotary part, the system skips over two rotary parts connected with the certain rotary part to solve and highlights the rotary parts, and reminds a user to modify the shape of the main shaft near the two rotary parts.
Drawings
FIG. 1 is a basic flow chart of a method for generating a large-scale series transmission mechanism in an embodiment of the invention.
FIG. 2 is a schematic diagram of the results of a three-dimensional model design.
Detailed Description
The invention is further illustrated by the following figures and examples.
As shown in FIG. 1, the method for generating the large-scale envelope-based series transmission mechanism comprises the following implementation steps:
(1) for every two adjacent revolving parts in the machine with finished part layout, according to the space transformation and the size of the shaft sleeve of the revolving parts, an envelope surface which rotates for one circle is constructed, and the method specifically comprises the following sub-steps:
(1.1) for every two adjacent rotating parts, calculating a coordinate transformation matrix T from a local coordinate system to a world coordinate system of the two rotating parts 1 ,T 2 ；
And (1.2) reading the shaft sleeve sizes of two adjacent rotary parts in the step (1.1). All rotating parts have the same bushing dimension, set as r 0 ；
(1.3) enveloping surfaces F1 and F2 of the transmission rod and the transmission fork which respectively rotate for one circle are constructed, the two enveloping surfaces are congruent round table sides, and the same initialization parameters are as follows: the included angle theta between the generatrix of the circular truncated cone and the axis and the height h of the circular truncated cone. The expressions of F1 and F2 in the respective coordinate systems of the rotating parts are:
to F 1 The method comprises the following steps:
to F is aligned with 2 The method comprises the following steps:
wherein: z belongs to [0, h ]]，φ∈[0,2π]. For ease of design and manufacture, the lengths of the drive link and the drive fork tend to be the same, which means h 1 ＝h 2 H, the included angles between the generatrix and the axis are also equal to theta 1 ＝θ 2 ＝θ。
In order to ensure the feasibility of large-scale rotary mechanical motion, the motion rod must be consistently inserted into the transmission fork groove, and the motion rod and the motion fork need to meet the following requirements:
T 1 (F θ1,h (z 1 ,φ 1 ))＝T 2 (F θ2,h (z 2 ,φ 2 )) (3)
to prevent the design mechanism from being oversized and narrow the solution range, θ ∈ [ π/6, π/3], h ∈ [0.6dz,0.9dz ] are defined.
(2) And (3) analyzing the spatial relationship of the axes of the envelope surfaces of the transmission rod and the transmission fork for every two adjacent rotary parts, and directly providing feasible envelope surface parameters if the axes are superposed. The method specifically comprises the following substeps:
(2.1) coordinate transformation matrix T of the coordinate transformation matrix of (1.1) 1 ,T 2 Calculating expressions A1 and A2 of the envelope axes of the transmission rod and the transmission fork in world coordinates;
(2.2) the spatial relationship of A1, A2 was analyzed. If a1 and a2 coincide, a feasible solution can be obtained directly, i.e. h is 0.6d z ，θ＝π/3。
(3) If the axes in the step (2) are parallel, intersected or out-of-plane, iteratively searching envelope surface parameters to find feasible envelope surface sizes so as to ensure that the transmission rod and the transmission fork are always in contact, and specifically comprising the following substeps:
(3.1) finding a possible solution by taking the initial value of θ ═ 5 °, h ═ 0.1, z ═ 0.1, and Φ ═ 5 °.
(3.2) taking a point in the round table of the transmission rod, F 1 (z 1 ,φ)＝(x 1 ,y 1 ,z 1 ) And calculating the coordinate transformation of the point in the original transmission fork circular table coordinate transformation system, namely (x) 2 ,y 2 ,z 2 )＝T(x 1 ,y 1 ,z 1 ). Will (x) 2 ,y 2 ) Brought to F 2 Is obtained from the expression of 2 ′。
(3.3) calculation of Δ z ＝z 2 -z 2 '. If Δ z >0, replacing the value of theta and returning to the step (3.2); if Δ z <0, replacing the value of phi andreturning to the step (3.2); if there is a for any value of phi z <0, the feasible solution is the current value of θ, h.
(3.4) if no feasible solution exists in the step (3.3), the reason is that the rotary parts are too sparse or the joint angles are too large, the system skips two connected rotary parts to solve and highlights the two connected rotary parts, and a user is reminded to modify the shape of the main shaft near the two rotary parts.
(4) If a feasible envelope surface is obtained, generating a three-dimensional model of the transmission rod and the transmission fork according to the size of the envelope surface, and specifically comprising the following substeps:
(4.1) the length l of the driving rod and the driving fork is (1+ lambda) h/cos theta. A safety factor lambda is adopted, so that the separation of the transmission rod and the transmission fork at the extreme position is avoided, wherein lambda is 0.1. Depth l of transmission fork groove g ＝0.2l。
(4.2) installation phase of Transmission rod phi 1 ∈[0,2π]Is random, the mounting phase phi of the transmission fork 2 According to the obtained theta, h and phi 1 And solved in equation (3).
(4.3) solving the parameters and generating the transmission device of each rotating part to obtain the integral three-dimensional model design result, as shown in figure 2.
(5) If the envelope surface is not feasible, no feasible transmission mechanism solution exists, highlight display is carried out on the two related adjacent rotary parts at the moment, the highlight display is fed back to a user, and the user is reminded of modifying the shape of the main shaft near the two rotary parts.
(6) And (4) executing the steps (1) to (4) on all adjacent two rotary parts in the machine to finish the automatic solution and generation of the transmission mechanism.
Claims (5)
1. A method for generating a large-scale series transmission mechanism based on an envelope is characterized by comprising the following steps:
(1) for every two adjacent rotary parts in the complex rotary machine with finished part layout, according to the space transformation and the size of a shaft sleeve of the rotary parts, an envelope surface for one circle of rotation of the rotary parts and the envelope surface for one circle of rotation of the rotary parts are constructed;
(2) for every two adjacent rotary parts, analyzing the spatial relationship of the axes of the transmission rod and the envelope surface of the transmission fork, and if the axes are overlapped, directly providing feasible envelope surface parameters;
(3) if the axes in the step (2) are parallel, intersected or different, iteratively searching envelope surface parameters, and searching feasible envelope surface sizes to ensure that the transmission rod is always in contact with the transmission fork;
(4) if a feasible envelope surface is obtained, generating a three-dimensional model of the transmission rod and the transmission fork according to the size of the envelope surface;
(5) if the envelope surface is not feasible, no feasible transmission mechanism solution exists, highlighting the two related adjacent rotary parts at the moment, feeding back to a user, and reminding the user to modify the shape of the main shaft near the two rotary parts;
(6) and (5) executing the steps (1) to (5) on all adjacent two rotary parts in the machine to finish the automatic solving and generation of the transmission mechanism.
2. An envelope-based large-scale series transmission generation method as claimed in claim 1, wherein said step (1) comprises the following sub-steps:
(1.1) for every two adjacent rotating parts, calculating a coordinate transformation matrix T from a local coordinate system to a world coordinate system of the two rotating parts 1 ,T 2 ；
(1.2) reading the size of the shaft sleeves of two adjacent rotary parts in the step (1.1); all rotating parts have the same bushing dimension, set as r 0 ；
(1.3) constructing an envelope surface F of the transmission rod and the transmission fork which respectively rotate for one circle 1 ,F 2 The two enveloping surfaces are congruent circular truncated cone side surfaces and have the same initialization parameters: the included angle theta between the generatrix of the circular truncated cone and the axis and the height h of the circular truncated cone are included; f 1 ,F 2 The expressions in the respective rotating part coordinate systems are:
to F 1 The method comprises the following steps:
to F 2 The method comprises the following steps:
wherein: z belongs to [0, h ]]，φ∈[0,2π]For ease of design and manufacture, the lengths of the transfer bar and the transfer fork tend to be the same, which means h 1 ＝h 2 H, the included angles between the generatrix and the axis are also equal to theta 1 ＝θ 2 ＝θ；
In order to ensure the feasibility of large-scale rotary mechanical motion, the motion rod must be uniformly inserted into the transmission fork groove, and the motion rod and the motion fork need to meet the following requirements:
to prevent the design mechanism from being oversized and narrow the solution range, θ ∈ [ π/6, π/3], h ∈ [0.6dz,0.9dz ] are defined.
3. An envelope-based large-scale series transmission generation method as claimed in claim 2, wherein said step (2) comprises the following sub-steps:
(2.1) transforming the matrix T according to the coordinates described in (1.1) 1 ,T 2 Calculating the expression A of the envelope surface axes of the transmission rod and the transmission fork in the world coordinate 1 ,A 2 ；
(2.2) analyzing the spatial relationship of A1 and A2; if A is 1 ,A 2 Coincidence, then a feasible solution can be obtained directly, i.e. h is 0.6d z ，θ＝π/3。
4. An envelope-based method for generating a large-scale series transmission according to claim 1, wherein said step (3) of iteratively searching envelope parameters for feasible envelope dimensions comprises the sub-steps of:
(3.1) initially taking a value theta of 5 degrees, h of 0.1, z of 0.1 and phi of 5 degrees, and searching for a possible solution;
(3.2) taking a point in the round table of the transmission rod, F 1 (z 1 ,φ)＝(x 1 ,y 1 ,z 1 ) And calculating the coordinate transformation of the point in the original transmission fork circular table coordinate transformation system, namely (x) 2 ,y 2 ,z 2 )＝T(x 1 ,y 1 ,z 1 ) (ii) a Will (x) 2 ,y 2 ) Brought to F 2 In the expression of (b) to obtain z 2 ′；
(3.3) calculation of Δ z ＝z 2 -z 2 '; if Δ z >0, replacing the value of theta and returning to the step (3.2); if Δ z <0, replacing the phi value and returning to the step (3.2); if there is a for any value of phi z <0, the feasible solution is the current value of theta, h;
(3.4) if no feasible solution exists in the step (3.3), the reason is that the rotary parts are too sparse or the joint angles are too large, the system skips two connected rotary parts to solve and highlights the two connected rotary parts, and a user is reminded to modify the shape of the main shaft near the two rotary parts.
5. The envelope-based method for generating a large-scale series transmission according to claim 1, wherein in step (4), for determining the feasible envelope surface, generating a three-dimensional model of the transmission rod and the transmission fork according to the size of the envelope surface comprises the following sub-steps:
(4.1) the length l of the transmission rod and the transmission fork is equal to (1+ lambda) h/cos theta, a safety coefficient lambda is adopted, the separation of the transmission rod and the transmission fork at the limit position is avoided, the lambda is equal to 0.1, and the depth l of a transmission fork groove is equal to g ＝0.2l；
(4.2) installation phase of Transmission rod phi 1 ∈[0,2π]Is random, the mounting phase phi of the driving fork 2 According to the obtained theta, h, phi 1 Solving in equation (3);
and (4.3) after solving of each parameter is completed, generating a transmission device of each rotary part according to the parameter to obtain an integral three-dimensional model design result.
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