CN110287627A - A method for generating large-scale series transmission mechanism based on envelope - Google Patents
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Abstract
本发明公开了一种基于包络的大规模串联传动机构生成方法，该方法能够针对由大量回转零件组成的复杂回转机械，自动求解所有回转零件之间的串联传动机构。在完成所有回转零件布局的基础上，构造传动机构中的杆和叉的运动包络面，对包络面的不同的相交情况进行分析，搜索合适的包络面参数，从而得到可行的杆和叉参数，形成传动机构解决方案。本发明方法能够显著降低大规模复杂回转机械中串联传动机构的设计难度，使设计师不再需要机械设计的专业知识即可借助本方法自动求解生成可行的传动机构，保障所设计机械的运动可行性。
The invention discloses a method for generating a large-scale series transmission mechanism based on an envelope, which can automatically solve the series transmission mechanism among all the rotating parts for a complex rotating machine composed of a large number of rotating parts. On the basis of completing the layout of all rotary parts, construct the motion envelope surfaces of the rod and fork in the transmission mechanism, analyze the different intersections of the envelope surfaces, and search for suitable parameters of the envelope surface, so as to obtain feasible rods and forks. Fork parameters, form the transmission mechanism solution. The method of the invention can significantly reduce the difficulty of designing a series transmission mechanism in a large-scale complex rotary machine, so that the designer can automatically solve and generate a feasible transmission mechanism with the help of the method without needing professional knowledge of mechanical design, so as to ensure that the motion of the designed machine is feasible. sex.
Description
技术领域technical field
本发明涉及机械设计方法领域，尤其涉及一种基于包络的大规模串联传动机构生成方法。The invention relates to the field of mechanical design methods, in particular to a method for generating a large-scale serial transmission mechanism based on an envelope.
背景技术Background technique
由大规模回转零件组成的复杂回转机械，如大规模回转机械、回转式建筑等，融合了工程学与艺术学之美，为艺术提供了丰富的审美体验，由于其复杂的结构和周期性的动态效果，具有非常的吸引力。然而，它们的设计是非常困难的，许多现有作品是由跨学科的专家或者团队经过多次试错后设计出来，设计效率较低。其中零件之间的传动机构的设计是最困难的部分，即使对于有技术背景的工程师而言，也几乎不可能通过手绘的方式求解可行的传动机构。而使用纯手动计算则需要求解大量参数并需要大量迭代，效率非常低下。开发自动化、参数化的传动机构设计方法，根据回转零件位置关系自动求解传动结构可以大大提高设计效率与准确性，使得设计师甚至新手也能够快速方便地设计此类复杂回转机械。Complex rotary machinery composed of large-scale rotary parts, such as large-scale rotary machinery, rotary buildings, etc., integrates the beauty of engineering and art, and provides a rich aesthetic experience for art, due to its complex structure and periodic dynamics. The effect is very attractive. However, their design is very difficult, and many existing works are designed by interdisciplinary experts or teams after many trials and errors, and the design efficiency is low. The design of the transmission mechanism between the parts is the most difficult part. Even for engineers with technical background, it is almost impossible to solve the feasible transmission mechanism by hand-painting. Using pure manual calculation requires solving a large number of parameters and requires a lot of iterations, which is very inefficient. Developing an automatic and parametric transmission mechanism design method, and automatically solving the transmission structure according to the positional relationship of the rotating parts can greatly improve the design efficiency and accuracy, enabling designers and even novices to quickly and easily design such complex rotating machinery.
发明内容SUMMARY OF THE INVENTION
为了克服传统手动分析计算大规模串联传动机构效率低，准确性差的问题，本发明的目的是提供了一种具有较强适应性和可靠性、能够满足各种形态的回转式复杂回转机械的基于包络的大规模串联传动机构生成方法。In order to overcome the problems of low efficiency and poor accuracy of the large-scale series transmission mechanism in the traditional manual analysis and calculation, the purpose of the present invention is to provide a rotary complex rotary machine with strong adaptability and reliability, which can meet the needs of various forms. A large-scale serial transmission mechanism generation method for envelopes.
本发明的目的是通过以下技术方案来实现的：一种基于包络的大规模串联传动机构生成方法，包括以下步骤：The object of the present invention is to be achieved through the following technical solutions: a method for generating a large-scale series transmission mechanism based on an envelope, comprising the following steps:
(1)对已经完成零件布局的复杂回转机械中的每两个相邻回转零件，根据回转零件的空间变换和轴套尺寸，构造二者各自旋转一周的包络面；(1) For every two adjacent rotary parts in the complex rotary machinery that has completed the part layout, according to the space transformation of the rotary parts and the size of the bushing, construct the envelope surface of each one rotation of the two;
(2)对每两个相邻回转零件，分析传动杆和传动叉包络面轴线的空间关系，如果轴线重合，则直接给出可行的包络面参数。(2) For every two adjacent rotating parts, analyze the spatial relationship between the axis of the envelope surface of the transmission rod and the transmission fork. If the axes are coincident, the feasible envelope surface parameters are directly given.
(3)如果(2)中的轴线平行、相交或异面，则对包络面参数进行迭代搜索，寻找可行的包络面尺寸，以保证传动杆和传动叉始终接触；(3) If the axes in (2) are parallel, intersecting or out of plane, iteratively search the envelope surface parameters to find a feasible envelope surface size to ensure that the transmission rod and the transmission fork are always in contact;
(4)若求得可行的包络面，则根据包络面的尺寸生成传动杆和传动叉的三维模型；(4) If a feasible envelope surface is obtained, the three-dimensional model of the transmission rod and the transmission fork is generated according to the size of the envelope surface;
(5)若没有可行的包络面，则没有可行的传动机构解，此时对所涉及的两相邻回转零件进行高亮显示，反馈给用户，提醒用户修改两回转零件附近的主轴形状。(5) If there is no feasible envelope surface, there is no feasible solution for the transmission mechanism. At this time, the two adjacent rotating parts involved are highlighted and fed back to the user to remind the user to modify the spindle shape near the two rotating parts.
(6)对机械中所有的相邻两个回转零件执行(1)-(4)步，完成传动机构的自动求解和生成。(6) Steps (1)-(4) are performed on all adjacent two rotating parts in the machine to complete the automatic solution and generation of the transmission mechanism.
进一步地，所述步骤(1)具体包括以下子步骤：Further, the step (1) specifically includes the following substeps:
(1.1)对每两个相邻回转零件，求出两回转零件局部坐标系到世界坐标系的坐标变换矩阵T1,T2；(1.1) For every two adjacent rotating parts, obtain the coordinate transformation matrix T 1 , T 2 from the local coordinate system of the two rotating parts to the world coordinate system;
(1.2)读取(1.1)中两相邻回转零件的轴套尺寸。所有回转零件都具有相同的轴套尺寸，设为r0；(1.2) Read the bushing dimensions of the two adjacent rotating parts in (1.1). All rotary parts have the same bushing size, set as r 0 ;
(1.3)构造传动杆和传动叉各自旋转一周的包络面F1,F2，两包络面为全等的圆台侧面，具有相同的初始化参数：圆台母线和轴线夹角θ，圆台高度h。F1,F2在各自回转零件坐标系内的表达式为：(1.3) Construct the envelope surfaces F1 and F2 for each rotation of the transmission rod and the transmission fork. The two envelope surfaces are congruent truncated truncated sides and have the same initialization parameters: the angle θ between the truncated truncated busbar and the axis, and the truncated truncated height h. The expressions of F1 and F2 in their respective rotating parts coordinate systems are:
对F1，有：For F1, there are :
对F2，有：For F2, there are :
其中：Z∈[0,h]，φ∈[0,2π]。为了便于设计和制造，传动杆和传动叉的长度往往相同，这意味着h1＝h2＝h，它们与母线和轴的夹角也相等:θ1＝θ2＝θ。where: Z∈[0,h], φ∈[0,2π]. For ease of design and manufacture, the length of the transmission rod and the transmission fork are often the same, which means that h 1 =h 2 =h, and the angle between them and the bus bar and the shaft is also equal: θ 1 =θ 2 =θ.
为保证大规模回转机械运动的可行性，运动杆必须一致插在传动叉槽中，运动杆和运动叉需满足：In order to ensure the feasibility of large-scale rotary mechanical movement, the moving rod must be inserted into the transmission fork slot, and the moving rod and the moving fork must meet the following requirements:
T1(Fθ1,h(z1,φ1))＝T2(Fθ2,h(z2,φ2)) (3)T 1 (F θ1,h (z 1 ,φ 1 ))=T 2 (F θ2,h (z 2 ,φ 2 )) (3)
为防止设计机构尺寸过大并且缩小求解范围，限定θ∈[π/6,π/3]，h∈[0.6dz,0.9dz]。In order to prevent the design mechanism from being too large and narrow the solution range, θ∈[π/6, π/3], h∈[0.6dz, 0.9dz] are defined.
进一步地，所述步骤(2)具体包括以下子步骤：Further, the step (2) specifically includes the following substeps:
(2.1)根据(1.1)所述的坐标变换矩阵坐标变换矩阵T1,T2，计算传动杆和传动叉包络面轴线在世界坐标内的表达式A1,A2；(2.1) According to the coordinate transformation matrix T 1 , T 2 described in (1.1), calculate the expressions A1, A2 of the envelope axes of the transmission rod and the transmission fork in world coordinates;
(2.2)分析A1,A2的空间关系。如果A1,A2重合，则可直接得到可行解，即h＝0.6dz，θ＝π/3。(2.2) Analyze the spatial relationship between A1 and A2. If A1 and A2 coincide, a feasible solution can be obtained directly, that is, h=0.6d z , θ=π/3.
进一步地，所述步骤(3)中，所述对于对包络面参数进行迭代搜索，寻找可行的包络面尺寸包括子步骤：Further, in the step (3), the iterative search for the envelope surface parameters to find a feasible envelope surface size includes sub-steps:
(3.1)初始取值θ＝5°、h＝0.1、z＝0.1、φ＝5°，寻找可能解。(3.1) The initial values of θ=5°, h=0.1, z=0.1, and φ=5° are used to find possible solutions.
(3.2)在传动杆圆台中取一点，F1(z1,φ)＝(x1,y1,z1)，并在原传动叉圆台坐标变换系统中计算所取点的坐标变换，即(x2,y2,z2)＝T(x1,y1,z1)。将(x2,y2)带到F2的表达式中得到z2′。(3.2) Take a point in the circular truncated transmission rod, F 1 (z 1 , φ)=(x 1 , y 1 , z 1 ), and calculate the coordinate transformation of the point in the original transmission fork truncated truncated coordinate transformation system, namely ( x 2 , y 2 , z 2 )=T(x 1 , y 1 , z 1 ). Bringing (x 2 , y 2 ) into the expression for F 2 yields z 2 ′.
(3.3)计算Δz＝z2-z2′。如果Δz>0，更换θ的值并返回步骤(3.2)；如果Δz<0，更换φ的值并返回步骤(3.2)；如果对任意φ的值都有Δz<0，可行解为当前θ，h的值。(3.3) Calculate Δ z =z 2 −z 2 ′. If Δ z > 0, change the value of θ and return to step (3.2); if Δ z < 0, change the value of φ and return to step (3.2); if Δ z < 0 for any value of φ, the feasible solution is The current value of θ, h.
(3.4)如果在(3.3)中没有可行解，则原因为回转零件过于稀疏或者关节角度过大，系统将跳过相连接的两个回转零件求解并对其进行高亮显示，提醒用户修改两回转零件附近的主轴形状。(3.4) If there is no feasible solution in (3.3), the reason is that the rotary parts are too sparse or the joint angle is too large, the system will skip the solution of the two connected rotary parts and highlight them, reminding the user to modify the two Spindle shape near the revolved part.
进一步地，所述步骤(4)中，所述对于求得可行的包络面，根据包络面的尺寸生成传动杆和传动叉的三维模型具体包括以下子步骤：Further, in the step (4), for obtaining a feasible envelope surface, generating the three-dimensional model of the transmission rod and the transmission fork according to the size of the envelope surface specifically includes the following sub-steps:
(4.1)传动杆和传动叉的长度l＝(1+λ)h/cosθ。采用安全系数λ，避免了传动杆和传动叉在极限位置的分离，本文中λ＝0.1。传动叉槽的深度lg＝0.2l。(4.1) The length of the transmission rod and the transmission fork l=(1+λ)h/cosθ. The safety factor λ is adopted to avoid the separation of the transmission rod and the transmission fork at the limit position, and λ=0.1 in this paper. The depth of the transmission fork groove is lg =0.2l.
(4.2)传动杆的安装相位φ1∈[0,2π]是随机的，传动叉的安装相位φ2根据求得的θ,h,φ1带入等式(3)中求解。(4.2) The installation phase ϕ 1 ∈ [0,2π] of the transmission rod is random, and the installation phase ϕ 2 of the transmission fork is brought into equation (3) according to the obtained θ, h, ϕ 1 to solve.
(4.3)求解并生成各回转零件的传动装置后，得到整体的三维模型设计结果。(4.3) After solving and generating the transmission device of each rotating part, the overall 3D model design result is obtained.
本发明具有的有益效果是：The beneficial effects that the present invention has are:
1、可以针对不同形态和位置的大规模回转机械回转零件快速设计大规模回转机械的传动机构，大大提高设计效率。1. The transmission mechanism of large-scale rotary machinery can be quickly designed for rotary parts of large-scale rotary machinery in different shapes and positions, which greatly improves the design efficiency.
2、对于大规模回转机械的回转零件形态和位置进行计算，分析传动机构设计的可行性。如果根据某回转零件设计结构可行性不存在，系统将跳过与某回转零件相连接的两个回转零件求解并对其进行高亮显示，提醒用户修改两回转零件附近的主轴形状。2. Calculate the shape and position of the rotating parts of the large-scale rotating machinery, and analyze the feasibility of the transmission mechanism design. If the feasibility of designing a structure based on a rotary part does not exist, the system will skip the solution of the two rotary parts connected to a rotary part and highlight them, reminding the user to modify the shape of the main shaft near the two rotary parts.
附图说明Description of drawings
图1是本发明实施例中大规模串联传动机构生成方法的基本流程图。FIG. 1 is a basic flow chart of a method for generating a large-scale series transmission mechanism in an embodiment of the present invention.
图2是三维模型设计结果示意图。Figure 2 is a schematic diagram of the design results of the 3D model.
具体实施方式Detailed ways
下面结合附图和实施例对本发明作进一步说明。The present invention will be further described below with reference to the accompanying drawings and embodiments.
如图1所示，本发明的基于包络的大规模串联传动机构生成方法，包含以下实施步骤：As shown in Figure 1, the envelope-based large-scale serial transmission mechanism generation method of the present invention comprises the following implementation steps:
(1)对已经完成零件布局的机械中的每两个相邻回转零件，根据回转零件的空间变换和轴套尺寸，构造二者各自旋转一周的包络面，具体包括以下子步骤：(1) For every two adjacent rotating parts in the machine that has completed the part layout, according to the space transformation of the rotating parts and the size of the bushing, construct the envelope surface of each one rotation of the two, which specifically includes the following sub-steps:
(1.1)对每两个相邻回转零件，求出两回转零件局部坐标系到世界坐标系的坐标变换矩阵T1,T2；(1.1) For every two adjacent rotating parts, obtain the coordinate transformation matrix T 1 , T 2 from the local coordinate system of the two rotating parts to the world coordinate system;
(1.2)读取(1.1)中两相邻回转零件的轴套尺寸。所有回转零件都具有相同的轴套尺寸，设为r0；(1.2) Read the bushing dimensions of the two adjacent rotating parts in (1.1). All rotary parts have the same bushing size, set as r 0 ;
(1.3)构造传动杆和传动叉各自旋转一周的包络面F1,F2，两包络面为全等的圆台侧面，具有相同的初始化参数：圆台母线和轴线夹角θ，圆台高度h。F1,F2在各自回转零件坐标系内的表达式为：(1.3) Construct the envelope surfaces F1 and F2 for each rotation of the transmission rod and the transmission fork. The two envelope surfaces are congruent truncated truncated sides and have the same initialization parameters: the angle θ between the truncated truncated busbar and the axis, and the truncated truncated height h. The expressions of F1 and F2 in their respective rotating parts coordinate systems are:
对F1，有：For F1, there are :
对F2，有：For F2, there are :
其中：Z∈[0,h]，φ∈[0,2π]。为了便于设计和制造，传动杆和传动叉的长度往往相同，这意味着h1＝h2＝h，它们与母线和轴的夹角也相等:θ1＝θ2＝θ。where: Z∈[0,h], φ∈[0,2π]. For ease of design and manufacture, the transmission rod and the transmission fork are often of the same length, which means h 1 =h 2 =h, and their included angle with the busbar and the shaft is also equal: θ 1 =θ 2 =θ.
为保证大规模回转机械运动的可行性，运动杆必须一致插在传动叉槽中，运动杆和运动叉需满足：In order to ensure the feasibility of large-scale rotary mechanical movement, the moving rod must be inserted into the transmission fork slot, and the moving rod and the moving fork must meet the following requirements:
T1(Fθ1,h(z1,φ1))＝T2(Fθ2,h(z2,φ2)) (3)T 1 (F θ1,h (z 1 ,φ 1 ))=T 2 (F θ2,h (z 2 ,φ 2 )) (3)
为防止设计机构尺寸过大并且缩小求解范围，限定θ∈[π/6,π/3]，h∈[0.6dz,0.9dz]。In order to prevent the design mechanism from being too large and narrow the solution range, θ∈[π/6, π/3], h∈[0.6dz, 0.9dz] are defined.
(2)对每两个相邻回转零件，分析传动杆和传动叉包络面轴线的空间关系，如果轴线重合，则直接给出可行的包络面参数。具体包括以下子步骤：(2) For every two adjacent rotating parts, analyze the spatial relationship between the axis of the envelope surface of the transmission rod and the transmission fork. If the axes are coincident, the feasible envelope surface parameters are directly given. Specifically, it includes the following sub-steps:
(2.1)根据(1.1)所述的坐标变换矩阵坐标变换矩阵T1,T2，计算传动杆和传动叉包络面轴线在世界坐标内的表达式A1,A2；(2.1) According to the coordinate transformation matrix T 1 , T 2 described in (1.1), calculate the expressions A1, A2 of the envelope axes of the transmission rod and the transmission fork in world coordinates;
(2.2)分析A1,A2的空间关系。如果A1,A2重合，则可直接得到可行解，即h＝0.6dz，θ＝π/3。(2.2) Analyze the spatial relationship between A1 and A2. If A1 and A2 coincide, a feasible solution can be obtained directly, that is, h=0.6d z , θ=π/3.
(3)如果(2)中的轴线平行、相交或异面，则对包络面参数进行迭代搜索，寻找可行的包络面尺寸，以保证传动杆和传动叉始终接触，具体包括以下子步骤：(3) If the axes in (2) are parallel, intersecting or different planes, perform an iterative search on the envelope surface parameters to find a feasible envelope surface size to ensure that the transmission rod and the transmission fork are always in contact, specifically including the following sub-steps :
(3.1)初始取值θ＝5°、h＝0.1、z＝0.1、φ＝5°，寻找可能解。(3.1) The initial values of θ=5°, h=0.1, z=0.1, and φ=5° are used to find possible solutions.
(3.2)在传动杆圆台中取一点，F1(z1,φ)＝(x1,y1,z1)，并在原传动叉圆台坐标变换系统中计算所取点的坐标变换，即(x2,y2,z2)＝T(x1,y1,z1)。将(x2,y2)带到F2的表达式中得到z2′。(3.2) Take a point in the circular truncated transmission rod, F 1 (z 1 , φ)=(x 1 , y 1 , z 1 ), and calculate the coordinate transformation of the point in the original transmission fork truncated truncated coordinate transformation system, namely ( x 2 , y 2 , z 2 )=T(x 1 , y 1 , z 1 ). Bringing (x 2 , y 2 ) into the expression for F 2 yields z 2 ′.
(3.3)计算Δz＝z2-z2′。如果Δz>0，更换θ的值并返回步骤(3.2)；如果Δz<0，更换φ的值并返回步骤(3.2)；如果对任意φ的值都有Δz<0，可行解为当前θ，h的值。(3.3) Calculate Δ z =z 2 −z 2 ′. If Δ z > 0, change the value of θ and return to step (3.2); if Δ z < 0, change the value of φ and return to step (3.2); if Δ z < 0 for any value of φ, the feasible solution is The current value of θ, h.
(3.4)如果在(3.3)中没有可行解，则原因为回转零件过于稀疏或者关节角度过大，系统将跳过相连接的两个回转零件求解并对其进行高亮显示，提醒用户修改两回转零件附近的主轴形状。(3.4) If there is no feasible solution in (3.3), the reason is that the rotary parts are too sparse or the joint angle is too large, the system will skip the solution of the two connected rotary parts and highlight them, reminding the user to modify the two Spindle shape near the revolved part.
(4)若求得可行的包络面，则根据包络面的尺寸生成传动杆和传动叉的三维模型，具体包括以下子步骤：(4) If a feasible envelope surface is obtained, the three-dimensional model of the transmission rod and the transmission fork is generated according to the size of the envelope surface, which specifically includes the following sub-steps:
(4.1)传动杆和传动叉的长度l＝(1+λ)h/cosθ。采用安全系数λ，避免了传动杆和传动叉在极限位置的分离，本文中λ＝0.1。传动叉槽的深度lg＝0.2l。(4.1) The length of the transmission rod and the transmission fork l=(1+λ)h/cosθ. The safety factor λ is adopted to avoid the separation of the transmission rod and the transmission fork at the limit position, and λ=0.1 in this paper. The depth of the transmission fork groove is lg =0.2l.
(4.2)传动杆的安装相位φ1∈[0,2π]是随机的，传动叉的安装相位φ2根据求得的θ,h，,φ1带入等式(3)中求解。(4.2) The installation phase φ 1 ∈ [0,2π] of the transmission rod is random, and the installation phase φ 2 of the transmission fork is brought into equation (3) according to the obtained θ, h, φ 1 and solved.
(4.3)求解各参数并生成各回转零件的传动装置后，得到整体的三维模型设计结果，如图2所示。(4.3) After solving each parameter and generating the transmission device of each rotating part, the overall 3D model design result is obtained, as shown in Figure 2.
(5)若没有可行的包络面，则没有可行的传动机构解，此时对所涉及的两相邻回转零件进行高亮显示，反馈给用户，提醒用户修改两回转零件附近的主轴形状。(5) If there is no feasible envelope surface, there is no feasible solution for the transmission mechanism. At this time, the two adjacent rotating parts involved are highlighted and fed back to the user to remind the user to modify the spindle shape near the two rotating parts.
(6)对机械中所有的相邻两个回转零件执行(1)-(4)步，完成传动机构的自动求解和生成。(6) Steps (1)-(4) are performed on all adjacent two rotating parts in the machine to complete the automatic solution and generation of the transmission mechanism.
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