WO2019119504A1 - 基于多目标法的旋盖机凸轮曲线设计方法 - Google Patents

基于多目标法的旋盖机凸轮曲线设计方法 Download PDF

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WO2019119504A1
WO2019119504A1 PCT/CN2017/119424 CN2017119424W WO2019119504A1 WO 2019119504 A1 WO2019119504 A1 WO 2019119504A1 CN 2017119424 W CN2017119424 W CN 2017119424W WO 2019119504 A1 WO2019119504 A1 WO 2019119504A1
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cam curve
cam
displacement
capping machine
curve
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French (fr)
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吴佳
何雪明
刘振超
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Jiangnan University
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Jiangnan University
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B67—OPENING, CLOSING OR CLEANING BOTTLES, JARS OR SIMILAR CONTAINERS; LIQUID HANDLING
    • B67B—APPLYING CLOSURE MEMBERS TO BOTTLES JARS, OR SIMILAR CONTAINERS; OPENING CLOSED CONTAINERS
    • B67B3/00—Closing bottles, jars or similar containers by applying caps
    • B67B3/20—Closing bottles, jars or similar containers by applying caps by applying and rotating preformed threaded caps
    • B67B3/2013—Closing bottles, jars or similar containers by applying caps by applying and rotating preformed threaded caps by carousel-type capping machines
    • B67B3/2033—Closing bottles, jars or similar containers by applying caps by applying and rotating preformed threaded caps by carousel-type capping machines comprising carousel co-rotating capping heads
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B67—OPENING, CLOSING OR CLEANING BOTTLES, JARS OR SIMILAR CONTAINERS; LIQUID HANDLING
    • B67B—APPLYING CLOSURE MEMBERS TO BOTTLES JARS, OR SIMILAR CONTAINERS; OPENING CLOSED CONTAINERS
    • B67B3/00—Closing bottles, jars or similar containers by applying caps
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H53/00—Cams or cam-followers, e.g. rollers for gearing mechanisms
    • F16H53/02—Single-track cams for single-revolution cycles; Camshafts with such cams
    • F16H53/025—Single-track cams for single-revolution cycles; Camshafts with such cams characterised by their construction, e.g. assembling or manufacturing features

Definitions

  • the invention relates to a cam curve design method of a capping machine based on a multi-objective method, and belongs to the technical field of cam design of a capping machine.
  • the cam mechanism can perform various shifting movements almost, and the speed can be adjusted as needed, and the precision is high and the cost is low, so the cam mechanism is applied in modern machinery.
  • people's requirements for the efficiency, precision and reliability of various types of automatic machinery are also constantly improved.
  • the engineer Gradually began to pay attention to the dynamic characteristics of the cam mechanism, and the development of new cam mechanisms is also developing very rapidly in the direction of combining dynamics and kinematics. It has become a very important task to design a cam mechanism to develop a general curve with better dynamics and kinematics.
  • the design method of the cam curve of the capping machine is to connect the key points when the capping machine completes the relevant action with a straight line and round the joint at the key point.
  • This method can satisfy the speed of the cam curve continuously, but when the cam is running at high speed, due to the flexible impact, the dynamic stress of the component is relatively large, and the capping machine is large in noise and easy to wear when working in the field, and the running efficiency is low. Therefore, the cam curve is redesigned by polynomial fitting and k-order harmonic function.
  • the obtained cam curve characteristic parameters such as maximum speed V max , maximum acceleration A max , maximum jump J max and maximum jump Q max are all obtained.
  • the characteristic parameter value is reduced, and its continuity and conductability are improved, and the kinematics performance and dynamic performance are greatly improved.
  • polynomial interpolation will cause the polynomial power to be too high, which is not conducive to processing.
  • the characteristic parameter values of the cam curve are simultaneously optimal, that is, the characteristic values are as small as possible, but it is difficult to implement. Therefore, this method of redesigning the cam curve cannot pre-balance these parameters, and only the items with smaller eigenvalues can be focused on different purposes, and other characteristic parameters are appropriately relaxed, so that all parameter characteristic values reach a relatively balanced optimization. .
  • the invention is to solve the problem that the existing method of redesigning the cam curve cannot optimize the parameter item according to the importance degree, and the cam mechanism has poor running stability, and provides a cam curve design method of the capping machine based on the multi-objective method.
  • the method for designing a cam curve of a capping machine based on a multi-objective method according to the present invention comprises the following steps:
  • Step 1 Obtain the key point data of the capping machine cam for function determination
  • Step 2 The key point data is dimensionless, and the dimensionless time T and the dimensionless displacement S are obtained;
  • Step 3 Write a polynomial fitting cam curve displacement function, compare the fitting error with the set allowable error, and if the comparison result is greater than the set threshold, manually insert the local control point until the comparison result is within the set threshold. Combining the constraints of key point displacement, using the least squares method, the polynomial fitting cam curve expression and map are obtained; n is a positive integer;
  • Step 4 Select the cam curve optimization target, set the weight coefficient, and construct the optimized cam curve.
  • Another method for designing a cam curve of a capping machine based on the multi-objective method according to the present invention comprises the following steps:
  • Step 1 Obtain the key point data of the capping machine cam for function determination
  • Step 2 The key point data is dimensionless, and the dimensionless time T and the dimensionless displacement S are obtained;
  • Step 3 Write a fitting program of the cam curve, determine the order of k based on the modified cam curve displacement function of the k-th harmonic function; add the local control point, and use the least squares method to fit the key point and local control Point, solve for the cam curve expression and its map;
  • Step 4 Select the cam curve optimization target, set the weight coefficient, and construct the optimized cam curve.
  • the polynomial fitting method controls the polynomial power from the beginning, and can reduce the processing difficulty under the condition of satisfying the local displacement control.
  • the harmonic function method can be infinitely guided, and the derivative function is also a harmonic function, which can effectively ensure the continuity of the cam curve and improve the operating efficiency of the mechanism. After multi-objective optimization of these two curves, not only can it guarantee its excellent performance, but also make the design process more realistic according to the requirements, so that the performance parameters can be more reasonablely improved.
  • G1 is continuous tangent
  • G2 is continuous curvature
  • G3 is continuous in curvature change rate
  • G4 is continuous in rate of change of curvature change rate.
  • FIG. 1 is a schematic structural view of a cam mechanism of a capping machine according to an embodiment of the present invention
  • Figure 2 is a schematic view of the cam of Figure 1;
  • Figure 3 is a time-and-displacement cam curve of the 7th degree polynomial multi-objective optimization method design
  • Figure 4 is a time and velocity cam curve of the 7th degree polynomial multi-objective optimization method design
  • Figure 5 is a time and acceleration cam curve of the 7th degree polynomial multi-objective optimization method design
  • Figure 6 is a time and hop cam curve of the 7th degree polynomial multi-objective optimization method design
  • Figure 7 is a time and hop cam curve of the 7th degree polynomial multi-objective optimization method design
  • Figure 8 is a time-and-dynamic torque cam curve of the seventh-order polynomial multi-objective optimization method design
  • Figure 9 is a time and displacement cam curve of the improved second-order harmonic function multi-objective optimization method design
  • Figure 10 is a time and velocity cam curve of a modified second-order harmonic function multi-objective optimization method design
  • Figure 11 is a time and acceleration cam curve of the improved second-order harmonic function multi-objective optimization method design
  • Figure 12 is a time and hop cam curve of the improved second-order harmonic function multi-objective optimization method design
  • Figure 13 is a time and hop cam curve of the improved second-order harmonic function multi-objective optimization method design
  • Figure 14 is a graph showing the time and dynamic load torque cam curve of the improved second-order harmonic function multi-objective optimization method design
  • Figure 15 is a comparison chart of time and displacement curves before and after multi-objective optimization of polynomial and harmonic cam curves of the present invention.
  • Figure 16 is a comparison chart of time and velocity curves before and after multi-objective optimization of polynomial and harmonic cam curves of the present invention.
  • 17 is a comparison chart of time and acceleration curves before and after multi-objective optimization of polynomial and harmonic cam curves of the present invention.
  • Figure 20 is a comparison of the time and dynamic load torque curves before and after multi-objective optimization of the polynomial and harmonic cam curves of the present invention.
  • the method for designing a cam curve of a capping machine based on a multi-objective method according to the present embodiment includes the following steps:
  • Step 1 Obtain the key point data of the capping machine cam for function determination
  • Step 2 The key point data is dimensionless, and the dimensionless time T and the dimensionless displacement S are obtained;
  • Step 3 Write a polynomial fitting cam curve displacement function, compare the fitting error with the set allowable error, and if the comparison result is greater than the set threshold, manually insert the local control point until the comparison result is within the set threshold. Combining the constraints of key point displacement, using the least squares method, the polynomial fitting cam curve expression and map are obtained; n is a positive integer;
  • Step 4 Select the cam curve optimization target, set the weight coefficient, and construct the optimized cam curve.
  • the data of the cam follower of the capping machine reaches the corresponding displacement point at the corresponding angle as a key point, and these key points generally support the capping machine to complete the functions of grasping, injecting, and capping; in step 3, MATLAB writes a polynomial fitting program.
  • the local control point can be manually inserted to reduce The error, and effectively control the shape of the cam curve, make the curve trend more in line with the actual situation, and then combine the constraints on the displacement of the key points, using the least squares method to obtain the cam curve expression and map designed by the polynomial fitting method.
  • C 0 is the initial coefficient
  • C 1 is the first coefficient
  • C n is the Nth coefficient.
  • Step 1 Obtain the key point data of the capping machine cam for function determination
  • Step 2 The key point data is dimensionless, and the dimensionless time T and the dimensionless displacement S are obtained;
  • Step 3 Write a fitting program of the cam curve, determine the order of k based on the modified cam curve displacement function of the k-th harmonic function; add the local control point, and use the least squares method to fit the key point and local control Point, solve for the cam curve expression and its map;
  • Step 4 Select the cam curve optimization target, set the weight coefficient, and construct the optimized cam curve.
  • the k is greater than or equal to two.
  • the data of the cam follower of the capping machine reaches the corresponding displacement point at the corresponding angle as a key point, and these key points generally support the capping machine to complete the functions of grasping, injecting, and capping; in step 3, MATLAB writes a cam curve fitting program.
  • the performance of the first-order curve is the same as that of the cycloid curve or the simple harmonic curve, so k
  • the rounding is started from 2; at the same time, in order to control the local shape and better adjust the cam curve, a series of local control points are added, and the least squares sum is used to fit the key points and the local control points are solved to obtain c n , ⁇ n and The value of the cam curve and its map are obtained.
  • c n is the amplitude
  • ⁇ n is the angular frequency
  • the invention adopts a multi-objective optimization method to optimize the cam curve of the polynomial fitting or the harmonic function fitting, and not only can we balance these parameter values according to actual conditions and requirements, and set the importance degree thereof to optimize it to different degrees. Moreover, the optimized characteristic value fluctuation can be reduced, which is very beneficial to the stability of the cam mechanism during operation, and effectively ensures the running accuracy of the mechanism.
  • Multi-objective optimization functions can generally be written as:
  • f p (x) is a single objective function that needs to be optimized
  • st g i (x) > 0 is a multi-objective optimization inequality constraint
  • h i (x) is an equality constraint equation
  • m is a positive integer
  • I is a positive integer
  • the method for optimizing the characteristic parameter values in step 4 is: optimizing the cam curve based on the multi-objective optimization method.
  • the optimization target is determined: the comprehensive performance of the cam curve is empirically distinguished by comparing characteristic values such as maximum speed V max , maximum acceleration A max , maximum jump J max , maximum jump Q max and dynamic load torque characteristic parameter AV max . Therefore, the maximum speed V max , the maximum acceleration A max , the maximum jump J max and the maximum jump Q max and the dynamic load torque characteristic parameter AV max are selected as cam curve optimization targets.
  • the weight coefficient using the linear weighting method, adding the weight coefficient ⁇ i to the maximum speed V max , the maximum acceleration A max , the maximum jump J max and the maximum jump Q max and the dynamic load torque characteristic parameter AV max And then sum and calculate.
  • the weights are changed according to the relevant design requirements.
  • cam curve can be compared and optimized, and the maximum speed, the maximum value of the acceleration, the maximum value of the jump, the maximum value of the jump, and the fluctuation thereof are observed to verify the optimization effect.
  • the present invention is directed to the existing defects in the design method of connecting the key points by straight lines and rounding at the joints when designing the cam curve of the capping machine, and the key determined by retaining the original cam mechanism for realizing the function.
  • the multi-objective method is used to optimize the cam curve to improve the guideability and continuity of the cam curve at the key points, effectively solving the cam mechanism. Impact, wear, fatigue damage and noise during operation.
  • the invention adopts a multi-objective optimization method to design a cam curve of a capping machine.
  • the key points determined by the capping machine to complete the capping function (generally expressed as a certain displacement to be reached at an angle) are obtained.
  • the expression of each key point is first transformed into the relationship between time and displacement, and then the time and displacement are not dimensioned.
  • the local control points are appropriately added, and the key points and local control points are fitted by multi-objective optimization, and the cam curve expression and the cam curve map are output.
  • the optimized cam curve can be compared with a single polynomial fitting and a cam curve designed by a harmonic function fitting to select an optimal cam curve design method.
  • the capping machine cam mechanism is mainly composed of a cam center shaft 10, a cam 20, a follower 30, a follower upper roller 40, and a follower lower roller 50.
  • the running cam 20 remains fixed, the cam central shaft 10 rotates relative to the cam 20, and the follower upper roller 40 and the follower lower roller 50 roll along the cam profile about the cam central axis 10, pushing the cam follower 30 up and down the hub. mobile.
  • the cam follower used for the capping machine needs to reach the corresponding displacement point at a corresponding angle to complete the action from the bottle opening, the capping, the bottle feeding to the capping.
  • These displacement points are referred to as key points, and the design tolerance for the key points is specified to be 1 mm. It is known that the cam mechanism is out of the bottle position point P1 point (0°) to P2 point (230°) until the end of the screw cap (290). °) For the two horizontal displacements that have been determined, the starting point of the screw cap (170°) to the point of P2 (230°) is also a predetermined motion law.
  • the capping machine Since the main working section of the existing cam is in the return period, the capping machine needs to complete the main capping, bottle feeding and capping in the returning period, and the design of the curve directly affects the capping speed of the capping machine and The quality of the screw cap is therefore optimized for the return curve, that is, the cam curve from the point P1 to the start of the cap.
  • the cam curve of the cam curve P1 point to the start point of the screw cap is designed by using the seventh-order polynomial multi-objective optimization method.
  • the cam curve can be expressed as:
  • the objective function can be written as:
  • V max cam curve taking a lower limit value, and no upper limit V max, V max does not require too much, V max of the commonly used standard cam curve design almost than 3 hours, in order to reduce the calculation
  • the upper limit of the optimization target V max can be taken as 3 when needed. Therefore, the feasible range of V max is 1 to 3.
  • the other AV max feasible domains take 4 to 12, the J max feasible domain takes 30 to 350, the Q max feasible domain takes 40 to 20000, and the AV max feasible domain takes 3 to 21.
  • the cam curve of the cam curve P1 to the starting point of the screw cap is designed by using the improved second-order harmonic optimization method.
  • the displacement function of the harmonic cam curve from point P1 to the beginning of the cap can be expressed as:
  • the decrease is 86.5%; the maximum jump J max is reduced from 1292 to 203.2, which is 84.27%; the maximum jump Q max is reduced from 13450 to 1344, which is reduced by 90%, and the dynamic load torque characteristic parameter AV max is 52.93. It dropped to 14.41, a decrease of 72.78%. All characteristic parameters have a large decline, and the maximum jump Q max is reduced by 90%, and the kinematics and dynamics performance are more obvious.
  • the maximum speed V max decreased from 2.002 to 1.9, which was reduced by 5.09%; the maximum acceleration A max decreased from 8.860 to 7.398, which was reduced by 16.0%; the maximum jump J max decreased from 68.34 to 53.59.
  • the optimized second-order harmonic cam curve is considered as the optimal cam curve.
  • the three-dimensional model can be imported into the UG processing module to generate the machining path, and the capping machine cam can be processed on the machining center.
  • the multi-objective optimization method of the present invention is very effective for the design of the cam curve.
  • different weight optimization cam curves can be given to the target according to different engineering conditions according to different importance of the optimization target.
  • the cam designed by the method of the invention has higher continuity of the cam curve, and when the rotation speed is increased, the mechanism will not be subjected to severe vibration, and the production efficiency of the capping machine is greatly improved.
  • the capping machine cam mechanism in the specific embodiment as an example, after the rotation speed is increased, the capping ability of the single capping head of the capping machine will be increased from the original 1800 caps per hour to 2600 caps per hour, and the capping The efficiency is increased by 30.8%. Since the cam mechanism is designed with 18 capping heads, a production line can complete the capping work of 46,800 bottles per hour, which will bring considerable benefits to the beverage filling enterprises.
  • the method of the invention is not limited to the cam of the capping machine, but is also applicable to cams in packaging machines such as filling machines and bottle blowing machines.
  • the cam curve design method of the invention can greatly improve the running performance of the mechanical system under the premise of high-speed driving of the machine, effectively control the unfavorable factors such as noise and vibration during the operation of the machine, and improve the operating efficiency.

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Abstract

基于多目标法的旋盖机凸轮曲线设计方法，属于旋盖机凸轮设计技术领域，为了解决现有重新设计凸轮曲线的方法不能根据重要程度来优化参数项，使凸轮机构运行稳定性差的问题。它包括：获取旋盖机凸轮为实现功能确定的关键点数据；将关键点数据无因次化，得到无因次时间T与无因次位移S；编写n次多项式拟合凸轮曲线位移函数，手动插入局部控制点，结合关键点位移的约束条件，利用最小二乘法，得到多项式拟合凸轮曲线表达式与图谱；选取凸轮曲线优化目标，设置权重系数，构建优化后的凸轮曲线。该方法用于凸轮曲线的设计。

Description

基于多目标法的旋盖机凸轮曲线设计方法 技术领域
本发明涉及基于多目标法的旋盖机凸轮曲线设计方法，属于旋盖机凸轮设计技术领域。
背景技术
凸轮机构几乎能够完成各种变速运动，而且能够按照需要调节速度，并且精度高、成本低，所以现代机械中应用凸轮机构比较多。伴随着社会不断地发展，人们对各类自动机械的效率、精度以及可靠性等方面的要求也不断的提高，另外由于凸轮的转速不断地加快，为了能够让凸轮运行的更加平稳、高效，工程师渐渐地开始重视凸轮机构的动力学特性，研发新型凸轮机构也朝着动力学、运动学相结合的方向非常快速地发展。研究出动力学、运动学性能都比较好的通用曲线已经成为设计凸轮机构的极重要的任务。
有许多方法可以提升凸轮机构的运动学与动力学性能，而研究凸轮机构的凸轮曲线是改善其运动学与动力学性能最有效的方式。传统研究凸轮曲线的方法是将目前常用的一些运动曲线进行组合以满足凸轮的实际运动需求，但是这种组合的运动曲线在高阶导数处并不连续，因此无法满足凸轮机构运行速度不断提高的需求。
目前旋盖机凸轮曲线的设计方法是：将旋盖机完成相关动作时的各个关键点用直线相连，并在关键点连接处倒圆。这种方法能满足凸轮曲线的速度连续，但是当凸轮高速运转时，由于存在柔性冲击，构件的动应力比较大，旋盖机在现场工作时噪声大、易磨损，运行效率很低。因此又采用多项式拟合、k阶谐波函数等方法重新设计凸轮曲线，这样获得的凸轮曲线特性参数如最大速度V max、最大加速度A max、最大跃度J max和最大跳度Q max等均较原凸轮曲线的特性参数值有所降低，并且其连续性与可导性随之提高，运动学性能与动力学性能大幅改善。但是，在利用多项式设计凸轮曲线时，经常会遇到局部位移控制条件过多的情况，运用多项式插值法会导致多项式幂次过高，不利于加工。在设计中，还通常期望凸轮曲线的特性参数值同时最优，即特性值都尽量小，但是很难实现。因此，这种重新设计凸轮曲线的方法并不能预先权衡这些参数，只能针对不同用途把特征值较小的项作为重点，并适当放宽其它特性参数，使所有参数特性值达到一个相对平衡的优化。
发明内容
本发明是为了解决现有重新设计凸轮曲线的方法不能根据重要程度来优化参数项，使凸轮机构运行稳定性差的问题，提供了一种基于多目标法的旋盖机凸轮曲线设计方法。
本发明所述一种基于多目标法的旋盖机凸轮曲线设计方法，它包括以下步骤：
步骤一：获取旋盖机凸轮为实现功能确定的关键点数据；
步骤二：将关键点数据无因次化，得到无因次时间T与无因次位移S；
步骤三：编写n次多项式拟合凸轮曲线位移函数，将拟合误差与设定的允许误差进行比较，若比较结果大于设定阈值，则手动插入局部控制点，直至比较结果处于设定阈值内；再结合关键点位移的约束条件，利用最小二乘法，得到多项式拟合凸轮曲线表达式与图谱；n为正整数；
步骤四：选取凸轮曲线优化目标，设置权重系数，构建优化后的凸轮曲线。
本发明所述又一种基于多目标法的旋盖机凸轮曲线设计方法，它包括以下步骤：
步骤一：获取旋盖机凸轮为实现功能确定的关键点数据；
步骤二：将关键点数据无因次化，得到无因次时间T与无因次位移S；
步骤三：编写凸轮曲线的拟合程序，基于改进的k阶谐波函数的凸轮曲线位移函数，确定k的阶数；加入局部控制点，利用最小二乘法和式来拟合关键点与局部控制点，求解获得凸轮曲线表达式及其图谱；
步骤四：选取凸轮曲线优化目标，设置权重系数，构建优化后的凸轮曲线。
本发明的优点：本发明相对于旋盖机原凸轮曲线设计方法与多项式插值的设计方法，其多项式拟合法从一开始就控制多项式幂次，能够在满足局部位移控制的条件下，减轻加工难度；谐波函数法可以无限次可导，且导函数还是谐波函数，可以有效保证凸轮曲线连续性，提高机构运行效率。对这两种曲线进行多目标优化后，不仅能够保证其优良性能，而且可以根据需求使设计过程更加符合实际，使各性能参数更加合理地提高。
经过多目标优化后的凸轮曲线，相比于原设计方法所得凸轮曲线的G1连续，可达到G2、G3甚至G4连续，曲线具有更好的光顺性，并且加速度波动幅度更小，能够有效减轻凸轮机构的噪声和振动，动力学性能得到改善。其中G1为切线连续，G2为曲率连续，G3为曲率变化率连续，G4为曲率变化率的变化率连续。
附图说明
图1是本发明具体实施方式所述旋盖机凸轮机构的结构示意图；
图2是图1中凸轮的示意图；
图3是7次多项式多目标优化法设计的时间与位移凸轮曲线图谱；
图4是7次多项式多目标优化法设计的时间与速度凸轮曲线图谱；
图5是7次多项式多目标优化法设计的时间与加速度凸轮曲线图谱；
图6是7次多项式多目标优化法设计的时间与跃度凸轮曲线图谱；
图7是7次多项式多目标优化法设计的时间与跳度凸轮曲线图谱；
图8是7次多项式多目标优化法设计的时间与动载转矩凸轮曲线图谱；
图9是改进2阶谐波函数多目标优化法设计的时间与位移凸轮曲线图谱；
图10是改进2阶谐波函数多目标优化法设计的时间与速度凸轮曲线图谱；
图11是改进2阶谐波函数多目标优化法设计的时间与加速度凸轮曲线图谱；
图12是改进2阶谐波函数多目标优化法设计的时间与跃度凸轮曲线图谱；
图13是改进2阶谐波函数多目标优化法设计的时间与跳度凸轮曲线图谱；
图14是改进2阶谐波函数多目标优化法设计的时间与动载转矩凸轮曲线图谱；
图15是本发明多项式和谐波凸轮曲线多目标优化前后时间与位移曲线对比图谱；
图16是本发明多项式和谐波凸轮曲线多目标优化前后时间与速度曲线对比图谱；
图17是本发明多项式和谐波凸轮曲线多目标优化前后时间与加速度曲线对比图谱；
图18是本发明多项式和谐波凸轮曲线多目标优化前后时间与跃度曲线对比图谱；
图19是本发明多项式和谐波凸轮曲线多目标优化前后时间与跳度曲线对比图谱；
图20是本发明多项式和谐波凸轮曲线多目标优化前后时间与动载转矩曲线对比图谱。
具体实施方式
具体实施方式一：下面结合图1至图20说明本实施方式，本实施方式所述基于多目标法的旋盖机凸轮曲线设计方法，它包括以下步骤：
步骤一：获取旋盖机凸轮为实现功能确定的关键点数据；
步骤二：将关键点数据无因次化，得到无因次时间T与无因次位移S；
步骤三：编写n次多项式拟合凸轮曲线位移函数，将拟合误差与设定的允许误差进行比较，若比较结果大于设定阈值，则手动插入局部控制点，直至比较结果处于设定阈值内；再结合关键点位移的约束条件，利用最小二乘法，得到多项式拟合凸轮曲线表达式与图谱；n为正整数；
步骤四：选取凸轮曲线优化目标，设置权重系数，构建优化后的凸轮曲线。
步骤一中，将旋盖机凸轮从动件在相应角度达到对应位移点的数据作为关键点，这些关键点一般支持旋盖机完成抓盖、进瓶、旋盖等功能；步骤三中，通过MATLAB编写多项式拟合程序，n次多项式拟合凸轮曲线位移函数可表示为：S＝C 0+C 1T+...+C nT n(本发明主要使用5次、6次、7次多项式),为了将拟合误差控制在一定范围内，编程时预先设定设计允许误差，当拟合误差与设定允许误差相差较大即超过设定阈值时，可手动插入局部控制点，减小误差，并有效控制凸轮曲线形状，使曲线走向更符合实际情况，然后结合对关键点位移 的约束条件，利用最小二乘法，得到多项式拟合法设计的凸轮曲线表达式与图谱。其中C 0为初始系数，C 1为第1系数，C n为第N系数。
具体实施方式二：下面结合图1至图20说明本实施方式，本实施方式所述基于多目标法的旋盖机凸轮曲线设计方法，它包括以下步骤：
步骤一：获取旋盖机凸轮为实现功能确定的关键点数据；
步骤二：将关键点数据无因次化，得到无因次时间T与无因次位移S；
步骤三：编写凸轮曲线的拟合程序，基于改进的k阶谐波函数的凸轮曲线位移函数，确定k的阶数；加入局部控制点，利用最小二乘法和式来拟合关键点与局部控制点，求解获得凸轮曲线表达式及其图谱；
步骤四：选取凸轮曲线优化目标，设置权重系数，构建优化后的凸轮曲线。
所述k大于或者等于2。
步骤一中，将旋盖机凸轮从动件在相应角度达到对应位移点的数据作为关键点，这些关键点一般支持旋盖机完成抓盖、进瓶、旋盖等功能；步骤三中，通过MATLAB编写凸轮曲线拟合程序，基于改进的k阶谐波函数的凸轮曲线位移函数可表示为：
Figure PCTCN2017119424-appb-000001
对于k的选取，由于k值越小，机构产生共振的可能性越小，而k＝1时，即为一阶，一阶的曲线性能与摆线曲线或简谐曲线运动规律相同，因此k一般先从2开始取整；同时为了控制局部形状以及更好的调节凸轮曲线，加入一系列局部控制点，利用最小二乘法和式来拟合关键点与局部控制点求解得到c n、ω n及
Figure PCTCN2017119424-appb-000002
的值，进而得到凸轮曲线表达式及其图谱。式中c n为振幅，ω n为角频率，
Figure PCTCN2017119424-appb-000003
为相位角。
本发明采用多目标优化的方式对多项式拟合或谐波函数拟合的凸轮曲线进行优化设计，不仅可以根据实际情况和要求预先权衡这些参数值，设置其重要程度，使之不同程度地得到优化，而且可以使优化后的特性值波动减小，这十分有利于凸轮机构运行时的稳定，并有效保证机构运行精度。
采用多目标优化时，优化目标之间一般会形成相互约束，导致所有目标不能够一起最优化。因此在应用多目标优化来解决实际问题的时候，一般会根据目标重要性的不一样，赋予各目标重要性对应的权值，将其中比较重要的目标当作主要的优化对象。因此为了相对较优的实现运动学和动力学特性，需要权衡各优化目标，使重要目标达到最优，其它目标较优。多目标优化函数一般可写为：
Figure PCTCN2017119424-appb-000004
式中f p(x)为单个需要优化的目标函数，s.t g i(x)>0为多目标优化不等式约束，s.t h i(x)＝0为等式约束。h i(x)为等式约束方程，m为正整数，I为正整数；
采用线性加权法来优化数个目标时，一般会根据目标重要性的不一样，根据重要程度，分别给p个目标函数f j(x)赋予一定的权系数λ 1，然后构建新的目标函数，即是所有的目标函数加权求和，求出新目标函数的最优值。其数学模型可以写为：
Figure PCTCN2017119424-appb-000005
以上两种实施方式中，步骤四优化特性参数值的方法均为：基于多目标优化的方法优化凸轮曲线。首先确定优化目标：通过比较最大速度V max、最大加速度A max、最大跃度J max、最大跳度Q max和动载转矩特性参数AV max等特性值，根据经验分辨该凸轮曲线的综合性能，因此选取最大速度V max、最大加速度A max、最大跃度J max和最大跳度Q max和动载转矩特性参数AV max作为凸轮曲线优化目标。然后设置权重系数：采用线性加权法，把权重系数λ i加入到最大速度V max、最大加速度A max、最大跃度J max和最大跳度Q max和动载转矩特性参数AV max等目标中，然后求和计算。在具体应用时，根据相关的设计要求，变化权值。
最后，可对比优化所得的凸轮曲线图谱，观察速度最大值、加速度最大值、跃度最大值、跳度最大值等以及其波动情况，验证优化效果。
本发明针对现有在设计旋盖机凸轮曲线时，仅采用直线将各关键点连接，并在连接处倒圆的设计方法所带来的缺陷，在保留原凸轮机构为实现功能而确定的关键点前提下，以多项式拟合或谐波函数拟合的方法为基础，采用多目标方式对凸轮曲线进行优化设计，提高凸轮曲线在关键点处的可导性和连续性，有效解决凸轮机构在运行时出现的冲击，磨损、疲劳破坏和噪声等问题。
本发明采用多目标优化的方法设计旋盖机凸轮曲线。首先，得到旋盖机为完成旋盖功能而确定的各个关键点(一般表达为某个角度需达到的某个位移)。其次，为了避免量纲带 来的影响，先将各关键点的表达方式转化为时间与位移的关系，再将时间与位移无因次化。最后，在控制曲线形状与误差的基础上适当添加局部控制点，用多目标优化的方式拟合关键点与局部控制点，输出凸轮曲线表达式及凸轮曲线图谱。
为了验证本发明方法的有效性，可以将优化后的凸轮曲线与单一的多项式拟合及谐波函数拟合设计的凸轮曲线进行对比，选出最优的凸轮曲线设计方法。
下面给出一个应用实例来具体阐述凸轮曲线的设计过程；
如图1所示，旋盖机凸轮机构主要由凸轮中心轴10、凸轮20、从动件30、从动件上滚子40与从动件下滚子50等部件构成。运行时凸轮20保持固定，凸轮中心轴10相对凸轮20旋转，从动件上滚子40与从动件下滚子50沿凸轮轮廓绕凸轮中心轴10滚动，推动凸轮从动件30沿轮毂上下移动。
如图2所示，使用的旋盖机凸轮从动件需在相应的角度到达对应的位移点，以完成从出瓶、抓盖、进瓶到旋盖的动作。将这些位移点称之为关键点，规定对关键点的设计允许误差为1mm，已知该凸轮机构出瓶位置点P1点(0°)至P2点(230°)直至旋盖结束点(290°)为已定的两段水平位移，旋盖开始点(170°)至P2点(230°)也为已定的一段运动规律。由于现有凸轮主要工作段在回程期，旋盖机需要在回程期完成主要的抓盖、进瓶和旋盖等动作，该段曲线设计的好坏直接影响了旋盖机的旋盖速度和旋盖质量，因此主要对回程期，即P1点至旋盖开始点的凸轮曲线进行优化设计。
采用具体实施方式一所述的方法，如图3至图8所示，利用7次多项式多目标优化法设计得出凸轮曲线P1点至旋盖开始点的凸轮曲线图谱。7次多项式位移曲线可写为：S＝x 1+x 2T 1+x 3T 2+x 4T 3+x 5T 4+x 6T 5+x 7T 6+x 8T 7，那么凸轮曲线可以表示为：
Figure PCTCN2017119424-appb-000006
其中，S为位移，T区间为0～1，x为系数，x＝[x 1,x 2,x 3,x 4,x 5,x 6,x 7,x 8]，V为速度，A为加速度，J为跃度，Q为跳度，AV为动载转矩特性参数；凸轮曲线优化目标为最大速度V max、 最大加速度A max、最大跃度J max和最大跳度Q max和动载转矩特性参数AV max。
那么f 1(x)＝V max＝max|V|，f 2(x)＝A max＝max|A|，f 3(x)＝J max＝max|J|，f 4(x)＝Q max＝max|Q|，f 5(x)＝AV max＝max|AV|。将最大速度V max、最大加速度A max权重系数设为0.35，其他特性参数权重系数设为0.1，那么λ 1＝λ 2＝0.35，λ 3＝λ 4＝λ 5＝0.35。
目标函数可以写为：
Figure PCTCN2017119424-appb-000007
凸轮曲线存在V max的下限值，下限值取1，并且V max没有上限，设计时不需要太大的V max，常用的标准凸轮曲线的V max几乎都比3小，为了减少计算所需要的时间，可以将优化目标V max上限值取为3。因此V max可行域取1～3。其它AV max可行域取4～12，J max可行域取30～350，Q max可行域取40～20000，AV max可行域取3～21。另外为了保证位移曲线在各个关键点的误差不大于1mm，设置各关键点的变化范围。图谱显示优化后的凸轮曲线V max＝1.95，A max＝9.465，J max＝203.2，Q max＝1344，AV max＝14.41。
采用具体实施方式二的方法，如图9至图14所示，利用改进2阶谐波优化法设计得出凸轮曲线P1点至旋盖开始点的凸轮曲线图谱。P1点至旋盖开始点段谐波凸轮曲线位移函数可以表示为：
S＝x 1sin(x 2T+x 3)+x 4sin(x 5T+x 6)，
仿照7次多项式凸轮曲线优化方法，可以得到改进2阶谐波优化凸轮曲线：
Figure PCTCN2017119424-appb-000008
图谱显示优化后的凸轮曲线V max＝1.9，A max＝7.396，J max＝53.59，Q max＝388.2，AV max＝8.932。
如图15至图20所示，将采用7次多项式优化的凸轮曲线与改进2阶谐波优化的凸轮曲线与未进行优化前的曲线对比可以发现，7次多项式拟合凸轮曲线在优化前的性能是最差的，各种特性值波动都较大，但是整体七次多项式拟合凸轮曲线经过优化后，最大速度V max由2.34 降到1.95，降低了16.67％；最大加速度A max由69.91降到了9.465，降低了86.5％；最大跃度J max由1292降到了203.2，降低了84.27％；最大跳度Q max由13450降到了1344，降低了90％，动载转矩特性参数AV max由52.93降到了14.41，降低了72.78％。所有特性参数下降幅度都很大，其中最大跳度Q max更是降低了90％，运动学和动力学性能提升比较明显。改进2阶谐波凸轮曲线优化后，最大速度V max由2.002降到1.9，降低了5.09％；最大加速度A max由8.806降到了7.398，降低了16.0％；最大跃度J max由68.34降到了53.59，降低了21.58％；最大跳度Q max由533降到了388.3，降低了27.15％，动载转矩特性参数AV max由10.98降到了8.911，降低了18.84％。所有特性参数下降幅度虽然不及多项式凸轮曲线优化，但是下降幅度也较大，其中最大跳度Q max更是降低了27.15％，运动学和动力学性能提升也是比较明显的。最终认为优化后的改进2阶谐波凸轮曲线为最优凸轮曲线，可以将其三维模型导入UG加工模块中，生成加工轨迹，在加工中心上完成该旋盖机凸轮的加工。
因此，本发明的多目标优化法用于凸轮曲线的设计非常有效，在实际工程设计中，可以根据优化目标重要性的不同，按照不一样的工程情况给目标赋予不同的权重优化凸轮曲线。
运用本发明所述方法设计的凸轮，由于凸轮曲线连续性提高，当转速提高时，机构将不会出现剧烈振动，旋盖机生产效率大大提高。以具体实施方案中的旋盖机凸轮机构为例，转速提高后，旋盖机单个旋盖头的旋盖能力将由原来每小时可旋盖1800个，提高至每小时可旋盖2600个，旋盖效率提升30.8％，由于该凸轮机构设计有18个旋盖头，因此一条生产线每小时可完成46800瓶饮料的旋盖工作，这将为饮料灌装企业带来十分可观的效益。
本发明方法不仅仅局限于旋盖机凸轮，对于灌装机、吹瓶机等包装机械中的凸轮也同样适用。本发明的凸轮曲线设计方法，可以在机器高速驱动的前提下，大幅度提高机械系统的运行性能，有效控制机器运行时噪声、振动等不利因素，提高运行效率。
本发明以较佳实施例公开如上，但其并非用以限定本发明，任何熟悉此技术的人员，在不脱离本发明的精神和范围内所做的改动与修饰，都属于本发明的保护范围以内。

Claims (9)

  1. 一种基于多目标法的旋盖机凸轮曲线设计方法，其特征在于，它包括以下步骤：
    步骤一：获取旋盖机凸轮为实现功能确定的关键点数据；
    步骤二：将关键点数据无因次化，得到无因次时间T与无因次位移S；
    步骤三：编写n次多项式拟合凸轮曲线位移函数，将拟合误差与设定的允许误差进行比较，若比较结果大于设定阈值，则手动插入局部控制点，直至比较结果处于设定阈值内；再结合关键点位移的约束条件，利用最小二乘法，得到多项式拟合凸轮曲线表达式与图谱；n为正整数；
    步骤四：选取凸轮曲线优化目标，设置权重系数，构建优化后的凸轮曲线。
  2. 根据权利要求1所述的基于多目标法的旋盖机凸轮曲线设计方法，步骤一中，将旋盖机凸轮从动件在相应角度达到对应位移点的数据作为关键点，这些关键点支持旋盖机完成抓盖、进瓶、旋盖功能。
  3. 根据权利要求1所述的基于多目标法的旋盖机凸轮曲线设计方法，步骤三中，通过MATLAB编写多项式拟合程序，n次多项式拟合凸轮曲线位移函数可表示为S＝C 0+C 1T+...+C nT n，其中C 0为初始系数，C 1为第1系数...C n为第N系数。
  4. 一种基于多目标法的旋盖机凸轮曲线设计方法，其特征在于，它包括以下步骤：
    步骤一：获取旋盖机凸轮为实现功能确定的关键点数据；
    步骤二：将关键点数据无因次化，得到无因次时间T与无因次位移S；
    步骤三：编写凸轮曲线的拟合程序，基于改进的k阶谐波函数的凸轮曲线位移函数，确定k的阶数；加入局部控制点，利用最小二乘法和式来拟合关键点与局部控制点，求解获得凸轮曲线表达式及其图谱；
    步骤四：选取凸轮曲线优化目标，设置权重系数，构建优化后的凸轮曲线。
  5. 根据权利要求4所述的基于多目标法的旋盖机凸轮曲线设计方法，其特征在于，步骤一中，将旋盖机凸轮从动件在相应角度达到对应位移点的数据作为关键点，这些关键点支持旋盖机完成抓盖、进瓶、旋盖功能。
  6. 根据权利要求4所述的基于多目标法的旋盖机凸轮曲线设计方法，其特征在于，步骤三中，通过MATLAB编写凸轮曲线的拟合程序，基于改进的k阶谐波函数的凸轮曲线位移函数可表示为：
    Figure PCTCN2017119424-appb-100001
    其中，c n为振幅，ω n为角频率，
    Figure PCTCN2017119424-appb-100002
    为相位角。
  7. 根据权利要求6所述的基于多目标法的旋盖机凸轮曲线设计方法，其特征在于，所述k大于或者等于2。
  8. 如权利要求1-7任一所述的基于多目标法的旋盖机凸轮曲线设计方法的应用。
  9. 一种基于权利要求1-7任一所述的基于多目标法的旋盖机凸轮曲线设计方法的设备。
PCT/CN2017/119424 2017-12-19 2017-12-28 基于多目标法的旋盖机凸轮曲线设计方法 Ceased WO2019119504A1 (zh)

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