柔性电子齿轮箱设计及精度控制方法研究
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摘要
电子齿轮箱是一种特殊的多轴同步运动控制技术,可以实现复杂的多轴耦合联动关系,具有传动比范围宽、传动精度高、调整方便等特点。电子齿轮箱的基本功能是代替机械传动链,实现两个或多个运动的定速比或变速比控制,保证各轴运动之间严格的同步关系。在数控齿轮加工机床中,采用电子齿轮箱控制模块,可以实现多坐标轴按照给定的约束关系进行同步运动。采用软件式电子齿轮箱控制策略,不仅可以实现滚齿机和插齿机等齿轮机床加工常规圆柱齿轮对多轴联动的要求,还能实现非圆齿轮加工的变比传动要求。在齿轮的展成加工过程中,齿轮形状的产生依赖于刀具与工件的耦合运动及进给附加运动的多轴联动关系,该运动关系由电子齿轮箱控制实现,其精度控制不仅包含刀具路径轨迹本身的轮廓精度,还包含从运动轴与主运动轴之间的同步精度。
本文设计了适用于齿轮数控展成加工的柔性电子齿轮箱结构,使其在自主研发的齿轮加工数控系统中实现,并深入研究了电子齿轮箱的精度控制方法。论文的主要研究内容如下：
1.通过对滚齿、插齿及非圆齿轮加工原理的分析和研究,推导出滚齿加工数学模型、插齿加工数学模型及非圆齿轮加工数学模型,构建了一种主从式复合结构的柔性电子齿轮箱,通过电子齿轮箱控制系数和数控轴定义的改变,形成滚齿加工电子齿轮箱、插齿加工电子齿轮箱(电子螺旋导轨)及非圆齿轮加工电子齿轮箱,提出柔性电子齿轮箱的概念,充分展现了软件式电子齿轮箱具有易改变、可重构的柔性特征。
2.提出将柔性电子齿轮箱与插补模块相结合,形成柔性电子齿轮箱插补模块,在嵌入式多CPU数控系统硬件平台上,采用模块化可重构思想,设计了数控系统总体架构,详细剖析了数控系统软件内部的信息流向,将柔性电子齿轮箱无缝地嵌入在齿轮加工数控系统中。在自行开发的嵌入式齿轮加工数控系统中实现了柔性电子齿轮箱的NC控制,通过程序运行实验数据与理论计算数据的对比分析,说明了柔性电子齿轮箱软件执行的正确性。
3.详细研究了数控系统常用轮廓精度和跟踪精度的基本控制策略,分析其控制结构和试用条件,建立了柔性电子齿轮箱的基本控制模型。根据柔性电子齿轮箱的结构特点,选择合适的增益匹配方式,推导出增益匹配数学模型,并在闭环数控实验平台上验证了增益匹配模型的有效性。考虑到增益匹配在一定程度上会带来跟踪精度的降低,结合柔性电子齿轮箱运动过程中刀具轨迹的特点,将交叉耦合控制模型应用在有多轴联动要求的进给轴之间,建立其交叉耦合补偿模型,并在闭环数控实验平台上验证了交叉耦合控制模型的有效性。由于本文所提出的电子齿轮箱控制模型对工作台回转轴的跟踪精度有较高要求,故研究了零相前馈控制方法,可以在精确建立系统模型并且系统超前信号已知的情况下实现单轴的高精度跟踪控制。
4.研究了由前馈控制器和交叉耦合控制器构成的复合式交叉耦合控制器的实现原理,并详细分析了该控制结构的设计步骤及系统稳定性,证明该控制器可以同时提高系统的轮廓精度和跟踪精度。以圆柱斜齿轮的轴向滚切为例,从加工工艺和几何的角度分析了电子齿轮箱控制误差的产生原因,并对相关误差的计算公式进行推导,结合主从式电子齿轮箱的结构特点与复合式交叉耦合控制器的设计原理,构建了复合式交叉耦合柔性电子齿轮箱结构模型,采用Matlab仿真的形式验证了复合式交叉耦合柔性电子齿轮箱具有较好的控制效果。.研究了模糊控制原理和生物免疫调节机理,将两者与PID控制相结合,构成模糊免疫PID控制器,并将这种智能控制算法应用在复合式交叉耦合电子齿轮箱的位置控制环节,仿真结果表明该控制方法可以进一步提高电子齿轮箱的控制精度。
5.将复合式交叉耦合柔性电子齿轮箱模型与主从式电子齿轮箱模型分别嵌入齿轮加工数控系统中,采用轴向滚切法进行实验,实验结果表明复合式交叉耦合柔性电子齿轮箱具有较好的控制精度,并在此基础上做了对角滚切实验及电子齿轮箱控制精度分析,验证了圆柱齿轮滚切加工电子齿轮箱软件具有精确的控制功能；采用电子螺旋导轨实现圆柱斜齿轮插齿加工运动控制实验,并对运动过程中各轴的位置轨迹及各轴的跟踪误差进行采集和分析,结果表明电子螺旋导轨可以精确实现圆柱斜齿轮的插齿加工运动控制；采用非圆滚齿加工电子齿轮箱实现一阶椭圆齿轮的加工运动控制,采用非圆插齿电子齿轮箱实现三阶椭圆齿轮的加工运动控制,并分别对运动过程数据进行了采样分析,实验结果表明柔性电子齿轮箱可以精确实现非圆齿轮加工所要求的多轴联动运动控制关系。
6.最后本文将电子齿轮箱控制软件成功的应用于自主研发的齿轮加工数控系统中,并将该数控系统与重庆机床厂生产的YS3118CNC5滚齿机床及天津第一机床总厂生产的YK5132B插齿机床配套。在自主研发的滚齿数控系统的控制下,完成了标准测试齿轮的加工,其中滚齿机床所加工的标准直齿轮精度可达5级,标准斜齿轮精度可达7级,插齿机床所加工的标准直齿轮精度可达6级。充分证明了本文所提出的柔性电子齿轮箱在实际加工应用中的高精度、可靠性和实用性。
Electronic Gearbox (EGB) is a special multi-axis synchronous motion control method. It not only can realize the complex coupling axes control, but also has many outstanding features, such as the wide range transmission ratio, high transmission precision and convenient adjustment. The basic function of Electronic Gearbox is to take the place of traditional mechanical transmission chain, implement two or more movements control with constant or variable speed ratio, and guarantee the strict synchronous relationship between axial movements. In CNC gear cutting machine tools, Electronic Gearbox control module can realize the synchronous multi-axis movements following the given constrained relationships. Using the software control strategy of Electronic Gearbox not only can satisfy the requirements of the cylindrical gear hobbing and gear shaping multi-axis movements, but also can satisfy the variable ratio transmission requirements of non-circular gear machining. Gear generating depends on the coupling movements of hob cutter axis, gear blank axis and the additional movement of feeding axes, which are controlled by the Electronic Gearbox. The gear machining accuracy contains both the contour precision of cutting tool path and the synchronization precision of tool axis and gear blank axis.
A flexible Electronic Gearbox for generating process was designed by this dissertation, and it was enforced in the home-made gear machining CNC. Then, its accuracy control methods were studied in depth. The main research content of the dissertation is as follows.
1. The mathematical models of gear hobbing, gear shaping and non-circular gear machining were deduced, through analyzing and studying the gear machining principle. A Master-slave flexible Electronic Gearbox structure was built. Gear hobbing Electronic Gearbox, gear shaping Electronic Gearbox (i.e. the Electronic screw guide) and the non-circular gear machining Electronic Gearbox can be obtained respectively, through changing the Electronic Gearbox coefficient and the CNC axes redefinition. Then, the concept of flexible Electronic Gearbox was proposed, and the changeability and reconfigurable flexible characteristics were fully demonstrated.
2. The flexible Electronic Gearbox interpolation module was proposed and the overall architecture of CNC software was designed based on the modularized and reconfigurable idea. The internal information flow of CNC software was analyzed in detail, and the flexible Electronic Gearbox was embedded in the gear machining CNC system seamlessly. The flexible Electronic Gearbox control through NC programming was realized in the CNC system which was developed by our institute. Through experimental verification, the control accuracy meets the requirements of gear machining inner-link transmission.
3. The common basic control strategy of contouring accuracy and tracking accuracy in CNC system, the control structures and application conditions were studied in detail, then, the basic control model of flexible Electronic Gearbox was established. An appropriate gain matching method was chosen and the gain matching mathematical model was deduced, according to the flexible Electronic Gearbox structure characteristic. The gain matching experiments were conducted on the closed-loop experimental platform, and the validity of the model was verified. Besides, considering that gain matching method can bring poor tracking precision to a certain extent, the cross-coupling compensation model was established combined with the characteristics of tool path in the process of Electronic Gearbox control movement. Then the cross-coupling control was used between the feed axes, the experiments were also conducted on the closed-loop experimental platform, and the validity of this model was verified. Finally, zero phase error tracking control method was studied because the Electronic Gearbox control model of this dissertation has higher request for slave axis tacking precision. It can realize uniaxial high-precision tracking control under the condition of the accurate system model has been established and the leading signal was known.
4. The realization principle of the integrated controller which consists of feedforward controller and cross-coupling controller was studied, and then its design procedures and stability were analyzed in detail. It was proved that the integrated controller can improve both contouring accuracy and tracking accuracy. In the case of cylindrical helical gear axial hobbing process, the causes of Electronic Gearbox control error were analyzed, and the relevant error calculation formulas were derived from the point of processing technology and geometric aspects. The flexible Electronic Gearbox cross-coupling controller (ECCC) was designed based on the structure characteristics of the common Master-slave Electronic Gearbox and the design principle of integrated controller. MATLAB simulation proved that the flexible Electronic Gearbox cross-coupling controller has a better control effect. What's more, the fuzzy control principle and biological immune regulation mechanism were studied, and a fuzzy immune PID controller was obtained which consists of fuzzy control, biological immune controller and PID controller. Then the intelligent control algorithm was used in the flexible Electronic Gearbox cross-coupling controller, the simulation results showed that the proposed control method can further improve the control precision of the Electronic Gearbox.
5. The flexible Electronic Gearbox cross-coupling controller and the common Master-slave Electronic Gearbox controller were embedded in the gear machining CNC system respectively. Then the axial hobbing experiments were conducted, the experiments results showed that the flexible Electronic Gearbox cross-coupling controller has better control precision. On this basis, the following experiments were conducted:diagonal hobbing motion control using the flexible hobbing Electronic Gearbox; cylindrical helical gear shaping motion control using electronic screw guide; one order elliptic gear machining motion control using non-circular gear hobbing Electronic Gearbox; and the three order elliptic gear machining motion control using non-circular gear shaping Electronic Gearbox. All the experiments results showed that the flexible Electronic Gearbox proposed by this dissertation has the expected control effect.
6. Finally, the flexible Electronic Gearbox control software was applied to the home-made gear machining CNC by the dissertation successfully. Then, the CNC systems were installed on the YS3118CNC5hobbing machine and the YK5132B gear shaping machine, which were produced by Chongqing Machine Tool Works and the Tianjin NO.1Machine Tool Works respectively. The standard testing gears were successfully machined by the two machine tools. Thereinto, the spur gear machined by the hobbing machine can reach precision grade5, the helical gear machined by the hobbing machine can reach precision grade7, and the spur gear machined by the shaping machine can reach precision grade6. The experimental results were fully proved that the proposed flexible Electronic Gearbox was high-precision, reliable and practicable in the actual engineering application.
本文设计了适用于齿轮数控展成加工的柔性电子齿轮箱结构,使其在自主研发的齿轮加工数控系统中实现,并深入研究了电子齿轮箱的精度控制方法。论文的主要研究内容如下：
1.通过对滚齿、插齿及非圆齿轮加工原理的分析和研究,推导出滚齿加工数学模型、插齿加工数学模型及非圆齿轮加工数学模型,构建了一种主从式复合结构的柔性电子齿轮箱,通过电子齿轮箱控制系数和数控轴定义的改变,形成滚齿加工电子齿轮箱、插齿加工电子齿轮箱(电子螺旋导轨)及非圆齿轮加工电子齿轮箱,提出柔性电子齿轮箱的概念,充分展现了软件式电子齿轮箱具有易改变、可重构的柔性特征。
2.提出将柔性电子齿轮箱与插补模块相结合,形成柔性电子齿轮箱插补模块,在嵌入式多CPU数控系统硬件平台上,采用模块化可重构思想,设计了数控系统总体架构,详细剖析了数控系统软件内部的信息流向,将柔性电子齿轮箱无缝地嵌入在齿轮加工数控系统中。在自行开发的嵌入式齿轮加工数控系统中实现了柔性电子齿轮箱的NC控制,通过程序运行实验数据与理论计算数据的对比分析,说明了柔性电子齿轮箱软件执行的正确性。
3.详细研究了数控系统常用轮廓精度和跟踪精度的基本控制策略,分析其控制结构和试用条件,建立了柔性电子齿轮箱的基本控制模型。根据柔性电子齿轮箱的结构特点,选择合适的增益匹配方式,推导出增益匹配数学模型,并在闭环数控实验平台上验证了增益匹配模型的有效性。考虑到增益匹配在一定程度上会带来跟踪精度的降低,结合柔性电子齿轮箱运动过程中刀具轨迹的特点,将交叉耦合控制模型应用在有多轴联动要求的进给轴之间,建立其交叉耦合补偿模型,并在闭环数控实验平台上验证了交叉耦合控制模型的有效性。由于本文所提出的电子齿轮箱控制模型对工作台回转轴的跟踪精度有较高要求,故研究了零相前馈控制方法,可以在精确建立系统模型并且系统超前信号已知的情况下实现单轴的高精度跟踪控制。
4.研究了由前馈控制器和交叉耦合控制器构成的复合式交叉耦合控制器的实现原理,并详细分析了该控制结构的设计步骤及系统稳定性,证明该控制器可以同时提高系统的轮廓精度和跟踪精度。以圆柱斜齿轮的轴向滚切为例,从加工工艺和几何的角度分析了电子齿轮箱控制误差的产生原因,并对相关误差的计算公式进行推导,结合主从式电子齿轮箱的结构特点与复合式交叉耦合控制器的设计原理,构建了复合式交叉耦合柔性电子齿轮箱结构模型,采用Matlab仿真的形式验证了复合式交叉耦合柔性电子齿轮箱具有较好的控制效果。.研究了模糊控制原理和生物免疫调节机理,将两者与PID控制相结合,构成模糊免疫PID控制器,并将这种智能控制算法应用在复合式交叉耦合电子齿轮箱的位置控制环节,仿真结果表明该控制方法可以进一步提高电子齿轮箱的控制精度。
5.将复合式交叉耦合柔性电子齿轮箱模型与主从式电子齿轮箱模型分别嵌入齿轮加工数控系统中,采用轴向滚切法进行实验,实验结果表明复合式交叉耦合柔性电子齿轮箱具有较好的控制精度,并在此基础上做了对角滚切实验及电子齿轮箱控制精度分析,验证了圆柱齿轮滚切加工电子齿轮箱软件具有精确的控制功能；采用电子螺旋导轨实现圆柱斜齿轮插齿加工运动控制实验,并对运动过程中各轴的位置轨迹及各轴的跟踪误差进行采集和分析,结果表明电子螺旋导轨可以精确实现圆柱斜齿轮的插齿加工运动控制；采用非圆滚齿加工电子齿轮箱实现一阶椭圆齿轮的加工运动控制,采用非圆插齿电子齿轮箱实现三阶椭圆齿轮的加工运动控制,并分别对运动过程数据进行了采样分析,实验结果表明柔性电子齿轮箱可以精确实现非圆齿轮加工所要求的多轴联动运动控制关系。
6.最后本文将电子齿轮箱控制软件成功的应用于自主研发的齿轮加工数控系统中,并将该数控系统与重庆机床厂生产的YS3118CNC5滚齿机床及天津第一机床总厂生产的YK5132B插齿机床配套。在自主研发的滚齿数控系统的控制下,完成了标准测试齿轮的加工,其中滚齿机床所加工的标准直齿轮精度可达5级,标准斜齿轮精度可达7级,插齿机床所加工的标准直齿轮精度可达6级。充分证明了本文所提出的柔性电子齿轮箱在实际加工应用中的高精度、可靠性和实用性。
Electronic Gearbox (EGB) is a special multi-axis synchronous motion control method. It not only can realize the complex coupling axes control, but also has many outstanding features, such as the wide range transmission ratio, high transmission precision and convenient adjustment. The basic function of Electronic Gearbox is to take the place of traditional mechanical transmission chain, implement two or more movements control with constant or variable speed ratio, and guarantee the strict synchronous relationship between axial movements. In CNC gear cutting machine tools, Electronic Gearbox control module can realize the synchronous multi-axis movements following the given constrained relationships. Using the software control strategy of Electronic Gearbox not only can satisfy the requirements of the cylindrical gear hobbing and gear shaping multi-axis movements, but also can satisfy the variable ratio transmission requirements of non-circular gear machining. Gear generating depends on the coupling movements of hob cutter axis, gear blank axis and the additional movement of feeding axes, which are controlled by the Electronic Gearbox. The gear machining accuracy contains both the contour precision of cutting tool path and the synchronization precision of tool axis and gear blank axis.
A flexible Electronic Gearbox for generating process was designed by this dissertation, and it was enforced in the home-made gear machining CNC. Then, its accuracy control methods were studied in depth. The main research content of the dissertation is as follows.
1. The mathematical models of gear hobbing, gear shaping and non-circular gear machining were deduced, through analyzing and studying the gear machining principle. A Master-slave flexible Electronic Gearbox structure was built. Gear hobbing Electronic Gearbox, gear shaping Electronic Gearbox (i.e. the Electronic screw guide) and the non-circular gear machining Electronic Gearbox can be obtained respectively, through changing the Electronic Gearbox coefficient and the CNC axes redefinition. Then, the concept of flexible Electronic Gearbox was proposed, and the changeability and reconfigurable flexible characteristics were fully demonstrated.
2. The flexible Electronic Gearbox interpolation module was proposed and the overall architecture of CNC software was designed based on the modularized and reconfigurable idea. The internal information flow of CNC software was analyzed in detail, and the flexible Electronic Gearbox was embedded in the gear machining CNC system seamlessly. The flexible Electronic Gearbox control through NC programming was realized in the CNC system which was developed by our institute. Through experimental verification, the control accuracy meets the requirements of gear machining inner-link transmission.
3. The common basic control strategy of contouring accuracy and tracking accuracy in CNC system, the control structures and application conditions were studied in detail, then, the basic control model of flexible Electronic Gearbox was established. An appropriate gain matching method was chosen and the gain matching mathematical model was deduced, according to the flexible Electronic Gearbox structure characteristic. The gain matching experiments were conducted on the closed-loop experimental platform, and the validity of the model was verified. Besides, considering that gain matching method can bring poor tracking precision to a certain extent, the cross-coupling compensation model was established combined with the characteristics of tool path in the process of Electronic Gearbox control movement. Then the cross-coupling control was used between the feed axes, the experiments were also conducted on the closed-loop experimental platform, and the validity of this model was verified. Finally, zero phase error tracking control method was studied because the Electronic Gearbox control model of this dissertation has higher request for slave axis tacking precision. It can realize uniaxial high-precision tracking control under the condition of the accurate system model has been established and the leading signal was known.
4. The realization principle of the integrated controller which consists of feedforward controller and cross-coupling controller was studied, and then its design procedures and stability were analyzed in detail. It was proved that the integrated controller can improve both contouring accuracy and tracking accuracy. In the case of cylindrical helical gear axial hobbing process, the causes of Electronic Gearbox control error were analyzed, and the relevant error calculation formulas were derived from the point of processing technology and geometric aspects. The flexible Electronic Gearbox cross-coupling controller (ECCC) was designed based on the structure characteristics of the common Master-slave Electronic Gearbox and the design principle of integrated controller. MATLAB simulation proved that the flexible Electronic Gearbox cross-coupling controller has a better control effect. What's more, the fuzzy control principle and biological immune regulation mechanism were studied, and a fuzzy immune PID controller was obtained which consists of fuzzy control, biological immune controller and PID controller. Then the intelligent control algorithm was used in the flexible Electronic Gearbox cross-coupling controller, the simulation results showed that the proposed control method can further improve the control precision of the Electronic Gearbox.
5. The flexible Electronic Gearbox cross-coupling controller and the common Master-slave Electronic Gearbox controller were embedded in the gear machining CNC system respectively. Then the axial hobbing experiments were conducted, the experiments results showed that the flexible Electronic Gearbox cross-coupling controller has better control precision. On this basis, the following experiments were conducted:diagonal hobbing motion control using the flexible hobbing Electronic Gearbox; cylindrical helical gear shaping motion control using electronic screw guide; one order elliptic gear machining motion control using non-circular gear hobbing Electronic Gearbox; and the three order elliptic gear machining motion control using non-circular gear shaping Electronic Gearbox. All the experiments results showed that the flexible Electronic Gearbox proposed by this dissertation has the expected control effect.
6. Finally, the flexible Electronic Gearbox control software was applied to the home-made gear machining CNC by the dissertation successfully. Then, the CNC systems were installed on the YS3118CNC5hobbing machine and the YK5132B gear shaping machine, which were produced by Chongqing Machine Tool Works and the Tianjin NO.1Machine Tool Works respectively. The standard testing gears were successfully machined by the two machine tools. Thereinto, the spur gear machined by the hobbing machine can reach precision grade5, the helical gear machined by the hobbing machine can reach precision grade7, and the spur gear machined by the shaping machine can reach precision grade6. The experimental results were fully proved that the proposed flexible Electronic Gearbox was high-precision, reliable and practicable in the actual engineering application.
引文
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