摘要
随着科技的不断发展，各行各业对产品精度的要求越来越高。重型数控机床因其结构尺寸空间大、运动范围大，各零部件制造安装精度受限，因而会产生较大的几何误差，同时重型数控机床因其质量和惯量大，驱动系统所需功率较大，零部件发热较为严重，产生较为明显的热变形，因而形成较大的热误差，严重制约数控机床精度的提高。误差补偿技术是提高数控机床精度的一项重要技术手段，本文在对现有误差补偿技术进行分析和研究的基础上，结合“高档数控机床与基础制造装备”科技重大专项以及生产企业急需解决的滑枕热伸长误差较大等实际问题，针对重型数控机床在实施误差补偿技术时存在的技术难点，以重型数控落地铣镗床为研究对象，重点研究了综合误差建模、误差测量与辨识以及误差补偿实施等关键技术难题。
误差建模是误差补偿的关键技术之一，本文尝试采用共形几何代数原理建立数控机床的综合误差模型。首先借助共形几何代数中的几何积对刚体运动中的旋转运动和平移运动进行统一表达；然后采用共形几何代数法对三轴机床的误差元素重新划分为平移误差元和旋转误差元，并分析了多体系统中两相邻体之间的运动；接下来，针对无误差的机床理想运动和有误差的机床实际运动分别建立了相应的数学模型，在此基础上根据刀尖点和工件上正被切削的点在空间中是同一点推导了机床误差模型的一般表达式；最后，以重型数控落地铣镗床为例，建立了基于共形几何代数的误差模型，并对模型的精度进行了分析。
实施误差补偿之前还需要能够对所要补偿的误差进行测量与辨识，以便掌握误差的特点和规律。本文针对重型数控机床工作空间尺寸大、误差辨识难的现状，提出一种用于重型数控机床大尺寸空间误差测量与辨识的方法。该方法利用激光跟踪仪进行误差的测量，在对激光跟踪仪测量误差进行分析的基础上，提出利用共形几何代数法进行误差辨识的原理。最后以重型数控落地铣镗床为研究对象，进行了几何误差的测量与辨识实验，用最小二乘多项式拟合的方法建立了几何误差元素的数学模型。
重型数控落地铣镗床的热误差占了较大比例，本文首先针对企业急需解决的重型数控落地铣镗床滑枕热伸长误差较为明显的问题，提出并实现了一种重型数控落地铣镗床滑枕热伸长误差的实时在线检测与补偿系统。该系统避免了在滑枕上安装温度传感器，能够适应各种工况，它采用一种热膨胀系数几乎为零的因瓦合金杆作为检测标准，利用位移传感器直接在线实时测量出滑枕的热伸长变形量，并将其实时反馈给数控系统，从而实现重型数控机床滑枕热伸长误差的实时补偿。然后针对其余部分热变形严重的问题，提出了一种热误差分离与建模的新方法。该方法首先在机床上根据一定的原则布置适量的温度传感器以测量相应点的温度变化，并用激光跟踪仪测量热误差，然后对实验获得的误差数据，利用基于共形几何代数的综合误差模型进行几何误差与热误差的分离，以得到相应的热误差参数，同时结合有关的温度传感器优化布置策略，选出相应的热误差关键点，最后采用多元线性回归理论建立了热误差的数学模型。
误差补偿实施策略是误差补偿技术实现的关键，本文在分析研究综合误差补偿功能的基础上，提出了一种用于西门子840D数控系统的综合误差补偿实施策略，并开发了相应的补偿系统。该系统通过手轮偏置功能与数控系统进行实时交互，实现了补偿系统与数控系统的无缝集成。开发了误差补偿器的硬件系统和软件系统，研究了机床坐标位置读取的方法、关键点温度的采集方法以及第三手轮在西门子840D数控系统中的应用，为了实现并行处理，采用了多线程编程技术，实现了误差补偿系统和机床数控系统的联接。
设计了重型数控落地铣镗床误差模型验证与补偿实验，并取得了一定效果，为数控机床误差补偿技术的实际应用奠定了基础。
With the continual development of science and technology, the demands forproducts’ precision are higher and higher in various fields. As a result of their largestructures and movement ranges, heavy-duty CNC machine tools’ geometric errorsare obvious; and due to their weighty mass and higher driving power, they willgenerate much heat, consequently their thermal induced errors is also prominent.Error compensation technologies are concernful means of improving machinetools’ precision. In this thesis, existing error compensation technologies researchstatus were analyzed firstly, then combining Major National S&T Program andmanufacturing enterprises’ requirements, for example ram thermal elongation erroris obvious and so on, aiming at the problems when error compensation technologyis implemented for heavy-duty CNC machine tools, the error compensationtechnology of heavy-duty CNC floor-typed boring and milling machine tools,which includes error modeling, error measurement, error identification and errorcompensation implementation, was researched.
Error modeling is one of key technologies in error compensation field.Conformal geometric algebra theory was attempted to apply in the error modelingtechnology field, and a new error modeling method which was based on conformalgeometric algebra was proposed in this thesis. Firstly, rotations and translations ofrigid body movement was expressed as a uniform formula with the geometricproduct of conformal geometric algebra; then, components of errors in3-axesmachine tools were classified into translation components and rotation components;and the movement of adjacent bodies in multi-body system were researched. Idealmovement in which error movements wasn’t calculated and actual movements inwhich error movements was calculated were researched and modeled withconformal geometric algebra theory; and then the machine tool’s error model wasconstructed according to the tip of tool is the same with the point which is cuttingin the workpiece. Finally, take a heavy-duty CNC floor-typed boring and millingmachine tool as an example, error model based on conformal geometric algebrawas obtained and the precisions of the error model were researched.
To obtain the characteristic of machine tools’ error, error measurement anderror identification are needed firstly before error compensation are implemented.Researching the problems on measuring small errors in large movement ranges, anew measurement and identification method for heavy-duty CNC machine tools’large movement ranges was proposed, which was finished by measuring volumeerrors with a laser tracker firstly, then components of the errors were identified based on conformal geometric algebra model. Basing on the analyzing of themeasurement error for the laser tracker, the error identification principle wasproposed. Finally, geometric errors in a heavy-duty CNC floor-typed boring andmilling machine tool were measured and identified, and the mathematic models ofgeometric error components were constructed through least square polynomialfitting method.
Thermal errors are the main of heavy-duty CNC machine tools’ volume errors,and an on-line measuring and compensating system was proposed for the ramthermal elongation error firstly in this thesis. Temperature sensors mounted on theram were not required in this system which can be used in various operatingconditions. An invar pole whose thermal expand coefficient is near to zero wasused as a benchmark, and a displacement sensor, which could obtain ram’selongation value and sent it to CNC system, was installed in one end of invar pole.Then, a new thermal error modeling method was proposed. Firstly, suitabletemperature sensors were mounted on the machine tool, and thermal error weremeasured with a laser tracker, then to get thermal error parameters, thermal errorsobtained from the experiments were separated from geometric errors. At the sametime, basing on temperature sensors optimizing distribution strategies, key pointsof thermal errors were selected. Finally, a multiple linear regression model wasconstructed.
The implementation strategy of error compensation is another key technology.Basing on handwheel offset function of CNC system, a novel error compensationimplementing strategy were proposed, and an error compensator was developed torealize the error compensation implementing on machine tools with Siemens840DCNC systems, which communicates with CNC system by the handwheel offsetfunction and substitutes for electronic handwheel of CNC system. The errorcompensator’s hardware and software systems, in which coordinates positionsacquiring, temperature collecting and third handwheel application in Sinumerik840D were included, were researched. And multithread technique was used toparallel run to avoid CPU’s long-playing employment by one task, were developed.
Error model validation and compensation experiments on a heavy-duty CNCfloor-typed boring and milling machine tool were designed, which laid afoundation for applying error compensation technology in the industries.
引文
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