WO2020037747A1 - 一种面向动态精度的数控系统插补生成运动指令评价方法 - Google Patents

一种面向动态精度的数控系统插补生成运动指令评价方法 Download PDF

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WO2020037747A1
WO2020037747A1 PCT/CN2018/106300 CN2018106300W WO2020037747A1 WO 2020037747 A1 WO2020037747 A1 WO 2020037747A1 CN 2018106300 W CN2018106300 W CN 2018106300W WO 2020037747 A1 WO2020037747 A1 WO 2020037747A1
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time
frequency
command
interpolation
acceleration
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吕盾
赵艳超
赵万华
卢秉恒
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西安交通大学
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
    • G05B19/4103—Digital interpolation
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35026—Design of machine tool, of cnc machine

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  • the invention belongs to the technical field of numerically controlled machine tools, and in particular relates to a method for evaluating motion instructions generated by interpolation of a numerically controlled system with dynamic accuracy.
  • the CNC system as the brain of the machine tool, is an important part of the CNC machine tool.
  • the function of the CNC system is to interpolate the tool path of the part (represented by the NC code) to generate motion instructions for each axis of the machine tool.
  • the servo feed system of each axis of the machine tool receives these.
  • the movement instruction drives the relative movement of the tool and the workpiece to complete the part processing.
  • the motion instructions generated by interpolation In the case of high-feedrate and large-curvature tool path machining, the motion instructions generated by interpolation often contain more frequency components, causing the machine tool to produce dynamic errors such as significant following errors and mechanical resonances. In order to achieve high machining accuracy and surface quality of the part, in addition to the requirements of the geometric accuracy of the tool path, the motion instructions generated by interpolation must also make the CNC machine tool easy to achieve high dynamic accuracy. However, due to the differences in interpolation algorithms and speed planning strategies, different CNC systems interpolate the same machining program, and the generated motion instructions still have some differences. Therefore, it is necessary to evaluate the motion instructions generated by the CNC system interpolation, reflecting the ability of the CNC system to realize the dynamic accuracy of the machine tool.
  • the time-domain analysis method alone can be used to directly observe the change in the amplitude of the motion command of the interpolation production with time, but the frequency component in the motion command cannot be obtained; and the frequency-domain analysis method is used to analyze the motion command generated by interpolation. Only the frequency component in the entire motion instruction can be obtained, and the tool path position corresponding to the frequency component cannot be determined.
  • an object of the present invention is to provide a method for evaluating motion instructions for interpolation of a numerical control system of dynamic accuracy, which can simultaneously obtain the frequency component and the change relationship of its amplitude with time (tool path).
  • a method of evaluating motion instructions for a CNC system based on dynamic accuracy interpolation includes the following steps:
  • the time-frequency analysis method is used to time-frequency transform the commanded speed, commanded acceleration, and commanded acceleration sequence of each axis to obtain the commanded time-frequency chart, commanded time-frequency chart, and commanded acceleration of each axis.
  • the time-varying curve P ⁇ a (t) and its maximum value P ⁇ a max of the low-order mechanical natural frequency near the command acceleration are calculated respectively.
  • the time-varying curve P ⁇ j (t) and its maximum value P ⁇ j max of the frequency band near the natural frequency of the second-order machine reflects the ability of the CNC system to generate motion commands to suppress the resonance of the machine tool.
  • step 3 for each time section of the command speed time-frequency map, command acceleration time-frequency map, and command jerk time-frequency map, the frequency corresponding to the time when the amplitude drops to within 2% of the maximum amplitude is taken as The command bandwidth at this time.
  • the change curve P (t) of the command speed high frequency band ratio with time, that is, the tool path reflects the ability of the CNC system to generate motion instructions to achieve position following accuracy at different times, that is, at different tool path positions, and at the same time
  • the maximum value Pmax of the command speed in the high frequency band reflects the corresponding tool when the position tracking accuracy is the worst. Path location.
  • the calculation method of the command speed high frequency band ratio with time is calculated by taking the time axis as a reference, taking a cross section of each time of the command speed time-frequency map, and combining with the CNC machine tool feed The position loop bandwidth of the axis.
  • a represents the position loop bandwidth of the feed axis of the CNC machine tool, and is determined by identifying the feed axis of the CNC machine tool;
  • b represents the command bandwidth at time t i ;
  • h is the step size in the complex rectangle integration formula;
  • m and M are equal fractions of the respective integration interval in the complex rectangle integration formula;
  • the maximum value Pmax of the command speed high frequency band ratio is defined as the maximum value of the P (t) curve.
  • the commanded acceleration time-frequency diagram and the commanded acceleration time-frequency diagram reflect the ability of the CNC system to generate motion commands to suppress the resonance of the machine tool.
  • the commanded acceleration time-frequency diagram reflects the low frequency component, and the commanded acceleration time-frequency diagram reflects the high frequency. ingredient.
  • the change curve P ⁇ a (t) of the frequency ratio near the natural frequency of the commanded low-order mechanical frequency of the commanded acceleration reflects the ability of the CNC system interpolation to generate motion instructions to suppress the resonance of the machine tool caused by the natural frequency of the low-frequency natural frequency in the mechanical system of the CNC machine tool;
  • the maximum value of the frequency band near the natural frequency of the commanded acceleration near the natural frequency P ⁇ a max reflects the position of the corresponding tool path when the ability to suppress the middle and low frequency resonance is the worst.
  • the time-varying curve P ⁇ j (t) of the frequency band near the natural frequency of the commanded acceleration of the high-order machine reflects the ability of the CNC system to generate motion instructions to suppress the machine tool resonance caused by the high-frequency natural frequency of the CNC machine tool system;
  • the maximum value of the frequency band near the natural frequency of the commanded acceleration of the high-order machine P ⁇ j max reflects the corresponding tool path position when the ability to suppress high-frequency resonance is the worst.
  • the command jerk over time P ⁇ j (t) of The calculation method is: take the time axis as the reference, take the cross section of the command acceleration time-frequency diagram and the command jerk time-frequency diagram at each time, and calculate the start time t 0 to the end time t n
  • the ratio of time where the ratio of the frequency band near the natural frequency at time t i (t 0 ⁇ t i ⁇ t n ) is calculated as shown in formula (1-2):
  • c represents the low-order or high-order natural frequency of the mechanical part of the feed axis of the CNC machine tool, which is obtained by performing a modal test on the mechanical system;
  • b represents the command bandwidth at time t i ;
  • d represents the upper and lower limits of the frequency band near the natural frequency.
  • Integral width Time-frequency graph amplitude at time t i As a function of the frequency f, h is the step size in the complex rectangle integral formula; r and R are equal fractions of the respective integration interval in the complex rectangle integral formula.
  • the present invention proposes a new method for evaluating the quality of motion commands generated by CNC system interpolation, which can evaluate the ability of CNC system interpolation to generate motion instructions to achieve position following accuracy, and the suppression of machine tool resonance by CNC system interpolation generated motion instructions ability.
  • the present invention can provide a basis and basis for evaluating the advantages and disadvantages of interpolation strategies, speed planning strategies, and tool path planning for R & D manufacturers of CNC systems, and can also help CNC machine tool manufacturers and users to provide an evaluation basis when selecting CNC systems.
  • FIG. 1 is a flowchart of an evaluation method of the present invention.
  • FIG. 2 is a time-frequency diagram of the interpolation instruction speed according to the embodiment.
  • FIG. 3 is a time-frequency diagram of the interpolation instruction acceleration according to the embodiment.
  • FIG. 4 is a time-frequency diagram of the interpolation instruction jerk according to the embodiment.
  • FIG. 5 is a time-frequency cross-sectional view of the interpolation command speed according to the embodiment.
  • FIG. 6 is a schematic diagram of corresponding indexes of interpolation instruction speed according to the embodiment.
  • FIG. 7 is a time-frequency cross-sectional view of the interpolation command acceleration according to the embodiment.
  • FIG. 8 is a schematic diagram of corresponding indexes of interpolation instruction acceleration in the embodiment.
  • a method for evaluating motion instructions generated by a numerical control system for dynamic accuracy interpolation includes the following steps:
  • Time-frequency diagram of command acceleration and time-frequency diagram of command acceleration are Using time-frequency analysis methods such as wavelet analysis and short-time Fourier transform, time-frequency transformation is performed on the acquired command speed, command acceleration, and command jerk sequence for each axis to obtain the corresponding command speed time-frequency map of each axis.
  • Time-frequency diagram of command acceleration and time-frequency diagram of command acceleration are Using time-frequency analysis methods such as wavelet analysis and short-time Fourier transform, time-frequency transformation is performed on the acquired command speed, command acceleration, and command jerk sequence for each axis to obtain the corresponding command speed time-frequency map of each axis.
  • the command speed time-frequency diagram combined with the position axis bandwidth of the feed axis, and taking the time axis as a reference, take a section of each time of the command speed time-frequency diagram, calculate the command high frequency band ratio at each time, and get the high command speed.
  • the frequency band ratio changes with time, that is, the change curve P (t) of the tool path and the maximum value of the command speed high frequency band ratio Pmax, in order to reflect the ability of the CNC system to generate motion instructions to achieve position following accuracy;
  • the commanded acceleration time-frequency diagram and the commanded acceleration time-frequency diagram are taken at each time to calculate the instruction.
  • Time-varying curve of the frequency band ratio near the natural frequency of the low-order mechanical acceleration of the acceleration P ⁇ a (t) and its maximum value P ⁇ a max and time-varying curve of the frequency band ratio near the natural frequency of the high-order mechanical natural frequency of the commanded acceleration P ⁇ j ( t) and its maximum value P ⁇ j max which reflects the ability of the CNC system to generate motion commands to suppress the resonance of the machine tool.
  • step 3 for each time section of the command speed time-frequency map, command acceleration time-frequency map, and command jerk time-frequency map, the frequency corresponding to the time when the amplitude drops to within 2% of the maximum amplitude is taken as The command bandwidth at this time.
  • the CNC machine tool feed system generally adopts closed-loop control.
  • the position closed-loop system when the frequency of the input command exceeds the bandwidth of the servo feed system, the servo feed system cannot reproduce the input command well, resulting in the following error. Therefore, the time-frequency diagram of the command speed reflects the ability of the CNC system to generate motion instructions to achieve position following accuracy through interpolation.
  • the resonance of the machine tool during the machining process is an important cause of machining error and surface quality.
  • the command acceleration and command jerk reflect the inertial force and its changes during the feed process, and are important sources of excitation that cause mechanical resonance. Therefore, the commanded acceleration time-frequency diagram and the commanded acceleration time-frequency diagram reflect the ability of the CNC system to generate motion commands to suppress the resonance of the machine tool. Among them, the commanded acceleration time-frequency diagram reflects the low-frequency component, and the commanded acceleration time-frequency diagram reflects high. Frequency component.
  • the following uses an axis X axis of an NC machine tool as an example for description. After inputting a code to be processed in the CNC system, the X axis interpolation instructions are collected, and the interpolation instructions are analyzed using a time-frequency analysis method to obtain Figures 2 and 3 The command speed time-frequency diagram, command acceleration time-frequency diagram, and command jerk time-frequency diagram shown in FIG. 4.
  • a represents the position loop bandwidth of the feed axis of the CNC machine tool, and is determined by identifying the feed axis of the CNC machine tool;
  • b represents the command bandwidth at time t i ;
  • h is the step size in the complex rectangle integration formula;
  • m and M are equal fractions of the respective integration intervals in the complex rectangle integration formula.
  • c represents the low-order or high-order natural frequency of the mechanical part of the feed axis of the CNC machine tool, which is obtained by performing a modal test on the mechanical system;
  • b represents the command bandwidth at time t i ;
  • d represents the upper and lower limits of the frequency band near the natural frequency.
  • h is the step size in the complex rectangle integration formula, and r and R are equal fractions of the respective integration interval in the complex rectangle integration formula.

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Abstract

公开了一种面向动态精度的数控系统插补生成运动指令评价方法，该方法先采集经过插补后输出给各轴伺服系统的指令速度、指令加速度及指令加加速度序列；然后进行时频变换，得到相应的时频图；最后根据指令速度时频图计算指令速度高频段占比随时间即刀具路径的变化曲线，以此反映数控系统插补生成运动指令实现位置跟随精度的能力；根据指令加速度时频图、指令加加速度时频图分别计算指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线、指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线，以此反映数控系统插补生成运动指令对机床谐振的抑制能力。该方法能够同时获得频率成分及其幅值随时间的变化关系。

Description

一种面向动态精度的数控系统插补生成运动指令评价方法 技术领域
本发明属于数控机床技术领域，特别涉及一种面向动态精度的数控系统插补生成运动指令评价方法。
技术背景
数控系统作为机床的大脑，是数控机床的重要组成部分，数控系统的作用是将零件的刀具路径(用NC代码表示)插补生成机床各轴的运动指令，机床各轴伺服进给系统接收这些运动指令，驱动刀具和工件相对运动，完成零件加工。
在高进给率及大曲率刀具路径加工的场合，插补生成的运动指令往往包含较多的频率成分，使机床产生显著的跟随误差及机械谐振等动态误差。为了达到零件高的加工精度和表面质量，插补生成的运动指令除了满足刀具路径几何精度的要求之外，还须使数控机床易于实现高的动态精度。但由于插补算法和速度规划策略等算法的差异，不同数控系统对同一段加工程序进行插补，生成的运动指令仍然有一定的差异。因此需要对数控系统插补生成运动指令进行评价，反映数控系统对机床动态精度的实现能力。
插补生成运动指令是否易于数控机床实现高的动态精度，目前尚无系统的评价方法。当前，单独采用时域分析方法可以直观的观察插补生产运动指令幅值随时间的变化情况，但不能获得运动指令中的频率成分；而单独采用频域分析方法对插补生成运动指令进行分析仅能获得整段运动指令中的频率成分，不能确定频率成分对应的刀具路径位置。
发明内容
为了克服上述现有技术的缺点，本发明的目的在于提供一种面向动态精 度的数控系统插补生成运动指令评价方法，能够同时获得频率成分及其幅值随时间(刀具路径)的变化关系。
为了达到上述目的，本发明采取的技术方案为：
一种面向动态精度的数控系统插补生成运动指令评价方法，包括以下步骤：
1)在待评价数控系统中运行曲率剧烈变化刀具路径的NC代码，并采集经过插补后输出给各轴伺服系统的指令速度、指令加速度及指令加加速度序列；
2)采用时频分析方法，对采集到的每个轴的指令速度、指令加速度及指令加加速度序列进行时频变换，得到相应各轴指令速度时频图、指令加速度时频图及指令加加速度时频图；
3)根据指令速度时频图计算指令速度高频段占比随时间即刀具路径的变化曲线P(t)和指令速度高频段占比的最大值Pmax，以此反映数控系统插补生成运动指令实现位置跟随精度的能力；，
根据指令加速度时频图、指令加加速度时频图分别计算指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)及其最大值P ωa max、指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)及其最大值P ωj max，以此反映数控系统插补生成运动指令对机床谐振的抑制能力。
所述的步骤3)中对于指令速度时频图、指令加速度时频图及指令加加速度时频图中每个时刻截面，以幅值下降到最大幅值的2％以内时所对应的频率作为该时刻的指令频宽。
所述的指令速度高频段占比随时间即刀具路径的变化曲线P(t)反映了在不同时间即不同刀具路径位置处，数控系统插补生成运动指令实现位置跟随 精度的能力，且同一时刻占比越大，数控系统插补生成运动指令实现位置跟随精度的能力则越差；所述的指令速度高频段占比的最大值Pmax反映了实现位置跟随精度能力最差时，所对应的刀具路径位置。
所述的指令速度高频段占比随时间即刀具路径的变化曲线P(t)的计算方法为：以时间轴为基准，对指令速度时频图的每个时刻取截面，结合数控机床进给轴的位置环带宽，计算起始时刻t 0到终止时刻t n每时刻的指令高频段占比，其中t i(t 0<t i≦t n)时刻指令高频段占比的计算如式(1-1)所示：
Figure PCTCN2018106300-appb-000001
其中，a表示数控机床进给轴位置环带宽，通过对数控机床进给轴进行辨识确定；b表示t i时刻的指令频宽；
Figure PCTCN2018106300-appb-000002
表示t i时刻时频图幅值
Figure PCTCN2018106300-appb-000003
随频率f变化的函数关系；h为复化矩形积分公式中的步长；m和M分别为复化矩形积分公式中各自积分区间的等分数；最终得到各时刻高频段占比P随时间t的变化曲线P(t)。
对于所述的指令速度高频段占比的最大值Pmax，定义为P(t)曲线的最大值。
所述的指令加速度时频图与指令加加速度时频图反映数控系统插补生成运动指令对机床谐振的抑制能力，其中指令加速度时频图反应中低频成分，指令加加速度时频图反映高频成分。
所述的指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)反映数控系统插补生成运动指令对数控机床机械系统中低频段固有频率引起机床谐振的抑制能力；指令加速度的低阶机械固有频率附近频段占比的最大值P ωa max反映了对中低频谐振抑制能力最差时，所对应的刀具路径位置。
所述的指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)反映数控系统插补生成运动指令对数控机床机械系统高频段固有频率引起机床谐振的抑制能力；指令加加速度的高阶机械固有频率附近频段占比的最大值P ωj max反映了对高频谐振抑制能力最差时，所对应的刀具路径位置。
所述的指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)、指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)的计算方法为：以时间轴为基准，分别对于指令加速度时频图和指令加加速度时频图每个时刻取截面，结合数控机床机械部分固有频率，计算起始时刻t 0到终止时刻t n每时刻的占比，其中t i(t 0<t i≦t n)时刻固有频率附近频段占比的计算如式(1-2)所示：
Figure PCTCN2018106300-appb-000004
其中，c表示数控机床进给轴的机械部分低阶或高阶固有频率，通过对机械系统进行模态测试获得；b表示t i时刻的指令频宽；d表示固有频率附近频段积分上下限的积分宽度；
Figure PCTCN2018106300-appb-000005
表示t i时刻时频图幅值
Figure PCTCN2018106300-appb-000006
随频率f的变化的函数关系,h为复化矩形积分公式中的步长；r和R分别为复化矩形积分公式中各自积分区间的等分数。最终得指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)和指令加加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)；P ωa(t)曲线和P ωj(t)的最大值即为P ωa max和P ωj max。
本发明具有以下有益效果：
1、本发明提出了一种新的数控系统插补生成运动指令质量评价的方法，可以评价数控系统插补生成运动指令实现位置跟随精度的能力以及数控系统 插补生成运动指令对机床谐振的抑制能力。
2、本发明可以为数控系统研发生产商评价插补策略、速度规划策略以及刀具路径规划的优劣提供基础和依据，还能够帮助数控机床生产厂商以及用户在选择数控系统的时提供评价依据。
附图说明
图1为本发明评价方法的流程图。
图2为实施例插补指令速度时频图。
图3为实施例插补指令加速度时频图。
图4为实施例插补指令加加速度时频图。
图5为实施例插补指令速度时频截面图。
图6为实施例插补指令速度对应指标示意图。
图7为实施例插补指令加速度时频截面图。
图8为实施例插补指令加速度对应指标示意图。
具体实施方式
下面结合附图和实施例对本发明做详细描述。
参照图1，一种面向动态精度的数控系统插补生成运动指令评价方法，包括以下步骤：
1)在待评价数控系统中运行曲率剧烈变化刀具路径的NC代码，并采集经过插补后输出给各轴伺服系统的指令速度、指令加速度及指令加加速度序列；
2)采用小波分析、短时傅里叶变换等时频分析方法，对采集到的每个轴的指令速度、指令加速度及指令加加速度序列进行时频变换，得到相应各轴指令速度时频图、指令加速度时频图及指令加加速度时频图；
3)根据指令速度时频图，结合进给轴位置环带宽，以时间轴为基准，对 指令速度时频图的每个时刻取截面，计算各时刻的指令高频段占比，得到指令速度高频段占比随时间即刀具路径的变化曲线P(t)和指令速度高频段占比的最大值Pmax，以此反映数控系统插补生成运动指令实现位置跟随精度的能力；
根据指令加速度时频图和指令加加速度时频图，结合数控机床机械部分固有频率，以时间轴为基准，分别对于指令加速度时频图和指令加加速度时频图每个时刻取截面，计算指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)及其最大值P ωa max和指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)及其最大值P ωj max，以此反映数控系统插补生成运动指令对机床谐振的抑制能力。
所述的步骤3)中对于指令速度时频图、指令加速度时频图及指令加加速度时频图中每个时刻截面，以幅值下降到最大幅值的2％以内时所对应的频率作为该时刻的指令频宽。
数控机床进给系统一般采用闭环控制，对于位置闭环系统，当输入的指令的频宽超过伺服进给系统带宽时，伺服进给系统不能良好的复现输入指令，从而导致跟随误差的产生。因此，所述的指令速度时频图反映数控系统插补生成运动指令实现位置跟随精度的能力。
机床在加工过程中的谐振是影响加工误差和表面质量的一个重要原因。当数控系统插补生成运动指令的频率成分在机械部分固有频率附近幅值较大时，会激起机床的机械谐振。指令加速度和指令加加速度反映了进给过程中惯性力及其变化，是引起机械谐振的重要激励源。因此所述的指令加速度时频图与指令加加速度时频图反映数控系统插补生成运动指令对机床谐振的抑制能力，其中指令加速度时频图反应中低频成分，指令加加速度时频图反映高频成分。
下面以数控机床的一个轴X轴为实施例进行说明，在数控系统中输入待加工代码后采集X轴的插补指令，将插补指令运用时频分析方法进行分析，得到图2、图3和图4所示的指令速度时频图、指令加速度时频图及指令加加速度时频图。
对指令速度时频图各个时刻取截面图，如取t＝29.83s时刻的截面图如图5所示，再根据数控机床位置环带宽及频宽的定义，依据式(1-1)计算每个时刻的指令高频段占比：
Figure PCTCN2018106300-appb-000007
其中，a表示数控机床进给轴位置环带宽，通过对数控机床进给轴进行辨识确定；b表示t i时刻的指令频宽；
Figure PCTCN2018106300-appb-000008
表示t i时刻时频图幅值
Figure PCTCN2018106300-appb-000009
随频率f变化的函数关系；h为复化矩形积分公式中的步长；m和M分别为复化矩形积分公式中各自积分区间的等分数。最终得到相应指标高频段占比P随时间t的变化曲线P(t)，以及P(t)曲线的最大值P max，其所对应的时间Tv即实现位置跟随精度能力的最差位置，如图6所示。
再根据指令加速度时频图各个时刻取截面图，如取t＝29.83s时刻的截面图如图7所示，再根据数控机床位置环带宽及频宽的定义，依据式(1-2)计算每个时刻的固有频率附近频段占比：
Figure PCTCN2018106300-appb-000010
其中，c表示数控机床进给轴的机械部分低阶或高阶固有频率，通过对机械系统进行模态测试获得；b表示t i时刻的指令频宽；d表示固有频率附近频段积分上下限的积分宽度；
Figure PCTCN2018106300-appb-000011
表示t i时刻时频图幅值
Figure PCTCN2018106300-appb-000012
随频率f的变化的函数关系；h为复化矩形积分公式中的步长，r和R分别为复化矩形积分公式中各自积分区间的等分数。最终得到相应指标指令加速度的低阶机械固有 频率附近频段占比随时间的变化曲线P ωa(t)及其最大值P ωa max，其所对应的时间Ta即中低频谐振抑制能力的最差位置，如图8所示。与指令加速度类似，重复上述步骤可得指令加加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)及其最大值P ωj max。
对于其他轴的插补指令评价重复上述步骤，最后得到每个轴的指令速度、指令加速度和指令加加速度的评价指标，完成对数控系统插补生成运动指令的评价。

Claims (8)

  1. 一种面向动态精度的数控系统插补生成运动指令评价方法，其特征在于，包括以下步骤：
    1)在待评价数控系统中运行曲率剧烈变化刀具路径的NC代码，并采集经过插补后输出给各轴伺服系统的指令速度、指令加速度及指令加加速度序列；
    2)采用时频分析方法，对采集到的每个轴的指令速度、指令加速度及指令加加速度序列进行时频变换，得到相应各轴指令速度时频图、指令加速度时频图及指令加加速度时频图；
    3)根据指令速度时频图计算指令速度高频段占比随时间即刀具路径的变化曲线P(t)和指令速度高频段占比的最大值Pmax，以此反映数控系统插补生成运动指令实现位置跟随精度的能力；’
    根据指令加速度时频图、指令加加速度时频图分别计算指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)及其最大值P ωa max、指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)及其最大值P ωj max，以此反映数控系统插补生成运动指令对机床谐振的抑制能力。
  2. 根据权利要求1所述的一种面向动态精度的数控系统插补生成运动指令评价方法，其特征在于：所述的步骤3)中对于指令速度时频图、指令加速度时频图及指令加加速度时频图中每个时刻截面，以幅值下降到最大幅值的2％以内时所对应的频率作为该时刻的指令频宽。
  3. 根据权利要求1所述的一种面向动态精度的数控系统插补生成运动指令评价方法，其特征在于：所述的指令速度高频段占比随时间即刀具路径的变化曲线P(t)反映了在不同时间即不同刀具路径位置处，数控系统插补生成 运动指令实现位置跟随精度的能力，且同一时刻占比越大，数控系统插补生成运动指令实现位置跟随精度的能力则越差；所述的指令速度高频段占比的最大值Pmax反映了实现位置跟随精度能力最差时，所对应的刀具路径位置。
  4. 根据权利要求1所述的一种面向动态精度的数控系统插补生成运动指令评价方法，其特征在于：所述的指令速度高频段占比随时间即刀具路径的变化曲线P(t)的计算方法为：以时间轴为基准，对指令速度时频图的每个时刻取截面，结合数控机床进给轴的位置环带宽，计算起始时刻t 0到终止时刻t n每时刻的指令高频段占比，其中t i(t 0<t i≦t n)时刻指令高频段占比的计算如式(1-1)所示：
    Figure PCTCN2018106300-appb-100001
    其中，a表示数控机床进给轴位置环带宽，通过对数控机床进给轴进行辨识确定；b表示t i时刻的指令频宽；
    Figure PCTCN2018106300-appb-100002
    表示t i时刻时频图幅值
    Figure PCTCN2018106300-appb-100003
    随频率f变化的函数关系；h为复化矩形积分公式中的步长；m和M分别为复化矩形积分公式中各自积分区间的等分数；最终得到各时刻高频段占比P随时间t的变化曲线P(t)；对于所述的指令速度高频段占比的最大值Pmax，P(t)曲线的最大值即为最大值Pmax。
  5. 根据权利要求1所述的一种面向动态精度的数控系统插补生成运动指令评价方法，其特征在于：所述的指令加速度时频图与指令加加速度时频图反映数控系统插补生成运动指令对机床谐振的抑制能力，其中指令加速度时频图反应中低频成分，指令加加速度时频图反映高频成分。
  6. 根据权利要求1所述的一种面向动态精度的数控雄雌同插补生成运动指令评价方法，其特征在于：所述的指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)反映数控系统插补生成运动指令对数控机床 机械系统中低频段谐振的抑制能力；指令加速度的低阶机械固有频率附近频段占比的最大值P ωa max反映了对中低频谐振抑制能力最差时，所对应的刀具路径位置。
  7. 根据权利要求1所述的一种面向动态精度的数控系统插补生成运动指令评价方法，其特征在于：所述的指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)反映数控系统插补生成运动指令对数控机床机械系统高频段谐振的抑制能力；指令加加速度的高阶机械固有频率附近频段占比的最大值P ωj max反映了对高频谐振抑制能力最差时，所对应的刀具路径位置。
  8. 根据权利要求1所述的一种面向动态精度的数控系统插补生成运动指令评价方法，其特征在于：所述的指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)、指令加加速度的高阶机械固有频率附近频段占比随时间的变化曲线P ωj(t)的计算方法为：以时间轴为基准，分别对于指令加速度时频图和指令加加速度时频图每个时刻取截面，结合数控机床机械部分固有频率，计算起始时刻t 0到终止时刻t n每时刻的占比，其中t i(t 0<t i≦t n)时刻固有频率附近频段占比的计算如式(1-2)所示：
    Figure PCTCN2018106300-appb-100004
    其中，c表示数控机床进给轴的机械部分低阶或高阶固有频率，通过对机械系统进行模态测试获得；b表示t i时刻的指令频宽；d表示固有频率附近频段积分上下限的积分宽度；
    Figure PCTCN2018106300-appb-100005
    表示t i时刻时频图幅值
    Figure PCTCN2018106300-appb-100006
    随频率f的变化的函数关系；h为复化矩形积分公式中的步长；r和R分别为复化矩形积分公式中各自积分区间的等分数；最终得指令加速度的低阶机械固有频率附近频段占比随时间的变化曲线P ωa(t)和指令加加速度的低阶机械固有频率附近频段 占比随时间的变化曲线P ωj(t)；P ωa(t)曲线和P ωj(t)的最大值即为P ωa max和P ωj max。
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