WO2016127826A1 - 曲线速度规划方法、装置及其数控加工路径数据处理方法 - Google Patents
曲线速度规划方法、装置及其数控加工路径数据处理方法 Download PDFInfo
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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
- G05B19/19—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 positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
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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
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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
- G05B19/416—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 control of velocity, acceleration or deceleration
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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
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/34—Director, elements to supervisory
- G05B2219/34141—B-spline, NURBS non uniform rational b-spline
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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
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/37—Measurements
- G05B2219/37347—Speed, velocity
Definitions
- the invention relates to the technical field of numerical control machining, in particular to a curve speed planning method and device based on NURBS curve interpolation and a numerical control processing path data processing method using NURBS curve interpolation speed planning.
- CAM computer-aided manufacturing
- NURBS non-uniform B-spline
- the back-tracking method or the two-way acceleration method is used to avoid the acceleration of the deceleration phase from exceeding the limit.
- the number of backtracking calculations is unpredictable in order to obtain a speed curve that meets the acceleration requirement, and there is no feasible estimation method for the deceleration of the velocity at the end of the acceleration phase at each retrospective, and only through multiple calculations.
- Temptation At the same time, after the backtracking, the interpolation point should be recalculated, and the speed of the interpolation point should be re-estimated.
- Such an algorithm is computationally intensive and time consuming, and cannot guarantee to complete the multi-interpolation point backtracking and recalculate in an interpolation period.
- the application space in real-time interpolation is limited.
- the two-way acceleration method when the initial speed difference between the two ends is large, the one with the larger initial speed stops the interpolation and waits for the other side to interpolate until the other side's interpolation speed reaches the requirement to meet the encounter. Since the two-way simultaneous interpolation is started, if the forward interpolation needs to wait for the reverse interpolation for more than one cycle in the actual machining, the forward interpolation speed and position will be caused. Uncontrollable, so the algorithm cannot be used in this case.
- the technical problem to be solved by the present invention is to provide a curve speed planning method and device based on NURBS curve interpolation and a numerical control processing path data processing method using NURBS curve interpolation speed planning, which can pre-calculate the interpolation of the acceleration in the deceleration phase beyond the limit. Point to avoid excessive speed at the end of the acceleration phase and cause the acceleration to exceed the limit.
- the present invention provides a method for processing numerically controlled machining path data, the method comprising: acquiring numerically controlled machining path data having a NURBS curve; and acquiring an acceleration a i in a parameter step size ⁇ u i on the NURBS curve; And comparing an acceleration a i around the NURBS curve with a maximum allowable acceleration to determine an acceleration sensitive point, and determining an acceleration sensitive interval according to the determined acceleration sensitive point; determining an intermediate point of the acceleration sensitive interval as the sensitive interval a boundary point of internal acceleration and deceleration; calculating a velocity value of the intermediate point as a target speed; and planning for accelerating and decelerating the acceleration sensitive interval according to the target speed to obtain a NC of the planned NURBS curve Processing path data.
- the step of comparing the acceleration of the NURBS curve with the maximum allowable acceleration to determine the acceleration sensitive point, and determining the acceleration sensitive interval according to the determined acceleration sensitive point comprises: calculating the curvature 1/ ⁇ i of the NURBS curve and to determine the maximum allowable speed profile according to the chord deviation ⁇ max constraints and limitations of the centripetal acceleration a max; and calculating each parameter step acceleration in ⁇ u i, and when the parameter step size ⁇ u i acceleration a i
- the end point of the parameter step corresponding to the acceleration with the smallest minimum allowable acceleration difference is determined as the acceleration sensitive point.
- determining the acceleration sensitive interval according to the determined acceleration sensitive point comprises: calculating the curvature 1/ ⁇ i of the NURBS curve and to determine the maximum allowable speed profile according to the chord deviation ⁇ max constraints and limitations of the centripetal acceleration a max; and calculating each parameter step acceleration in ⁇ u i, and when the parameter step size ⁇ u i acceleration a i
- the step of accelerating and decelerating the acceleration sensitive section according to the target speed to obtain the NC machining path data of the planned NURBS curve includes: determining whether the parameter corresponding to the interpolation point enters the acceleration a sensitive interval; and when it is determined that the parameter corresponding to the interpolation point enters the acceleration sensitive interval, starting from one end of the acceleration sensitive interval as a starting point to accelerate toward the intermediate point, and from the intermediate point to another The side end is decelerated as the end point.
- the present invention also provides a speed control method based on NURBS curve interpolation, the method comprising: calculating a curvature 1/ ⁇ i around a NURBS curve, and according to a constraint condition and a centripetal of the chord height error ⁇ max
- the limit of the acceleration a max determines the maximum allowable speed curve. Calculating the acceleration in each parameter step ⁇ u i and determining when the acceleration a i in the parameter step ⁇ u i is greater than the maximum allowable acceleration and the acceleration a i+n in the parameter step ⁇ u i+n is less than the maximum allowable acceleration
- the end point of the parameter step corresponding to the acceleration with the smallest allowable acceleration difference is the acceleration sensitive point.
- the maximum allowable speed curve is divided into multiple segments according to the minimum value, and the corresponding parameter value u mid is determined according to the intermediate point of the acceleration sensitive interval of each speed curve segment, and the velocity value of the intermediate point is calculated. It is determined whether the parameter u corresponding to the interpolation point enters the acceleration sensitive interval. And when it is determined that the parameter u corresponding to the interpolation point enters the acceleration sensitive interval, starting from one end point of the acceleration sensitive section as a starting point to accelerate to the intermediate point, and decelerating from the intermediate point to the other end point as an end point, Wherein, the intermediate point acceleration is 0.
- u i is the parameter value of the current interpolation point
- the numerator represents the velocity value
- the denominator represents the approximate replacement of the arc segment by the chord segment between the two interpolation points on the NURBS curve.
- V mid V m +a m (u mid -u m );
- V mid V m + n + a m + n (u mid - u m + n ).
- a m and a m+n are respectively accelerations corresponding to the two end points of the acceleration sensitive section of the velocity curve segment, and u m and u m+n are corresponding parameters, respectively.
- the value of v mid is the minimum value between the calculated value calculated by the second and third formulas and the maximum allowable speed.
- the starting point acceleration is a slope value of the starting point of the acceleration sensitive area, and the starting acceleration of decelerating to the other side end point at the intermediate point is 0, and the end point acceleration is a slope of the end point of the acceleration sensitive area.
- the present invention also provides a speed control apparatus based on NURBS curve interpolation, comprising: a maximum allowable speed curve determining unit for using a curvature rate 1/ ⁇ i and a string height error ⁇ max according to a NURBS curve.
- the limit condition and the limit condition of the centripetal acceleration a max determine the maximum allowable speed curve.
- Acceleration sensitive point determining unit an acceleration calculation parameters in step ⁇ u i, a i and the acceleration in the parameter determining step ⁇ u i is greater than the maximum permissible acceleration and the step size parameter in acceleration ⁇ u i + n a i + n
- the intermediate point speed value determining unit is configured to determine a corresponding parameter value u mid according to an intermediate point of the acceleration sensitive section of each speed curve segment into which the maximum allowable speed curve is divided into minimum values, and calculate a speed value of the intermediate point .
- an interpolation point calculation unit configured to determine whether the parameter u corresponding to the interpolation point enters the acceleration sensitive interval, and when determining that the parameter u corresponding to the interpolation point enters the acceleration sensitive interval, from one end of the acceleration sensitive interval As the starting point, the acceleration to the intermediate point is started, and the end point is decelerated from the intermediate point to the other end point, wherein the intermediate point acceleration is zero.
- the intermediate point speed value determining unit determines that the speed value of the intermediate point is the maximum allowable speed.
- the acceleration sensitive point determining unit calculates the acceleration in each parameter step size ⁇ ui by using the following first formula:
- u i is the parameter value of the current interpolation point
- the numerator represents the velocity value
- the denominator represents the approximate replacement of the arc segment by the chord segment between the two interpolation points on the NURBS curve.
- the velocity value of the intermediate point uses the following second and third formulas to calculate the velocity value of the intermediate point:
- V mid V m +a m (u mid -u m );
- V mid V m + n + a m + n (u mid - u m + n );
- a m and a m+n are respectively accelerations corresponding to the two end points of the acceleration sensitive section of the velocity curve segment, and u m and u m+n are respectively corresponding parameters; the value of v mid is passed through the second and third The minimum value between the calculated value calculated by the formula and the maximum allowable speed.
- the starting point acceleration is a slope value of the starting point of the acceleration sensitive area, and the initial acceleration decelerating to the other side end point at the intermediate point is 0, and the end point acceleration is a slope of the end point of the acceleration sensitive area. .
- the present invention further provides a data machine tool, comprising a numerical control system, a servo motor and an executing component, the data system is configured to: acquire numerical control machining path data with a NURBS curve; and obtain a parameter step size on the NURBS curve Acceleration a i in ⁇ u i ; comparing the acceleration a i around the NURBS curve with the maximum allowable acceleration to determine an acceleration sensitive point, and determining an acceleration sensitive interval according to the determined acceleration sensitive point; determining the middle of the acceleration sensitive interval a point as a demarcation point of acceleration and deceleration in the sensitive interval; calculating a velocity value of the intermediate point as a target speed; and planning acceleration and deceleration of the acceleration sensitive interval according to the target speed to obtain
- the NC machining path data of the planned NURBS curve; the servo motor receives the NC machining path data of the planned NURBS curve, and controls the execution component to perform NC machining according to the received NC machining path data.
- the step of comparing the acceleration of the NURBS curve with the maximum allowable acceleration to determine the acceleration sensitive point, and determining the acceleration sensitive interval according to the determined acceleration sensitive point comprises: calculating the curvature 1/ ⁇ i of the NURBS curve And determining the maximum allowable speed curve according to the constraint condition of the chord height error ⁇ max and the constraint condition of the centripetal acceleration a max ; calculating the acceleration a i in each parameter step ⁇ u i and the acceleration a in the parameter step ⁇ u i When i is greater than the maximum allowable acceleration and the acceleration a i+n in the parameter step size ⁇ u i+n is less than the maximum allowable acceleration, determining the end point of the parameter step corresponding to the acceleration with the smallest minimum allowable acceleration difference is acceleration sensitivity Point and determine the acceleration sensitive interval based on the determined acceleration sensitive point.
- the step of calculating the velocity value of the intermediate point comprises: dividing the maximum allowable speed curve into a plurality of segments according to a minimum value, and determining a corresponding parameter value according to an intermediate point of the acceleration sensitive interval of each velocity curve segment. Mid , and calculate the velocity value of the intermediate point.
- u i is the parameter value of the current interpolation point
- the numerator represents the velocity value
- the denominator represents the approximate replacement of the arc segment by the chord segment between the two interpolation points on the NURBS curve
- V mid V m +a m (u mid -u m );
- V mid V m + n + a m + n (u mid - u m + n );
- a m and a m+n are respectively accelerations corresponding to the two end points of the acceleration sensitive section of the velocity curve segment, and u m and u m+n are respectively corresponding parameters; the value of v mid is passed through the second and third The minimum value between the calculated value calculated by the formula and the maximum allowable speed.
- the step of accelerating and decelerating the acceleration sensitive section according to the target speed to obtain the NC machining path data of the planned NURBS curve includes: determining whether the parameter corresponding to the interpolation point enters the acceleration a sensitive interval; when it is determined that a parameter corresponding to the interpolation point enters the acceleration sensitive interval, starting from an end point of the acceleration sensitive interval as a starting point to accelerate toward the intermediate point, and from the intermediate point to the other side The endpoint decelerates as an end point.
- the invention provides a curve speed planning method and device based on NURBS curve interpolation and a numerical control processing path data processing method using NURBS curve interpolation speed planning, by predicting acceleration sensitive points and using the system in an acceleration-sensitive interval.
- the maximum acceleration is re-executed for S-type speed planning. Therefore, NURBS interpolation can be accelerated and decelerated in strict accordance with the new speed curve without worrying about speed and acceleration exceeding the limit.
- the new speed curve deviates from the original maximum allowable speed curve only at the acceleration sensitive point, the machining efficiency is maximized under the speed and acceleration limits.
- the algorithm can be interpolated without backtracking, and there is no need to wait for the interpolation result of one party. The calculation amount is light, and the real-time performance of the interpolation is guaranteed.
- FIG. 1 is a schematic diagram showing a relationship between a parameter u and a NURBS curve curvature and a maximum allowable speed function in the prior art
- FIG. 2 is a schematic flow chart of a method for processing data of a numerical control processing path according to an embodiment of the present invention
- FIG. 3 is a schematic flow chart of a speed control method based on NURBS curve interpolation according to another embodiment of the present invention.
- FIG. 4 is a schematic diagram of determining an acceleration sensitive point according to a parameter u and a maximum allowable speed according to an embodiment of the present invention
- FIG. 5 is a schematic diagram of speed planning in an embodiment of the present invention.
- FIG. 6 is a schematic diagram of functional modules of a speed control device based on NURBS curve interpolation according to an embodiment of the present invention
- FIG. 7 is a schematic structural diagram of a numerical control machine tool according to an embodiment of the present invention.
- the NURBS curve is a piecewise polynomial curve, usually written as a unary function form of the parameter u :
- N i,p (u) is a non-uniform rational B-spline basis function determined by the node vector U and satisfies the Cox-de Boor recursive relations (2) and (3):
- Each parameter u corresponds to a point on the NURBS curve. Therefore, the task of NURBS curve interpolation is to select a series of u in the parameter domain and calculate the points on the curves corresponding to these u (ie the machining segments in the machining path of the tool).
- the parameter value of the current point is u(t i ), so the interpolation point after an interpolation period T corresponds to the following parameter Taylor(u i ):
- NURBS curve interpolation is usually implemented by approximating the arc segment between the two interpolation points u i and u i+1 , and the maximum distance between the string segment and the arc segment is the maximum interpolation string height error.
- the maximum value of the feed rate needs to be limited.
- the arc height approximation method can be used to obtain the string height error:
- ⁇ L i1 is the feed step size under acceleration and deceleration constraints, a max maximum normal acceleration, and:
- the maximum speed allowed at the interpolation point can be obtained by calculating the curvature of the curve of the interpolation point.
- the speed from the current interpolation point to the next interpolation point cannot exceed the maximum speed allowed.
- FIG. 2 is a schematic flowchart of a speed control method based on NURBS curve interpolation according to an embodiment of the present invention.
- step S10 the NC machining path data with the NURBS curve is acquired.
- step S11 the acceleration a i in the parameter step size ⁇ u i on the NURBS curve is obtained.
- Step S12 comparing the accelerations around the NURBS curve with the maximum allowable acceleration to determine an acceleration sensitive point, and determining an acceleration sensitive interval according to the determined acceleration sensitive point.
- the maximum allowable acceleration is determined according to the curvature 1/ ⁇ i of the NURBS curve, the constraint condition of the chord height error ⁇ max , and the constraint condition of the centripetal acceleration a max . Determining an acceleration corresponding to the minimum allowable acceleration difference when the acceleration a i in the parameter step ⁇ u i is greater than the maximum allowable acceleration and the acceleration a i+n in the parameter step ⁇ u i+n is less than the maximum allowable acceleration
- the endpoint of the parameter step is the acceleration sensitive point.
- step S13 an intermediate point of the acceleration sensitive interval is determined as a demarcation point of acceleration and deceleration in the sensitive interval.
- step S14 the velocity value of the intermediate point is calculated as the target speed.
- Step S15 Perform acceleration and deceleration planning on the acceleration sensitive section according to the target speed, to obtain NC machining path data of the planned NURBS curve.
- the end point of the acceleration sensitive section is used as a starting point to accelerate toward the intermediate point, and the intermediate point is decelerated from the intermediate point to the other end point, thereby realizing Plan the acceleration and deceleration of the acceleration sensitive section.
- FIG. 3 is a schematic flowchart of a speed control method based on NURBS curve interpolation according to another embodiment of the present invention.
- Step S20 calculating a curvature 1/ ⁇ i around the NURBS curve, and determining a maximum allowable speed according to a constraint condition of the chord height error ⁇ max (formula (5)) and a constraint condition of the centripetal acceleration a max (formula (9)) Curve (ie maximum allowable velocity V max throughout the NURBS curve).
- step S21 the acceleration in each parameter step size ⁇ u i is calculated and compared with the maximum allowable acceleration. If the acceleration a i in the parameter step size ⁇ u i is greater than the maximum allowable acceleration, and the acceleration a i+n in ⁇ u i+n is less than the maximum allowable acceleration, then the parameter step corresponding to the acceleration with the smallest minimum allowable acceleration difference is determined.
- the long endpoint is the acceleration sensitive point.
- u i is the parameter value of the current interpolation point
- the numerator represents the velocity value
- the denominator represents the approximate replacement of the arc segment by the chord segment between the two interpolation points on the NURBS curve. Since the string segment is smaller than the arc segment length, the calculated value of the acceleration is larger than the true value. If the required acceleration value is less than the maximum allowable acceleration, then the true value of the acceleration will not exceed the limit of the maximum allowable acceleration.
- an acceleration sensitive point as shown in FIG. 3, such as a star mark point, can be obtained.
- Step S22 dividing the maximum allowable speed curve determined in step S20 into multiple segments according to the minimum value (the maximum allowable speed curve for each segment is hereinafter referred to as the speed curve segment), that is, the velocity curve between each two velocity troughs is one segment (full curve The starting point and the ending point are also considered as speed troughs).
- the acceleration sensitive point of the segment of the velocity curve is determined, and the corresponding acceleration-sensitive interval (hereinafter referred to as the sensitive interval) and the parameter value u mid corresponding to the intermediate point of the sensitive interval are determined, and the velocity value of the intermediate point is calculated.
- the two endpoints of the sensitive interval are respectively extended according to the current slope and intersected at one point, and the intersection is called an intermediate point, and the parameter value u mid corresponding to the intermediate point is the accelerated interpolation stage of the speed curve segment.
- the end point is also the starting point for the deceleration interpolation phase.
- V mid V m +a m (u mid -u m ) (11)
- V mid V m+n +a m+n (u mid -u m+n ) (12)
- a m and a m+n are respectively accelerations corresponding to the two end points of the acceleration sensitive section of the velocity curve segment, and u m and u m+n are corresponding parameters, respectively.
- the section included in 1 to 2 points, 3 to 4 points, 5 to 6 points, 7 to 8 points, 9 to 10 points, and 11 to 12 points is a sensitive section.
- the sensitive interval between 3 to 4 points and 5 to 6 points is taken as an example.
- step S23 real-time interpolation is started, and the parameter u corresponding to the interpolation point is determined according to formula (4) and it is determined whether the parameter u enters the determined sensitive interval. If yes, go to step S24, otherwise, go to step S25.
- Step S24 starting from the end of one side (such as the left side) of the sensitive section, accelerating to the intermediate point, and after reaching the intermediate point, decelerating to the other side (such as the right side), wherein the intermediate point acceleration is 0. Then the process ends.
- the starting point acceleration is the slope value of the point
- the acceleration and the jerk are both maintained as required by the formula (8), and the initial acceleration is 0, and the final acceleration is the slope of the other side (right side) end point.
- the acceleration from the left side to the middle point of the sensitive section is a process of type S acceleration
- the initial acceleration is not 0,
- the final acceleration is 0,
- the final speed must not exceed v mid
- the acceleration end point must not exceed u mid .
- each cycle of the acceleration process is used as a basis for whether or not to use positive acceleration, and finally can be flexibly accelerated to the intermediate point.
- the process of deceleration from the intermediate point is also a process of S-type deceleration.
- the initial acceleration is 0, the final acceleration is not 0, the final velocity is as close as possible to v 6 , and the acceleration end point must not exceed u 6 .
- the user-specified feed rate limit causes the maximum allowable speed curve to appear in a uniform speed range (for example, the point 4 to point 5 in Fig. 4), it is likely that the acceleration from the end point of the sensitive section to the uniform speed section in a short time has already occurred. At the end, the efficiency loss due to the acceleration limitation is reduced to a minimum.
- the color deepening is the speed planning from the end of the sensitive interval to the intermediate point. This means that starting from the adjacent velocity valley on the left side of the color deepening line segment, acceleration along the color un-deep line segment and the color deepening line segment is both satisfying the speed limit and satisfying the acceleration limit.
- step S25 the interpolation point is calculated according to the maximum allowable speed according to the formula (8). Then the process ends.
- FIG. 6 is a schematic diagram of functional modules of a speed control device based on NURBS curve interpolation according to an embodiment of the present invention.
- the device 30 includes:
- the maximum allowable speed curve determining unit 31 is configured to determine a maximum allowable speed curve based on the curvature 1/ ⁇ i of the NURBS curve and the constraint condition of the chord height error ⁇ max and the constraint condition of the centripetal acceleration a max .
- the acceleration sensitive point determining unit 32 is configured to calculate the acceleration in each parameter step size ⁇ u i , and determine that the acceleration a i in the parameter step size ⁇ u i is greater than the maximum allowable acceleration and the acceleration a i+ in the parameter step size ⁇ u i+n When n is less than the maximum allowable acceleration, the end point of the parameter step corresponding to the acceleration with the smallest difference of the maximum allowable acceleration is determined to be an acceleration sensitive point.
- the intermediate point speed value determining unit 33 is configured to determine a corresponding parameter value u mid according to an intermediate point of the acceleration sensitive section of each speed curve segment into which the maximum allowable speed curve is divided into minimum values, and calculate the speed of the intermediate point value. as well as
- the interpolation point calculation unit 34 is configured to determine whether the parameter u corresponding to the interpolation point enters the acceleration sensitive interval, and when determining that the parameter u corresponding to the interpolation point enters the acceleration sensitive interval, from one end of the acceleration sensitive interval As the starting point, the acceleration to the intermediate point is started, and the end point is decelerated from the intermediate point to the other end point, wherein the intermediate point acceleration is zero.
- FIG. 7 is a schematic structural diagram of a numerical control machine tool according to an embodiment of the present invention.
- the numerical control machine tool 70 includes a numerical control system 71, a servo motor 72, and an executing unit 73.
- the numerical control system 71 is configured to acquire numerical control machining path data with a NURBS curve; acquire an acceleration a i in the parameter step size ⁇ u i on the NURBS curve; compare the acceleration a i around the NURBS curve with a maximum allowable acceleration to determine Acceleration sensitive point, and determining an acceleration sensitive interval according to the determined acceleration sensitive point; determining an intermediate point of the acceleration sensitive interval as a demarcation point of acceleration and deceleration in the sensitive interval; calculating a velocity value of the intermediate point to As the target speed; the acceleration and deceleration planning of the acceleration sensitive section is performed according to the target speed, to obtain the NC machining path data of the planned NURBS curve, and the NC machining path data of the planned NURBS curve is sent to Servo motor 72.
- the numerical control system 71 can plan the numerical control processing path data by using FIG. 1 and its corresponding method embodiment. Moreover, the numerical control system 71 specifically determines the acceleration, the acceleration sensitive point, the velocity value of the intermediate point in each parameter step size ⁇ ui, and the acceleration and deceleration of the acceleration sensitive interval according to the target speed. Corresponding to the method embodiment. That is, the numerical control system 71 can also perform the above-described embodiment shown in FIG. 2 to perform speed control based on NURBS curve interpolation, thereby implementing the planning of the above-mentioned numerical control processing path data.
- the servo motor 72 receives the NC machining path data of the planned NURBS curve, and performs numerical control machining according to the received NC machining path data control executing unit 73, so that the executing unit 73 performs machining according to the planned NC machining path.
- the executing component 73 can Think of industrial robots, tools and other parts required for processing.
- the invention provides a curve speed planning method and device based on NURBS curve interpolation and a numerical control processing path data processing method using NURBS curve interpolation speed planning, by predicting acceleration sensitive points and using the system in an acceleration-sensitive interval.
- the maximum acceleration is re-executed for S-type speed planning. Therefore, NURBS interpolation can be accelerated and decelerated in strict accordance with the new speed curve without worrying about speed and acceleration exceeding the limit.
- the new speed curve deviates from the original maximum allowable speed curve only at the acceleration sensitive point, the machining efficiency is maximized under the speed and acceleration limits.
- the algorithm can be interpolated without backtracking, and there is no need to wait for the interpolation result of one party. The calculation amount is light, and the real-time performance of the interpolation is guaranteed.
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Abstract
一种基于NURBS曲线插补的曲线速度规划方法、装置及应用NURBS曲线插补速度规划的数控加工路径数据处理方法,该处理方法包括:获取具有NURBS曲线的数控加工路径数据(S10),获取所述NURBS曲线上参数步长Δu i内的加速度a i(S11);将各加速度与最大允许加速度比较确定加速度敏感点和敏感区间(S12);确定加速度敏感区间的中间点作为加减速分界点(S13);计算中间点的速度值作为目标速度(S14);根据目标速度对加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据(S15)。该处理方法能够预先计算减速阶段加速度超出限制的插补点,从而避免加速阶段末速度过高而导致加速度超出限制。
Description
本发明涉及数控加工技术领域,尤其涉及一种基于NURBS曲线插补的曲线速度规划方法、装置及应用NURBS曲线插补速度规划的数控加工路径数据处理方法。
数控加工***中,CAM(computer Aided Manufacturing,计算机辅助制造)软件常常将复杂曲线分解为细密的小线段,作为数控***的插补轨迹。近年来,CAM逐渐使用NURBS(非均匀B样条)曲线的形式来拟合复杂曲线,并将NURBS的参数发送给数控加工***作为插补数据。这样能够大大减小传输文件的提交,并且由于避免了频繁的加速和减速,使加工效率远远高于小线段加工,因此NURBS插补正在成为数控加工的主流趋势。
由于NURBS曲线的曲率是非线性变化的,这使得加工过程中必须实时计算插补速度和加速度,避免超出加工误差限制和机床加速能力限制。尽管现有的插补算法通常能够在允许的最大速度曲线的限制下进行加速段的插补,但这些算法无法考虑减速阶段的速度突变,导致加速度超出最大向心加速度的限制。
因此,现有技术中通过回溯法或双向加速法来避免减速阶段的加速度超出限制。但是,使用回溯法时,为了得到符合加速度要求的速度曲线而回溯计算的次数是无法预测的,并且每次回溯时加速阶段末速度的递减量没有可行的估计方法,只能通过多次计算来试探。同时,回溯之后插补点要重新计算,插补点的速度也要重新估计,这样的算法计算量巨大,非常耗时,无法保证在一个插补周期内完成多插补点回溯并重新计算,因此在实时插补中的应用空间有限。使用双向加速法时,两端初始速度差距较大时会造成初速度较大的一侧停止插补而等待另一侧插补,直至另一侧插补速度到达满足相遇的要求为止。由于双向同时开始插补,实际加工中如果正向插补需要等待反向插补一个以上的周期,会造成正向插补速度和位置
无法控制,因此这种情况下无法使用该算法。
【发明内容】
本发明要解决的技术问题是提供一种基于NURBS曲线插补的曲线速度规划方法、装置及应用NURBS曲线插补速度规划的数控加工路径数据处理方法,能够预先计算减速阶段加速度超出限制的插补点,从而避免加速阶段末速度过高而导致加速度超出限制。
为解决上述问题,本发明提供一种数控加工路径数据的处理方法,所述方法包括:获取具有NURBS曲线的数控加工路径数据;获取所述NURBS曲线上参数步长Δui内的加速度ai;将所述NURBS曲线各处的加速度ai与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间;确定所述加速度敏感区间的中间点,以作为所述敏感区间内加速和减速的分界点;计算所述中间点的速度值,以作为目标速度;以及根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据。
其中,所述将所述NURBS曲线各处的加速度与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间的步骤包括:计算NURBS曲线各处的曲率1/ρi,并根据弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线;以及计算各参数步长Δui内的加速度,并当参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于所述最大允许加速度时,确定与所述最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间。
其中,所述根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据的步骤包括:判断插补点对应的参数是否进入所述加速度敏感区间;以及当确定插补点对应的参数进入所述加速度敏感区间时,从所述加速度敏感区间的一侧端点作为起始点开始向所述中间点加速,并从所述中间点向另一侧端点作为终点减速。
为解决上述问题,本发明还提供一种基于NURBS曲线插补的速度控制方法,该方法包括:计算NURBS曲线各处的曲率1/ρi,并根据弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线。计算各参数步长Δui内的加速度,并当参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于该最大允许加速度时,确定与该最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点。将该最大允许速度曲线按极小值分成多段,并根据每个速度曲线段的加速度敏感区间的中间点确定对应的参数值umid,并计算该中间点的速度值。判断插补点对应的参数u是否进入该加速度敏感区间。以及当确定插补点对应的参数u进入该加速度敏感区间时,从该加速度敏感区间的一侧端点作为起始点开始向该中间点加速,并从该中间点向另一侧端点作为终点减速,其中,该中间点加速度为0。
其中,利用如下第一公式计算各参数步长Δui内的加速度:
其中,ui为当前插补点的参数值,分子表示速度值,分母表示用NURBS曲线上两插补点之间的弦线段近似代替弧线段。
其中,利用如下第二、三公式计算该中间点的速度值:
第二公式:Vmid=Vm+am(umid-um);
第三公式:Vmid=Vm+n+am+n(umid-um+n)。
其中,am、am+n分别为速度曲线段的加速度敏感区间两个端点对应的加速度,um、um+n分别为对应的参数。vmid的值为通过该第二、三公式计算得出的计算值和该最大允许速度之间的最小值。
其中,当该中间点的速度值大于该最大允许速度时,设定该中间点的速度值为该最大允许速度。
其中,该起始点加速度为该加速度敏感区域起始点的斜率值,在该中间点向另一侧端点减速的起始加速度为0,该终点加速度为该加速度敏感区域终点的斜率。
为解决上述问题,本发明还提供一种基于NURBS曲线插补的速度控制装置,包括:最大允许速度曲线确定单元,用于根据NURBS曲线各处的曲
率1/ρi,以及弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线。加速度敏感点确定单元,用于计算各参数步长Δui内的加速度,以及判断参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于该最大允许加速度时,确定与该最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点。中间点速度值确定单元,用于根据将该最大允许速度曲线按极小值分成的每段速度曲线段的加速度敏感区间的中间点确定对应的参数值umid,并计算该中间点的速度值。以及插补点计算单元,用于判断插补点对应的参数u是否进入该加速度敏感区间,并当确定插补点对应的参数u进入该加速度敏感区间时,从该加速度敏感区间的一侧端点作为起始点开始向该中间点加速,并从该中间点向另一侧端点作为终点减速,其中,该中间点加速度为0。
其中,当该中间点的速度值大于该最大允许速度时,该中间点速度值确定单元确定该中间点的速度值为该最大允许速度。
其中,所述加速度敏感点确定单元利用如下第一公式计算各参数步长Δui内的加速度:
其中,ui为当前插补点的参数值,分子表示速度值,分母表示用NURBS曲线上两插补点之间的弦线段近似代替弧线段。
其中,所述中间点的速度值利用如下第二、三公式计算所述中间点的速度值:
第二公式:Vmid=Vm+am(umid-um);
第三公式:Vmid=Vm+n+am+n(umid-um+n);
其中,am、am+n分别为速度曲线段的加速度敏感区间两个端点对应的加速度,um、um+n分别为对应的参数;vmid的值为通过所述第二、三公式计算得出的计算值和所述最大允许速度之间的最小值。
其中,所述起始点加速度为所述加速度敏感区域起始点的斜率值,在所述中间点向另一侧端点减速的起始加速度为0,所述终点加速度为所述加速度敏感区域终点的斜率。
为解决上述问题,本发明还提供一种数据机床,包括数控***、伺服
电机以及执行部件,所述数据***用于:获取具有NURBS曲线的数控加工路径数据;获取所述NURBS曲线上参数步长Δui内的加速度ai;将所述NURBS曲线各处的加速度ai与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间;确定所述加速度敏感区间的中间点,以作为所述敏感区间内加速和减速的分界点;计算所述中间点的速度值,以作为目标速度;根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据;所述伺服电机接收所述规划后的NURBS曲线的数控加工路径数据,并按照所述接收到的数控加工路径数据控制执行部件进行数控加工。
其中,所述将所述NURBS曲线各处的加速度与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间的步骤包括:计算NURBS曲线各处的曲率1/ρi,并根据弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线;计算各参数步长Δui内的加速度ai,并当参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于所述最大允许加速度时,确定与所述最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间。
其中,所述计算所述中间点的速度值的步骤包括:将所述最大允许速度曲线按极小值分成多段,并根据每个速度曲线段的加速度敏感区间的中间点确定对应的参数值umid,并计算所述中间点的速度值。
其中,利用如下第一公式计算各参数步长Δui内的加速度:
其中,ui为当前插补点的参数值,分子表示速度值,分母表示用NURBS曲线上两插补点之间的弦线段近似代替弧线段;以及
利用如下第二、三公式计算所述中间点的速度值:
第二公式:Vmid=Vm+am(umid-um);
第三公式:Vmid=Vm+n+am+n(umid-um+n);
其中,am、am+n分别为速度曲线段的加速度敏感区间两个端点对应的加速度,um、um+n分别为对应的参数;vmid的值为通过所述第二、三公式计
算得出的计算值和所述最大允许速度之间的最小值。
其中,所述根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据的步骤包括:判断插补点对应的参数是否进入所述加速度敏感区间;当确定插补点对应的参数进入所述加速度敏感区间时,从所述加速度敏感区间的一侧端点作为起始点开始向所述中间点加速,并从所述中间点向另一侧端点作为终点减速。
本发明提供的一种基于NURBS曲线插补的曲线速度规划方法、装置及应用NURBS曲线插补速度规划的数控加工路径数据处理方法,通过预测加速度敏感点,并在加速度敏感的区间使用***允许的最大加速度重新做S型速度规划。因此,NURBS插补可以严格按照新的速度曲线来加速和减速,而无需担心速度和加速度超出限制。另外,由于新的速度曲线仅在加速度敏感点偏离原最大允许速度曲线,是在速度和加速度限制下实现了加工效率最大化。同时,该算法可以一次插补无需回溯、也无需等待某一方的插补结果,运算量轻,插补的实时性得到了保证。
图1为现有技术中参数u与NURBS曲线曲率、最大允许速度函数关系示意图;
图2为本发明实施方式中的一种数控加工路径数据处理方法的流程示意图;
图3为本发明另一实施方式中的一种基于NURBS曲线插补的速度控制方法的流程示意图;
图4为本发明实施方式中的根据参数u、最大允许速度确定加速度敏感点的示意图;
图5为本发明实施方式中的速度规划示意图;
图6为本发明实施方式中的一种基于NURBS曲线插补的速度控制装置的功能模块示意图;
图7为本发明一实施方式提供的数控机床的结构示意图。
为详细说明本发明的技术内容、构造特征、所实现目的及效果,以下结合附图和实施例对本发明进行详细说明。
以下将首先对NURBS曲线插补算法的基本原理进行说明:
1、NURBS曲线是分段多项式曲线,通常写成关于参数u的一元函数形式:
其中,p为阶数(多项式最高次数),Pi为控制点(限制曲线形状的多边形的笛卡尔坐标),wi为权重(曲线被控制点吸引的程度),ui为节点(分段区间的始末点参数值),u为NURBS曲线的自变量,U={U1,U2,……,Un+1},称为节点矢量。Ni,p(u)是非均匀有理B样条基函数,由节点矢量U确定,并满足Cox-de Boor递推关系式(2)和(3):
2、NURBS曲线插补的速度控制:
设定NURBS曲线为:P(u)=(x(u),y(u),z(u));
其中,时间函数u是曲线参数,记为u(ti)=ui,u(ti+1)=ui+1。每个参数u对应于NURBS曲线上的一个点。故NURBS曲线插补的任务是在参数域内选择一系列的u并计算这些u对应的曲线(即刀具的加工路径中的加工段)上的点。
当前点的参数值为u(ti),因此一个插补周期T之后的插补点对应参数u(ti+1)满足以下泰勒展开:
3、弦高误差对进给速度与进给步长的影响:
NURBS曲线插补通常采用两插补点ui、ui+1间的弦线段逼近弧段来实
现,弦线段与弧线段之间的最大距离即为最大插补弦高误差。在定周期数控插补时,为了保证插补轨迹满足一定精度要求,需要对进给速度的最大值进行限定。
用圆弧近似方法可求得弦高误差为:
其中,ρi为ui处的曲率半径,V为编程进给速度,T为插补周期。由公式(5)可得:
假设限定最大弦高误差为δmax,则由公式(6)得到:
其中,ΔLi为第i段进给步长。从上式可知每段进给步长必须满足最大弦高误差的限定条件。同时,为了满足数控机床***加工精度的要求,NURBS曲线每插补周期进给步长还必须考虑加减速和最大法向加速度的约束,即:
其中,ΔLi1为加减速约束下的进给步长,amax最大法向加速度,并且:
amax=V(ui)2ρi (9)
因此,根据如上公式并如图1(a)和(b)所示,通过计算插补点的曲线曲率,可以得到插补点处允许的最大速度。从当前插补点加速到下一插补点的末速度,不能超过允许的最大速度。
请参阅图2,为本发明实施方式中的一种基于NURBS曲线插补的速度控制方法流程示意图。
步骤S10,获取具有NURBS曲线的数控加工路径数据。
步骤S11,获取该NURBS曲线上参数步长Δui内的加速度ai。
步骤S12,将该NURBS曲线各处的加速度与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间。
在本实施方式中,最大允许加速度根据NURBS曲线各处的曲率1/ρi、弦高误差δmax的限制条件以及向心加速度amax的限制条件确定。当参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于该最大允许加速度时,确定与该最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点。
步骤S13,确定该加速度敏感区间的中间点,以作为该敏感区间内加速和减速的分界点。
步骤S14,计算该中间点的速度值,以作为目标速度。
步骤S15,根据该目标速度对该加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据。
其中,当插补点对应的参数u进入加速度敏感区间时,从加速度敏感区间的一侧端点作为起始点开始向所述中间点加速,并从中间点向另一侧端点作为终点减速,从而实现对该加速度敏感区间进行加速和减速的规划。
请参阅图3,为本发明另一实施方式中的一种基于NURBS曲线插补的速度控制方法流程示意图。
步骤S20,计算NURBS曲线各处的曲率1/ρi,并根据弦高误差δmax的限制条件(公式(5))和向心加速度amax的限制条件(公式(9))确定最大允许速度曲线(即NURBS曲线各处的最大允许速度Vmax)。
步骤S21,计算各参数步长Δui内的加速度,并与最大允许加速度比较。如果参数步长Δui内的加速度ai大于最大允许加速度,而Δui+n内的加速度ai+n小于最大允许加速度时,则确定与该最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点。
其中,设定参数步长Δu的值为极小值,例如Δu=10-5,因此可以将参数步长Δu内的加速过程视为匀加速过程。
具体地,利用如下公式(10)计算各参数步长Δui内的加速度:
其中,ui为当前插补点的参数值,分子表示速度值,分母表示用NURBS曲线上两插补点之间的弦线段近似代替弧线段。由于,弦线段比弧线段长度小,因此加速度的计算值比真实值偏大。如果要求偏大的加速度值小于
最大允许加速度,那么各处加速度的真实值就一定不会超出最大允许加速度的限制。
进一步地,取各参数步长Δui终点的加速度值与最大允许加速度值比较,可以得到如图3所示的加速度敏感点,如星形标记点。
步骤S22,将如步骤S20确定的最大允许速度曲线按极小值分成多段(每段最大允许速度曲线以下简称速度曲线段),即每两个速度波谷之间的速度曲线为一段(全曲线的起点和终点也视为速度波谷)。确定一段速度曲线段的加速度敏感点,并判断对应的加速度敏感的区间(以下简称为敏感区间)以及该敏感区间的中间点对应的参数值umid,并计算中间点的速度值。
具体地,将该敏感区间的两个端点分别按当前的斜率做延长线并相交于一点,该交点称为中间点,该中间点对应的参数值umid就是该速度曲线段的加速插补阶段的终点,同时也是减速插补阶段的起点。当中间点速度如果大于最大允许速度,则取最大允许速度。
其中,利用如下公式(11)、(12)计算该中间点的速度值:
Vmid=Vm+am(umid-um) (11)
Vmid=Vm+n+am+n(umid-um+n) (12)
其中,am、am+n分别为速度曲线段的加速度敏感区间两个端点对应的加速度,um、um+n分别为对应的参数。
如图4所示,其中,1~2点、3~4点、5~6点、7~8点、9~10点、11~12点所包含的区间为敏感区间。此处以3~4点、5~6点之间的敏感区间为例加以说明。
计算3点和6点的加速度a3、a6作为斜率,可以分别得到通过3点(u3,v3)和6点(u6,v6)的直线方程l1、l2:
l1:v=v3+a3(u-u3)
l2:v=v6+a6(u-u6)
联立以上方程可以得出交点(即中间点)坐标(umid,vmid)。其中,vmid的值为计算值和最大允许速度之间的最小值。需要说明的是,由于斜率a3、a6是加速和减速阶段允许的最大加速度,所以只要重新规划的速度曲线在这两条直线的下方,就一定满足***加速度的限制。以这种方式求出的中间点,一定会处在两条直线正下方的包围之内,也就是说,可以保证加速
和减速的终点和起始点都必然在满足加速度限制的范围之内,因此中间点的坐标是合理可接受的。
步骤S23,启动实时插补,根据公式(4)确定插补点对应的参数u并判断该参数u是否进入该确定的敏感区间。若是,则进入步骤S24,否则,进入步骤S25。
步骤S24,从该敏感区间的一侧(如左侧)端点开始,向该中间点加速,到达该中间点后,向另一侧(如右侧)端点减速,其中,该中间点时加速度为0。然后,流程结束。
其中,起始点加速度为该点的斜率值,加速度和加加速度都要保持如公式(8)的要求,并且起始加速度为0,末加速度为该另一侧(右侧)端点的斜率。
具体地,从该敏感区间左侧向中间点加速是一个类S型加速的过程,初始加速度不为0,末加速度为0,末速度不得超过vmid,加速终点不得超过umid。以此为加速条件,在加速过程的每个周期都作为是否使用正加加速度的依据,最终能够柔性地加速到中间点。从中间点开始减速的过程同样是一个类S型减速的过程,初始加速度为0,末加速度不为0,末速度尽可能贴近v6,加速终点不得超过u6。
由于用户指定进给率限制而使最大允许速度曲线出现匀速段的情况(例如图4中点4~点5区间),很可能在很短的时间内从敏感区间端点到匀速段的加速就已经结束,由于加速度限制而导致的效率损失被降低到最小化。
如图5所示,颜色加深部分是从敏感区间端点到中间点重做的速度规划。这意味着,从颜色加深线段的左侧的相邻速度谷底开始,沿着颜色未加深线段和颜色加深线段加速是既满足速度限制又满足加速度限制的。
步骤S25,根据公式(8)按照最大允许速度计算插补点。然后流程结束。
请参阅图6,为本发明一实施方式提供的基于NURBS曲线插补的速度控制装置的功能模块示意图。该装置30包括:
最大允许速度曲线确定单元31,用于根据NURBS曲线各处的曲率1/ρi,以及弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线。
加速度敏感点确定单元32,用于计算各参数步长Δui内的加速度,以及判断参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于该最大允许加速度时,确定与该最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点。
中间点速度值确定单元33,用于根据将该最大允许速度曲线按极小值分成的每段速度曲线段的加速度敏感区间的中间点确定对应的参数值umid,并计算该中间点的速度值。以及
插补点计算单元34,用于判断插补点对应的参数u是否进入该加速度敏感区间,并当确定插补点对应的参数u进入该加速度敏感区间时,从该加速度敏感区间的一侧端点作为起始点开始向该中间点加速,并从该中间点向另一侧端点作为终点减速,其中,该中间点加速度为0。
请参阅图7,为本发明一实施方式提供的数控机床的结构示意图。本实施方式中,数控机床70包括数控***71、伺服电机72以及执行部件73。
数控***71用于获取具有NURBS曲线的数控加工路径数据;获取所述NURBS曲线上参数步长Δui内的加速度ai;将所述NURBS曲线各处的加速度ai与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间;确定所述加速度敏感区间的中间点,以作为所述敏感区间内加速和减速的分界点;计算所述中间点的速度值,以作为目标速度;根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据,并将规划后的的NURBS曲线的数控加工路径数据发送至伺服电机72。
具体,该数控***71可采用图1及其对应方法实施例对数控加工路径数据进行规划。并且,该数控***71具体确定各参数步长Δui内的加速度、加速度敏感点、中间点的速度值、根据所述目标速度对所述加速度敏感区间进行加速和减速的规划可参阅图2及其对应方法实施例所述。即,该数控***71还可执行上述图2所示实施例进行基于NURBS曲线插补的速度控制,进而实现上述数控加工路径数据的规划。
伺服电机72接收该规划后的NURBS曲线的数控加工路径数据,并按照所述接收到的数控加工路径数据控制执行部件73进行数控加工,以使执行部件73按照规划后的数控加工路径进行加工。其中,该执行部件73可
以为工业机器人、刀具等加工所需零件。
本发明提供的一种基于NURBS曲线插补的曲线速度规划方法、装置及应用NURBS曲线插补速度规划的数控加工路径数据处理方法,通过预测加速度敏感点,并在加速度敏感的区间使用***允许的最大加速度重新做S型速度规划。因此,NURBS插补可以严格按照新的速度曲线来加速和减速,而无需担心速度和加速度超出限制。另外,由于新的速度曲线仅在加速度敏感点偏离原最大允许速度曲线,是在速度和加速度限制下实现了加工效率最大化。同时,该算法可以一次插补无需回溯、也无需等待某一方的插补结果,运算量轻,插补的实时性得到了保证。
以上所述仅为本发明的实施方式,并非因此限制本发明的专利范围,凡是利用本发明说明书及附图内容所作的等效结构或等效流程变换,或直接或间接运用在其他相关的技术领域,均同理包括在本发明的专利保护范围内。
Claims (20)
- 一种数控加工路径数据的处理方法,其中,所述方法包括:获取具有NURBS曲线的数控加工路径数据;获取所述NURBS曲线上参数步长Δui内的加速度ai;将所述NURBS曲线各处的加速度ai与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间;确定所述加速度敏感区间的中间点,以作为所述敏感区间内加速和减速的分界点;计算所述中间点的速度值,以作为目标速度;以及根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据。
- 如权利要求1所述的数控加工路径数据的处理方法,其中,所述将所述NURBS曲线各处的加速度与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间的步骤包括:计算NURBS曲线各处的曲率1/ρi,并根据弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线;以及计算各参数步长Δui内的加速度ai,并当参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于所述最大允许加速度时,确定与所述最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间。
- 如权利要求1所述的数控加工路径数据的处理方法,其中,所述根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据的步骤包括:判断插补点对应的参数是否进入所述加速度敏感区间;以及当确定插补点对应的参数进入所述加速度敏感区间时,从所述加速度敏感区间的一侧端点作为起始点开始向所述中间点加速,并从所述中间点向另一侧端点作为终点减速。
- 一种基于NURBS曲线插补的速度控制方法,其中,所述方法包括:计算NURBS曲线各处的曲率1/ρi,并根据弦高误差δmax的限制条件 和向心加速度amax的限制条件确定最大允许速度曲线;计算各参数步长Δui内的加速度ai,并当参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于所述最大允许加速度时,确定与所述最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点;将所述最大允许速度曲线按极小值分成多段,并根据每个速度曲线段的加速度敏感区间的中间点确定对应的参数值umid,并计算所述中间点的速度值;判断插补点对应的参数u是否进入所述加速度敏感区间;以及当确定插补点对应的参数u进入所述加速度敏感区间时,从所述加速度敏感区间的一侧端点作为起始点开始向所述中间点加速,并从所述中间点向另一侧端点作为终点减速,其中,所述中间点加速度为0。
- 如权利要求4所述的基于NURBS曲线插补的速度控制方法,其中,利用如下第二、三公式计算所述中间点的速度值:第二公式:Vmid=Vm+am(umid-um);第三公式:Vmid=Vm+n+am+n(umid-um+n);其中,am、am+n分别为速度曲线段的加速度敏感区间两个端点对应的加速度,um、um+n分别为对应的参数;vmid的值为通过所述第二、三公式计算得出的计算值和所述最大允许速度之间的最小值。
- 如权利要求4所述的基于NURBS曲线插补的速度控制方法,其中,当所述中间点的速度值大于所述最大允许速度时,设定所述中间点的速度值为所述最大允许速度。
- 如权利要求6所述的基于NURBS曲线插补的速度控制方法,其中,当所述中间点的速度值大于所述最大允许速度时,设定所述中间点的速度 值为所述最大允许速度。
- 如权利要求4所述的基于NURBS曲线插补的速度控制方法,其中,所述起始点加速度为所述加速度敏感区域起始点的斜率值,在所述中间点向另一侧端点减速的起始加速度为0,所述终点加速度为所述加速度敏感区域终点的斜率。
- 一种基于NURBS曲线插补的速度控制装置,其中,包括:最大允许速度曲线确定单元,用于根据NURBS曲线各处的曲率1/ρi,以及弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线;加速度敏感点确定单元,用于计算各参数步长Δui内的加速度,以及判断参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于所述最大允许加速度时,确定与所述最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点;中间点速度值确定单元,用于根据将所述最大允许速度曲线按极小值分成的每段速度曲线段的加速度敏感区间的中间点确定对应的参数值umid,并计算所述中间点的速度值;以及插补点计算单元,用于判断插补点对应的参数u是否进入所述加速度敏感区间,并当确定插补点对应的参数u进入所述加速度敏感区间时,从所述加速度敏感区间的一侧端点作为起始点开始向所述中间点加速,并从所述中间点向另一侧端点作为终点减速,其中,所述中间点加速度为0。
- 如权利要求10所述的基于NURBS曲线插补的速度控制装置,其中,所述中间点的速度值利用如下第二、三公式计算所述中间点的速度值:第二公式:Vmid=Vm+am(umid-um);第三公式:Vmid=Vm+n+am+n(umid-um+n);其中,am、am+n分别为速度曲线段的加速度敏感区间两个端点对应的加速度,um、um+n分别为对应的参数;vmid的值为通过所述第二、三公式计算得出的计算值和所述最大允许速度之间的最小值。
- 如权利要求10所述的基于NURBS曲线插补的速度控制装置,其中,当所述中间点的速度值大于所述最大允许速度时,所述中间点速度值确定单元确定所述中间点的速度值为所述最大允许速度。
- 如权利要求12所述的基于NURBS曲线插补的速度控制装置,其中,当所述中间点的速度值大于所述最大允许速度时,所述中间点速度值确定单元确定所述中间点的速度值为所述最大允许速度。
- 如权利要求10所述的基于NURBS曲线插补的速度控制装置,其中,所述起始点加速度为所述加速度敏感区域起始点的斜率值,在所述中间点向另一侧端点减速的起始加速度为0,所述终点加速度为所述加速度敏感区域终点的斜率。
- 一种数据机床,其中,包括数控***、伺服电机以及执行部件,所述数据***用于:获取具有NURBS曲线的数控加工路径数据;获取所述NURBS曲线上参数步长Δui内的加速度ai;将所述NURBS曲线各处的加速度ai与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间;确定所述加速度敏感区间的中间点,以作为所述敏感区间内加速和减速的分界点;计算所述中间点的速度值,以作为目标速度;根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据;以及所述伺服电机接收所述规划后的NURBS曲线的数控加工路径数据,并按照所述接收到的数控加工路径数据控制执行部件进行数控加工。
- 如权利要求16所述的数控机床,其中,所述将所述NURBS曲线各处的加速度与最大允许加速度比较以确定加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间的步骤包括:计算NURBS曲线各处的曲率1/ρi,并根据弦高误差δmax的限制条件和向心加速度amax的限制条件确定最大允许速度曲线;以及计算各参数步长Δui内的加速度ai,并当参数步长Δui内的加速度ai大于最大允许加速度且参数步长Δui+n内的加速度ai+n小于所述最大允许加速度时,确定与所述最大允许加速度差值最小的加速度对应的参数步长的端点为加速度敏感点,并根据确定的加速度敏感点确定加速度敏感区间。
- 如权利要求17所述的数控机床,其中,所述计算所述中间点的速度值的步骤包括:将所述最大允许速度曲线按极小值分成多段,并根据每个速度曲线段的加速度敏感区间的中间点确定对应的参数值umid,并计算所述中间点的速度值。
- 如权利要求16所述的数控机床,其中,所述根据所述目标速度对所述加速度敏感区间进行加速和减速的规划,以得到规划后的NURBS曲线的数控加工路径数据的步骤包括:判断插补点对应的参数是否进入所述加速度敏感区间;以及当确定插补点对应的参数进入所述加速度敏感区间时,从所述加速度敏感区间的一侧端点作为起始点开始向所述中间点加速,并从所述中间点向另一侧端点作为终点减速。
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