CN110989504B - Interval self-adaptive planning method for five-axis machining feed speed - Google Patents

Interval self-adaptive planning method for five-axis machining feed speed Download PDF

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CN110989504B
CN110989504B CN201911327146.6A CN201911327146A CN110989504B CN 110989504 B CN110989504 B CN 110989504B CN 201911327146 A CN201911327146 A CN 201911327146A CN 110989504 B CN110989504 B CN 110989504B
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interval
speed
allowable
feeding
mth
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CN110989504A (en
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宋得宁
钟宇光
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Harbin Engineering University
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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
    • G05B19/4163—Adaptive control of feed or cutting velocity
    • 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
    • G05B2219/36—Nc in input of data, input key till input tape
    • G05B2219/36521—Select by combination of detected force, acceleration, speed, work rate

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Abstract

The invention belongs to the technical field of robots and high-grade numerical control machines, and particularly relates to a five-axis machining feed speed interval adaptive planning method. The method is based on applying the look-ahead window to isolate the influence of the appearance of the curve outside the window on the planning of the feeding speed in the current interval, calculates the allowable feeding parameters of the current interval and the look-ahead interval based on the differential principle, plans the feeding speed profile of the current interval according to the allowable feeding parameters of the previous interval, the current interval and the look-ahead interval, realizes the area-by-area look-ahead planning of the whole feeding speed of the long spline curve path, has high calculation efficiency, and can fully utilize the machine tool performance on the premise of meeting the constraint of the driving capability of the feeding shaft.

Description

Interval self-adaptive planning method for five-axis machining feed speed
Technical Field
The invention belongs to the technical field of robots and high-grade numerical control machines, and particularly relates to a five-axis machining feed speed interval adaptive planning method.
Background
For a high-grade five-axis linkage numerical control system, spline curve interpolation is a necessary advanced interpolation function, and in order to realize spline curve interpolation processing, reasonable planning on the feeding speed of a curve path is a foundation and a precondition. If the feeding speed is too high, one or more of the five feeding shafts exceed the driving capability range to induce machining vibration, and if the feeding speed is too low, the machining efficiency is inevitably influenced, so that how to plan the five-axis numerical control machining feeding speed which fully utilizes the performance of the machine tool under the constraint condition of satisfying the driving capability of the feeding shafts becomes one of the problems which must be solved for developing a high-grade five-axis linkage numerical control system.
Prior art document 1 "The optimal feed planning on five-axis parameter tools with geometry and kinetic constraints for CNC machine tools", Liu et al, International Journal of Production Research, 2017, 55 (13): 3715-3731, which obtains the five-axis linkage feeding speed satisfying the axis driving constraint condition based on the linear programming strategy by linearizing the considered multiple constraints. Document 2 "interactive fed scheduling method with defined high-order constraints in parameter addressing", Liang et al, International Journal of Advanced Manufacturing Technology, 2017, 92 (5-8): 2001-2015, which represents the five-axis machining feed rate as a spline curve, obtains a final feed rate profile that satisfies all considered constraints through multiple iterative adjustments. However, the above method is mainly suitable for a conventional spline curve path with a short length, for a path with a large length, it is difficult to apply the method because of a large calculation load when performing iterative planning on the whole path, and if performing sectional planning on the whole long spline curve path, the speed needs to be reduced to zero at a transition position, thereby affecting the stability of the feeding motion. Therefore, a five-axis feed rate planning method specially aiming at the long spline curve path needs to be further researched.
Disclosure of Invention
The invention aims to provide a five-axis machining feed speed interval adaptive planning method.
The purpose of the invention is realized by the following technical scheme: the method comprises the following steps:
step 1: calculating the arc length of the forward-looking interval;
in order to ensure that the feeding movement has enough distance to realize safe braking, the displacement required by reducing the maximum feeding speed to zero is used as the arc length of a prospective interval; then the arc length S of the look-ahead interval in the S-shaped acceleration and deceleration modewComprises the following steps:
Figure BDA0002328659750000011
wherein v ismaxIs the maximum feed speed; a ist，maxIs the maximum tangential acceleration; j is a function oft，maxMaximum tangential jerk;
step 2: calculating allowable motion parameters of the current interval;
obtain the arc length s of the look-ahead windowwThen, for the m arc length is swThe spline curve path interval is subjected to coarse interpolation, and the calculation method of the coarse interpolation point parameters comprises the following steps:
Figure BDA0002328659750000021
wherein m is the serial number of the current interval; r (u) is a nose point path spline; o (u) is a spline of the path in the arbor direction;scompensating for the coarse interpolation arc length;
Figure BDA0002328659750000022
the total number of the coarse interpolation points of the mth interval;
Figure BDA0002328659750000023
an ith coarse interpolation point parameter in an mth interval;
the rough interpolation point and the shaft direction can be respectively expressed as
Figure BDA0002328659750000024
And
Figure BDA0002328659750000025
obtaining the ith physical axis position coordinate of the mth interval through the reverse kinematic transformation of the five-axis machine tool
Figure BDA0002328659750000026
m is 1, 2, …, calculating the first derivative vector of the ith physical axis position to the arc length of the path of the cusp point in the mth interval
Figure BDA0002328659750000027
Second order director
Figure BDA0002328659750000028
Third-order vector
Figure BDA0002328659750000029
Figure BDA00023286597500000210
Given feed shaft drive energyForce constraints, i.e. maximum feed shaft speed
Figure BDA00023286597500000211
Maximum feed shaft acceleration
Figure BDA00023286597500000212
And maximum feed shaft jerk
Figure BDA00023286597500000213
Calculating the adjustment coefficient at the ith coarse interpolation point in the mth interval
Figure BDA00023286597500000214
Figure BDA00023286597500000215
Calculating allowable speed of the mth interval
Figure BDA00023286597500000216
Allowable acceleration
Figure BDA00023286597500000217
And allowable jerk
Figure BDA00023286597500000218
Comprises the following steps:
Figure BDA00023286597500000219
and step 3: looking ahead at the next feed speed planning interval;
look ahead the (m +1) th interval, calculate the allowable speed of the (m +1) th interval
Figure BDA00023286597500000220
Allowable acceleration
Figure BDA00023286597500000221
And permit to use and addAcceleration of a vehicle
Figure BDA0002328659750000031
Judging whether the (m +1) th interval is an ending interval of the curve path; if yes, the allowable speed of the interval is updated
Figure BDA0002328659750000032
Comprises the following steps:
Figure BDA0002328659750000033
wherein s isfIs the arc length of the end interval;
calculating the ending speed of the current mth interval
Figure BDA0002328659750000034
Figure BDA0002328659750000035
Starting speed of m-th interval
Figure BDA0002328659750000036
Taking the actual ending speed of the previous interval;
and 4, step 4: self-adaptive planning of the feeding speed of the current interval;
the feed speed profile of the mth interval is planned in the following 4 cases:
case 1:
Figure BDA0002328659750000037
at this time, the velocity from the start is calculated
Figure BDA0002328659750000038
Is accelerated to
Figure BDA0002328659750000039
Required displacement
Figure BDA00023286597500000310
From
Figure BDA00023286597500000311
Slowing down to an end speed
Figure BDA00023286597500000312
Required displacement of
Figure BDA00023286597500000313
Let the maximum achievable feed speed in the mth interval be vcJudgment of
Figure BDA00023286597500000314
Figure BDA00023286597500000315
Whether or not to be established, and if so,
Figure BDA00023286597500000316
otherwise, vcComprises the following steps:
Figure BDA00023286597500000317
wherein
Figure BDA00023286597500000318
To be driven from
Figure BDA00023286597500000319
Up/down to
Figure BDA00023286597500000320
Required displacement; in the m-th interval, the feed speed is planned to be from
Figure BDA00023286597500000321
Increase speed to vcFrom v againcDown to
Figure BDA00023286597500000322
Two processes of (2);
case 2:
Figure BDA00023286597500000323
at the moment, the starting speed and the ending speed are equal to the maximum allowable speed of the current interval, and the feeding speed is planned to be a constant speed process in the mth interval;
case 3:
Figure BDA00023286597500000324
at this time, the ending speed is equal to the maximum allowable speed of the current interval and is greater than the starting speed, and thus, the feeding speed is programmed to be a slave in the m-th interval
Figure BDA00023286597500000325
To
Figure BDA00023286597500000326
The speed raising process of (2);
case 4:
Figure BDA00023286597500000327
at this time, the starting speed is equal to the maximum allowable speed of the current interval and is greater than the ending speed, and thus, the feeding speed is programmed to be a slave in the m-th interval
Figure BDA00023286597500000328
To
Figure BDA00023286597500000329
The deceleration process of (2);
and 5: feed rate planning for ending interval
Let m be m +1, judge whether the m-th interval is the end interval, if yes, let m be m +1
Figure BDA0002328659750000041
Marking the mth section of feeding by adopting the method in the step 4)Speed; otherwise, repeating the step 3) to the step 5) to realize the region-by-region self-adaptive planning of the feeding speed of the longer spline curve path.
The invention has the beneficial effects that:
the invention relates to a five-axis numerical control machining feeding speed interval self-adaptive planning method suitable for a long spline curve path, which is based on applying a look-ahead window to isolate the influence of the appearance of a curve outside the window on the planning of the feeding speed of a current interval, calculates the allowable feeding parameters of the current interval and the look-ahead interval based on a differential principle, plans the feeding speed profile of the current interval according to the allowable feeding parameters of the previous interval, the current interval and the look-ahead interval, realizes the area-by-area look-ahead planning of the whole feeding speed of the long spline curve path, has high calculation efficiency, and can fully utilize the machine tool performance on the premise of meeting the constraint of the driving capability of a feeding shaft.
Drawings
FIG. 1 is an overall flow diagram of the present invention.
FIG. 2 is a five-axis spline path geometric model diagram.
Fig. 3 is a graph of the projected feed rate for the method of the present invention.
FIG. 4 is a graph of linear axis feed axis velocity, acceleration, and jerk as programmed by the method of the present invention.
FIG. 5 is a graph of the rotating shaft feed shaft speed, acceleration and jerk as programmed by the method of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention aims to overcome the defects of the prior art, and provides a five-axis machining feeding speed interval adaptive planning method. The technical scheme is that the interval self-adaptive planning method for the five-axis machining feed speed is characterized in that the method is based on a differential principle, allowable motion parameters of a current interval are determined, a deceleration distance in an S-shaped acceleration and deceleration mode is calculated to serve as the length of a forward-looking window interval, and the end speed of the current interval is determined by looking ahead at the next interval, so that the zone-by-zone self-adaptive planning is carried out on the feed speed of a long spline curve path. The method comprises the following specific steps:
1) calculating the arc length of the prospective interval
In order to ensure that the feeding movement has enough distance to realize safe braking, the displacement required by reducing the maximum feeding speed to zero is used as the arc length of a prospective interval; recording the maximum feeding speed, the maximum tangential acceleration and the maximum tangential jerk as v respectivelymax、at，maxAnd jt，maxThen, under S-shaped acceleration and deceleration mode, the arc length S of the prospective sectionwComprises the following steps:
Figure BDA0002328659750000051
2) calculating allowable motion parameters of current interval
The serial number of the current interval is recorded as m, the spline of the nose point path is recorded as R (u), and the spline of the arbor direction path is recorded as O (u), so as to obtain the arc length s of the foresight windowwThen, for the m arc length is swThe spline curve path interval is subjected to coarse interpolation, and the coarse interpolation arc length is taken as compensationsThe coarse interpolation point parameters are calculated as:
Figure BDA0002328659750000052
wherein the content of the first and second substances,
Figure BDA0002328659750000053
represents the total number of coarse interpolation points of the mth interval,
Figure BDA0002328659750000054
representing the ith rough interpolation point parameter in the mth interval; thus, the rough interpolation point and the shaft direction can be respectively expressed as
Figure BDA0002328659750000055
And
Figure BDA0002328659750000056
obtaining the ith physical axis position coordinate of the mth interval through the reverse kinematic transformation of the five-axis machine tool
Figure BDA0002328659750000057
And m is 1, 2, a first derivative vector of the ith physical axis position to the arc length of the path of the tool tip point in the mth interval is calculated
Figure BDA0002328659750000058
Second order director
Figure BDA0002328659750000059
Third-order vector
Figure BDA00023286597500000510
Figure BDA00023286597500000511
Given feed shaft drive capability constraints, i.e. maximum feed shaft speed
Figure BDA00023286597500000512
Maximum feed shaft acceleration
Figure BDA00023286597500000513
And maximum feed shaft jerk
Figure BDA00023286597500000514
Calculating the adjustment coefficient at the ith coarse interpolation point in the mth interval
Figure BDA00023286597500000515
Figure BDA00023286597500000516
Calculating allowable speed of the mth interval
Figure BDA00023286597500000517
Allowable acceleration
Figure BDA00023286597500000518
And allowable jerk
Figure BDA00023286597500000519
Comprises the following steps:
Figure BDA00023286597500000520
3) look ahead next feed speed plan interval
Look ahead the (m +1) th interval, calculate the allowable speed of the (m +1) th interval according to the formula (5)
Figure BDA00023286597500000521
Allowable acceleration
Figure BDA00023286597500000522
And allowable jerk
Figure BDA00023286597500000523
Judging whether the (m +1) th interval is an ending interval of the curve path; if yes, the allowable speed of the interval is updated
Figure BDA0002328659750000061
Comprises the following steps:
Figure BDA0002328659750000062
wherein s isfIs the arc length of the end interval;
next, the end speed of the current m-th interval is calculated
Figure BDA0002328659750000063
Figure BDA0002328659750000064
Starting speed of m-th interval
Figure BDA0002328659750000065
Taking the actual ending speed of the previous interval;
4) feed rate adaptive planning for current interval
The feed speed profile of the mth interval is planned in the following 4 cases:
case (1):
Figure BDA0002328659750000066
at this time, the velocity from the start is calculated
Figure BDA0002328659750000067
Is accelerated to
Figure BDA0002328659750000068
Required displacement
Figure BDA0002328659750000069
From
Figure BDA00023286597500000610
Slowing down to an end speed
Figure BDA00023286597500000611
Required displacement of
Figure BDA00023286597500000612
Let the maximum achievable feed speed in the mth interval be vcJudgment of
Figure BDA00023286597500000613
Figure BDA00023286597500000614
Whether or not toAnd if so, the first and second sensors are connected,
Figure BDA00023286597500000615
otherwise, vcComprises the following steps:
Figure BDA00023286597500000616
wherein
Figure BDA00023286597500000617
To be driven from
Figure BDA00023286597500000618
Up/down to
Figure BDA00023286597500000619
Required displacement; in the m-th interval, the feed speed is planned to be from
Figure BDA00023286597500000620
Increase speed to vcFrom v againcDown to
Figure BDA00023286597500000621
Two processes of (2);
case (2):
Figure BDA00023286597500000622
at the moment, the starting speed and the ending speed are equal to the maximum allowable speed of the current interval, and the feeding speed is planned to be a constant speed process in the mth interval;
case (3):
Figure BDA00023286597500000623
at this time, the ending speed is equal to the maximum allowable speed of the current interval and is greater than the starting speed, and thus, the feeding speed is programmed to be a slave in the m-th interval
Figure BDA00023286597500000624
To
Figure BDA00023286597500000625
The speed raising process of (2);
case (4):
Figure BDA00023286597500000626
at this time, the starting speed is equal to the maximum allowable speed of the current interval and is greater than the ending speed, and thus, the feeding speed is programmed to be a slave in the m-th interval
Figure BDA00023286597500000627
To
Figure BDA00023286597500000628
The deceleration process of (2);
5) feed rate planning for ending interval
Let m be m +1, judge whether the m-th interval is the end interval, if yes, let m be m +1
Figure BDA00023286597500000629
Marking the m-th section of feeding speed by adopting the method in the step 4); otherwise, repeating the step 3) to the step 5) to realize the region-by-region self-adaptive planning of the feeding speed of the longer spline curve path.
The invention has the beneficial effects that: the method is based on the application of a look-ahead window, the influence of the appearance of a curve outside the window on the feed speed planning of the current interval is isolated, the allowable feed parameters of the current interval and the look-ahead interval are calculated based on a differential principle, and the feed speed profile of the current interval is planned according to the allowable feed parameters of the previous interval, the current interval and the look-ahead interval, so that the regional look-ahead planning of the overall feed speed of the long spline curve path is realized, the calculation efficiency is high, and the machine tool performance can be fully utilized on the premise of meeting the constraint of the drive capability of a feed shaft.
The detailed description of the embodiments of the invention is provided with reference to the accompanying drawings.
FIG. 1 is a flowchart of the overall method, and FIG. 2 is a geometric model of a five-axis spline curve path in a spatial rectangular coordinate system, wherein the total arc length of the curve path is 2107.7 mm; taking the curve path shown in fig. 2 as an example, a five-axis numerical control machine tool structure having three linear axes (X-axis, Y-axis, Z-axis) and two rotation axes (B-axis, C-axis) rotating around Y, Z axes is selected, and the driving capability of the feeding axis is constrained to be
Figure BDA0002328659750000071
Figure BDA0002328659750000072
Figure BDA0002328659750000073
The maximum feeding speed is 40mm/s, the method is adopted to plan the feeding speed of the long spline curve path, and the specific implementation process is described in detail below with reference to the attached drawing 1.
Let m equal to 1, start speed
Figure BDA0002328659750000074
Secondly, calculating the arc length of the forward-looking interval by using the formula (1), wherein the calculation result is sw＝2.4mm；
Calculating allowable speed of mth interval by formula (5)
Figure BDA0002328659750000075
Allowable acceleration
Figure BDA0002328659750000076
And allowable jerk
Figure BDA0002328659750000077
Fourthly, the allowable speed of the (m +1) th interval is calculated by using the formula (5) to look ahead
Figure BDA0002328659750000078
Allowable acceleration
Figure BDA0002328659750000079
And allowable jerk
Figure BDA00023286597500000710
Utilizing the method of the step 4) in the invention content to carry out self-adaptive planning on the feeding speed of the current interval to obtain the feeding speed profile of the mth interval;
sixthly, m is equal to m + 1;
seventhly, judging whether an ending interval is reached, if so, controlling the ending speed
Figure BDA00023286597500000711
Carrying out self-adaptive planning on the feeding speed of the current interval by using the method of the step 4) in the invention content to obtain a feeding speed profile of an ending interval; otherwise, returning to the fourth step to finish the area-by-area self-adaptive planning of the feeding speed.
Fig. 3 shows a feed rate profile planned by the method of the present invention, and it can be seen that the planned feed rate is continuous over the entire long spline path, and there is no speed reduction to zero.
Fig. 4 shows the feed shaft speed, acceleration and jerk of the linear axes planned by the method of the present invention, which shows that the motion parameters of the three linear axes are effectively limited within the set constraint range.
Fig. 5 shows the rotating shaft feed shaft speed, acceleration and jerk planned by the method of the present invention, and it can be seen that the motion parameters of both rotating shafts are also effectively limited within the set constraint range.
In conclusion, the five-axis machining feeding speed interval self-adaptive planning method can realize efficient feeding speed planning on the long spline curve path under the constraint of the driving capability of the feeding shaft, and has important significance for the development of the five-axis linkage spline curve interpolation technology and the improvement of the technical level of a high-grade numerical control system, so that the method can provide beneficial reference for numerical control system manufacturers.
The invention discloses a self-adaptive planning method for a five-axis machining feed speed interval, belongs to the technical field of robots and high-grade numerical control machines, and relates to a self-adaptive planning method for a feed speed interval, which is specially used for a long spline curve path in a five-axis linkage numerical control machining process. The method comprises the steps of applying a look-ahead window with the length equal to the braking distance in an S-shaped acceleration and deceleration mode to isolate the influence of the appearance of an outer curve of the window on the planning of the feeding speed at the current position, determining allowable motion parameters of the current interval under the constraint of the driving capability of five feeding shafts based on a differential principle, and planning the feeding speed profile of the current interval by combining the ending speed of the previous interval and the allowable speed of the look-ahead interval, thereby ensuring the continuous smoothness of the whole feeding speed profile. The method can realize the high-efficiency planning of the feeding speed of the longer five-axis linkage curve path, and has important significance for improving the development level of the five-axis numerical control technology.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A five-axis machining feed speed interval adaptive planning method is characterized by comprising the following steps:
step 1: calculating the arc length of the forward-looking interval;
in order to ensure that the feeding movement has enough distance to realize safe braking, the displacement required by reducing the maximum feeding speed to zero is used as the arc length of a prospective interval; then the arc length S of the look-ahead interval in the S-shaped acceleration and deceleration modewComprises the following steps:
Figure FDA0002744011310000011
wherein v ismaxIs the maximum feed speed; a ist，maxIs at mostTangential acceleration; j is a function oft，maxMaximum tangential jerk;
step 2: calculating allowable motion parameters of the current interval;
obtaining the arc length s of the prospective intervalwThen, for the m arc length is swThe spline curve path interval is subjected to coarse interpolation, and the calculation method of the coarse interpolation point parameters comprises the following steps:
Figure FDA0002744011310000012
wherein m is the serial number of the current interval; r (u) is a nose point path spline; o (u) is a spline of the path in the arbor direction;scompensating for the coarse interpolation arc length;
Figure FDA0002744011310000013
the total number of the coarse interpolation points of the mth interval;
Figure FDA0002744011310000014
an ith coarse interpolation point parameter in an mth interval;
the rough interpolation point and the shaft direction can be respectively expressed as
Figure FDA0002744011310000015
And
Figure FDA0002744011310000016
obtaining the ith physical axis position coordinate of the mth interval through the reverse kinematic transformation of the five-axis machine tool
Figure FDA0002744011310000017
Calculating a first derivative vector of the ith physical axis position to the arc length of the path of the tool tip point in the mth interval
Figure FDA0002744011310000018
Second order director
Figure FDA0002744011310000019
Third-order vector
Figure FDA00027440113100000110
Figure FDA00027440113100000111
Given feed shaft drive capability constraints, i.e. maximum feed shaft speed
Figure FDA00027440113100000112
Maximum feed shaft acceleration
Figure FDA00027440113100000117
And maximum feed shaft jerk
Figure FDA00027440113100000114
Calculating the adjustment coefficient at the ith coarse interpolation point in the mth interval
Figure FDA00027440113100000115
Figure FDA00027440113100000116
Calculating allowable speed of the mth interval
Figure FDA0002744011310000021
Allowable acceleration
Figure FDA0002744011310000022
And allowable jerk
Figure FDA0002744011310000023
Comprises the following steps:
Figure FDA0002744011310000024
and step 3: looking ahead at the next feed speed planning interval;
look ahead the (m +1) th interval, calculate the allowable speed of the (m +1) th interval
Figure FDA0002744011310000025
Allowable acceleration
Figure FDA0002744011310000026
And allowable jerk
Figure FDA0002744011310000027
Judging whether the (m +1) th interval is an ending interval of the curve path; if yes, the allowable speed of the interval is updated
Figure FDA0002744011310000028
Comprises the following steps:
Figure FDA0002744011310000029
wherein s isfIs the arc length of the end interval;
calculating the ending speed of the current mth interval
Figure FDA00027440113100000210
Figure FDA00027440113100000211
Starting speed of m-th interval
Figure FDA00027440113100000212
Taking the actual ending speed of the previous interval;
and 4, step 4: self-adaptive planning of the feeding speed of the current interval;
the feed speed profile of the mth interval is planned in the following 4 cases:
case 1:
Figure FDA00027440113100000213
at this time, the velocity from the start is calculated
Figure FDA00027440113100000214
Is accelerated to
Figure FDA00027440113100000215
Required displacement
Figure FDA00027440113100000216
From
Figure FDA00027440113100000217
Slowing down to an end speed
Figure FDA00027440113100000218
Required displacement of
Figure FDA00027440113100000219
Let the maximum achievable feed speed in the mth interval be vcJudgment of
Figure FDA00027440113100000220
Figure FDA00027440113100000221
Whether or not to be established, and if so,
Figure FDA00027440113100000222
otherwise, vcComprises the following steps:
Figure FDA00027440113100000223
wherein
Figure FDA00027440113100000224
To be driven from
Figure FDA00027440113100000225
Up/down to
Figure FDA00027440113100000226
Required displacement; in the m-th interval, the feed speed is planned to be from
Figure FDA00027440113100000227
Increase speed to vcFrom v againcDown to
Figure FDA00027440113100000228
Two processes of (2);
case 2:
Figure FDA00027440113100000229
at the moment, the starting speed and the ending speed are equal to the maximum allowable speed of the current interval, and the feeding speed is planned to be a constant speed process in the mth interval;
case 3:
Figure FDA00027440113100000230
at this time, the ending speed is equal to the maximum allowable speed of the current interval and is greater than the starting speed, and thus, the feeding speed is programmed to be a slave in the m-th interval
Figure FDA0002744011310000031
To
Figure FDA0002744011310000032
The speed raising process of (2);
case 4:
Figure FDA0002744011310000033
at this time, the starting speed is equal to the maximum allowable speed of the current interval and is greater than the ending speed, and thus, the feeding speed is programmed to be a slave in the m-th interval
Figure FDA0002744011310000034
To
Figure FDA0002744011310000035
The deceleration process of (2);
and 5: feed rate planning for ending interval
Let m be m +1, judge whether the m-th interval is the end interval, if yes, let m be m +1
Figure FDA0002744011310000036
Marking the m-th section of feeding speed by adopting the method in the step 4); otherwise, repeating the step 3) to the step 5) to realize the region-by-region self-adaptive planning of the feeding speed of the longer spline curve path.
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