CN114273681B - Ring surface worm helicoid processing system and method based on serial mechanical arm - Google Patents
Ring surface worm helicoid processing system and method based on serial mechanical arm Download PDFInfo
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Abstract
The invention relates to a toroidal worm helicoid processing system and a toroidal worm helicoid processing method based on a serial mechanical arm, wherein the system comprises a processing platform and a mechanical arm, the processing platform is clamped and provided with a toroidal worm to be processed, the tail end of the mechanical arm is connected with a processing tool through an electric spindle, the toroidal worm rotates on the processing platform according to a set rotating speed, and the mechanical arm controls the working position and the processing force of the processing tool according to a set processing track and a set command so as to complete the processing of the toroidal worm. Compared with the prior art, the invention realizes the high-efficiency automatic processing of the enveloping worm, simultaneously ensures the processing precision, can effectively improve the consistency of the processing efficiency and the batch production, reduces the production cost, and is particularly suitable for processing the enveloping worm with large size.
Description
Technical Field
The invention relates to the technical field of processing of enveloping worms, in particular to a system and a method for processing a helicoid of an enveloping worm based on a serial mechanical arm.
Background
Compared with cylindrical worm transmission, the enveloping worm transmission has the advantages of strong bearing capacity, small volume, high transmission efficiency and long service life, is widely applied to transmission devices of mining and metallurgy, petrifaction, hoisting and transportation, ships, power and light industrial machinery, and particularly has more superior performance than the straight-profile enveloping worm transmission, such as plane, double conical surface and the like.
At present, the processing steps of the helicoid of the enveloping worm comprise two parts of rough processing and finish processing, wherein the rough processing is completed by turning or milling, and the finish processing is completed by grinding, the traditional grinding mode is carried out on a special machine tool with a rotary table, the centre distance is adjusted by moving the rotary table along the radial direction of the worm during processing, the transmission ratio is adjusted by matching a hanging wheel, even if the numerical control machine tool is adopted for processing, a special grinding head with a complex structure is required to be configured, and a special tool is required for the tool setting process.
For the processing of the spiral surface of the plane enveloping ring surface worm, a special grinding head is required to be arranged on a B-axis turntable of a machine tool, the B axis and the C axis are linked to grind the spiral surface on one side, when the other side of the spiral surface is processed, the worm is required to be arranged in a turning way, or the grinding head rotates for 360 degrees around the B axis to be processed in a reverse direction, and secondary clamping and reverse processing inevitably cause the increase of repeated positioning error and lower efficiency;
for the processing of the helicoids of the conical surface enveloping ring worm, although the helicoids on the left side and the right side can be formed simultaneously, the special grinding head has a complex structure, the machine tool is complex to adjust, the processing period is long, the cost is high, the processing range is limited by the diameter of the rotary table, the special grinding head is not favorable for the efficient automatic processing of the enveloping worm, and the development and application requirements of the existing enveloping worm are difficult to meet.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a system and a method for processing the helicoid of the enveloping worm based on a series mechanical arm so as to realize efficient and automatic processing of the enveloping worm and ensure the processing precision.
The purpose of the invention can be realized by the following technical scheme: the utility model provides a torus worm helicoid system of processing based on mechanical arm establishes ties, includes processing platform and arm, the centre gripping installation remains to process the torus worm on the processing platform, the end of arm is connected with the processing cutter through electric main shaft, the torus worm takes place to rotate according to setting for the rotational speed on the processing platform, the arm is according to the working position and the processing power of processing cutter of processing orbit and instruction control of setting for to accomplish the processing to the torus worm.
Further, an electric motor is arranged on the processing platform, and an output shaft of the electric motor is connected with the enveloping worm to be processed.
Further, the processing cutter is a grinding cutter or a turning cutter.
A toroidal worm helicoid processing method based on a serial mechanical arm comprises the following steps:
s1, establishing a kinematic model of a machining system, and calibrating a base coordinate system;
s2, generating a spiral surface processing path of the enveloping worm;
s3, planning the spiral surface track of the enveloping worm;
s4, preliminarily determining a machining track and a control instruction of the mechanical arm;
s5, aiming at the helicoid of the toroidal worm to be machined, establishing a mechanical arm machining simulation model, and adjusting a machining track and a control instruction of the mechanical arm according to a simulation result;
s6, generating a control program for processing the helicoid of the toroidal worm by the mechanical arm in an off-line manner according to the adjusted processing track and the control instruction of the mechanical arm;
s7, mounting the enveloping worm to be machined to a machining platform, and mounting a machining tool at the tail end of the mechanical arm through an electric spindle;
the enveloping worm to be processed rotates according to the set rotating speed, and meanwhile, the mechanical arm correspondingly controls the processing cutter according to the control program to complete the processing of the helicoid of the enveloping worm to be processed.
Further, the specific process of step S1 is: establishing a closed-chain kinematic relationship among the mechanical arm, the processing tool and the processing platform, namely a mechanical arm base, a mechanical arm tail end, the processing tool, a processing position point and a processing platform base;
and then calibrating the processing system by using a laser tracker, wherein the coordinate system of the laser tracker is a fixed measurement coordinate system, respectively calibrating transformation matrixes of the base coordinate systems of the mechanical arm and the processing platform relative to the measurement coordinate system, and calculating to obtain a relative transformation matrix between the base coordinate systems of the mechanical arm and the processing platform based on a relative coordinate transformation principle.
Further, the specific process of step S2 is: firstly, selecting a plurality of characteristic points on a spiral line, and fitting based on a trigonometric function method to obtain a processing track equation;
then discretizing a machining track equation to obtain a unit tangent vector and a unit internal normal vector of a corresponding discrete point, and determining machining pose information of the tail end of the mechanical arm, wherein path points on the machining track comprise two directions of the unit tangent vector and the unit internal normal vector, and the posture of a machining tool at the tail end of the mechanical arm is determined according to the two vector directions;
according to the processing technological requirements of the helicoid of the enveloping worm, the attitude of the processing tool at the tail end of the mechanical arm is specified as follows: during the machining operation, the normal vector f of the path point on the machining path and the X of the grinding tool TCP coordinate system t The directions are overlapped and are the directions of constant force control of the machining tool at the tail end of the mechanical arm and the Y of a TCP coordinate system t The direction is the tangent vector tau of the path point and points to the next processing point, and is also the moving direction of the processing tool, Z of the processing tool TCP coordinate system t The cross direction w = f × τ of the normal vector f of the direction and the path point and the tangent vector τ coincides with the right-hand rule.
Further, the specific process of step S3 is: given the speed of rotation omega of the worm 1 And the transmission ratio i of the worm gear pair according to i = omega 1 /ω 2 Calculating to obtain the rotation speed omega of the tail end of the grinding tool 2 ；
When the machining tool starts from the initial position and rotates anticlockwise to the final position along the mechanical arm, the worm rotates around the axis of the worm in the positive direction, and the speed direction of the worm is outward along the paper surface; when the machining tool rotates clockwise from the initial position to the final position along with the mechanical arm, the worm rotates around the axis in the reverse direction, the speed direction is inward along the paper surface, and the machining surface of the machining tool is tangent to the main base circle of the worm wheel all the time in the rotation process of the mechanical arm.
Further, in the step S3, for the planar double-enveloping worm, the machining tool rotates counterclockwise with the mechanical arm to machine a left-side spiral surface of the worm, and the machining tool rotates clockwise with the mechanical arm to machine a right-side spiral surface of the worm;
for the conical surface double-enveloping ring surface worm, the machining tool machines the helicoids on the left side and the right side of the worm simultaneously in the anticlockwise and clockwise rotation processes of the mechanical arm;
for a multi-head ring surface worm, after a machining tool rotates along with a mechanical arm to machine a spiral surface of a first head of the worm, the initial installation position of the worm needs to rotate 360/z around the rotation axis of the worm 1 Angle, wherein z 1 And (4) counting the number of the heads of the worm, continuously processing the helicoid of the second head, and continuously updating the processing track until the helicoid of the multi-head ring surface worm is processed.
Further, the specific process of step S4 is: the mechanical arm is based on a position control mode, so that the machining track is accurately tracked, the machining contact force is collected in real time through a six-dimensional force sensor arranged at the tail end of the mechanical arm, and the tail end X of a machining tool is machined based on an impedance control algorithm t Constant machining force control of direction.
Further, the specific process of step S5 is: the proportion of the built physical platform to the physical platform is 1:1, adopting a Solidworks and Matlab/Simulink module to jointly build a spiral surface system simulation platform of the processing ring surface worm of the serial mechanical arm;
after the simulation is finished, a rotation angle sequence diagram, a joint angle track tracking error diagram and an expected track and actual track comparison diagram of each joint of the serial mechanical arm are generated;
and determining whether the series mechanical arm stably and continuously moves according to the joint angle sequence diagram, the joint angle track tracking error diagram and the expected track and actual track comparison diagram to determine the accuracy of the processing track and the control instruction, so as to adjust the processing track and the control instruction of the mechanical arm.
Compared with the prior art, the processing platform and the mechanical arm are arranged, and the processing platform is used for clamping and mounting the enveloping worm to be processed, so that the enveloping worm rotates on the processing platform according to the set rotating speed; the tail end of the mechanical arm is connected with a machining tool through an electric spindle, and the mechanical arm is used for controlling the working position and the machining force of the machining tool according to the set machining track and the set command, so that the machining of the enveloping worm is completed, the automatic machining of the enveloping worm is realized, repeated positioning operation is not needed, the machining efficiency is improved, and the machining precision is guaranteed.
According to the method, firstly, a closed-chain kinematic model of the mechanical arm, a machining tool and a machining platform is established, a machining path of the helicoid of the toroidal worm is generated, a machining track is planned, and the machining track and a control instruction of the mechanical arm are determined by combining with simulation model adjustment, so that the accuracy of the set machining track and the control instruction is ensured, and the precision of machining the toroidal worm can be effectively improved.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention;
FIG. 2 is a schematic diagram of a coordinate system of the grinding system in the embodiment;
FIG. 3 is a schematic diagram of a grinding trace in the embodiment;
FIG. 4 is a diagram illustrating normal vectors and tangent vectors of path points in an embodiment;
FIG. 5 is a schematic view illustrating the grinding operation of the robot arm according to the embodiment;
FIG. 6 is a diagram illustrating pose constraint relationships in an embodiment;
FIG. 7 is a schematic diagram of a control architecture for a robot arm according to one embodiment;
the notation in the figure is: 1. the machining device comprises a mechanical arm, 2, a machining platform, 3, a ring surface worm, 4, an electric spindle, 5 and a machining tool.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
As shown in fig. 1, a toroidal worm helicoid processing system based on serial mechanical arms comprises a processing platform 2 and a mechanical arm 1, wherein a toroidal worm 3 to be processed is clamped and mounted on the processing platform 2, the tail end of the mechanical arm 1 is connected with a processing tool 5 through an electric spindle 4, the toroidal worm 3 rotates on the processing platform 2 according to a set rotating speed, and the mechanical arm 1 controls the working position of the processing tool 5 according to a set processing track and a set command so as to complete the processing of the toroidal worm 3.
Wherein, the processing platform 2 is provided with an electric motor, and an output shaft of the electric motor is connected with the enveloping worm 3 to be processed so as to drive the enveloping worm 3 to rotate.
According to the processing requirement, the processing cutter 5 can be a grinding cutter or a turning cutter.
The system is applied to practice to realize a toroidal worm helicoid processing method based on a series mechanical arm, and the method comprises the following steps:
s1, establishing a kinematic model of a processing system, and calibrating a base coordinate system, specifically:
establishing a closed-chain kinematic relationship among the mechanical arm, the processing tool and the processing platform, namely a mechanical arm base, a mechanical arm tail end, the processing tool, a processing position point and a processing platform base;
then, calibrating the processing system by using a laser tracker, wherein the coordinate system of the laser tracker is a fixed measurement coordinate system, respectively calibrating transformation matrixes of the base coordinate systems of the mechanical arm and the processing platform relative to the measurement coordinate system, and calculating to obtain a relative transformation matrix between the base coordinate systems of the mechanical arm and the processing platform based on a relative coordinate transformation principle;
s2, generating a spiral surface processing path of the enveloping worm, specifically:
firstly, selecting a plurality of characteristic points on a spiral line, and fitting based on a trigonometric function method to obtain a processing track equation;
then discretizing a machining track equation to obtain a unit tangent vector and a unit internal normal vector of a corresponding discrete point, and determining the machining pose information of the tail end of the mechanical arm, wherein path points on the machining track comprise the unit tangent vector and the unit internal normal vector, and the posture of a machining tool at the tail end of the mechanical arm is determined according to the two vector directions;
according to the processing technological requirements of the helicoid of the enveloping worm, the attitude of the processing tool at the tail end of the mechanical arm is specified as follows: during the machining operation, the normal vector f of the path point on the machining path and the X of the grinding tool TCP coordinate system t The directions are overlapped and are the directions of constant force control of the machining tool at the tail end of the mechanical arm and the Y of a TCP coordinate system t The direction is the tangent line vector tau of the path point and points to the next processing point, and is also the moving direction of the processing cutter, and the processing cutter TCP is arranged onZ of the mark system t The direction and the cross direction w = f × τ of the normal vector f of the path point and the tangent vector τ coincide, and meet the right-hand rule;
s3, planning a helicoid track of the enveloping worm, specifically:
given the speed of rotation omega of the worm 1 And the transmission ratio i of the worm gear pair according to i = omega 1 /ω 2 Calculating to obtain the rotation speed omega of the tail end of the grinding tool 2 ；
When the machining tool starts from the initial position and rotates anticlockwise to the final position along the mechanical arm, the worm rotates around the axis of the worm in the positive direction, and the speed direction of the worm is outward along the paper surface; when the machining tool rotates clockwise from the initial position to the final position along with the mechanical arm, the worm rotates reversely around the axis of the worm, the speed direction of the worm is inward along the paper surface, and the machining surface of the machining tool is always tangent to the main base circle of the worm gear in the rotating process of the mechanical arm;
for the planar double-enveloping ring surface worm, a machining tool rotates anticlockwise with a mechanical arm to machine a left side spiral surface of the worm, and the machining tool rotates clockwise with the mechanical arm to machine a right side spiral surface of the worm;
for the conical surface double-enveloping ring surface worm, the machining tool machines the helicoids on the left side and the right side of the worm simultaneously in the anticlockwise and clockwise rotation processes of the mechanical arm;
for a multi-head ring surface worm, after a machining tool rotates along with a mechanical arm to machine a spiral surface of a first head of the worm, the initial installation position of the worm needs to rotate 360/z around the rotation axis of the worm 1 Angle, wherein z 1 Counting the heads of the worm, then continuously processing the helicoid of the second head, and continuously updating the processing track until the helicoid of the multi-head ring surface worm is processed;
s4, preliminarily determining the machining track and the control instruction of the mechanical arm, specifically:
the mechanical arm is based on a position control mode, so that the machining track is accurately tracked, the machining contact force is collected in real time through a six-dimensional force sensor arranged at the tail end of the mechanical arm, and the tail end X of a machining tool is machined based on an impedance control algorithm t Constant machining force control of direction;
s5, aiming at the helicoid of the toroidal worm to be machined, establishing a mechanical arm machining simulation model, and adjusting the machining track and the control instruction of the mechanical arm according to the simulation result, specifically:
the proportion of the built physical platform to the physical platform is 1:1, adopting a Solidworks and Matlab/Simulink module to jointly build a spiral surface system simulation platform of the processing ring surface worm of the serial mechanical arm;
after the simulation is finished, a rotation angle sequence diagram, a joint angle track tracking error diagram and an expected track and actual track comparison diagram of each joint of the serial mechanical arm are generated;
determining whether the series mechanical arm stably and continuously moves or not according to each joint corner angle sequence diagram, and determining the accuracy of a processing track and a control instruction according to a joint angle track tracking diagram, a joint angle track tracking error diagram and an expected track and actual track comparison diagram, so as to adjust the processing track and the control instruction of the mechanical arm;
s6, generating a control program for processing the helicoid of the toroidal worm by the mechanical arm in an off-line manner according to the adjusted processing track and the control instruction of the mechanical arm;
s7, mounting the enveloping worm to be machined to a machining platform, and mounting a machining tool at the tail end of the mechanical arm through an electric spindle;
the enveloping worm to be processed rotates according to the set rotating speed, and meanwhile, the mechanical arm correspondingly controls the processing cutter according to the control program to complete the processing of the helicoid of the enveloping worm to be processed.
In the embodiment, the spiral surface of the enveloping worm is subjected to finish machining, so that a grinding tool is selected and installed at the tail end of the mechanical arm. In this embodiment, a modified torus worm pair is taken as an example, and the relevant parameters are as follows: number of enveloping worm heads z 1 Number of worm gear teeth z =4 2 =40, mesh center distance a =160mm, gear ratio i =10, diameter d of tip circle of worm a =267mm, diameter d of worm root f =250mm, worm wheel end face modulus m t =10.45mm, diameter of main base circle d b =95mm, length of worm work L w =90mm, mechanical arm corner
The range of values of (A) is 0 to 0.8rad.
A mechanical arm with the model number of ER20-C10 is adopted, the load of the mechanical arm is 20Kg, the self weight of the mechanical arm is 220Kg, the arm span is 1722mm, and a machine tool based on a serial mechanical arm grinding system comprises the mechanical arm, a grinding platform, a ring surface worm, an electric spindle and a grinding tool. The grinding platform is mainly used for clamping the enveloping worm, and the rotating speed of the enveloping worm during grinding is set according to the technical requirements of the machined enveloping worm; the electric spindle and the grinding tool are arranged at the tail end of the mechanical arm, the mechanical arm clamps the grinding tool, and the enveloping worm is processed according to the grinding track and the control method.
Based on the method process proposed by the technical scheme, the application process of the embodiment includes:
1. a coordinate system for grinding the helicoids of the enveloping worms using a tandem robot arm was established as shown in figure 2. Wherein T is w Representing the world coordinate system, T b1 Indicating the base coordinate system, T, of the tandem robot arm f1 Representing the coordinate system of the end of the arm, T t Representing the grinding tool end coordinate system, T b2 Representing the central coordinate system, T, of the grinding table j Representing the coordinate system T of any discrete point on the grinding path of the helicoid of the enveloping worm w And T b1 And (4) overlapping. The series mechanical arm and the grinding platform form a closed-chain kinematic relationship, and the expression of the mechanical arm 1 base, the mechanical arm 1 tail end, the grinding tool, the grinding point and the grinding platform 2 base is as follows: b1 T f1 f1 T t t T j j T b2 ＝ b1 T b2 ， j t b2 determined according to the specific grinding track requirements, is a known matrix, b1 T b2 is determined by the calibration of the base coordinate system, f1 T t determined by calibration of a TCP tool according to the installation mode, tt T j is an identity matrix, so that b1 T f1 ＝ b1 T b2 ( j T b2 ) -1 ( t T j ) -1 ( f1 T) -1 Can obtain b1 T f1 And determining a coordinate system of the end of the mechanical arm grinding tool according to the coordinate system, and then solving the motion angle of each joint according to the inverse kinematics. Through a laser tracker calibration system, wherein a laser tracker coordinate system is a fixed measurement coordinate system, transformation matrixes T of base coordinate systems of the serial mechanical arm and the grinding platform relative to the measurement coordinate system are respectively calibrated 1 ,T 2 . Based on the principle of relative coordinate transformation, by formula b1 T b2 ＝T 2 -1 T 1 Calculating to obtain a relative pose homogeneous matrix between the serial mechanical arm and a base coordinate system of the grinding platform b2 T b1 。
2. Taking 20 characteristic points on the 4-head annular worm indexing annular spiral line, fitting the points based on a trigonometric function method to generate a spiral line to obtain a grinding track equation, and discretizing the track equation to obtain surface normal vectors of corresponding discrete points, thereby determining the grinding pose information of the tail end of the serial mechanical arm; the path point on the grinding track comprises two directions of a unit tangent vector tau and a unit internal normal vector f, as shown in fig. 4, and then the attitude of the end grinding tool of the serial robot is further determined according to the two vector directions, and the attitude of the end grinding tool of the serial robot arm is specified as follows according to the processing requirements of the toroidal worm: during the machining operation, the normal vector f of the path point on the grinding path and the X of the grinding tool TCP coordinate system t The directions are overlapped, and simultaneously, the direction is controlled by the constant force at the tail end of the grinding tool of the serial mechanical arm, and the Y of a TCP coordinate system t The direction is the tangent vector tau of the path point and points to the next grinding point, which is also the direction of the movement of the grinding tool. Z of TCP coordinate system of grinding tool t The cross direction w = f × τ of the normal vector f of the direction and the path point and the tangent vector τ coincides with the right-hand rule.
3. Given the speed of rotation omega of the worm 1 =1400r/min and the gear ratio of the worm gear pair i =10, according to i = ω 1 /ω 2 Calculating to obtain the rotation speed omega of the tail end of the grinding tool 2 =140r/min. As shown in FIG. 5, the grinding tool rotates counterclockwise along with the arm from the initial position AWhen the grinding tool rotates to the end position A, the worm rotates around the axis of the grinding tool in the positive direction (the speed direction is outward along the paper surface), when the grinding tool rotates clockwise from the initial position B to the end position A along the mechanical arm, the worm rotates around the axis of the grinding tool in the negative direction (the speed direction is inward along the paper surface), and in the rotation process of the mechanical arm, the machining surface of the grinding tool always rotates with the radius r b The main base circle of the worm gear is tangent, and the rotation center of the mechanical arm is O d At a rotation angle of
Center distance O of worm gear pair d O 1 =160mm, radius of worm tooth top circle R a =133.5mm. For the planar worm with the secondary enveloping ring surface, a grinding tool rotates anticlockwise with a mechanical arm to machine a left spiral surface of the worm, and the grinding tool rotates clockwise with the mechanical arm to machine a right spiral surface of the worm; for the conical surface secondary enveloping ring surface worm, the grinding tool simultaneously processes the left and right spiral surfaces of the worm in the anticlockwise and clockwise rotation processes of the mechanical arm; for a multi-head enveloping worm, after a grinding tool rotates with a mechanical arm to machine the spiral surface of the first head of the worm, the initial installation position of the worm needs to rotate 360/4=90 ° around the rotation axis of the worm, then the spiral surface of the second head is machined according to the method, and the grinding track is continuously updated until the machining of the spiral surface of the multi-head enveloping worm is completed.
According to the processing technology requirement, the serial mechanical arm needs to carry out constant grinding force control while working along the grinding track, so that in the Cartesian operation space of the mechanical arm, the mechanical arm is subjected to force/position operation space decomposition, namely in X t Direction of constant force control, Y t 、Z t The direction is controlled, and the pose constraint relation is shown in fig. 6. During grinding, the serial arm holds the grinding tool while maintaining the constant force control direction coincident with the normal direction f of the path point, so that the X-ray in the coordinate system of the grinding tool of the serial arm t The direction is controlled by constant force and is always kept horizontal, namely the grinding attitude is b1 R T ＝[1 0 0] T In Y, at t ，Z t Direction position control following grinding railAnd (4) tracing. Calculating the position of the end of the grinding tool from the kinematic model b1 P T ＝[x t y t z t ] T ＝ b1 T b2 ( j T b2 ) -1 ( t T j ) -1 [x j y j z j 1] T . Finally, the kinematic angle of each joint can be obtained by inverse solution of kinematics. The transformation matrix T comprises a position vector P and a rotation matrix R, wherein:
P＝[p x p y p z ] T
4. the serial mechanical arm accurately tracks the grinding track based on a position control mode, and the control structure is shown in fig. 7. Because the control cycle of the built control system is short, the characteristic of integral is not considered, and the serial mechanical arm adopts a single-joint PD control mode. Desired position θ of each joint ti Calculated by inverse kinematics, the joint position θ i Velocity of joint
The driving quantity of each joint of the mechanical arm is acquired by a six-dimensional force sensor in real time
Wherein k is pi Is a proportionality coefficient, k vi Are differential coefficients.
Control parameter k in servo control system for each joint pi 、k vi The adjustment of (2) continuously adjusting the proportionality coefficient according to the amplitude of the deviation oscillation to quickly reduce the errorAnd then, the differential coefficient is adjusted to reduce the oscillation frequency of the deviation, the change of the track is quickly and accurately tracked, and the motion controlled process of the whole serial mechanical arm is ensured to be stable. And each joint in the joint servo control system is regarded as a single-input single-output system, each joint is independently controlled, and then synchronous linkage control of each joint is completed through a periodic synchronous interpolation mode of a driver, so that accurate motion control of the serial mechanical arm is realized.
The contact force information of the series mechanical arm and the enveloping worm is acquired in real time through a six-dimensional force sensor arranged at the tail end of the series mechanical arm, and X is obtained after filtering and gravity compensation of the force sensor t Directional actual grinding force F, which is in contact with the desired contact force F d Deviation f of e As an input to a second order low pass filter, output X t And feeding back the correction value to a reference motion track of the robot in the X direction in a Cartesian operation space through a selection matrix S, S', updating the motion track of the mechanical arm, calculating the angle of each joint through the kinematics of the mechanical arm, continuously acquiring grinding force contact information by a six-dimensional force sensor at the tail end of the mechanical arm when the mechanical arm enters the next grinding period, repeatedly executing the steps, and continuously updating the grinding track until the task of grinding the helicoid of the toroidal worm is completed.
5. And (3) building a simulation environment, and firstly, developing kinematics, trajectory planning and control algorithm of the serial mechanical arm grinding system by using an M file and an S function in MATLAB/Simulink. A grinding system CAD model is established by utilizing SolidWorks three-dimensional software, then the system CAD model is exported into an XML format file and a STEP model which can be read by MATLAB through a Simscape Multibody Link plug-in, finally the STEP model of the system is loaded into MATLAB/Simulink through reading the XML format file, and the Simscape simulation model of the grinding system is generated by combining algorithms such as kinematics and trajectory planning. Generally, an original system simulation model imported into Simulink cannot be directly controlled, the model needs to be further optimized and relevant control parameter configuration, including STEP model path modification, rotation input and output quantity configuration, mechanical arm initial posture joint angle configuration, joint Rotation positive direction setting and the like, and finally the model is packaged into an independent module. And then, performing kinematics, trajectory planning and control algorithm development of the grinding system by using an M file and an S function in MATLAB/Simulink, performing related algorithm simulation based on a simulation platform, dynamically verifying the feasibility of the algorithm through a built simulation environment, and further analyzing the algorithm performance by using a Scope component and a To Workspace component To store data.
And (3) generating angle, speed and acceleration change graphs of all joints of the mechanical arm, wherein if the curves in the change graphs are stable and continuous, the kinematic model of the grinding toroidal worm helicoid system of the serial mechanical arm built in the step one is correct. Secondly, generating a comparison graph of the actual track and the expected track and a tracking error graph of the joint angle track, wherein if the actual track can move according to the expected track and the error is small, the serial mechanical arm is correct based on a PD position control mode; to the tail end X of the mechanical arm t And applying an external force in the direction, observing whether the track graph can adapt to the external force to adjust and then return to the grinding path again, if the mechanical arm can adapt to the change of the external force to adjust the motion track, and when the interference force is zero, the serial mechanical arm can quickly and stably continue to track the expected track, so that the grinding constant force control of the serial mechanical arm based on the position impedance control algorithm is feasible.
6. Aiming at the simulation result, the process of grinding the helicoid of the enveloping worm of the serial mechanical arm is adjusted, and the program of grinding the helicoid of the enveloping worm of the mechanical arm is generated off line after comprehensive adjustment.
In the embodiment, finish machining is performed on the enveloping worm, and if only rough machining is needed in practical application, the grinding tool of the embodiment is replaced by a turning tool.
In conclusion, the technical scheme provided by the invention can realize the automatic processing of the enveloping worm, avoid repeated positioning, effectively ensure the consistency of the precision of the enveloping worm in batch production, improve the processing efficiency and reduce the production cost, and is particularly suitable for processing the enveloping worm with large size.
Claims (8)
1. The toroidal worm helicoid processing system based on the serial mechanical arm is characterized by comprising a processing platform (2) and a mechanical arm (1), wherein a toroidal worm (3) to be processed is clamped and mounted on the processing platform (2), the tail end of the mechanical arm (1) is connected with a processing tool (5) through an electric spindle (4), the toroidal worm (3) rotates on the processing platform (2) according to a set rotating speed, and the mechanical arm (1) controls the working position and the processing force of the processing tool (5) according to a set processing track and a set instruction so as to complete the processing of the toroidal worm (3);
the toroidal worm helicoid processing system is applied to realize a toroidal worm helicoid processing method based on a series mechanical arm, and comprises the following steps:
s1, establishing a kinematic model of a machining system, and calibrating a base coordinate system;
s2, generating a spiral surface processing path of the enveloping worm;
s3, planning the spiral surface track of the enveloping worm;
s4, preliminarily determining a machining track and a control instruction of the mechanical arm;
s5, aiming at the helicoid of the toroidal worm to be machined, establishing a mechanical arm machining simulation model, and adjusting the machining track and the control instruction of the mechanical arm according to the simulation result;
s6, according to the adjusted machining track and the control instruction of the mechanical arm, a control program for machining the spiral surface of the ring surface worm by the mechanical arm is generated in an off-line mode;
s7, mounting the enveloping worm to be machined to a machining platform, and mounting a machining tool at the tail end of the mechanical arm through an electric spindle;
the enveloping worm to be processed rotates according to the set rotating speed, and the mechanical arm correspondingly controls the processing cutter according to the control program to complete the processing of the helicoid of the enveloping worm to be processed;
the specific process of the step S2 is as follows: firstly, selecting a plurality of characteristic points on a spiral line, and fitting based on a trigonometric function method to obtain a processing track equation;
then discretizing a machining track equation to obtain a unit tangent vector and a unit internal normal vector of a corresponding discrete point, and determining the machining pose information of the tail end of the mechanical arm, wherein path points on the machining track comprise the unit tangent vector and the unit internal normal vector, and the posture of a machining tool at the tail end of the mechanical arm is determined according to the two vector directions;
according to the processing technological requirements of the helicoid of the enveloping worm, the attitude of the processing tool at the tail end of the mechanical arm is specified as follows: during the machining operation, the normal vector f of the path point on the machining path and the X of the grinding tool TCP coordinate system t The directions are overlapped and are the directions of constant force control of the machining tool at the tail end of the mechanical arm and the Y of a TCP coordinate system t The direction is the tangent vector tau of the path point and points to the next processing point, and is also the moving direction of the processing tool, Z of the processing tool TCP coordinate system t The direction w = f × τ is coincident with the direction w = f × τ of the cross product of the normal vector f of the direction and the path point and the tangent vector τ, and conforms to the right-hand rule.
2. The toroidal worm helicoidal machining system based on serial mechanical arms according to claim 1, characterized in that the machining platform (2) is provided with an electric motor, the output shaft of which is connected with the toroidal worm (3) to be machined.
3. The toroidal worm helicoidal machining system based on serial mechanical arms according to claim 1, characterized in that the machining tool (5) is a grinding tool or a turning tool.
4. The toroidal worm helicoid processing system based on serial mechanical arm according to claim 1, wherein the specific process of step S1 is: establishing a closed-chain kinematic relationship among the mechanical arm, the processing tool and the processing platform, namely a mechanical arm base, the tail end of the mechanical arm, the processing tool, a processing position point and a processing platform base;
and then calibrating the processing system by using a laser tracker, wherein the coordinate system of the laser tracker is a fixed measurement coordinate system, respectively calibrating transformation matrixes of the base coordinate systems of the mechanical arm and the processing platform relative to the measurement coordinate system, and calculating to obtain a relative transformation matrix between the base coordinate systems of the mechanical arm and the processing platform based on a relative coordinate transformation principle.
5. The toroidal worm helicoid processing system based on serial mechanical arms as claimed in claim 1, wherein the specific process of step S3 is: given the speed of rotation omega of the worm 1 And the transmission ratio i of the worm gear pair according to i = omega 1 /ω 2 Calculating to obtain the rotation speed omega of the tail end of the grinding tool 2 ；
When the machining tool starts from the initial position and rotates anticlockwise to the final position along the mechanical arm, the worm rotates around the axis of the worm in the positive direction, and the speed direction of the worm is outward along the paper surface; when the machining tool rotates clockwise from the initial position to the final position along with the mechanical arm, the worm rotates reversely around the axis of the worm, the speed direction of the worm is inward along the paper surface, and the machining surface of the machining tool is always tangent to the main base circle of the worm wheel in the rotation process of the mechanical arm.
6. The toroidal worm helicoid processing system based on serial mechanical arms as claimed in claim 5, wherein in step S3, for a planar double-enveloping toroidal worm, the processing tool rotates clockwise with the mechanical arm to process the left helicoid of the worm, and the processing tool rotates clockwise with the mechanical arm to process the right helicoid of the worm;
for the conical surface double-enveloping ring surface worm, the machining tool machines the helicoids on the left side and the right side of the worm simultaneously in the anticlockwise and clockwise rotation processes of the mechanical arm;
for a multi-start ring surface worm, after a processing tool rotates along with a mechanical arm to process a spiral surface of a first head of the worm, the initial installation position of the worm needs to rotate 360/z around the rotation axis of the worm 1 Angle, wherein z 1 And (4) counting the number of the heads of the worm, continuously processing the helicoid of the second head, and continuously updating the processing track until the helicoid of the multi-head ring surface worm is processed.
7. The toroidal worm helicoid processing system based on serial mechanical arm according to claim 1, wherein the specific process of step S4 is: the mechanical arm is based on a position control mode to accurately track a processing trackThe six-dimensional force sensor arranged at the tail end of the mechanical arm is used for acquiring the machining contact force in real time and machining the tail end X of the cutter based on an impedance control algorithm t Constant machining force control of direction.
8. The toroidal worm helicoid processing system based on serial mechanical arms as claimed in claim 1, wherein the specific process of step S5 is: the proportion of the built physical platform to the physical platform is 1:1, adopting a Solidworks and Matlab/Simulink module to jointly build a spiral surface system simulation platform of the processing ring surface worm of the serial mechanical arm;
after the simulation is finished, a rotation angle sequence diagram, a joint angle track tracking error diagram and an expected track and actual track comparison diagram of each joint of the serial mechanical arm are generated;
and determining whether the series mechanical arm stably and continuously moves according to the joint angle sequence diagram, the joint angle track tracking error diagram and the expected track and actual track comparison diagram to determine the accuracy of the processing track and the control instruction, so as to adjust the processing track and the control instruction of the mechanical arm.
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