CN114273681B - Toroidal worm helical surface machining system and method based on tandem manipulator - Google Patents

Abstract

The invention relates to a helical surface processing system and method of a toroidal worm based on a series mechanical arm. The system includes a processing platform and a mechanical arm. The toroidal worm to be processed is clamped and installed on the processing platform, and the end of the mechanical arm is connected by an electric spindle. There is a processing tool, and the toroidal worm rotates on the processing platform according to the set speed. The mechanical arm controls the working position and processing force of the processing tool according to the set processing trajectory and instructions to complete the processing of the toroidal worm. Compared with the prior art, the present invention realizes high-efficiency automatic processing of toroidal worms while ensuring machining accuracy, can effectively improve processing efficiency and batch production consistency, and reduce production costs, and is especially suitable for processing large-sized torus worm.

Description

Toroidal worm helical surface machining system and method based on tandem manipulator

technical field

The invention relates to the technical field of toroidal worm machining, in particular to a toroidal worm helical surface machining system and method thereof based on tandem mechanical arms.

Background technique

Compared with the cylindrical worm drive, the toroidal worm drive has the advantages of strong load capacity, small size, high transmission efficiency and long service life, and has been widely used in mining and metallurgy, petrochemical, lifting and transportation, ships, power and light industrial machinery The transmission device, especially the secondary enveloping toroidal worm drive such as plane and double cone, has more superior performance than the straight profile toroidal worm drive.

At present, the processing steps of the helical surface of the toroidal worm include rough machining and finishing. Among them, the rough machining is completed by turning or milling, and the finishing is completed by grinding. The traditional grinding method is to The center distance is adjusted by moving the rotary table along the radial direction of the worm during processing, and the transmission ratio is adjusted by matching the hanger wheel. Even if the CNC machine tool is used for processing, it is necessary to configure a special grinding head with a complex structure. The knife process requires special tooling.

For the machining of the plane enveloping toroidal worm helicoid, a special grinding head needs to be installed on the B-axis turntable of the machine tool, and the B-axis and the C-axis are linked to realize the grinding of one side of the helicoid. When processing the other side of the helicoid, It is also necessary to reverse the installation of the worm, or rotate the grinding head 360° around the B axis for reverse processing, and the secondary clamping and reverse processing will inevitably lead to increased repeat positioning errors and low efficiency;

For the processing of the helical surface of the cone, torus, and worm, although the left and right helicoids can be formed at the same time, the structure of the special grinding head is complicated, the adjustment of the machine tool is cumbersome, the processing cycle is long, and the cost is high, and the processing range is limited by the diameter of the rotary table. , all of the above are not conducive to the efficient automatic processing of toroidal worms, and it is difficult to meet the current development and application requirements of toroidal worms.

Contents of the invention

The object of the present invention is to provide a helical surface processing system and method for toroidal worms based on tandem mechanical arms in order to overcome the defects of the above-mentioned prior art, so as to realize efficient automatic processing of toroidal worms while ensuring machining accuracy.

The purpose of the present invention can be achieved through the following technical solutions: a toroidal worm helical surface processing system based on series mechanical arms, including a processing platform and a mechanical arm, the toroidal worm to be processed is clamped and installed on the processing platform, the The end of the mechanical arm is connected with a processing tool through the electric spindle, and the toroidal worm rotates on the processing platform according to the set speed. The mechanical arm controls the working position and processing force of the processing tool according to the set processing trajectory and instructions. To complete the processing of the toroidal worm.

Further, an electric motor is arranged on the processing platform, and the output shaft of the electric motor is connected with the toroidal worm to be processed.

Further, the processing tool is a grinding tool or a turning tool.

A method for machining the helical surface of a toroidal worm based on a tandem mechanical arm, comprising the following steps:

S1. Establish the kinematics model of the processing system and calibrate the base coordinate system;

S2, generate the helical surface processing path of the toroidal worm;

S3, planning the trajectory of the helical surface of the toroidal worm;

S4. Preliminarily determine the processing trajectory and control instructions of the mechanical arm;

S5. For the helical surface of the toroidal worm to be processed, establish a machining simulation model of the manipulator, and adjust the machining trajectory and control instructions of the manipulator according to the simulation results;

S6. According to the adjusted machining trajectory and control instructions of the mechanical arm, a control program for machining the helical surface of the toroidal worm with the mechanical arm is generated offline;

S7. Install the toroidal worm to be processed on the processing platform, and install the processing tool at the end of the mechanical arm through the electric spindle;

Make the toroidal worm to be processed rotate according to the set speed, and at the same time, the mechanical arm controls the processing tool according to the control program to complete the processing of the helical surface of the toroidal worm to be processed.

Further, the specific process of the step S1 is: establish the closed-chain kinematic relationship between the robotic arm, the processing tool and the processing platform, that is, the base of the robotic arm - the end of the mechanical arm - the processing tool - the processing position point - the base of the processing platform seat;

Then use the laser tracker to calibrate the processing system. The laser tracker coordinate system is a fixed measurement coordinate system, and the transformation matrix of the base coordinate system of the manipulator and the processing platform relative to the measurement coordinate system is calibrated respectively. Based on the principle of relative coordinate transformation, The relative transformation matrix between the base coordinate system of the manipulator and the processing platform is calculated.

Further, the specific process of the step S2 is as follows: first select a number of feature points on a helix, and obtain the processing trajectory equation based on trigonometric function fitting;

Then the processing trajectory equation is discretized to obtain the unit tangent vector and the unit normal vector of the corresponding discrete points, thereby determining the processing pose information at the end of the manipulator, where the path points on the processing trajectory include the unit tangent vector and the unit internal normal vector The two directions of the normal vector, according to these two vector directions, determine the attitude of the machining tool at the end of the robotic arm;

According to the processing requirements of the helical surface of the toroidal worm, the posture of the machining tool at the end of the mechanical arm is specified as follows: During the processing operation, the normal vector f of the path point on the machining track coincides with the _Xt direction of the TCP coordinate system of the grinding tool, At the same time, it is also the direction of the constant force control of the machining tool at the end of the mechanical arm. The Y _t direction of the TCP coordinate system is the tangent vector τ of the path point and points to the next processing point. It is also the moving direction of the machining tool. The Z of the TCP coordinate system of the machining tool is The _t direction coincides with the cross product direction w=f×τ of the normal vector f of the path point and the tangent vector τ, and conforms to the right-hand rule.

Further, the specific process of the step S3 is: given the rotational speed _ω1 of the worm and the transmission ratio i of the worm pair, the rotational speed _ω2 of the end of the grinding tool is calculated according to i= _ω1 / _ω2 ;

When the processing tool rotates counterclockwise with the mechanical arm to the end position from the initial position, the worm rotates positively around its axis, and the speed direction is outward along the paper surface; when the processing tool rotates clockwise with the mechanical arm to the end position from the initial position, the worm Rotate in reverse around its axis, and the speed direction is inward along the paper surface. During the rotation of the mechanical arm, the processing surface of the processing tool is always tangent to the main base circle of the worm wheel.

Further, in the step S3, for a planar quadratic enveloping toroidal worm, the machining tool rotates counterclockwise 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 side of the worm. Helicoid;

For the conical surface secondary enveloping toroidal worm, the machining tool simultaneously processes the left and right helical surfaces of the worm during the counterclockwise and clockwise rotation of the mechanical arm;

For the multi-head toroidal worm, after the machining tool rotates with the mechanical arm to process the helical surface of the first head of the worm, it is necessary to rotate the initial installation position of the worm around its rotation axis by an angle of 360/z ₁ , where z ₁ is the head of the worm number, and then continue to process the helicoid of the second head, and continuously update the machining track until the processing of the helicoid of the multi-head toroidal worm is completed.

Further, the specific process of step S4 is: the mechanical arm is based on the position control method to accurately track the processing trajectory, and the six-dimensional force sensor installed at the end of the mechanical arm is used to collect the processing contact force in real time, and the processing is performed based on the impedance control algorithm Constant machining force control in the X _t direction of the tool tip.

Further, the specific process of the step S5 is: build a simulation platform with a ratio of 1:1 to the real physical platform, and use Solidworks and Matlab/Simulink modules to jointly build a series manipulator to process the torus worm helical surface system simulation platform;

After the simulation is completed, the rotation angle sequence diagram of each joint of the serial manipulator, the joint angle trajectory tracking diagram, the joint angle trajectory tracking error diagram, and the comparison diagram between the expected trajectory and the actual trajectory are generated;

Determine whether the tandem manipulator moves smoothly and continuously from the angle sequence diagram of each joint, and determine the accuracy of the processing trajectory and control instructions according to the joint angle trajectory tracking diagram, joint angle trajectory tracking error diagram, and the comparison diagram between the expected trajectory and the actual trajectory , so as to adjust the machining trajectory and control instructions of the robotic arm.

Compared with the prior art, the present invention sets the processing platform and the mechanical arm, and uses the processing platform to clamp and install the toroidal worm to be processed, so that the toroidal worm rotates on the processing platform according to the set speed; and at the end of the mechanical arm The machining tool is connected to the electric spindle, and the mechanical arm is used to control the working position and processing force of the machining tool according to the set machining trajectory and instructions, so as to complete the machining of the toroidal worm, thereby realizing the automatic processing of the toroidal worm, and There is no need to perform repeated positioning operations, which not only improves the processing efficiency, but also ensures the processing accuracy.

The present invention first establishes the closed-chain kinematics model of the mechanical arm, the processing tool and the processing platform, generates the processing path of the helical surface of the torus worm, plans the processing trajectory, and adjusts the simulation model to determine the processing trajectory and control instructions of the mechanical arm. This ensures the accuracy of the set machining trajectory and control instructions, and can effectively improve the accuracy of machining the toroidal worm.

Description of drawings

Fig. 1 is a schematic diagram of the system structure of the present invention;

Fig. 2 is the coordinate system schematic diagram of grinding system in the embodiment;

Fig. 3 is the schematic diagram of grinding track in the embodiment;

Fig. 4 is the schematic diagram of path point normal vector and tangent vector in the embodiment;

Fig. 5 is a schematic diagram of the working principle of mechanical arm grinding in the embodiment;

Fig. 6 is a schematic diagram of pose constraint relationship in the embodiment;

7 is a schematic diagram of the control architecture of the robotic arm in the embodiment;

Explanation of marks in the figure: 1. Mechanical arm, 2. Processing platform, 3. Toroidal worm, 4. Electric spindle, 5. Processing tool.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Example

As shown in Figure 1, a toroidal worm helical surface processing system based on series mechanical arms includes a processing platform 2 and a mechanical arm 1. The toroidal worm 3 to be processed is clamped and installed on the processing platform 2, and the end of the mechanical arm 1 passes through the The electric spindle 4 is connected with a processing tool 5, the toroidal worm 3 rotates on the processing platform 2 according to the set speed, and the mechanical arm 1 controls the working position of the processing tool 5 according to the set processing trajectory and instructions to complete the toroidal worm 3 processing.

Wherein, the processing platform 2 is provided with a motor, and the output shaft of the motor is connected with the toroidal worm 3 to be processed to drive the toroidal worm 3 to rotate.

According to processing requirements, the processing tool 5 can be a grinding tool or a turning tool.

The above system is applied in practice to realize a method of machining the helical surface of the toroidal worm based on the tandem manipulator, including the following steps:

S1. Establish the kinematics model of the processing system and calibrate the base coordinate system, specifically:

Establish the closed-chain kinematics relationship between the robotic arm, the processing tool and the processing platform, that is, the base of the robotic arm - the end of the mechanical arm - the processing tool - the processing position point - the base of the processing platform;

Then use the laser tracker to calibrate the processing system. The laser tracker coordinate system is a fixed measurement coordinate system, and the transformation matrix of the base coordinate system of the manipulator and the processing platform relative to the measurement coordinate system is calibrated respectively. Based on the principle of relative coordinate transformation, Calculate the relative transformation matrix between the base coordinate system of the manipulator and the processing platform;

S2. Generate the machining path of the helical surface of the torus worm, specifically:

First select several feature points on a helical line, and obtain the machining trajectory equation based on trigonometric function fitting;

Then the processing trajectory equation is discretized to obtain the unit tangent vector and the unit normal vector of the corresponding discrete points, thereby determining the processing pose information at the end of the manipulator, where the path points on the processing trajectory include the unit tangent vector and the unit internal normal vector The two directions of the normal vector, according to these two vector directions, determine the attitude of the machining tool at the end of the robotic arm;

According to the processing requirements of the helical surface of the toroidal worm, the posture of the machining tool at the end of the mechanical arm is specified as follows: During the processing operation, the normal vector f of the path point on the machining track coincides with the _Xt direction of the TCP coordinate system of the grinding tool, At the same time, it is also the direction of the constant force control of the machining tool at the end of the mechanical arm. The Y _t direction of the TCP coordinate system is the tangent vector τ of the path point and points to the next processing point. It is also the moving direction of the machining tool. The Z of the TCP coordinate system of the machining tool is The _t direction coincides with the cross product direction w=f×τ of the normal vector f of the path point and the tangent vector τ, and conforms to the right-hand rule;

S3. Planning the trajectory of the helical surface of the torus worm, specifically:

Given the rotational speed ω ₁ of the worm and the transmission ratio i of the worm pair, calculate the rotational speed ω ₂ of the end of the grinding tool according to i=ω ₁ /ω ₂ ;

When the processing tool rotates counterclockwise with the mechanical arm to the end position from the initial position, the worm rotates positively around its axis, and the speed direction is outward along the paper surface; when the processing tool rotates clockwise with the mechanical arm to the end position from the initial position, the worm Rotate in reverse around its axis, and the speed direction is inward along the paper surface. During the rotation of the mechanical arm, the processing surface of the processing tool is always tangent to the main base circle of the worm wheel;

Wherein, for the planar quadratic enveloping toroidal worm, the processing tool rotates counterclockwise 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 secondary enveloping toroidal worm, the machining tool simultaneously processes the left and right helical surfaces of the worm during the counterclockwise and clockwise rotation of the mechanical arm;

For the multi-head toroidal worm, after the machining tool rotates with the mechanical arm to process the helical surface of the first head of the worm, it is necessary to rotate the initial installation position of the worm around its rotation axis by an angle of 360/z ₁ , where z ₁ is the head of the worm number, and then continue to process the helicoid of the second head, and continuously update the processing track until the processing of the helicoid of the multi-head toroidal worm is completed;

S4. Preliminarily determine the processing trajectory and control instructions of the robotic arm, specifically:

The mechanical arm is based on the position control method to accurately track the processing trajectory, and the six-dimensional force sensor installed at the end of the mechanical arm is used to collect the processing contact force in real time, and based on the impedance control algorithm to control the constant processing force in the X _t direction of the end of the processing tool;

S5. For the helical surface of the toroidal worm to be processed, establish a machining simulation model of the manipulator, and adjust the machining trajectory and control instructions of the manipulator according to the simulation results, specifically:

Build a simulation platform with a ratio of 1:1 to the actual physical platform, and use Solidworks and Matlab/Simulink modules to jointly build a simulation platform for the tandem mechanical arm processing torus worm helical surface system;

After the simulation is completed, the rotation angle sequence diagram of each joint of the serial manipulator, the joint angle trajectory tracking diagram, the joint angle trajectory tracking error diagram, and the comparison diagram between the expected trajectory and the actual trajectory are generated;

Determine whether the tandem manipulator moves smoothly and continuously from the angle sequence diagram of each joint, and determine the accuracy of the processing trajectory and control instructions according to the joint angle trajectory tracking diagram, joint angle trajectory tracking error diagram, and the comparison diagram between the expected trajectory and the actual trajectory , so as to adjust the machining trajectory and control instructions of the robotic arm;

S6. According to the adjusted machining trajectory and control instructions of the mechanical arm, a control program for machining the helical surface of the toroidal worm with the mechanical arm is generated offline;

S7. Install the toroidal worm to be processed on the processing platform, and install the processing tool at the end of the mechanical arm through the electric spindle;

Make the toroidal worm to be processed rotate according to the set speed, and at the same time, the mechanical arm controls the processing tool according to the control program to complete the processing of the helical surface of the toroidal worm to be processed.

的取值范围0～0.8rad。In this embodiment, the helical surface of the toroidal worm is finished, so the grinding tool is selected to be installed at the end of the mechanical arm. This embodiment takes the modified toroidal worm pair as an example, and the relevant parameters are: the number of toroidal worm heads z ₁ =4, the number of worm gear teeth z ₂ =40, the meshing center distance a=160mm, the transmission ratio i=10, the worm gear Top circle diameter d _a = 267mm, worm root circle diameter d _f = 250mm, worm wheel end face modulus m _t = 10.45mm, main base circle diameter d _b = 95mm, worm working length L _w = 90mm, mechanical arm rotation angle

The value range of 0～0.8rad.

A mechanical arm with a model of ER20-C10 is used, with a load of 20Kg, a self-weight of 220Kg, and an arm span of 1722mm. The machine tool based on the tandem mechanical arm grinding system includes a mechanical arm, a grinding platform, a toroidal worm, an electric spindle, Grinding knives. The grinding platform is mainly used to hold the toroidal worm. According to the technical requirements of the toroidal worm to be processed, the speed of the toroidal worm during grinding is set; the electric spindle and the grinding tool are installed at the end of the mechanical arm, and the mechanical arm holds the Grinding tools, according to the grinding trajectory and control method, the toroidal worm is processed.

Based on the method process proposed by this technical solution, the application process of this embodiment includes:

1. Establish a coordinate system for grinding the helical surface of the toroidal worm by using the tandem mechanical arm, as shown in Figure 2. Among them, T _w represents the world coordinate system, T _b1 represents the base coordinate system of the series manipulator, T _f1 represents the end coordinate system of the manipulator, T _t represents the end coordinate system of the grinding tool, T _b2 represents the center coordinate system of the grinding platform, and T _j Represents the coordinate system of any discrete point on the grinding path of the helical surface of the toroidal worm, and T _w coincides with T _b1 . A closed-chain kinematic relationship is formed between the mechanical arm and the grinding platform in series, and the expression of "the base of the mechanical arm 1 - the end of the mechanical arm 1 - the grinding tool - the grinding point - the base of the grinding platform 2" is: ^b1 T _f1 ^f1 T _t ^t T _j ^j T _b2 = ^b1 T _b2 , ^j t _b2 is determined according to the specific grinding trajectory requirements, it is a known matrix, ^b1 T _b2 is determined by the calibration of the base coordinate system, ^f1 T _t is determined by the TCP tool according to the installation method The calibration is confirmed, ^tt T _j is the identity matrix, so ^b1 T _f1 can be obtained from the formula ^b1 T _f1 = ^b1 T _b2 ( ^j T _b2 ) ^-1 ( ^t T _j ) ^-1 ( ^f1 T) ^-1 , and thus determined The mechanical arm grinds the tool end coordinate system, and then obtains the motion angle of each joint according to the inverse kinematics solution. Calibrate the system through the laser tracker, where the coordinate system of the laser tracker is a fixed measurement coordinate system, and calibrate the transformation matrices T ₁ , T ₂ of the base coordinate system of the serial manipulator and the grinding platform relative to the measurement coordinate system. Based on the principle of relative coordinate transformation, the relative pose homogeneous matrix ^b2 T _b1 between the series manipulator and the base coordinate system of the grinding platform is calculated by the formula ^b1 T _b2 =T ₂ ^-1 T ₁ .

2. Take 20 characteristic points on the indexing torus helix of the 4-head torus worm, and fit these points based on the trigonometric function method to generate a helix and obtain the grinding trajectory equation, as shown in Figure 3, and then The trajectory equation is discretized to obtain the surface normal vector of the corresponding discrete point, thereby determining the grinding pose information at the end of the series manipulator; the path point on the grinding trajectory includes the unit tangent vector τ and the unit normal vector f direction, as shown in Fig. 4, and then further determine the posture of the grinding tool at the end of the tandem robot according to the two vector directions. During the operation process, the normal vector f of the path point on the grinding track coincides with the X _t direction of the TCP coordinate system of the grinding tool _. is the tangent vector τ of the path point and points to the next grinding point, and is also the moving direction of the grinding tool. The Z _t direction of the TCP coordinate system of the grinding tool coincides with the cross product direction w=f×τ of the normal vector f of the path point and the tangent vector τ, and conforms to the right-hand rule.

蜗杆副的中心距O_dO₁＝160mm，蜗杆齿顶圆半径R_a＝133.5mm。对于平面二次包络环面蜗杆，磨削刀具随机械臂逆时针转动加工出蜗杆的左侧螺旋面，磨削刀具随机械臂顺时针转动加工出蜗杆的右侧螺旋面；对于锥面二次包络环面蜗杆，磨削刀具随机械臂逆时针和顺时针转动过程中都同时加工出蜗杆的左右两侧螺旋面；对于多头环面蜗杆，磨削刀具随机械臂转动加工出蜗杆第一个头的螺旋面以后，需要将蜗杆的初始安装位置绕其旋转轴线转动360/4＝90°，然后依照上述方法加工出第二个头的螺旋面，不断更新磨削轨迹，直至完成多头环面蜗杆螺旋面的加工。3. Given the rotational speed of the worm ω ₁ =1400r/min and the transmission ratio of the worm pair i=10, the rotational speed of the end of the grinding tool ω ₂ =140r/min is calculated according to i=ω ₁ /ω ₂ . As shown in Figure 5, when the grinding tool starts from the initial position A and rotates counterclockwise with the mechanical arm to the end position B, the worm rotates positively around its axis (the speed direction is outward along the paper surface), and the grinding tool starts from the initial position B When the mechanical arm rotates clockwise to the end position A, the worm rotates in the opposite direction around its axis (the speed direction is along the paper surface inward). During the rotation of the mechanical arm, the processing surface of the grinding tool is always aligned with the main base of the worm wheel with a radius of r _b The circle is tangent, the center of rotation of the manipulator is O _d , and the rotation angle is

The center distance of the worm pair O _d O ₁ =160mm, the radius of the worm addendum circle R _a =133.5mm. For the planar quadratic enveloping torus worm, the grinding tool rotates counterclockwise with the mechanical arm to process the left helicoid of the worm, and the grinding tool rotates clockwise with the mechanical arm to process the right helicoid of the worm; For the sub-enveloping toroidal worm, the grinding tool rotates counterclockwise and clockwise with the mechanical arm to process the helical surfaces on the left and right sides of the worm at the same time; for the multi-head toroidal worm, the grinding tool rotates with the mechanical arm to process the first After the helical surface of the first head, it is necessary to rotate the initial installation position of the worm 360/4=90° around its rotation axis, and then process the helicoid surface of the second head according to the above method, and continuously update the grinding track until the multi-head toroidal surface is completed Machining of worm helical surfaces.

According to the requirements of the processing technology, the tandem manipulator needs to control the constant grinding force while working along the grinding track. Therefore, in the Cartesian operation space of the manipulator, the force/position operation space of the manipulator is decomposed, that is, in The constant force control is performed in the X _t direction, and the position control is performed in the Y _t and Z _t directions. The pose constraint relationship is shown in Figure 6. During the grinding process, the tandem manipulator holds the grinding tool while keeping the constant force control direction coincident with the normal direction f of the path point, so the constant force control is performed in the _Xt direction of the tandem manipulator grinding tool coordinate system, And keep it horizontal all the time, that is, the grinding posture is ^b1 R _T =[1 0 0] ^T , and the position control is performed in the Y _t and Z _t directions to follow the grinding trajectory. From the kinematics model, the position of the end of the grinding tool ^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 motion angle of each joint can be obtained by kinematics inverse solution. The transformation matrix T contains the position vector P and the rotation matrix R, where:

P＝[p _x p _y p _z ] ^T

通过六维力传感器实时采集获得，则机械臂各关节驱动量

其中k_pi为比例系数，k_vi为微分系数。4. The tandem robotic arm accurately tracks the grinding trajectory based on the position control method, and the control architecture is shown in Figure 7. Since the control period of the control system built by the present invention is short, the characteristics of the integral are not considered, and the serial manipulator adopts the single-joint PD control mode. The expected position θ _ti of each joint is calculated by inverse kinematics, the joint position θ _i , joint velocity

Obtained by real-time acquisition by the six-dimensional force sensor, the driving force of each joint of the manipulator is

Among them, k _pi is a proportional coefficient, and k _vi is a differential coefficient.

For the adjustment of the control parameters k _pi and k _vi in the servo control system of each joint, the proportional coefficient is continuously adjusted according to the magnitude of the deviation oscillation to quickly reduce the error, and then the differential coefficient is adjusted to reduce the oscillation frequency of the deviation, so as to quickly and accurately track the trajectory Changes to ensure the stability of the entire series manipulator movement controlled process. Each joint in the joint servo control system is regarded as a single-input single-output system, and each joint is controlled independently, and then the synchronous linkage control of each joint is completed through the periodic synchronous interpolation mode of the driver, so as to realize the precise motion control of the serial manipulator.

The tandem manipulator collects the contact force information with the toroidal worm in real time through the six-dimensional force sensor installed at the end, and obtains the actual grinding force F in the X _t direction after filtering and gravity compensation of the force sensor, and its deviation from the expected contact force F _d f _e is used as the input of a second-order low-pass filter to output the position correction value Δx in the direction of X _t , and the correction value is fed back to the reference motion trajectory in the X direction of the Cartesian operation space of the robot through the selection matrix S, S', and the mechanical arm is updated The movement trajectory is calculated by the kinematics of the manipulator to obtain the angles of each joint. When the manipulator enters the next grinding cycle, the six-dimensional force sensor at the end of the manipulator continues to collect the contact information of the grinding force, and repeats the above steps to continuously update the grinding process. trajectory until the task of grinding the helicoid of the toroidal worm is completed.

5. To build a simulation environment, first use the M file and S function in MATLAB/Simulink to develop the kinematics, trajectory planning and control algorithm of the series manipulator grinding system. Use the SolidWorks 3D software to build the CAD model of the grinding system, and then export the system CAD model into an XML format file and STEP model that MATLAB can read through the Simscape Multibody Link plug-in, and finally load the system STEP model into MATLAB/ In Simulink, combined with kinematics, trajectory planning and other algorithms to generate a Simscape simulation model of the grinding system. Generally, the original system simulation model imported into Simulink cannot be directly controlled, and further optimization of the model and configuration of related control parameters are required, including STEP model path modification, Rotation input and output configuration, initial attitude joint angle configuration of the manipulator, and joint rotation positive direction setting. Wait, and finally package it into an independent module. Then use the M-file and S-function in MATLAB/Simulink to develop the kinematics, trajectory planning and control algorithm of the grinding system, carry out relevant algorithm simulation based on the simulation platform, and dynamically verify the feasibility of the algorithm through the built simulation environment, and use Scope component and To Workspace component save data to further analyze algorithm performance.

Generate the change diagram of the joint angle, velocity and acceleration of the manipulator. If the curve in the change diagram is smooth and continuous, the kinematics model of the tandem manipulator grinding toroidal worm helicoid system established in step 1 is correct. Secondly, generate the actual trajectory and expected trajectory comparison diagram and the joint angle trajectory tracking error diagram. If the actual trajectory can move according to the expected trajectory and the error is small, the serial manipulator based on the _PD position control method is correct; apply a External force, observe whether the trajectory map will adapt to the external force to adjust and return to the grinding path. If the mechanical arm can adapt to the change of external force and adjust the trajectory, and when the interference force is zero, the serial mechanical arm can continue to track quickly and stably. Trajectory, then based on the position impedance control algorithm, it is feasible to control the grinding constant force of the series manipulator.

6. According to the simulation results, the process of grinding the helical surface of the toroidal worm with the tandem manipulator is adjusted, and after comprehensive adjustment, the program for grinding the helicoid of the torus and worm with the manipulator is generated offline.

This embodiment is for the finishing machining of the toroidal worm. If only rough machining is required in practical applications, the grinding tool in this embodiment can be replaced with a turning tool.

In summary, the technical solution proposed by the present invention can realize the automatic processing of toroidal worms, avoid repeated positioning, effectively ensure the consistency of mass production of toroidal worms, improve processing efficiency and reduce production costs, and is especially suitable for processing Large size toroidal worm.

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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