Design and Research of Dual-Robot Collaborative Grinding

Polishing is the most important process for improving the surface quality of die-cast parts. For the complex grinding process of die-cast parts, using dual robots to grind from both sides of the workpiece can greatly improve the efficiency of robotic grinding.

Currently, most small and medium-sized enterprises (SMEs) still rely on manual grinding, which is extremely harmful to the physical and mental health of workers. A small number use industrial robots with end effectors to hold the workpiece for grinding, but this method is only suitable for small and medium-sized die-cast parts. Furthermore, most calculations of grinding forces are based on empirical formulas, resulting in rather coarse results. Since the cutting tool teeth shape is similar to that of a milling cutter, this is equivalent to studying milling forces. Numerous scholars have conducted extensive research on the calculation and modeling of milling forces, establishing a milling force model for helical end mills based on the frictional force and normal force on the rake face. However, the cutting force acts not only on the rake face of the tool but is generated by the interaction between the tool and the workpiece, thus limiting the model's scope.

This paper addresses the grinding problem of complex die-cast parts, employing a grinding method where an industrial robot's end effector holds the grinding tool. Dual-robot collaborative grinding allows for simultaneous grinding of both sides of the workpiece, resulting in higher automation and significantly improved grinding efficiency. The scheme establishes a mathematical model of grinding force based on the infinitesimal element method. The maximum cutting force during grinding is obtained using Matlab. Static analysis of the weak points in the fixture-workpiece assembly using ANSYS reveals that the maximum equivalent stress does not exceed 39% of the material's allowable stress. Furthermore, modal analysis yields the first six vibration modes and natural frequencies, with the highest frequency of 413.61Hz being less than one-quarter of the excitation frequency. This indicates that resonance does not occur when the grinding excitation force acts on the fixture-workpiece system, demonstrating the applicability of this scheme. The system also calculates the grinding force based on the infinitesimal element cutting principle, analyzing the stress and deformation of the die-cast part and the designed dedicated fixture assembly under the grinding force generated during dual-robot collaborative grinding.

Structure and Principle

The research adopted a robotic grinding method using grinding tools. Two robots are positioned on either side of the workpiece, grinding simultaneously from both sides. The grinding process layout is shown in Figure 1. A dedicated fixture is fixed on the grinding table to clamp the die-casting. The end effector of the industrial robot is connected to the grinding tool. The robot trajectory recording and I/O signal settings are pre-programmed, and the coordination between the two robots is debugged. After the operator clamps the blank, the two robots grind collaboratively according to the taught path. After grinding, the operator removes the ground workpiece and loads another blank. The fixture on each worktable only requires rotating a crank to clamp the blank. The collaborative grinding of the die-casting by the robots from both sides of the workpiece allows for orderly and efficient grinding, fully utilizing the workspace accessible to the robot arms and significantly improving grinding efficiency.

Figure 1. Dual-robot collaborative polishing platform

Mathematical modeling of polishing force

The grinding force calculation in this study is based on a milling force model using the principle of infinitesimal cutting. The mechanical model for milling generally adopts the cutting force model derived by Y. Altintas, which divides the helical cutting edge into a finite number of infinitesimal elements along the helix. The total cutting force acting on a single cutting edge at a given moment is obtained by numerical integration of each infinitesimal element on that cutting edge. The milling model and force diagram of a cylindrical helical end mill are shown in Figure 2. With the end mill centerline as the z-axis, the end mill face as the xy-plane, and the center of the end face as the origin, a coordinate system is established according to the right-hand rule. Each cutting edge is divided into a finite number of infinitesimal cutting edge elements along the end mill axis. β is the helix angle, and ψ is the hysteresis angle.

Based on Altintas's dynamic milling force model, the tangential, radial, and axial cutting forces of thickness dz acting on the j-th cutting edge are respectively represented as:

By summing the cutting forces of the cutting edges involved in the cutting, we can obtain the cutting force of the entire tool at the same moment and the same axial depth of cut. Finally, the relationship between the resultant cutting force in each direction and the rotational speed and axial depth of cut is shown in Figure 3.

Figure 3. Resultant cutting force diagram for each axis

Based on the above analysis and calculations, the cutting force is at its maximum at a speed of 10,000 rpm and an axial depth of cut of 10 mm. Combined with the actual cutting depth of 1 mm during grinding, the magnitudes of the cutting forces exerted by the tool on the workpiece in various directions are Fx = -49.019 N, Fy = 274.5 N, and Fz = 44.44 N, respectively. The next step is to analyze whether the stress and deformation of the workpiece can meet the production requirements at this maximum cutting force.

Simulation Analysis

The following steps were taken to analyze the stress and deformation of the assembly of the specialized fixture designed for collaborative grinding of complex castings by dual robots:

(1) Create a finite element model of the fixture workpiece system as shown in Figure 4.

(2) Setting parameters: The meshing method uses FaceMeshing for the contact area between the cylindrical pin and the workpiece, and tetrahedral elements for the other parts. Table 2 shows the setting of material parameters.

Table 2 Material Parameters

(3) Applying constraints and loads: The contact relationship between the fixture body and the workpiece is shown in Table 3 below. The friction coefficient is selected as 0.2 according to the friction coefficient table of commonly used materials in the Mechanical Design Handbook. The contact relationship between the cylindrical pins 1, 2, 3, and 4 and the workpiece 6 is frictional, and the contact relationship between them and the arc clamping plate 5 is bonded. The release relationship between the fixture body 8 and the cylindrical pins and the arc clamping plate is bonded.

The fixture is fixed at the bottom, and three sets of forces are applied to the weakest points of the workpiece during actual processing. The first set of forces is applied at points B and E, the second set at points A and E, and the third set at points C and D. Because the two robots work together to grind, the load is applied to two weak points of the workpiece simultaneously each time, as shown in Figure 4.

Cylindrical pins - 1, 2, 3, 4; Arc clamping plate - 5; Workpiece - 6; Fixture body - 7, 8

Figure 4. Load and constraint locations in the finite element model.

(4) Analysis and solution: Figure 5 below shows the deformation and stress cloud map after the third set of forces are applied. The analysis results after the three sets of constraint loads are statistically shown in Table 4.

Figure 5. Workpiece stress and deformation cloud map

Table 3 Statistical Results

As shown in Table 3, after the first set of loads, the maximum equivalent stress occurred at the lower right crossbeam of the workpiece, with a value of 84.475 MPa, and the largest deformation occurred at the connection between the cylindrical pin 2 and the workpiece, with a value of 0.10392 mm; after the second set of loads, the maximum equivalent stress occurred at one of the protruding ears of the workpiece, with a value of 90.306 MPa, and the largest deformation occurred at the upper left crossbeam of the workpiece, with a value of 0.10048 mm; after the third set of loads, the maximum equivalent stress occurred at the protrusion C of the workpiece, with a value of 117.81 MPa, and the largest deformation occurred on the inner side of the ring at workpiece C, with a value of 0.05461 mm.

According to the allowable stress value requirement of the workpiece material, after the grinding force generated by the tool is applied to the workpiece during the grinding process, the maximum equivalent stress of the workpiece and the fixture assembly should not exceed 295 MPa. All three sets of results are within the allowable stress range, and the maximum equivalent stress is 39% of the allowable stress, which meets the production requirements.

Modal analysis

Modal characteristics are the inherent vibrational properties of a structural system. Modal analysis is a numerical technique for calculating the vibrational properties of a structure, which include its natural frequencies and mode shapes. Modal analysis is the foundation of dynamic analysis and a modern method for studying the dynamic characteristics of structures.

The preprocessing for modal analysis in this study (finite element model, material parameters, mesh generation, contact and constraints) is consistent with that used in the static analysis. This section extracts the first six vibration modes from the modal analysis results of the fixture-workpiece system.

Since the main factors affecting the dynamic characteristics of machining are the lower-order natural frequencies and mode shapes, studying the first few natural frequencies and mode shapes can meet the needs of the analysis. The natural frequencies of the fixture-workpiece system obtained by the ANSYS Workbench Model analysis module are shown in Table 4 below.

Table 4 Modal frequencies of the fixture-workpiece system

In the first six deformation contour diagrams, the influence of the second natural frequency is the most significant. The second mode shape involves the workpiece torsion around the X and Y axes, with the largest deformation occurring at the lower right crossbeam. Since the grinding tool was started and maintained at approximately 10,000 rpm before the grinding process began, the excitation frequency acting on the workpiece was close to 1840 Hz. Since the natural frequencies of all orders of this fixture-workpiece system are much lower than the excitation frequency, this system will not resonate.

in conclusion

To address the limitations of grinding complex die-cast parts, a dual-robot collaborative grinding method was adopted. A dynamic grinding force model was established, and the grinding force load was applied to the fixture and workpiece assembly using the finite element analysis software ANSYS, and the results were solved. After applying the grinding force load to the weak points of the workpiece, the maximum stress on the workpiece and fixture did not exceed 39% of the allowable stress value of the material, indicating that the designed fixture meets the requirements. Furthermore, modal analysis of the fixture-workpiece system yielded the first six natural frequencies and mode shapes. The highest frequency, 413.61Hz, is less than 1/4 of the excitation frequency, clearly indicating that resonance will not occur when the grinding excitation force is applied to the fixture-workpiece system, demonstrating the design's stability. This has significant implications for improving the machining quality and efficiency of parts in automated production.

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