A multi-degree-of-freedom spherical motor torque detection experimental device and method

Abstract

The application discloses a kind of multi-degree-of-freedom spherical motor torque detection experimental device and method, belong to multi-degree-of-freedom spherical motor measurement technical field, including the base and bearing platform component placed in bottom layer, inner and outer ring component, XYZ three-axis mounting frame, XYZ three-axis drive sensing component;X-axis drive sensing component includes X-axis torque sensor, is installed in X-axis mounting frame, output shaft is connected with the first and second counterbore center point of inner ring component line assembly;Y-axis drive sensing component includes Y-axis torque sensor, is installed in Y-axis mounting frame;Z-axis drive sensing component includes Z-axis torque sensor, is installed in Z-axis mounting frame;XYZ three-axis torque sensor is respectively used to complete XYZ three-axis torque detection;Base is installed height adjustment seat, multi-degree-of-freedom spherical motor in turn, two ends are respectively installed two bearing platforms of bearing platform component.The application solves the problem that operation is complex and inefficient in manual positioning in contact torque detection method.

Description

Technical Field

[0001] This invention belongs to the field of measurement technology for multi-degree-of-freedom spherical motors, specifically relating to an experimental device and method for torque detection of multi-degree-of-freedom spherical motors. Background Technology

[0002] With the rapid development of modern industrial technology, multi-degree-of-freedom, high-precision motion actuators have been widely used in industrial production, aerospace, robotics, and other fields. Traditional multi-degree-of-freedom motion devices often rely on combinations of single-degree-of-freedom motion devices, resulting in problems such as complex structures, error accumulation, and difficulties in coordinated control, limiting their application in space-constrained scenarios. Therefore, actuators capable of independently performing multi-degree-of-freedom motion have attracted widespread attention from scholars both domestically and internationally.

[0003] Spherical structures facilitate multi-degree-of-freedom motion within space, leading to the development of various spherical motors based on principles such as induction, permanent magnet, and reluctance. Research on these motors focuses on torque modeling, attitude detection, and motion control. During operation, an accurate torque model is fundamental for closed-loop motion control, and the model's establishment relies on experimental torque data. However, because spherical motors possess multiple degrees of freedom and lack a fixed axis of rotation, their torque detection methods differ significantly from those of traditional single-degree-of-freedom motors.

[0004] Existing technologies include: (1) using MEMS (microelectromechanical systems) sensors for non-contact detection, and indirectly obtaining torque in multiple degrees of freedom by processing state variables; (2) using torque sensors to detect torque in a single degree of freedom, and obtaining torque in multiple degrees of freedom through repeated experiments; (3) using multiple torque sensors to detect torque in multiple degrees of freedom simultaneously, and manually positioning by rotary encoders and scales.

[0005] Problems with existing technologies: (1) In non-contact detection methods, zero-point drift and error accumulation of MEMS (microelectromechanical systems) cannot be avoided, and there are also accumulated errors in the processing of state variables. (2) In contact detection methods, the measured shaft for single-degree-of-freedom torque detection is unique and fixed, and multi-degree-of-freedom torque needs to be obtained through repeated experiments, which has problems with poor repeatability and poor system flexibility. (3) In contact detection methods, multi-degree-of-freedom torque detection is based on rotary encoders and scales and is carried out manually, which has problems with complex operation and low efficiency in large sample collection tasks. Summary of the Invention

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A multi-degree-of-freedom spherical motor torque detection experimental device includes: a base, a support assembly, an inner ring assembly, an outer ring assembly, an X-axis mounting bracket, a Y-axis mounting bracket, a Z-axis mounting bracket, an X-axis drive sensing assembly, a Y-axis drive sensing assembly, and a Z-axis drive sensing assembly; the base and support assembly are placed at the bottom layer; the X-axis drive sensing assembly includes an X-axis torque sensor, mounted on the X-axis mounting bracket, and the output shaft of the X-axis drive sensing assembly is collinearly assembled with the center point connection line of the first and second countersunk holes of the inner ring assembly, and the X-axis torque sensor is used to complete the X-axis torque detection; the Y-axis drive sensing assembly includes a Y-axis torque sensor, mounted on the Y-axis mounting bracket, and the output of the Y-axis high-precision planetary reducer in the Y-axis drive sensing assembly... The shaft is collinearly assembled with the center point connection lines of the third and fourth countersunk holes of the inner ring assembly, and also collinearly assembled with the center point connection lines of the first and third 6001 deep groove ball bearings of the outer ring assembly. The Y-axis torque sensor is used to complete the Y-axis torque detection. The Z-axis drive sensing assembly includes a Z-axis torque sensor, which is mounted on the Z-axis mounting bracket. The output shaft of the Z-axis drive sensing assembly is collinearly assembled with the central axis of the second 6001 deep groove ball bearing of the outer ring assembly. The Z-axis torque sensor is used to complete the Z-axis torque detection. The middle part of the base is used to install a height adjustment seat, and a multi-degree-of-freedom spherical motor is installed above the height adjustment seat. The first and second supports of the support assembly are installed at both ends, respectively.

[0008] A method for detecting the torque of a multi-degree-of-freedom spherical motor, used in the aforementioned experimental apparatus for detecting the torque of a multi-degree-of-freedom spherical motor, includes:

[0009] Step 1: Solve for the relative motion transformation matrix between the stator and rotor of the multi-degree-of-freedom spherical motor;

[0010] A fixed coordinate system O-UVW, which is fixed relative to the stator, and a moving coordinate system o-xyz, which moves with the rotor, are constructed. To describe the multi-degree-of-freedom motion of the rotor relative to the stator, the rotation process of the moving coordinate system o-xyz is decomposed. Each arbitrary orientation of the rotor uniquely corresponds to a moving coordinate system o-xyz, which can be obtained by performing three coordinate rotations starting from the fixed coordinate system O-UVW, with the rotation direction following the right-hand screw rule. First, the o-x1y1z1 coordinate system is obtained by rotating the O-UVW around the U-axis by an angle α. Then, the o-x2y2z2 coordinate system is obtained by rotating the O-UVW around the y1-axis by an angle β. Finally, the o-xyz coordinate system is obtained by rotating the O-x2-axis by an angle γ. The angular displacement matrix during these three rotations is... and angular velocity matrix They are respectively and ; These represent the angular velocities of rotation about each axis during the rotation process; the corresponding rotation matrix is ​​obtained by solving the cubic coordinate rotation problem. for:

[0011] (1)

[0012] The relative motion transformation matrix between the stator and rotor of a multi-degree-of-freedom spherical motor is as follows:

[0013] (2)

[0014] Step 2: Conduct a torque detection experiment;

[0015] Step 3: Construct the Stribeck friction model of the composite friction torque, and model the composite friction torque sequences of the x, y, and z axes obtained in Step 2 respectively;

[0016] Step 4: Power on the multi-degree-of-freedom spherical motor and conduct a constant speed tracking pre-experiment in the x, y, and z axes;

[0017] Step 5: Power on the multi-degree-of-freedom spherical motor and conduct a formal experiment of constant speed tracking in the x, y, and z axes, reducing the speed sequence based on step 4. The area in question;

[0018] Step 6, set the parameter matrix E for the x, y, and z axes:

[0019] (5)

[0020] in, These represent the positive and negative components of the Coulomb friction torque along the x, y, and z axes, respectively. These represent the components of the maximum static friction torque in the positive and negative directions of the x, y, and z axes, respectively. These represent the components of Stribeck's switching speed in the positive and negative directions of the x, y, and z axes, respectively. These are the components of the viscous friction coefficient in the positive and negative directions of the x, y, and z axes, respectively.

[0021] Step 7: Use the composite friction torque sequence obtained in Step 6. For the raw data of parameter identification, the Particle Swarm Optimization (PSO) algorithm is used to identify the parameters of equation (4), and the parameter matrix is ​​obtained. This leads to the Stribeck friction model in the x, y, and z axes. ;

[0022] Step 8: Power on the multi-degree-of-freedom spherical motor and use the multi-degree-of-freedom spherical motor torque detection experimental device to drive the multi-degree-of-freedom spherical motor along a predetermined trajectory in the x, y, and z axes to conduct a constant speed torque detection experiment.

[0023] Step 9: Transform T to the coordinate system O-UVW using equation (2) to obtain the torque of the multi-degree-of-freedom spherical motor in the fixed coordinate system O-UVW. :

[0024] (7)

[0025] in, Let be the rotation matrix of the three rotations in equation (1);

[0026] Step 10, the obtained three-degree-of-freedom torque data , , Stribeck friction model , , After compensation, the components of the output torque T of the multi-degree-of-freedom spherical motor on the x, y, and z axes are obtained. , , ;

[0027] Using equation (6), the output torque T is transformed from the moving coordinate system o-xyz to the fixed coordinate system O-UVW. After the transformation, the components of the output torque T in the U, V, and W axes are positioned based on the centroid of the rotor salient pole of the multi-degree-of-freedom spherical motor. .

[0028] The present invention has the following beneficial effects:

[0029] This invention designs an experimental device for detecting the torque of a multi-degree-of-freedom spherical motor with automatic tracking function. This device automatically drives the multi-degree-of-freedom spherical motor to any point on the spherical surface and collects the multi-degree-of-freedom torque data at that position, significantly improving the automation level of the detection process. It avoids the zero-point drift and accumulated errors caused by MEMS (Micro-Electro-Mechanical Systems) in non-contact detection methods; it solves the problems of repeatability and uniqueness of the measured shaft in single-degree-of-freedom torque detection in contact detection methods; and it solves the problems of operational complexity and low efficiency caused by manual positioning in contact detection methods. Attached Figure Description

[0030] Figure 1This is a schematic diagram of the experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to the present invention. In the diagram, 1-1-X-axis mounting bracket, 1-2-base, 1-3-first support platform, 1-4-multi-degree-of-freedom spherical motor, 1-5-height adjustment seat, 1-6-Y-axis torque sensor shaft, 1-7-first counterweight, 1-8-Y-axis 57 stepper motor, 1-9-Y-axis high-precision planetary reducer, 1-10-Y-axis mounting bracket, 1-11-Y-axis torque sensor, 1-12-Y-axis linkage bracket, 1-13-Y-axis reducer output flange, 1-14-X-axis conductive slip ring, 1-15-X-axis conductive slip ring shaft, 1-16-second support platform, 1-17-multi-degree-of-freedom spherical motor output shaft coupling, 1- 18-Z-axis torque sensor shaft, 1-19-Z-axis torque sensor, 1-20-Z-axis reducer output flange, 1-21-Z-axis conductive slip ring, 1-22-Z-axis 57 stepper motor, 1-23-Z-axis mounting bracket, 1-24-Z-axis high-precision planetary reducer, 1-25-Z-axis conductive slip ring bracket, 1-26-inverted U-shaped outer ring, 1-27-Y-axis conductive slip ring shaft, 1-28-Y-axis conductive slip ring, 1-29-second counterweight, 1-30-O-shaped inner ring, 1-31-X-axis torque sensor shaft, 1-32-X-axis torque sensor, 1-33-X-axis reducer output flange, 1-34-X-axis high-precision planetary reducer, 1-35-X-axis 57 stepper motor;

[0031] Figure 2 The diagram shows the structure of the first and second bearing platforms of the present invention, wherein (a) is a structural diagram of the first bearing platform and (b) is a structural diagram of the second bearing platform; 2-1-first aluminum alloy body, 2-2-second aluminum alloy body, 2-3-first bearing retaining ring, 2-4-first 6002 deep groove ball bearing, 2-5-second bearing retaining ring, 2-6-second 6002 deep groove ball bearing;

[0032] Figure 3 This is a schematic diagram of the inner ring assembly of the present invention, wherein 1-15-X-axis conductive slip ring shaft, 1-30-O-shaped inner ring, 1-31-X-axis torque sensor shaft, 3-1-first countersunk hole, 3-2-second countersunk hole, 3-3-third countersunk hole, and 3-4-fourth countersunk hole;

[0033] Figure 4This is a schematic diagram of the outer ring assembly of the present invention, wherein (a) is a side view of the outer ring assembly, and (b) is a structural diagram of the outer ring assembly in cross section AA; 1-6-Y-axis torque sensor shaft, 1-17-multi-degree-of-freedom spherical motor output shaft coupling, 1-18-Z-axis torque sensor shaft, 1-26-inverted U-shaped outer ring, 1-27-Y-axis conductive slip ring shaft, 4-1-aluminum alloy body, 4-2-first bearing retaining ring, 4-3-first 6001 deep groove ball bearing, 4-4-second bearing retaining ring, 4-5-second 6001 deep groove ball bearing, 4-6-third 6001 deep groove ball bearing, 4-7-third bearing retaining ring;

[0034] Figure 5 This is a schematic diagram of the X-axis mounting bracket of the present invention, wherein 5-1-the main steel structure of the X-axis mounting bracket;

[0035] Figure 6 This is a schematic diagram of the Y-axis mounting bracket of the present invention, wherein 6-1- is the main steel structure of the Y-axis mounting bracket;

[0036] Figure 7 This is a schematic diagram of the Z-axis mounting bracket of the present invention, wherein 7-1-the main steel structure of the Z-axis mounting bracket;

[0037] Figure 8 This is a schematic diagram of the X-axis drive sensing assembly of the present invention, wherein (a) is a schematic diagram of the X-axis driver and sensor, and (b) is a schematic diagram of the X-axis conductive slip ring; 1-14-X-axis conductive slip ring, 1-32-X-axis torque sensor, 1-33-X-axis reducer output flange, 1-34-X-axis high-precision planetary reducer, 1-35-X-axis 57 stepper motor, 8-1-first outer tube, 8-2-first inner tube;

[0038] Figure 9 This is a schematic diagram of the Y-axis drive sensing assembly of the present invention, wherein (a) is a schematic diagram of the Y-axis driver and sensor, and (b) is a schematic diagram of the Y-axis conductive slip ring; 1-8-Y-axis 57 stepper motor, 1-9-Y-axis high-precision planetary reducer, 1-11-Y-axis torque sensor, 1-12-Y-axis linkage bracket, 1-13-Y-axis reducer output flange, 1-28-Y-axis conductive slip ring, 9-1-second outer tube, 9-2-second inner tube;

[0039] Figure 10 This is a schematic diagram of the Z-axis drive sensing assembly of the present invention, wherein 1-19-Z-axis torque sensor, 1-20-Z-axis reducer output flange, 1-21-Z-axis conductive slip ring, 1-22-Z-axis 57 stepper motor, 1-24-Z-axis high-precision planetary reducer, 1-25-Z-axis conductive slip ring bracket, 10-1-third inner tube, 10-2-third outer tube;

[0040] Figure 11 This is a schematic diagram of the decomposition of the motion coordinate system o-xyz rotation process in the multi-degree-of-freedom spherical motor torque detection experimental method of the present invention. Among them, (a) is the initial state in which the fixed coordinate system O-UVW coincides with the motion coordinate system o-xyz, (b) is a schematic diagram of the o-x1y1z1 coordinate system obtained by rotating the fixed coordinate system O-UVW around the U(x1) axis by an angle α, (c) is a schematic diagram of the o-x2y2z2 coordinate system obtained by rotating the fixed coordinate system O-x1y1z1 around the y1(y2) axis by an angle β, and (d) is a schematic diagram of the o-xyz coordinate system obtained by rotating the fixed coordinate system O-x2y2z2 around the z2(z) axis by an angle γ.

[0041] Figure 12 The image shows the motion trajectory of the centroid of the rotor salient pole relative to the centroid of the stator winding in the multi-degree-of-freedom spherical motor torque detection experiment device of the present invention, where 1-rotor salient pole, 12-stator winding;

[0042] Figure 13 The torque of the multi-degree-of-freedom spherical motor detected by the torque detection experimental method of the present invention is shown in (a) as a component MAP of the torque in the U-axis direction, (b) as a component MAP of the torque in the V-axis direction, and (c) as a component MAP of the torque in the W-axis direction. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] like Figure 1 As shown, the multi-degree-of-freedom spherical motor torque detection experimental device (hereinafter referred to as the experimental device) of the present invention includes a base 1-2, a support assembly (including a first support 1-3 and a second support 1-16), an inner ring assembly, an outer ring assembly, an X-axis mounting bracket 1-1, a Y-axis mounting bracket 1-10, a Z-axis mounting bracket 1-23, an X-axis drive sensing assembly, a Y-axis drive sensing assembly, and a Z-axis drive sensing assembly. The base 1-2 and the support assembly (first support 1-3 and second support 1-16) serve as the foundation of the experimental device and are placed at the bottom layer.

[0046] The X-axis drive sensing component is installed on the X-axis mounting bracket 1-1. The output shaft of the X-axis drive sensing component is assembled collinearly with the center point connection line of the first counter bore 3-1 and the second counter bore 3-2 of the inner ring component. The X-axis torque sensor 1-32 included in the X-axis drive sensing component is used to complete the X-axis torque detection. The Y-axis drive sensing component is installed on the Y-axis mounting bracket 1-10. The output shaft of the high-precision planetary reducer 1-9 in the Y-axis drive sensing component is assembled collinearly with the center point connection line of the third counter bore 3-3 and the fourth counter bore 3-4 of the inner ring component. At the same time, it is assembled collinearly with the center point connection line of the first deep groove ball bearing 4-3 and the third deep groove ball bearing 4-6 of the outer ring component. The Y-axis torque sensor 1-11 included in the Y-axis drive sensing component is used to complete the Y-axis torque detection. The Z-axis drive sensing component is installed on the Z-axis mounting bracket 1-23. The output shaft of the Z-axis drive sensing component is assembled collinearly with the central axis of the second deep groove ball bearing 4-5 of the outer ring component. The Z-axis torque sensor 1-19 included in the Z-axis drive sensing component is used to complete the Z-axis torque detection.

[0047] The base 1-2 is in a middle shape. The middle part of the middle shape is used to install the height adjustment seat 1-5, and a multi-degree-of-freedom spherical motor 1-4 is installed above the height adjustment seat 1-5. The two ends of the middle shape are respectively installed with the first bearing block 1-3 and the second bearing block 1-16. Among them, the longer ends of the two ends of the middle shape of the base 1-2 are used to install the X-axis mounting bracket 1-1. The bearing block assembly includes the first bearing block 1-3 and the second bearing block 1-16. The O-shaped inner ring 1-30 of the inner ring component is installed between the first bearing block 1-3 and the second bearing block 1-16. The distance between the first bearing block 1-3 and the second bearing block 1-16 is greater than the maximum diameter of the O-shaped inner ring 1-30 of the inner ring component.

[0048] As Figure 2 shown in (a) of Figure 2As shown in (b), the second bearing platform 1-16 consists of a second aluminum alloy main body 2-2, a second bearing snap ring 2-5, and a second 6002 deep groove ball bearing 2-6. The first aluminum alloy main body 2-1 and the second aluminum alloy main body 2-2 are provided with counterbores with a diameter of 32 mm. The first bearing snap ring 2-3 and the first 6002 deep groove ball bearing 2-4 are installed in the counterbore of the aluminum alloy main body 2-1 by interference fit; similarly, the second bearing snap ring 2-5 is installed in the counterbore on the outer side surface of the aluminum alloy main body 2-2 by interference fit, and the second 6002 deep groove ball bearing 2-6. The first bearing snap ring 2-3 and the second bearing snap ring 2-5 are used to prevent the first 6002 deep groove ball bearing 2-4 and the second 6002 deep groove ball bearing 2-6 from generating axial displacement along the counterbore direction; the first aluminum alloy main body 2-1 is assembled at the longer end of the base 1-2, and the second aluminum alloy main body 2-2 is assembled at the shorter ends of the two middle parts of the base 1-2. M3 threaded mounting holes are reserved on the outer side surfaces of the first aluminum alloy main body 2-1 and the second aluminum alloy main body 2-2 for fixing the X-axis conductive slip ring 1-14 in the X-axis drive sensing component.

[0049] As Figure 3 shown, the inner ring assembly includes an O-shaped inner ring 1-30, an X-axis torque sensor shaft 1-31, and an X-axis conductive slip ring shaft 1-15; four square counterbores are equally spaced on the circumference of the O-shaped inner ring 1-30: the first counterbore 3-1, the second counterbore 3-2, the third counterbore 3-3, and the fourth counterbore 3-4. The diameter of the X-axis torque sensor shaft 1-31 is 15 mm, and it is press-fitted into the first 6002 deep groove ball bearing 2-4 of the first bearing platform 1-3 by interference fit. The two sides of the X-axis torque sensor shaft 1-31 are respectively assembled and locked with the X-axis torque sensor 1-32 and the first counterbore 3-1 on the side of the first bearing platform 1-3 of the O-shaped inner ring 1-30 by bolts. The diameter of the X-axis conductive slip ring shaft 1-15 is 15 mm, and it is press-fitted into the second 6002 deep groove ball bearing 2-6 of the second bearing platform 1-16 by interference fit. The two sides of the X-axis conductive slip ring shaft 1-15 are respectively assembled and locked with the X-axis conductive slip ring 1-14 in the X-axis drive sensing component and the second counterbore 3-2 on the side of the second bearing platform 1-16 of the O-shaped inner ring 1-30 by bolts. The inner ring assembly is connected to the first bearing platform 1-3 and the second bearing platform 1-16 based on the X-axis torque sensor shaft 1-31 and the X-axis conductive slip ring shaft 1-15, and can complete rotational movement around the center line connecting the centers of the first counterbore 3-1 and the second counterbore 3-2.

[0050] As Figure 4 shown, the outer ring assembly includes an inverted U-shaped outer ring 1-26, a Y-axis torque sensor shaft 1-6, a Y-axis conductive slip ring shaft 1-27, a Z-axis torque sensor shaft 1-18, and a multi-degree-of-freedom spherical motor output shaft coupling 1-17.

[0051] The inverted U-shaped outer ring 1-26 is composed of an aluminum alloy body 4-1, a first bearing retaining ring 4-2, a first 6001 deep groove ball bearing 4-3, a second bearing retaining ring 4-4, a second 6001 deep groove ball bearing 4-5, a third 6001 deep groove ball bearing 4-6, and a third bearing retaining ring 4-7. The opening of the inverted U-shaped outer ring 1-26 faces downwards. Its first 6001 deep groove ball bearing 4-3 and third 6001 deep groove ball bearing 4-6 are respectively mounted on the Y-axis torque sensor shaft 1-6 and the Y-axis conductive slip ring shaft 1-27. The Y-axis torque sensor shaft 1-6 and the Y-axis conductive slip ring shaft 1-27 are respectively mounted on the third countersunk hole 3-3 and the fourth countersunk hole 3-4 of the O-shaped inner ring 1-30. The opening spacing of the inverted U-shaped outer ring 1-26 is greater than the maximum width of the outer side of the O-shaped inner ring 1-30. Each of the three outer surfaces of the inverted U-shaped outer ring 1-26 has countersunk holes with a diameter of approximately 28 mm. A first 6001 deep groove ball bearing 4-3, a second 6001 deep groove ball bearing 4-5, and a third 6001 deep groove ball bearing 4-6 are respectively installed in these three countersunk holes using an interference fit. A first bearing retaining circlip 4-2, a second bearing retaining circlip 4-4, and a third bearing retaining circlip 4-7 are respectively installed on one side of each of the first 6001 deep groove ball bearing 4-3, the second 6001 deep groove ball bearing 4-5, and the third 6001 deep groove ball bearing 4-6 to prevent axial displacement along the countersunk hole direction.

[0052] The Y-axis torque sensor shaft 1-6 has a diameter of approximately 12 mm and passes through the first 6001 deep groove ball bearing 4-3 on one side of the opening of the inverted U-shaped outer ring 1-26 with an interference fit. Both sides of the Y-axis torque sensor shaft 1-6 are bolted to the square countersunk holes on one side of the Y-axis mounting bracket 1-10 and the O-shaped inner ring 1-30. The Y-axis conductive slip ring shaft 1-27 has a diameter of approximately 12 mm and is press-fitted into the third 6001 deep groove ball bearing 4-6 on the other side of the opening of the inverted U-shaped outer ring 1-26 with an interference fit. Both sides of the Y-axis conductive slip ring shaft 1-27 are bolted to the Y-axis conductive slip ring 1-28 and the O-shaped inner ring 1-30 in the Y-axis drive sensing assembly. The square countersunk hole on one side of the inner ring 1-30 is locked by bolt assembly; the Z-axis torque sensor shaft 1-18 has a diameter of about 12 mm and is press-fitted into the second 6001 deep groove ball bearing 4-5 on the closed side of the inverted U-shaped outer ring 1-26 with an interference fit; the two sides of the Z-axis torque sensor shaft 1-18 are respectively bolted to the Z-axis torque sensor 1-19 in the Z-axis drive sensing assembly and the multi-degree-of-freedom spherical motor output shaft coupling 1-17; the outer ring assembly can rotate around the line connecting the center points of the third countersunk hole 3-3 and the fourth countersunk hole 3-4 on the O-shaped inner ring 1-30, which are far away from the first bearing 1-3 and the second bearing 1-16.

[0053] like Figure 5As shown, the X-axis mounting bracket 1-1 has a U-shaped structure. The bottom surface of the main steel structure 5-1 of the X-axis mounting bracket has two elongated openings for locking the main steel structure 5-1 of the X-axis mounting bracket to the base 1-2 by installing M5 bolts. The two sides of the main steel structure 5-1 of the X-axis mounting bracket that are perpendicular to the ground have openings for installing X-axis drive sensing components.

[0054] like Figure 6 As shown, the Y-axis mounting bracket 1-10 has a U-shaped structure. The bottom and one side of the main steel structure 6-1 of the Y-axis mounting bracket are respectively provided with through holes for mounting the Y-axis 57 stepper motor 1-8 and the Y-axis high-precision planetary reducer 1-9. The other side of the main steel structure 6-1 of the Y-axis mounting bracket is provided with through holes for locking the Y-axis mounting bracket 1-10 with the Y-axis torque sensor shaft 1-6.

[0055] like Figure 7 As shown, the Z-axis mounting bracket 1-23 has an H-shaped structure. The middle horizontal surface and the upper section of the side of the main steel structure 7-1 of the Z-axis mounting bracket are provided with through holes for mounting the Z-axis 57 stepper motor 1-22 and the Z-axis high-precision planetary reducer 1-24. The two bottom horizontal surfaces of the main steel structure 7-1 of the Z-axis mounting bracket are provided with through holes for locking with the blind holes on the closed side of the inverted U-shaped outer ring 1-26 using M5 bolts. The lower sections of the two side surfaces of the main steel structure 7-1 of the Z-axis mounting bracket are provided with through holes for mounting the Z-axis conductive slip ring bracket 1-25.

[0056] like Figure 8 As shown in (a), the X-axis drive sensing assembly includes an X-axis 57 stepper motor 1-35, an X-axis high-precision planetary reducer 1-34, an X-axis reducer output flange 1-33, an X-axis torque sensor 1-32, and an X-axis conductive slip ring 1-14, connected in sequence. Figure 8 As shown in (b), the X-axis conductive slip ring 1-14 includes a first inner tube 8-2 and a first outer tube 8-1, which are coaxially nested together. Stable and uniformly frictional power supply and signal connection are achieved through sliding contact during relative motion. The center point connection lines of the aforementioned X-axis drive sensing component and the inner ring component's first countersunk hole 3-1 and second countersunk hole 3-2 are coaxially connected, and the axis passes through the center of the multi-degree-of-freedom spherical motor 1-4.

[0057] The X-axis 57-stepper motor 1-35 serves as the rotational motion power source, controlling the experimental device to complete movement along the X-axis at a given rotational angle and speed, making the rotational angle and speed controllable. The X-axis high-precision planetary reducer 1-34 adopts a coaxial design for its input and output ends. The X-axis 57-stepper motor 1-35 is locked to the input end of the X-axis high-precision planetary reducer 1-34 via an M4 bolt on the vertical surface of the X-axis mounting bracket 1-1. The X-axis high-precision planetary reducer 1-34 has a reverse self-locking function, and its output end is locked to another vertical surface of the X-axis mounting bracket 1-1 via an M5 bolt. The hollow shaft of the X-axis reducer output flange 1-33 mates with the output shaft of the X-axis high-precision planetary reducer 1-34, achieving circumferential fixation through a keyway. Its flange is locked to the X-axis torque sensor 1-32 with bolts, enabling the X-axis torque sensor 1-32 to perform both reverse self-locking and torque transmission and detection. The X-axis torque sensor 1-32 serves as the torque detection device of the experimental device, and is equipped with through-holes on both sides. The X-axis reducer output flange 1-33 with reverse self-locking function is locked by M6 bolts, and the X-axis torque sensor shaft 1-31 of the inner ring assembly is also included. The X-axis conductive slip ring 1-14 has a first inner tube 8-2 and a first outer tube 8-1 that can move relative to each other. The two are coaxially nested and cooperate with each other. The power supply and signal connection in the relative motion state is achieved through sliding contact. It is the electrical connection component between the moving inner ring assembly on the X-axis and the stationary base 1-2, first support 1-3, second support 1-16, X-axis mounting bracket 1-1, and X-axis drive sensing assembly. The first inner tube 8-2 is locked to the X-axis conductive slip ring shaft 1-14 of the inner ring assembly and rotates accordingly. The first outer tube 8-1 is locked to the second support 1-16 by M3 bolts and remains relatively stationary. When the X-axis torque sensor 1-32, Y-axis torque sensor 1-11, Y-axis 57 stepper motor 1-8, Z-axis torque sensor 1-19, and Z-axis 57 stepper motor 1-22 rotate around the X-axis, power supply and signal connection are completed between the X-axis conductive slip ring 1-14 and the first outer tube 8-1.

[0058] like Figure 9 As shown in (a), the Y-axis drive sensing assembly includes a Y-axis 57 stepper motor 1-8, a Y-axis high-precision planetary reducer 1-9, a Y-axis reducer output flange 1-13, a Y-axis torque sensor 1-11, and a Y-axis linkage bracket 1-12 connected in sequence. Figure 9As shown in (b), the Y-axis conductive slip ring 1-28 includes a second inner tube 9-2 and a second outer tube 9-1, which are coaxially nested together. Stable and uniformly frictional power supply and signal connection are achieved through sliding contact during relative motion. In addition to the Y-axis 57 stepper motor 1-8, the Y-axis drive sensing component is connected to the center points of the third countersunk hole 3-3 and the fourth countersunk hole 3-4 on the O-shaped inner ring 1-30 using a coaxial connection, and the axis passes through the center of the multi-degree-of-freedom spherical motor 1-4.

[0059] The Y-axis 57 stepper motor 1-8 serves as the rotational motion power source, controlling the experimental device to complete the movement in the Y-axis direction according to a given rotation angle and speed, making the rotation angle and speed controllable. The Y-axis high-precision planetary reducer 1-9 adopts an L-shaped design, with its input and output ends at a 90-degree angle. The Y-axis 57 stepper motor 1-8 is locked to the input end of the Y-axis high-precision planetary reducer 1-9 via the bottom surface of the Y-axis mounting bracket 1-10 using M4 bolts. The Y-axis high-precision planetary reducer 1-9 has a reverse self-locking function, and its output end is locked to the vertical surface of the Y-axis mounting bracket 1-10 using M5 bolts. The hollow shaft of the Y-axis reducer output flange 1-13 mates with the output shaft of the Y-axis high-precision planetary reducer 1-9, achieving circumferential fixation through a keyway. Its flange is locked to the Y-axis torque sensor 1-11 with bolts. The device simultaneously performs torque transmission and torque detection while possessing a reverse self-locking function. The Y-axis torque sensor 1-11 serves as the torque detection device of the experimental apparatus. It has a Y-axis reducer output flange 1-13 with a reverse self-locking function, which is locked to the Y-axis by M6 bolts, and a Y-axis linkage bracket 1-12 on both sides. One end of the Y-axis linkage bracket 1-12 is locked to the Y-axis torque sensor 1-11, and the other end is locked to the inverted U-shaped outer ring 1-26 by M4 bolts. The rotation axis of both ends of the bracket is the Y-axis. The Y-axis conductive slip ring 1-28 has a second inner tube 9-2 and a second outer tube 9-1, which are coaxially nested together. Through sliding contact, it achieves stable and frictionally uniform power supply and signal connection in the relative motion state. It is the electrical connection component between the moving outer ring assembly on the Y-axis and the stationary Y-axis mounting bracket 1-10 and Y-axis drive sensing assembly. The second outer tube 9-1 is locked to the inverted U-shaped outer ring 1-26 with M3 bolts and rotates accordingly. The second inner tube 9-2 is locked to the Y-axis conductive slip ring shaft 1-27 of the outer ring assembly. When the Y-axis torque sensor 1-11, Y-axis 57 stepper motor 1-8, Z-axis torque sensor 1-19, and Z-axis 57 stepper motor 1-22 rotate around the Y-axis, they complete the power supply and signal connection with the stationary Y-axis mounting bracket 1-10 and the Y-axis drive sensing assembly through the Y-axis conductive slip ring 1-28.

[0060] like Figure 10As shown, the Z-axis drive sensing assembly includes a Z-axis 57 stepper motor 1-22, a Z-axis high-precision planetary reducer 1-24, a Z-axis conductive slip ring bracket 1-25, a Z-axis conductive slip ring 1-21, a Z-axis reducer output flange 1-20, and a Z-axis torque sensor 1-19, connected in sequence. Except for the Z-axis 57 stepper motor 1-22, the above components are coaxially connected to the Z-axis torque sensor shaft 1-18 on the inverted U-shaped outer ring 1-26, and the shaft passes through the center of the multi-degree-of-freedom spherical motor 1-4. The Z-axis 57 stepper motor 1-22 serves as the rotational motion power source, controlling the experimental device to complete the movement in the Z-axis direction according to a given rotation angle and speed, making the rotation angle and speed controllable. The Z-axis high-precision planetary reducer 1-24 adopts an L-shaped design, and its input and output... The output ends form a 90-degree angle. The Z-axis 57 stepper motor 1-22 is locked to the input end of the Z-axis high-precision planetary reducer 1-24 via the side of the Z-axis mounting bracket 1-23 using M4 bolts. The Z-axis high-precision planetary reducer 1-24 has a reverse self-locking function, and its output end is locked to the middle surface of the Z-axis mounting bracket 1-23 using M5 bolts. The hollow shaft of the Z-axis reducer output flange 1-20 mates with the output shaft of the Z-axis high-precision planetary reducer 1-24, and is circumferentially fixed via a keyway. Its flange is connected to the Z-axis... Torque sensor 1-19 is bolted in place, providing torque transmission while also having a reverse self-locking function. The Z-axis torque sensor 1-19 serves as the torque detection device in the experimental setup, with its two sides connected to the output flange 1-20 of the Z-axis reducer (which has a reverse self-locking function) and the Z-axis torque sensor shaft 1-18, respectively, both secured with M6 bolts. The Z-axis conductive slip ring bracket 1-25 has an n-shaped structure with two elongated openings on each of its two sides for mounting M5 bolts to achieve torque transmission along the Z-axis. The conductive slip ring bracket 1-25 is locked to the Z-axis mounting bracket 1-23. Its bottom surface has a circular opening for the Z-axis reducer output flange 1-20 and the Z-axis conductive slip ring 1-21 to pass through. The Z-axis conductive slip ring 1-21 has a structure of a third inner tube 10-1 and a third outer tube 10-2 that move relative to each other. This structure can achieve a stable and frictionally uniform power supply and signal connection between the two in a relative motion state. It is the electrical connection component between the moving Z-axis drive sensing component and the stationary Z-axis mounting bracket 1-23.The third inner tube 10-1 is embedded in the hollow shaft of the output flange 1-20 of the Z-axis reducer. The third outer tube 10-2 and the Z-axis conductive slip ring bracket 1-25 of the Z-axis drive sensing assembly are locked together by M3 bolts and kept relatively stationary. When the Z-axis torque sensor 1-19 and the Z-axis 57 stepper motor 1-22 rotate around the Z-axis, the Z-axis conductive slip ring 1-21 and the stationary third outer tube 10-2 are connected for power supply and signal. Except for the Z-axis reducer output flange 1-20, the third inner tube 10-1, and the Z-axis torque sensor 1-19, the rest of the Z-axis drive sensing assembly is fixed relative to the inverted U-shaped outer ring 1-26, which together drive the Z-axis torque sensor shaft 1-18 to rotate around the Z-axis and also has sensing capability.

[0061] The height adjustment seat 1-5 is locked to the multi-degree-of-freedom spherical motor 1-4 and the base 1-2 on its upper and lower sides respectively by M5 bolts. It is used to adjust the relative height and horizontal position between the multi-degree-of-freedom spherical motor 1-4 and the base 1-2. The height adjustment seat 1-5 is used to make the multi-degree-of-freedom spherical motor torque detection experimental device adapt to multi-degree-of-freedom spherical motors 1-4 with different structures and sizes, and to ensure that the intersection of the X-axis, Y-axis and Z-axis of the test bench coincides with the center of the sphere of the multi-degree-of-freedom spherical motor 1-4.

[0062] A multi-axis motion controller coordinates the movement of the X-axis 57 stepper motor 1-35, Y-axis 57 stepper motor 1-8, and Z-axis 57 stepper motor 1-22 of the multi-degree-of-freedom spherical motor torque detection experimental device, jointly driving the device according to... Figure 12 The predetermined trajectory shown completes the tracking of the multi-degree-of-freedom spherical motors 1-4.

[0063] The first counterweight 1-7 and the second counterweight 1-29 are respectively installed on the bottom end of the open side of the inverted U-shaped outer ring 1-26 of the outer ring assembly and on the Y-axis conductive slip ring shaft 1-27. They are locked to the bottom end of the open side of the inverted U-shaped outer ring 1-26 and the Y-axis conductive slip ring shaft 1-27 by M5 bolts, respectively. They are used to provide counterweights for the outer ring assembly rotating around the Y-axis and the inner ring assembly rotating around the X-axis, so as to ensure that the center of mass of the outer ring assembly and its accessories, and the inner ring assembly and its accessories coincide with the center of the ball of the multi-degree-of-freedom spherical motor 1-4, thereby eliminating the adverse effects of gravity on torque detection.

[0064] Step 1: Solve for the relative motion transformation matrix between the stator and rotor of the multi-degree-of-freedom spherical motors 1-4.

[0065] A fixed coordinate system O-UVW, which is fixed relative to the stator, and a moving coordinate system o-xyz, which moves with the rotor, are constructed. To describe the multi-degree-of-freedom motion of the rotor relative to the stator, the rotation process of the moving coordinate system o-xyz is decomposed. In any rotor orientation, there is a unique corresponding moving coordinate system o-xyz. This moving coordinate system o-xyz can be obtained by performing three coordinate rotations starting from the fixed coordinate system O-UVW, with the direction of rotation following the right-hand screw rule. Figure 11 As shown, the gray coordinate system represents the new coordinate system generated after rotating the previous coordinate system, and the axis numbers in parentheses indicate that the newly generated coordinate axes coincide with the original coordinate axes. Figure 11 (a) represents the initial state before coordinate rotation, at which point o-xyz and O-UVW coincide. First, as... Figure 11 As shown in (b), the o-x1y1z1 coordinate system is obtained by rotating the O-UVW coordinate system around the U-axis by an angle α; subsequently, as shown in (b)... Figure 11 As shown in (c), rotating by an angle β around the y1 axis yields the o-x2y2z2 coordinate system; finally, as... Figure 11 As shown in (d), the motion coordinate system o-xyz is obtained by rotating about the z2 axis by an angle γ. The angular displacement matrix during the three rotations is... and angular velocity matrix They are respectively and . These are the angular velocities of rotation about each axis during the three rotations mentioned above. Figure 11 The cubic coordinate rotation solution yields the corresponding rotation matrix. for:

[0066] (1)

[0067] The relative motion transformation matrix between the stator and rotor of the multi-degree-of-freedom spherical motors 1-4 is as follows:

[0068] (2)

[0069] Step 2: Conduct a torque detection experiment. This specifically includes:

[0070] Step 21: Using a multi-axis motion controller to drive the torque detection experimental device of the multi-degree-of-freedom spherical motor, the rotor salient pole 1 of the multi-degree-of-freedom spherical motor 1-4 is dragged according to... Figure 12 The predetermined trajectory shown completes the tracking of the multi-degree-of-freedom spherical motors 1-4; Figure 12 The motion trajectory of the centroid of the rotor salient pole 1 of the multi-degree-of-freedom spherical motor 1-4 relative to the centroid of the stator winding 12 is shown. The centroid of the rotor salient pole 1 moves along the meridians of the spherical surface one by one, completing the traversal of the entire spherical surface. The torque data of the entire spherical surface is obtained through the torque sensor.

[0071] Step 22: The multi-axis motion controller controls the coordinated motion of the X-axis drive sensing component, Y-axis drive sensing component, and Z-axis drive sensing component to drag the centroid of the rotor salient pole 1 of the multi-degree-of-freedom spherical motor 1-4 along... Figure 12 During the torque detection process of the motion trajectory shown, the torque sensors detect the torque data corresponding to the traversal points in real time. The detection results of the X-axis torque sensor 1-32, Y-axis torque sensor 1-11, and Z-axis torque sensor 1-19 are as follows: , , ,in, , , The detection results of the above torque sensors are: the torques along the x, y, and z axes in the motion coordinate system o-xyz. The control torques output by the X-axis 57 stepper motor 1-35, the Y-axis 57 stepper motor 1-8, and the Z-axis 57 stepper motor 1-22 are also included. for , , ,in, , , The control torque output by each of the aforementioned stepper motors. The rotational angular displacement and rotational angular velocity output by the X-axis high-precision planetary reducer 1-34, the Y-axis high-precision planetary reducer 1-9, and the Z-axis high-precision planetary reducer 1-24 are expressed in matrix form: angular displacement matrix : and angular velocity matrix : The frictional torque existing at the connection points of the multi-degree-of-freedom spherical motor 1-4, X-axis conductive slip ring 1-14, Y-axis conductive slip ring 1-28, Z-axis conductive slip ring 1-21, and various rotating axes of the multi-degree-of-freedom spherical motor torque detection experimental device is represented as the composite frictional torque. , , ,in, , , Let be the components of the composite frictional torque along each axis of the motion coordinate system o-xyz. The output torque of the multi-degree-of-freedom spherical motor 1-4 is expressed as: , , ;in, , , The components of the output torque on each axis of the motion coordinate system o-xyz. and They are equal in size but opposite in direction, among which, Regarding the test results The combined frictional torque present in Compensation is performed to obtain the output torque T of the tested object: multi-degree-of-freedom spherical motor 1-4.

[0072] Step 3: Construct the Stribeck friction model for the composite friction torque. Model the composite friction torque sequences along the x, y, and z axes obtained in Step 2. The mathematical expressions are as follows:

[0073] (3)

[0074] For compound friction torque, The frictional torque is Coulomb torque. For the maximum static friction torque, For Stribeck switching speed, The coefficient of viscous friction, This indicates the components of the above parameters on the x, y, and z axes; This is an empirical parameter, typically taken as 0.5-2; for Figure 11 The angular velocities of rotation about the x, y, and z axes during the three rotations shown can be represented in matrix form as follows: The expression for the symbolic function sgn is:

[0075] (4)

[0076] Step 4: Power off the multi-degree-of-freedom spherical motors 1-4 and conduct a constant-speed tracking pre-experiment in the x, y, and z axes. The purpose is to confirm the speed range in which the Stribeck phenomenon occurs, so as to further narrow down the experimental speed range. This specifically includes the following steps:

[0077] Step 41: Simultaneously control three stepper motors (X-axis 57 stepper motor 1-35, Y-axis 57 stepper motor 1-8, and Z-axis 57 stepper motor 1-22) to move at the same speed and distance within the 0-200 rpm range. The rotational speed sequence repeats point by point to complete constant speed motion; It is a rotational speed sequence, where i takes values ​​from 1 to 41, meaning the sequence contains 41 rotational speed elements.

[0078] Step 42: During constant speed motion, the torque sequence is obtained using the X-axis torque sensor 1-32, Y-axis torque sensor 1-11, and Z-axis torque sensor 1-19, respectively. Torque sequences corresponding to the x, y, and z axes ; Respectively with the speed sequence There is a unique correspondence, that is The torque element is The mapping of medium speed elements, where the value of i is 1-41, that is, each of the three torque sequences contains 41 torque elements.

[0079] Step 43: Based on the torque sequence obtained in step 42 during constant speed motion, obtain the speed sequence. The corresponding composite friction torque sequence This allows us to determine the velocity range in which the Stribeck phenomenon occurs.

[0080] Step 5: Power off the multi-degree-of-freedom spherical motors 1-4 and conduct a formal experiment on constant speed tracking in the x, y, and z axes. Based on step 4, reduce the speed sequence. The specific steps involved are as follows:

[0081] Step 51: Simultaneously control three stepper motors (X-axis 57 stepper motor 1-35, Y-axis 57 stepper motor 1-8, and Z-axis 57 stepper motor 1-22) within the speed range of 0-5 rpm. The rotational speed sequence repeats point by point to complete constant speed motion.

[0082] Step 52: During constant speed motion, the torque sequence is obtained using the X-axis torque sensor 1-32, Y-axis torque sensor 1-11, and Z-axis torque sensor 1-19, respectively. Torque sequences corresponding to the x, y, and z axes ; Respectively with the speed sequence There is a unique correspondence, that is The torque element is The mapping of medium speed elements, where the value of i is 1-33, that is, each of the three sequences contains 33 torque elements.

[0083] Step 53, based on the torque sequence obtained in step 52 during constant speed motion. The rotational speed sequence was obtained. The corresponding composite friction torque sequence .

[0084] Step 6, set the parameter matrix E for the x, y, and z axes:

[0085] (5)

[0086] in, These represent the positive and negative components of the Coulomb friction torque along the x, y, and z axes, respectively. These represent the components of the maximum static friction torque in the positive and negative directions of the x, y, and z axes, respectively. These represent the components of Stribeck's switching speed in the positive and negative directions of the x, y, and z axes, respectively. These are the components of the viscous friction coefficient in the positive and negative directions of the x, y, and z axes, respectively.

[0087] Step 7: Use the composite friction torque sequence obtained in Step 6. For the raw data of parameter identification, the Particle Swarm Optimization (PSO) algorithm is used to identify the parameters of equation (4), and the parameter matrix is ​​obtained. This leads to the Stribeck friction model in the x, y, and z axes. The parameter matrix was identified. The parameters are shown in Table 1:

[0088] Table 1

[0089]

[0090] Step 8: Power on the multi-degree-of-freedom spherical motor 1-4, and use the multi-degree-of-freedom spherical motor torque detection experimental device to drive the multi-degree-of-freedom spherical motor 1-4 in the x, y, and z axes according to... Figure 12 A constant speed torque detection experiment was conducted on the predetermined trajectory shown, specifically including:

[0091] Step 81: Using a multi-axis motion controller, control the three stepper motors (X-axis 57 stepper motor 1-35, Y-axis 57 stepper motor 1-8, and Z-axis 57 stepper motor 1-22) of the multi-degree-of-freedom spherical motor torque detection experimental device according to a speed sequence within the 0-5 rpm speed range. To achieve constant speed motion; the constant speed torque detection experiment is conducted according to... Figure 12 The predetermined trajectory is shown, which contains 180 meridians with a distance of 2° between them. Therefore, the rotational speed sequence... These are the angular velocities of the x, y, and z axes respectively during the scanning along the i-th meridian; when scanning the i-th meridian, the rotational speeds of the x, y, and z axes are constant, respectively. The rotational speed changes only with the meridian.

[0092] Step 82: During the constant speed motion process, the speed sequence is acquired by the X-axis torque sensor 1-32, Y-axis torque sensor 1-11, and Z-axis torque sensor 1-19 respectively. The corresponding x, y, z torque sequences .

[0093] Step 83: During the process of the multi-degree-of-freedom spherical motor torque detection experimental device driving the multi-degree-of-freedom spherical motor 1-4, the multi-degree-of-freedom spherical motor 1-4 is always kept powered on to generate output torque. According to step 2 The torque sequences acquired by each torque sensor represent the output torque of the multi-degree-of-freedom spherical motors 1-4. Combined frictional torque The superposition of these factors results in a composite frictional torque. This can be represented using the Stribeck friction model.

[0094] Step 84, output torque of the multi-degree-of-freedom spherical motor The components along the x, y, and z axes can be represented as: , , Torque sensor detection results The components along the x, y, and z axes can be represented as: , , Composite friction torque The components on the x, y, and z axes are represented using the Stribeck friction model. , , Output torque for:

[0095] (6)

[0096] angular velocity matrix The x, y, and z axis output torques of the corresponding multi-degree-of-freedom spherical motors 1-4 can be expressed as the corresponding axes in the angular velocity matrix. Torque obtained from the lower sensor Combined frictional torque The sum of.

[0097] Step 9: The output torque T of the multi-degree-of-freedom spherical motor 1-4 obtained in step 8 is in the coordinate system o-xyz. In order to facilitate the comparison of the output torque under different rotor attitudes, T can be transformed to the coordinate system O-UVW using equation (2) to obtain the torque of the multi-degree-of-freedom spherical motor 1-4 in the fixed coordinate system O-UVW. :

[0098] (7)

[0099] in, Let be the rotation matrix of the three rotations in equation (1).

[0100] Step 10, the obtained three-degree-of-freedom torque data , , After Stribeck friction model , , After compensation, the components of the output torque T of the multi-degree-of-freedom spherical motor 1-4 on the x, y, and z axes are obtained. , , Using equation (7), the output torque T is transferred from... Figure 11 The motion coordinate system o-xyz is transformed into the fixed coordinate system O-UVW. After the transformation, the components of the output torque T on the U, V, and W axes are positioned based on the centroid of the rotor salient pole 1 of the multi-degree-of-freedom spherical motor 1-4, and the output torque components on the U, V, and W axes are respectively... Figure 13 of (a) Figure 13 (b) and Figure 13 As shown in (c); Figure 13 In this context, the point where the centroid of the rotor salient pole 1 is directly opposite the centroid of the stator winding 12 is the intersection of the 0° longitude and the 0° latitude. Figure 13 In the diagram, the horizontal axis represents the longitude of the centroid of rotor salient pole 1. The vertical axis represents the latitude of the centroid of rotor salient pole 1. The vertical axis represents the output torque components on the U, V, and W axes corresponding to the current longitude and latitude. .

[0101] The above description is merely an embodiment of the present invention and does not limit the scope of the invention. Any equivalent structural or procedural transformations made based on the description and drawings of this invention, or direct or indirect applications in other related system fields, are similarly included within the protection scope of this invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

Claims

1. An experimental device for detecting the torque of a multi-degree-of-freedom spherical motor, characterized in that, Including: Base, bearing platform assembly, inner ring assembly, outer ring assembly, X-axis mounting bracket, Y-axis mounting bracket, Z-axis mounting bracket, X-axis drive and sensing assembly, Y-axis drive and sensing assembly, Z-axis drive and sensing assembly; The base and the bearing platform assembly are placed at the bottom layer; The X-axis drive and sensing assembly includes an X-axis torque sensor installed on the X-axis mounting bracket. The output shaft of the X-axis drive and sensing assembly is coaxially assembled with the connection line of the center points of the first counter bore and the second counter bore of the inner ring assembly. The X-axis torque sensor is used to complete the X-axis torque detection; The Y-axis drive and sensing assembly includes a Y-axis torque sensor installed on the Y-axis mounting bracket. The output shaft of the high-precision planetary reducer of the Y-axis in the Y-axis drive and sensing assembly is coaxially assembled with the connection line of the center points of the third counter bore and the fourth counter bore of the inner ring assembly, and at the same time, is coaxially assembled with the connection line of the center points of the first 6001 deep groove ball bearing and the third 6001 deep groove ball bearing of the outer ring assembly. The Y-axis torque sensor is used to complete the Y-axis torque detection; The Z-axis drive and sensing assembly includes a Z-axis torque sensor installed on the Z-axis mounting bracket. The output shaft of the Z-axis drive and sensing assembly is coaxially assembled with the central axis of the second 6001 deep groove ball bearing of the outer ring assembly. The Z-axis torque sensor is used to complete the Z-axis torque detection; The middle part of the base is used to install the height adjustment base, and a multi-degree-of-freedom spherical motor is installed above the height adjustment base. The first bearing platform and the second bearing platform included in the bearing platform assembly are installed at both ends respectively.

2. The experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 1, characterized in that, The O-shaped inner ring of the inner ring assembly is installed between the first bearing platform and the second bearing platform, and the distance between the first bearing platform and the second bearing platform is greater than the maximum diameter of the O-shaped inner ring of the inner ring assembly; The first bearing platform includes a first aluminum alloy body, a first bearing snap ring, and a first 6002 deep groove ball bearing; The second bearing platform includes a second aluminum alloy body, a second bearing snap ring, and a second 6002 deep groove ball bearing; Counter bores are provided on the outer side surfaces of the first aluminum alloy body and the second aluminum alloy body; The first bearing snap ring and the first 6002 deep groove ball bearing are installed in the counter bores on the outer side surface of the aluminum alloy body; The second bearing snap ring and the second 6002 deep groove ball bearing are installed in the counter bores on the outer side surface of the aluminum alloy body; The first bearing snap ring and the second bearing snap ring are used to prevent the first 6002 deep groove ball bearing and the second 6002 deep groove ball bearing from generating axial displacement along the direction of the counter bore; The first aluminum alloy body is assembled at the longer ends of the two middle-shaped ends of the base, and the second aluminum alloy body is assembled at the shorter ends of the two middle-shaped ends of the base.

3. The experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 2, characterized in that, The inner ring assembly includes an O-shaped inner ring, an X-axis torque sensor shaft, and an X-axis conductive slip ring shaft; First counter bore, second counter bore, third counter bore, and fourth counter bore are equidistantly arranged on the circumference of the O-shaped inner ring; The X-axis torque sensor shaft is press-fitted into the first 6002 deep groove ball bearing by interference fit, and both sides of the X-axis torque sensor shaft are assembled and locked with the X-axis torque sensor and the first counter bore on the first bearing platform side of the O-shaped inner ring respectively; The X-axis conductive slip ring shaft is press-fitted into the second 6002 deep groove ball bearing by interference fit, and both sides of the X-axis conductive slip ring shaft are assembled and locked with the X-axis conductive slip ring of the X-axis drive and sensing assembly and the second counter bore on the second bearing platform side of the O-shaped inner ring respectively; The inner ring assembly is based on the X-axis torque sensor shaft and the X-axis conductive slip ring shaft, which are connected to the first and second supports to achieve rotational movement around the line connecting the center points of the first and second countersunk holes.

4. The experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 3, characterized in that, The outer ring assembly includes an inverted U-shaped outer ring, a Y-axis torque sensor shaft, a Y-axis conductive slip ring shaft, a Z-axis torque sensor shaft, and a multi-degree-of-freedom spherical motor output shaft coupling; The inverted U-shaped outer ring includes an aluminum alloy body, a first bearing retainer, a first 6001 deep groove ball bearing, a second bearing retainer, a second 6001 deep groove ball bearing, a third 6001 deep groove ball bearing, and a third bearing retainer. The opening of the inverted U-shaped outer ring faces downwards, and its first and third 6001 deep groove ball bearings are respectively mounted on the Y-axis torque sensor shaft and the Y-axis conductive slip ring shaft. The Y-axis torque sensor shaft and the Y-axis conductive slip ring shaft are respectively mounted on the third bearing retainer of the O-shaped inner ring. The outer ring has a hole and a fourth countersunk hole. The opening spacing of the inverted U-shaped outer ring is greater than the maximum width of the outer side of the O-shaped inner ring. Countersunk holes are distributed on the three outer sides of the inverted U-shaped outer ring. The first 6001 deep groove ball bearing, the second 6001 deep groove ball bearing, and the third 6001 deep groove ball bearing are installed in the three countersunk holes respectively. The first bearing retaining ring, the second bearing retaining ring, and the third bearing retaining ring are installed on one side of the first 6001 deep groove ball bearing, the second 6001 deep groove ball bearing, and the third 6001 deep groove ball bearing respectively.

5. The experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 4, characterized in that, The Y-axis torque sensor shaft passes through a first 6001 deep groove ball bearing on one side of the opening of the inverted U-shaped outer ring. Both sides of the Y-axis torque sensor shaft are respectively fitted and locked to the square countersunk holes on one side of the Y-axis mounting bracket and the O-shaped inner ring. The Y-axis conductive slip ring shaft is press-fitted into a third 6001 deep groove ball bearing on the other side of the opening of the inverted U-shaped outer ring. Both sides of the Y-axis conductive slip ring shaft are respectively fitted and locked to the square countersunk holes on one side of the Y-axis conductive slip ring and the O-shaped inner ring in the Y-axis drive sensing assembly. The Z-axis torque sensor shaft is press-fitted into a second 6001 deep groove ball bearing on the closed side of the inverted U-shaped outer ring. Both sides of the Z-axis torque sensor shaft are respectively fitted and locked to the Z-axis torque sensor and the multi-degree-of-freedom spherical motor output shaft coupling in the Z-axis drive sensing assembly. The outer ring assembly rotates around the line connecting the center points of the third and fourth countersunk holes on the O-shaped inner ring, away from the first and second bearing platforms.

6. The experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 5, characterized in that, The X-axis mounting bracket has a U-shaped structure. The bottom surface of the main steel structure of the X-axis mounting bracket has an opening for locking the main steel structure of the X-axis mounting bracket to the base. The two sides of the main steel structure of the X-axis mounting bracket that are perpendicular to the ground have openings for installing the X-axis drive sensor components. The Y-axis mounting bracket has a U-shaped structure. The bottom and one side of the main steel structure of the Y-axis mounting bracket are respectively provided with through holes for mounting the Y-axis 57 stepper motor and the Y-axis high-precision planetary reducer. The other side of the main steel structure of the Y-axis mounting bracket is provided with through holes for locking the Y-axis mounting bracket to the Y-axis torque sensor shaft. The Z-axis mounting bracket has an H-shaped structure. Through holes are provided on the middle horizontal surface and upper side sections of the main steel structure for mounting the Z-axis 57 stepper motor and the Z-axis high-precision planetary reducer. Through holes are also provided on the two bottom horizontal surfaces of the main steel structure for bolting to the blind holes on the closed side of the inverted U-shaped outer ring. Through holes are also provided on the lower side sections of the main steel structure for mounting the Z-axis conductive slip ring bracket.

7. The experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 6, characterized in that, The X-axis drive sensing assembly includes an X-axis 57 stepper motor, an X-axis high-precision planetary reducer, an X-axis reducer output flange, an X-axis torque sensor, and an X-axis conductive slip ring, connected in sequence. The X-axis drive sensing assembly and the inner ring assembly are coaxially connected at the center points of the first and second countersunk holes, and the axis passes through the center of the multi-degree-of-freedom spherical motor. The X-axis 57 stepper motor is locked to the X-axis high-precision planetary reducer via the X-axis mounting bracket; the reducer output end is locked to another vertical surface of the X-axis mounting bracket; the hollow shaft of the X-axis reducer output end flange is fitted with the reducer output shaft keyway, and the flange is locked to the X-axis torque sensor; the X-axis torque sensor shaft of the X-axis reducer output end flange and the inner ring assembly are locked on both sides of the X-axis torque sensor; the X-axis conductive slip ring includes a first inner tube and a first outer tube, which are coaxially nested; the first inner tube is locked to the X-axis conductive slip ring shaft for rotation, and the first outer tube is locked to the second support by bolts to remain stationary, realizing the electrical connection between the moving inner ring assembly and the stationary base, first support, second support, and X-axis mounting bracket.

8. The experimental apparatus for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 7, characterized in that, The Y-axis drive sensing assembly includes a Y-axis 57-stepper motor, a Y-axis high-precision planetary reducer, a Y-axis reducer output flange, a Y-axis torque sensor, and a Y-axis linkage bracket connected in sequence. These components are coaxially connected to the center points of the third and fourth countersunk holes on the O-shaped inner ring, with the axis passing through the center of the multi-degree-of-freedom spherical motor. The Y-axis 57-stepper motor is locked to the Y-axis high-precision planetary reducer via the bottom surface of the Y-axis mounting bracket, and the reducer output end is locked to the vertical surface of the Y-axis mounting bracket. The hollow shaft of the Y-axis reducer output flange engages with the keyway of the reducer output shaft, and the flange is locked to the Y-axis torque sensor. The Y-axis torque sensor is locked to both sides of the Y-axis reducer output flange and the Y-axis linkage bracket, which is locked to the inverted U-shaped outer ring. The Y-axis conductive slip ring includes a second inner tube and a second outer tube. The second outer tube is locked to the inverted U-shaped outer ring for rotation, while the second inner tube is locked to the Y-axis conductive slip ring shaft for stationary operation, thus achieving electrical connection between the moving outer ring assembly and the stationary Y-axis mounting bracket and Y-axis drive sensing assembly. The Z-axis drive sensing assembly includes a Z-axis 57-stepper motor, a Z-axis high-precision planetary reducer, a Z-axis conductive slip ring bracket, a Z-axis conductive slip ring, a Z-axis reducer output flange, and a Z-axis torque sensor connected in sequence. The Z-axis torque sensor shaft is coaxially connected to the Z-axis torque sensor shaft on the inverted U-shaped outer ring, and the shaft passes through the center of the multi-degree-of-freedom spherical motor. The Z-axis 57-stepper motor is locked to the Z-axis high-precision planetary reducer via the side of the Z-axis mounting bracket, and the reducer output end is locked to the middle surface of the Z-axis mounting bracket. The hollow shaft of the Z-axis reducer output flange engages with the reducer output shaft via a keyway, and the flange is locked to the Z-axis torque sensor, with the Z-axis torque sensor shaft locked on both sides. The Z-axis conductive slip ring bracket is n-shaped and locked to the Z-axis mounting bracket, with a circular opening on its bottom surface passing through the Z-axis reducer output flange and the Z-axis conductive slip ring.

9. The experimental device for detecting the torque of a multi-degree-of-freedom spherical motor according to claim 8, characterized in that, Also includes: Multi-axis motion controller, first counterweight, and second counterweight; The multi-axis motion controller coordinates the X-axis 57 stepper motor, Y-axis 57 stepper motor, and Z-axis 57 stepper motor of the multi-degree-of-freedom spherical motor torque detection experimental device to move in tandem, driving the device to track the multi-degree-of-freedom spherical motor along a predetermined trajectory. The first and second counterweights are respectively installed on the bottom end of the inverted U-shaped outer ring opening side of the outer ring assembly and the Y-axis conductive slip ring shaft, and are locked to the bottom end of the inverted U-shaped outer ring opening side and the Y-axis conductive slip ring shaft, respectively. They are used to provide counterweights for the outer ring assembly rotating around the Y-axis and the inner ring assembly rotating around the X-axis, ensuring that the center of mass of the outer ring assembly and its accessories, and the inner ring assembly and its accessories, coincide with the center of the sphere of the multi-degree-of-freedom spherical motor.

10. A method for detecting the torque of a multi-degree-of-freedom spherical motor, used in the experimental apparatus for detecting the torque of a multi-degree-of-freedom spherical motor as described in any one of claims 1 to 9, characterized in that, include: Step 1: Solve for the relative motion transformation matrix between the stator and rotor of the multi-degree-of-freedom spherical motor; A fixed coordinate system O-UVW, which is fixed relative to the stator, and a moving coordinate system o-xyz, which moves with the rotor, are constructed. To describe the multi-degree-of-freedom motion of the rotor relative to the stator, the rotation process of the moving coordinate system o-xyz is decomposed. Each arbitrary orientation of the rotor uniquely corresponds to a moving coordinate system o-xyz, which can be obtained by performing three coordinate rotations starting from the fixed coordinate system O-UVW, with the rotation direction following the right-hand screw rule. First, the o-x1y1z1 coordinate system is obtained by rotating the O-UVW around the U-axis by an angle α. Then, the o-x2y2z2 coordinate system is obtained by rotating the O-UVW around the y1-axis by an angle β. Finally, the o-xyz coordinate system is obtained by rotating the O-x2-axis by an angle γ. The angular displacement matrix during these three rotations is... and angular velocity matrix They are respectively and ; These represent the angular velocities of rotation about each axis during the rotation process; the corresponding rotation matrix is ​​obtained by solving the cubic coordinate rotation problem. for: （1） The relative motion transformation matrix between the stator and rotor of a multi-degree-of-freedom spherical motor is as follows: （2） Step 2: Conduct a torque detection experiment; Step 3: Construct the Stribeck friction model of the composite friction torque, and model the composite friction torque sequences of the x, y, and z axes obtained in Step 2 respectively; Step 4: Power on the multi-degree-of-freedom spherical motor and conduct a constant speed tracking pre-experiment in the x, y, and z axes; Step 5: Power on the multi-degree-of-freedom spherical motor and conduct a formal experiment of constant speed tracking in the x, y, and z axes, reducing the speed sequence based on step 4. The area in question; Step 6, set the parameter matrix E for the x, y, and z axes: （5） in, These represent the positive and negative components of the Coulomb friction torque along the x, y, and z axes, respectively. These represent the components of the maximum static friction torque in the positive and negative directions of the x, y, and z axes, respectively. These represent the components of Stribeck's switching speed in the positive and negative directions of the x, y, and z axes, respectively. These are the components of the viscous friction coefficient in the positive and negative directions of the x, y, and z axes, respectively. Step 7: Use the composite friction torque sequence obtained in Step 6. The raw data for parameter identification is used to perform parameter identification on equation (4) using the particle swarm optimization algorithm, and the parameter matrix is ​​obtained. This leads to the Stribeck friction model in the x, y, and z axes. ; Step 8: Power on the multi-degree-of-freedom spherical motor and use the multi-degree-of-freedom spherical motor torque detection experimental device to drive the multi-degree-of-freedom spherical motor along a predetermined trajectory in the x, y, and z axes to conduct a constant speed torque detection experiment. Step 9: Transform T to the coordinate system O-UVW using equation (2) to obtain the torque of the multi-degree-of-freedom spherical motor in the fixed coordinate system O-UVW. : （7） in, Let be the rotation matrix for the three rotations in equation (1); Step 10, the obtained three-degree-of-freedom torque data , , Stribeck friction model , , After compensation, the components of the output torque T of the multi-degree-of-freedom spherical motor on the x, y, and z axes are obtained. , , ; Using equation (6), the output torque T is transformed from the moving coordinate system o-xyz to the fixed coordinate system O-UVW. After the transformation, the components of the output torque T in the U, V, and W axes are positioned based on the centroid of the rotor salient pole of the multi-degree-of-freedom spherical motor. .

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