Preliminary knowledge of CMM

by:Top Talent     2020-07-20
One, three coordinate measuring machine
The Coordinate Measuring Machining (CMM) is a new type of high-precision precision measuring instrument developed in the 1960s. Its emergence, on the one hand, is due to the high-efficiency processing of automatic machine tools, CNC machine tools, and the processing of more and more complex-shaped parts. It requires fast and reliable measuring equipment to match it; And the development of precision machining technology provides a technical basis for the production of coordinate measuring machines. In 1960, British FERRANTI successfully developed the world's first coordinate measuring machine. By the end of the 1960s, more than 30 companies in nearly ten countries were producing CMM, but CMM was still in its infancy during this period. stage. After entering the 1980s, many companies represented by ZEISS, LEITZ, DEA, LK, Mitutoyo, SIP, FERRANTI, MOORE, etc. continuously introduced new products, which accelerated the development of CMM. Modern CMM can not only complete various complex measurements under computer control, but also can control the processing by exchanging information with CNC machine tools, and can also implement reverse engineering based on the measurement data. At present, CMM has been widely used in various sectors such as machinery manufacturing, automotive industry, electronics industry, aerospace industry and national defense industry, and has become an indispensable universal measurement equipment for modern industrial testing and quality control.
The composition and working principle of two and three coordinate measuring machines
(1) Composition of CMM
The CMM is a typical mechatronics device, which is composed of two parts: mechanical system and electronic system.
(1) Mechanical system: generally consists of three orthogonal linear motion axes. In the structure shown in Figure 9-1, the X-direction rail system is installed on the workbench, the moving bridge beam is the Y-direction rail system, and the Z-direction rail system is installed in the central carriage. Grating rulers are installed on the three direction axes to measure the displacement value of each axis. Manually-driven handwheels and motors driven by motor and numerical control are generally near each axis. The probe used to touch the surface of the tested part is installed at the end of the Z axis.
(2) Electronic system: It is generally composed of a grating counting system, a probe signal interface and a computer, etc. It is used to obtain measured coordinate point data and process the data.
(2) Working principle of CMM
The coordinate measuring machine is a universal digital measuring device based on coordinate measurement. It first converts the measurement of each measured geometric element into the measurement of the coordinate position of some point sets on these geometric elements. After measuring the coordinate position of these points, it then finds out the mathematical coordinates according to the spatial coordinate values ??of these points. Size and shape error, to measure the diameter of a cylindrical hole on the workpiece, you can touch the three points (point 1, 2, 3) on the wall of the inner hole in the section I perpendicular to the hole axis, according to these three points The coordinate value of can calculate the diameter of the hole and the center coordinate OI; if more points are touched in this section (points 1, 2, ..., n, n are the number of measured points), then the least square method or the smallest Conditional method calculates the roundness error of the cross-section circle; if multiple cross-section circles perpendicular to the hole axis (I, II, ..., m, m are the measured cross-section circle numbers) are measured, then the coordinate values ??of the measured points are used The cylindricity error of the hole and the circle center coordinates of each cross-section circle can be calculated, and then the hole axis position can be calculated according to each circle center coordinate value; if three points are touched on the hole end face A, the hole axis opposite end face can be calculated Position error. This shows that the working principle of CMM makes it very versatile and flexible. In principle, it can measure any parameter of any geometric element of any workpiece.
Three, three coordinate measuring machine classification
(1) Classification according to the technical level of CMM
1. Digital display and printing
This type of CMM is mainly used for geometric size measurement. It can display and print out the coordinate data of the measured points, but to obtain the required geometric size and position error, manual calculation is required. Its technical level is low, and it has been basically Reduce.
2. With computer for data processing
The technical level of this type of CMM is slightly higher, and it is currently widely used. The measurement is still manual or motorized, but processing the measurement data with a computer can complete data processing such as automatic correction calculation of workpiece installation tilt, coordinate transformation, hole center distance calculation, deviation value calculation and so on.
3. Computer digital control
This type of CMM has a high technical level, and can be automatically measured according to the prepared program like a CNC machine tool.
(2) Classification according to the measuring range of CMM
1. Small coordinate measuring machine
This type of CMM has a measuring range of less than 500mm in the direction of its longest coordinate axis (generally the X-axis direction), which is mainly used for the measurement of small precision molds, tools and tools.
2. Medium-sized coordinate measuring machine
The measurement range of this type of CMM in the direction of its longest coordinate axis is 500-2000mm, which is the most widely used model, mainly used for the measurement of box and mold parts.
3. Large coordinate measuring machine
The measurement range of this type of CMM in the direction of its longest coordinate axis is greater than 2000mm, which is mainly used for the measurement of large parts such as automobile and engine shells, aero engine blades.
(3) Classification according to the accuracy of CMM
1. Precision CMM
The single-axis maximum measurement uncertainty is less than 1×10-6L (L is the maximum range, the unit is mm), and the space maximum measurement uncertainty is less than (2~3)×10-6L, generally placed in measurement with constant temperature conditions Indoor, used for precision measurement.
2. Medium and low precision CMM
The single-axis maximum measurement uncertainty of low-precision CMM is about 1×10-4L, the maximum spatial measurement uncertainty is (2~3)×10-4L, and the single-axis maximum measurement uncertainty of medium-precision CMM is about 1×10-5L, the maximum spatial measurement uncertainty is (2~3)×10-5L. This type of CMM is generally placed in the production workshop for production process testing.
(4) Classification according to the structure of CMM
According to the structure, CMM can be divided into mobile bridge type, fixed bridge type, gantry type, cantilever type, column type, etc., see the next section.
Section 2 Mechanical Structure of CMM
1. Structure
The three-coordinate measuring machine is composed of three orthogonal linear motion axes. The mutual arrangement positions of the three coordinate axes (that is, the overall structure form) have a great influence on the accuracy of the measuring machine and the applicability of the measured workpiece.
2. Workbench
The workbenches of early CMMs are generally made of cast iron or cast steel, but in recent years, various manufacturers have widely used granite to manufacture workbenches, because granite deformation is small, good stability, and wear resistance , No rust, and the price
Cheap and easy to process. Some measuring machines are equipped with a lifting table to expand the measuring range of the Z axis, and some measuring machines are equipped with a rotating table to expand the measuring function.
Three, guide rail
The guide rail is the guiding device of the measuring machine, which directly affects the accuracy of the measuring machine, and therefore requires high linearity accuracy. The guide rails used in the coordinate measuring machine include sliding guide rails, rolling guide rails and air-floating guide rails, but sliding guide rails and air-floating guide rails are commonly used. Rolling guide rails are used less frequently because rolling guide rails have poor wear resistance and lower rigidity than sliding guide rails. . In the early CMMs, many models used sliding guides. The sliding guide rail has high precision and strong carrying capacity, but it has large friction resistance, easy to wear, easy to crawl when running at low speed, and it is not easy to run at high speed. There is a tendency to be gradually replaced by air floating guide rails. At present, most CMMs have adopted air static pressure guide rails (also known as air float guide rails and air cushion guide rails), which have many advantages, such as simple manufacturing, high precision, minimal friction, and smooth operation.
The development of air floatation technology has made great breakthroughs in the processing cycle and accuracy of the CMM. At present, many production plants are looking for high-strength light materials as guide rail materials, and some production plants have selected ceramic or high-membrane carbon fiber as the material for moving components on moving bridges and beams. In addition, in order to accelerate heat conduction and reduce thermal deformation, ZEISS company uses coated anti-aging alloy to manufacture the guide rail, making its aging deformation extremely small and making the temperature of each part more uniform, thus making the measurement accuracy of the whole machine It has been improved, but the requirements for ambient temperature can be relaxed.
Section 3 Measuring System of CMM
The measuring system of the three-coordinate measuring machine is composed of a scale system and a probe system. They are the key components of the three-coordinate measuring machine and determine the level of CMM measurement accuracy.
1. Ruler System
The scale system is used to measure the coordinate values ??of each axis. There are many types of scale systems currently used on coordinate measuring machines. They are roughly the same as the scale systems used on various machine tools and instruments. They can be divided into mechanical scales according to their properties. System (such as precision screw and differential drum, precision rack and pinion, rolling ruler), optical scale system (such as optical reading ruler, optical encoder, grating, laser interferometer) and electrical scale system ( Such as induction synchronizer, magnetic grid). According to the statistical analysis of the scale system used in the production of CMM at home and abroad, it is known that the most used is the grating, followed by the induction synchronizer and the optical encoder. Some high precision CMM scale systems use laser interferometers.
Second, the probe system
(1) Probe
The coordinate measuring machine uses a probe to pick up signals, so the performance of the probe directly affects the measurement accuracy and measurement efficiency. Without advanced probes, the functions of the measuring machine cannot be fully utilized. Probes used on CMMs can be divided into mechanical, optical, and electrical types according to structural principles; and can be divided into contact and non-contact types according to measurement methods.
1. Mechanical contact probe
The mechanical contact probe is a rigid probe. According to the shape of the touched part, it can be divided into conical probe, cylindrical probe, spherical probe, semi-circular probe, spot probe, V-block probe, etc. (As shown in Figure 9-5). The shape of this type of probe is simple and easy to manufacture, but the measurement force depends on the operator's experience and skills, so the measurement accuracy is poor and the efficiency is low. At present, except for a few manual measuring machines that use this type of probe, most measuring machines no longer use this type of probe.
2. Electrical contact probe
Electrical contact probes are currently used by most coordinate measuring machines, and can be divided into dynamic probes and static probes according to their working principles.
(1) Dynamic probe
The measuring rod is installed on the core, and the core is placed on three pairs of contacts through three steel balls distributed along the circumference of 1200. When the measuring rod is not subjected to the measuring force, the steel ball on the core and the three pairs of contacts All contacts are kept. When the spherical end of the measuring rod is in contact with the workpiece, no matter which direction of the X, Y, Z contact force is received, at least one steel ball will be out of contact with the contact, which will cause the circuit to be disconnected, resulting in a step. The jump signal directly or through the computer controls the sampling circuit to send the coordinate data along the three axes to the memory for data processing.
It can be seen that the probe is measured and sampled in the process of touching the surface of the workpiece, so it is called a dynamic probe, also known as a trigger probe. The dynamic probe has a simple structure, low cost, and can be used for high-speed measurement, but the accuracy is slightly lower, and the dynamic probe cannot stay on the surface of the workpiece in a contact state, so only discrete point-by-point measurement can be performed on the surface of the workpiece, and continuous scanning cannot be performed. measuring. At present, the vast majority of production plants use the trigger probes produced by the British RENISHAW company.
(2) Static probe
In addition to the trigger sampling function of the touch probe, the static probe is also equivalent to an ultra-small coordinate measuring machine. There is a three-dimensional geometry sensor in the probe. When the probe is in contact with the surface of the workpiece, there are corresponding displacement outputs in the three directions of X, Y, and Z, so that the servo system is automatically adjusted to stop the probe at the specified In terms of displacement, the three-dimensional coordinate data is collected when the probe is close to static, so it is called a static probe. When the static probe moves along the surface of the workpiece, it can always maintain contact and perform scanning measurement, so it is also called a scanning probe. Its main feature is high accuracy, which can be used for continuous scanning, but the manufacturing technology is difficult, the sampling speed is slow, and the price is expensive. It is suitable for high-precision measuring machines. At present, the static probes produced by LEITZ, ZEISS and KERRY all use inductive displacement sensors. At this time, the static probe is also called a three-way inductive probe. Figure 9-7 shows the structure of a double leaf spring stacked three-dimensional inductive probe produced by ZEISS.
The probe is in the form of a three-layer leaf spring guide, with three layers in three directions, each layer suspended by two leaf springs. The adapter 17 can be moved in the X direction by means of a parallelogram mechanism formed by two X-direction leaf springs 16. The parallelogram mechanism is fixed below the parallelogram mechanism formed by the Y-direction leaf spring 1. With the aid of the leaf spring 1, the adaptor can be moved in the Y direction. The Y-directional parallelogram mechanism is fixed below the parallelogram mechanism composed of the Z-direction leaf spring 3, and depending on its leaf spring, the adapter seat can be moved in the Z direction. In order to enhance the rigidity and stability of the leaf spring, the middle of the leaf spring is a metal clamping plate. To ensure sensitive and accurate measurement, the leaf spring should not be too thick, generally 0.1mm. Since the Z-direction guide rails are installed horizontally, three sets of springs 2, 14, 15 are used to balance them. There is a thread adjustment mechanism above the adjustable spring 14, and the balance force adjustment micromotor 10 rotates the balance force adjustment screw 11 to cause the balance force adjustment nut sleeve 13 to rise and fall to automatically adjust the balance force. In order to reduce the displacement caused by the shear force of the Z-direction spring, springs 2 and 15 are provided to balance the weight of the Y-direction and X-direction components of the probe.
There are three components in each layer of guide rail: ①Locking mechanism: As shown in Figure 9-7b, there is a groove in its positioning block 24, which precisely matches with the locking steel ball 23 on the locking lever 22, To determine the 'zero position' of the guide rail. When it needs to be opened, the motor 20 can be reversed by an angle, and then the guide rail is in a free state. When it needs to be locked, the motor can be turned forward by another angle. ② Displacement sensor: used to measure the magnitude of displacement, as shown in Figure 9-7c, on the two-layer guide rail, one side is fixed with a magnetic core 27, and the other side is fixed with a coil 26 and a coil bracket 25. ③Damping mechanism: used to reduce the influence of external vibration during high-resolution measurement. As shown in Fig. 9-7d, the upper damping bracket 28 and the lower damping bracket 31 which perform relative movement are respectively fixed with damping sheets 29 and 30, and a capillary gap is formed between the two damping sheets, and viscous silicone oil is placed in the middle to make the two-layer guide rail During movement, a damping force is generated to avoid oscillation caused by the leaf spring mechanism being too sensitive.
(3) Optical probe
In most cases, the optical probe has no mechanical contact with the measured object. This non-contact measurement has some outstanding advantages, mainly reflected in: 1) Because there is no measuring force, it is suitable for measuring various soft and thin Workpiece; 2) Because it is a non-contact measurement, it can quickly scan the surface of the workpiece; 3) Most optical probes have a relatively large range, which is difficult to achieve with general contact probes; 4) Can detect general mechanical measurements on the workpiece Difficult to detect the head. In recent years, optical probes have developed rapidly, and there are many types of optical probes currently used in coordinate measuring machines, such as triangulation probes, laser focusing probes, fiber optic probes, stereoscopic 3D probes, and contact type Grating probe, etc. The following is a brief introduction
The working principle of the triangulation probe. (Two) probe accessories
In order to expand the function of the probe, improve the measurement efficiency and detect different parts of various parts, it is often necessary to configure various accessories for the probe, such as the probe end, probe, connector, probe rotation attachment, etc.
1. Measuring end
For contact probes, the measuring tip is the part that directly contacts the surface of the workpiece to be measured. For different shapes of surfaces, different measuring tips are required. Figure 9-9 shows some common measuring tip shapes.

2. Probe
Probe is a replaceable probe. In some cases, in order to facilitate the measurement, you need to choose a different probe. The probe has a great influence on the measurement capability and measurement accuracy. When selecting, you should pay attention to: 1) The probe should be as short as possible under the premise of meeting the measurement requirements; 2) The probe diameter must be smaller than the diameter of the measurement end, and interference will not occur Under conditions, you should try to choose a large-diameter probe; 3) When a long probe is needed, you can choose a hard alloy probe to improve rigidity. If a particularly long probe is required, a lighter-weight ceramic probe can be used.
3. Connector
In order to connect the probe to the probe, the probe to the rotating body or the measuring machine spindle, various connectors are required. Commonly used are star probe connectors, connecting shafts, star probe seats, etc.
4. Rotary attachment
For the detection of some workpiece surfaces, such as some inclined surfaces, integral impeller blade surfaces, etc., only the probe perpendicular to the table will not be able to complete the required measurement. At this time, it is necessary to use a certain rotary attachment to make the probe or the entire The probe rotates at a certain angle before measuring, thereby expanding the function of the probe.
The commonly used rotary attachment is the probe rotary body shown in Figure 9-11a. It can rotate around the horizontal axis A and the vertical axis B. There is a precision indexing mechanism in its rotating mechanism, and its indexing principle is similar to the multi-tooth indexing plate. There are 48 cylinders evenly distributed along the circumference in the static plate, and there are 48 steel balls corresponding to it in the moving plate, so that the index can be realized in steps of 7.5o. Its rotation range around the vertical axis is 360o, a total of 48 positions, and its rotation range around the horizontal axis is 0o to 105o, a total of 15 positions. Since the rotation angle around the horizontal axis is 0o (that is, the probe is vertically downward), the rotation around the vertical axis does not change the position of the measuring end, so the measuring end can have a total of 48×14+1=673 positions in space. It can make the probe change the attitude to expand the ability to approach the workpiece from all directions. At present, most of the probe rotators used on the measuring machine are various probe rotators produced by RENISHAW,

Section 4 Control System of CMM
1. The function of the control system
The control system is one of the key components of the CMM. Its main functions are: reading space coordinate values, controlling the measuring and sighting system to respond and process the probe signals in real time, controlling the mechanical system to achieve the necessary movements for measurement, and monitoring the status of the coordinate measuring machine in real time to ensure the safety and security of the entire system. Reliability etc.
Second, the structure of the control system
According to the degree of automation, the coordinate measuring machine is divided into manual type, mobile type and CNC type. Early coordinate measuring machines were mainly manual type and motorized type. The measurement was performed by the operator directly or through the joystick to complete the sampling of various points, and then the data was processed in the computer. With the development of computer technology and numerical control technology, the CNC-type control system has become increasingly popular. It uses a program to control the coordinate measuring machine's automatic feed and data sampling, while completing data processing in the computer.
1. Manual and mobile control systems
This type of control system has a simple structure, convenient operation, low price, and is widely used in the workshop. The scale system of these two types of coordinate measuring machines is usually a grating, and the touch probe is generally a touch probe. Its working process is: When the touch probe touches the workpiece, the trigger signal is issued by the probe, and an interrupt signal is sent to the CPU through the probe control interface. The CPU executes the corresponding interrupt service program and reads the count interface unit in real time. Numerical value, calculate the corresponding space length, form the sampling coordinate values ??X, Y and Z, and send it to the sampling data buffer for subsequent data processing.
2. CNC type control system
The measurement feed of CNC type control system is controlled by computer. It can control the movement of each axis of the measuring machine through the program and monitor the running state of the measuring machine in real time, so as to realize automatic measurement. In addition, it can also be manually measured by the joystick. CNC type control system can be divided into two types: centralized control and distributed control.
(1) Centralized control
Centralized control is implemented by a main CPU for monitoring and sampling of coordinate values. It completes the tasks of receiving, interpreting and executing commands of the main computer, returning and real-time display of status information and data, keyboard input of control commands and safety monitoring. Its motion control is completed by an independent module, which is a relatively independent computer system, which completes single-axis servo control, three-axis linkage and motion status monitoring. From a functional point of view, the motion control CPU must not only complete the operation of the digital regulator, but also perform the interpolation operation, which has a large amount of calculation, and its real-time performance and measured feed speed depend on the speed of the CPU.
(2) Distributed control
Distributed control refers to the use of multiple CPUs in the system, each CPU completes a specific control, and at the same time these CPUs coordinate work and jointly complete the measurement task, so the speed is fast and the real-time nature of the control system is improved. In addition, the characteristic of distributed control is multi-CPU parallel processing. Because it is a unit type, it is easy to maintain and expand. If you want to add a turntable, you only need to expand a single-axis control unit in the system, define its address on the bus, and add the corresponding software.
3. Measurement feed control
The coordinate measuring machine other than the manual type controls the speed of the servo motor through the joystick or CNC program, so as to control the probe and the measuring table to move relative to the set trajectory, so as to realize the measurement of the workpiece. The measurement feed of the three-coordinate measuring machine is basically the same as the machining feed of the CNC machine tool, but its requirements for movement accuracy, movement stability and response speed are higher. The motion control of the CMM includes single-axis servo control and multi-axis linkage control. The single-axis servo control is relatively simple, and the motion control of each axis is completed by the respective single-axis servo controller. However, when the probe is required to move relative to the workpiece in a three-dimensional space according to a predetermined trajectory, the CPU needs to control the three axes to link with a certain algorithm to realize the spatial movement of the probe. Such control is controlled by the above single-axis servo control and interpolator Completed together. In the CMM control system, the interpolator is controlled by the CPU program. According to the set trajectory, the CPU continuously provides coordinate axis position commands to the three-axis servo control system, and the single-axis servo control system continuously tracks, so that the probe moves step by step from the starting point to the end point.
4. Communication of the control system
The communication of the control system includes internal communication and external communication. Internal communication refers to the mutual transfer of commands, parameters, status, data, etc. between the host computer and the control system. These are achieved through the communication bus connecting the host computer and the control system. External communication refers to the communication between the control system and other devices when the CMM is an integral part of the FMS system or CIMS system. At present, serial RS-232 standard and parallel IEEE-488 standard are mainly used for CMM communication.
Section 5 Software System of CMM
Modern coordinate measuring machines are equipped with computers, which collect data and output the required measurement results through calculation. The strength of its software system function directly affects the function of the measuring machine. Therefore, manufacturers of coordinate measuring machines attach great importance to the research and development of software systems, and the proportion of human and financial resources invested in this area is increasing. The following briefly introduces the software used in the CMM.
1. Programming software
In order for the coordinate measuring machine to realize automatic measurement, it is necessary to prepare the corresponding measurement program in advance. There are several ways to compile these measurement programs.
(1) Graphic and window programming methods
Graphic and window programming is the simplest way. It selects the measured element through the graphical menu, establishes the coordinate system, and selects the operation process and input parameters through the 'window' prompt to compile the measurement program. This method is only suitable for relatively simple programming of single geometric element measurement.
(2) Self-learning programming method
This programming method is on the CNC measuring machine, the operator guides the measurement process, and enters the corresponding instructions until the measurement is completed, and the computer automatically records the process and related information manually operated by the operator, and automatically generates the corresponding measurement program. If you want to measure the same kind of parts repeatedly, just call this measurement program and all the previously recorded measurement processes can be completed automatically. This method is suitable for batch testing and is also a relatively simple programming method.
(3) Offline programming
In this way, the special measuring machine language provided by the manufacturer of the three-coordinate measuring machine is used to pre-program the measuring program on other general-purpose computers, which has nothing to do with the turning on of the measuring machine. After programming the program, go to the measuring machine for trial operation. If errors are found, modify them. The advantage is that it can solve very complicated measurement work, the disadvantage is that it is easy to make mistakes.
(4) Automatic programming
In a computer integrated manufacturing system, a CAD/CAM system usually automatically generates a measurement program. On the one hand, the coordinate measuring machine reads the design drawing data file generated by the CAD system and automatically constructs the virtual workpiece. On the other hand, it accepts the actual workpiece processed by the CAM and automatically generates a measurement path according to the virtual workpiece to realize unmanned automatic measurement. The measurement program in this process is completely automatically generated by the system.
Second, the measurement software package
The measurement software package can contain many kinds of data processing programs to meet various engineering needs. Generally, the measurement software packages of the CMM are divided into general measurement software packages and special measurement software packages. The general measurement software package mainly refers to a software package for measuring basic geometric elements such as points, lines, surfaces, circles, cylinders, cones, spheres and their geometric errors and their interrelationships. Usually each coordinate measuring machine is equipped with this type of software package. The special measurement software package refers to various measurement software packages developed by the coordinate measuring machine manufacturers in order to improve the measurement efficiency and measurement accuracy of some specific measurement objects. If there are many coordinate measuring machines equipped with special measurement software packages for gears, cams and camshafts, threads, curves, curved surfaces and other common parts and surface measurements. Some measuring machines are also equipped with special measuring software packages for measuring automobile body, engine blades and other parts.
3. System debugging software
It is used to debug the measuring machine and its control system, and generally has the following software.
(1) Self-checking and fault analysis software package: used to check system faults and automatically display fault categories;
(2) Error compensation software package: used to detect the geometric error of the three-coordinate measuring machine. When the three-coordinate measuring machine is working, the error of the measuring machine is corrected according to the detection result;
(3) System parameter identification and control parameter optimization software package: used for general debugging of the CMM control system, and generates user operation files with optimized parameters;
(4) Accuracy test and acceptance measurement software package: used to measure inspection tools according to acceptance standards.
4. System working software
The measurement software system must be equipped with some working software that is of a coordinated and auxiliary nature, some of which are necessary and some are used to expand functions.
(1) Probe management software: used for probe calibration, probe rotation control, etc.;
(2) CNC operation software: used for probe motion control;
(3) System monitoring software: used to monitor the system (such as monitoring power supply, gas source, etc.);
(4) Compile system software: compile with this program to generate running object code;
(5) DMIS interface software: used to translate DMIS format files;
(6) Data file management software: used for various file management;
(7) Network communication software: used to realize two-way or one-way communication with other computers.
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