Over-positioning grinding method for hard and brittle tube with large length-to-diameter ratio

Abstract

An over-positioning grinding method for a hard and brittle tube with a large length-to-diameter ratio. The over-positioning grinding method comprises: using a rigid mandrel (1), a supporting plate (3) and a guide wheel (4) to perform over-positioning support on a hard and brittle tube (2); driving the guide wheel (4) to rotate forwards to feed the hard and brittle tube (2) with a large length-to-diameter ratio into a grinding area; rotating the guide wheel (4) reversely upon coming into contact with the hard and brittle tube (2) and driving same to advance; rotating a grinding wheel (5) reversely and feeding same toward the hard and brittle tube (2); and with the grinding and feeding of the grinding wheel (5), feeding the guide wheel (4) and the supporting plate (3) toward the hard and brittle tube (2), so as to always maintain the over-positioning support of the hard and brittle tube (1) by the guide wheel (4), the supporting plate (3) and the rigid mandrel (1), thereby enabling grinding of the hard and brittle tube (1) with the large length-to-diameter ratio. The over-positioning grinding method can improve the grinding accuracy of the outer circle of the hard and brittle tube while ensuring the coaxiality of the outer circle and the inner circle of the ground hard and brittle tube.

Description

Over-positioning grinding method for hard and brittle pipes with large length-to-diameter ratio Technical Field

[0001] This invention belongs to the field of grinding technology, specifically the field of external cylindrical grinding of hard and brittle materials, and particularly relates to an over-positioning grinding method for hard and brittle pipes with a large length-to-diameter ratio. Background Technology

[0002] Currently, high aspect ratio hard and brittle pipes are widely used in semiconductor, nuclear energy, chemical and other fields. High aspect ratio hard and brittle pipes used in special working conditions need to have high dimensional and shape accuracy. Due to the manufacturing process, the blank pipes of high aspect ratio hard and brittle pipes have large dimensional and shape accuracy errors, which cannot directly meet the use requirements. This means that it is necessary to process the hard and brittle pipes to ensure their accuracy. However, due to the structural characteristics of high aspect ratio hard and brittle pipes and the characteristics of high hardness and high brittleness, it is difficult to perform high-precision and high-efficiency precision forming of such parts. This greatly limits the application of such parts in various industries.

[0003] The existing processing of the outer diameter of hard and brittle pipe fittings generally uses external diameter grinding. However, the current processing method cannot improve the grinding accuracy of the outer diameter of the hard and brittle pipe fittings, and also ensure the coaxiality of the outer diameter and inner diameter of the hard and brittle pipe fittings after grinding. This will lead to inconsistent wall thickness of the hard and brittle pipe fittings after grinding. Summary of the Invention

[0004] In view of this, the present invention provides an over-positioning grinding method for hard and brittle pipes with a large length-to-diameter ratio. This method can provide over-positioning support for the hard and brittle pipes during the processing, thereby improving the grinding accuracy of the outer circle of the hard and brittle pipes and ensuring that the outer circle and inner circle of the hard and brittle pipes are coaxial after grinding, thus achieving high-precision processing of hard and brittle pipes with a large length-to-diameter ratio.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A method for over-positioning grinding of hard and brittle pipe fittings with a large length-to-diameter ratio, the specific grinding process is as follows:

[0007] S1, Assembly and positioning of hard and brittle pipe fittings: A rigid mandrel passes through the inner hole of a hard and brittle pipe fitting with a large length-to-diameter ratio and is clearance-fitted with the hard and brittle pipe fitting. The rigid mandrel is tensioned to keep the hard and brittle pipe fitting horizontal. Each end of the rigid mandrel and the position close to the hard and brittle pipe fitting is supported by a vibration damping device to reduce the vibration amplitude and frequency of the rigid mandrel during the processing of the hard and brittle pipe fitting. The support plate contacts the outer pipe surface of the hard and brittle pipe fitting and supports the hard and brittle pipe fitting.

[0008] S2, Determine the grinding area: Arrange the grinding wheel and guide wheel on both sides of the hard and brittle pipe, and keep the axes of the grinding wheel and guide wheel at the same height. Adjust their height so that there is a height difference between the axes of the guide wheel and the grinding wheel and the axis of the hard and brittle pipe. The grinding surface of the grinding wheel and the guide support surface of the guide wheel face each other. The grinding wheel, guide wheel and support plate form the grinding area of ​​the hard and brittle pipe, and the rigid mandrel is used to provide over-positioning support for the hard and brittle pipe.

[0009] S3, Guide Roller Positioning: Move the hard and brittle tube to the grinding area, and move the guide roller toward the hard and brittle tube until the guide support surface of the guide roller contacts and presses against the outer tube surface of the hard and brittle tube, so that there is a pre-pressure between the guide roller and the hard and brittle tube. The hard and brittle tube is moved out of the grinding area, and the guide roller is kept in place.

[0010] S4, Tool setting: Drive the guide wheel to rotate forward, and feed the hard and brittle tube with a large length-to-diameter ratio into the grinding area. The guide wheel contacts and drives the hard and brittle tube forward while rotating in the opposite direction. The grinding wheel rotates in the opposite direction and feeds a small amount towards the hard and brittle tube side to achieve the tool setting operation.

[0011] S5, Grinding of Hard and Brittle Pipes: Set the rotational speed and feed rate of the guide wheel and the rotational speed and feed rate of the grinding wheel, and set the grinding amount of the hard and brittle pipe. Drive the guide wheel to rotate forward, and feed the hard and brittle pipe with a large length-to-diameter ratio into the grinding area. The guide wheel contacts and drives the hard and brittle pipe forward while rotating in the opposite direction. The grinding wheel rotates in the opposite direction and feeds towards the hard and brittle pipe. As the grinding wheel grinds and feeds, the guide wheel and the support plate feed towards the hard and brittle pipe to always maintain the over-positioning support of the guide wheel, the support plate and the rigid mandrel on the hard and brittle pipe. As the hard and brittle pipe moves, the grinding of the hard and brittle pipe with a large length-to-diameter ratio is achieved.

[0012] Furthermore, in S5, the linear velocity of the grinding wheel is 30 m / s.

[0013] Furthermore, in S5, when the outer diameter of the grinding wheel is 400mm, the rotational speed of the grinding wheel is 1400rpm / min to 1500rpm / min.

[0014] Furthermore, in S5, the operating speed of the guide wheel is 15 rpm / min to 20 rpm / min.

[0015] Furthermore, the range of the clearance between the rigid mandrel and the hard and brittle tubular component is 0.2 to 0.5 mm.

[0016] Furthermore, the support plate is positioned close to the grinding wheel and obliquely supports the hard and brittle pipe. The supporting surface of the support plate is an inclined surface with an inclination angle of 30°.

[0017] Furthermore, the grinding wheel is a parallel grinding wheel.

[0018] Furthermore, the grinding wheel is a cup-shaped grinding wheel, and there is an offset angle θ between the axis of the cup-shaped grinding wheel and the axis of the hard and brittle pipe, where θ > 0.

[0019] Furthermore, in S2, the height difference between the axis of the guide wheel and the grinding wheel and the axis of the hard and brittle tube is obtained in the following way:

[0020] Let R be the outer radius of the rigid and brittle pipe fitting with a large length-to-diameter ratio. w The radius of the guide wheel is R. c The radius of the grinding wheel is R. g Let h be the height difference between the axis of the hard and brittle pipe and the axis of the grinding wheel; when the grinding wheel contacts the hard and brittle pipe, let A be the initial contact point between the grinding wheel and the hard and brittle pipe, and let l be the tangent at point A; when the guide wheel contacts the hard and brittle pipe, let B be the initial contact point between the guide wheel and the hard and brittle pipe; when the support plate contacts the hard and brittle pipe, let C be the initial contact point between the support plate and the hard and brittle pipe.

[0021] Let the axis of the rigid and brittle pipe be O, and the center of the guide wheel be O. c The center of the grinding wheel is O. g , ∠AOC=α, ∠BOC=φ, ∠AO g O c =β g ,∠O g O c B = β c β is the grinding angle of the grinding wheel, δ is the angle between OA and the horizontal line, and the inclination angle of the supporting surface of the support plate is γ, with O g Establish a rectangular coordinate system with the center of the circle, and let the point of tangency A lie in the coordinate system xO. g The coordinates in y are (x, y); when there is an offset angle θ between the axis of the grinding wheel and the axis of the hard and brittle pipe, the grinding wheel grinds at the offset angle θ. The projection of the profile of the grinding wheel in the section perpendicular to the feed speed direction is then in xO. g The equation of the elliptic curve in y can be expressed as:

[0022] Where y is the height difference between the tangent point A and the axis of the grinding wheel, and x is the horizontal distance from the tangent point A to the vertical axis y;

[0023] From formula (1), we obtain the following relationship: x = R g sinθcosβ g (2) y=R g sinβ g (3)

[0024] The slope of the tangent line l passing through the point of tangency A on the elliptic curve can be expressed as:

[0025] Since the tangent of the slope of tangent l is the angle between tangent l and the x-axis, the angle δ between tangent l and the x-axis can be obtained from formula (4):

[0026] Based on geometric relationships, the following formula is obtained: β c ≈h / (R w +R c (6) h=y+R w sinδ (7) β=β c +δ=π-φ-α (8)

[0027] Let δ, y, β c Substituting into equations (7) and (8), we get:

[0028] In trigonometric functions, when the angle is small, the following simplification occurs: cot(β g )≈1 / β g (12)

[0029] Therefore, substituting formulas (11) and (12) into formulas (9) and (10) yields: h = R g β g +R w β g sinθ (14)

[0030] Combining formulas (13) and (14), we get:

[0031] Furthermore, the process for obtaining the grinding angle β is as follows:

[0032] Based on geometric relationships, the following formula is obtained:

[0033] Stability growth coefficient A i The expression is:

[0034] Combining formulas (4)-(17), formula (18) can be transformed into a variable with only angles β and γ, and formula (18) becomes:

[0035] Based on the open-source software Python and the stability growth coefficient A i The stability plot is obtained when A i When the value is greater than 0, the region is stable. Based on the inclination angle γ of the support surface of the support plate, the range of values ​​for β within the stable region is selected.

[0036] The beneficial effects of this invention compared to the prior art are:

[0037] 1. The support plate provides oblique support to the surface of the hard and brittle tube. The guide wheel and grinding wheel also provide support and positioning for the tube. All three components—support plate, guide wheel, and grinding wheel—provide upward support, forming the grinding zone. The rigid mandrel has a clearance fit with the tube, ensuring not only its rotation and forward movement but also maintaining its horizontal position under tension. This presses the tube firmly into the grinding zone, providing multi-point support and positioning during processing. This over-positioning support not only ensures stable support for the tube but also provides a positioning reference for machining the outer diameter. Under this over-positioning support, the grinding accuracy of the outer diameter of the hard and brittle tube is improved, while ensuring that the outer and inner diameters are coaxial after grinding, enabling high-precision machining of hard and brittle tubes with large length-to-diameter ratios.

[0038] 2. The guide wheel adopts a single-leaf hyperboloid structure, which can not only drive the workpiece to rotate stably and achieve uniform machining of the outer circle of the workpiece, but also drive the workpiece to move forward at a uniform speed and achieve uniform machining of the workpiece in the length direction.

[0039] 3. Grinding wheels can be either parallel wheels or cup-shaped wheels. When a cup-shaped wheel is used, its rotation axis is perpendicular to the feed direction, making the grinding in the feed direction an external cylindrical grinding rather than a planar grinding. This reduces the grinding force, and the material removed from the outer cylindrical surface of the wheel has a smaller contact area, allowing for more precise cutting control of the workpiece. It is especially suitable for high-precision external cylindrical grinding, achieving higher surface quality and dimensional accuracy. Simultaneously, the cutting area of ​​the cup-shaped wheel is concentrated, resulting in less force during grinding and reducing the impact of cutting forces. The abrasive grain movement trajectory on the wheel end face is parallel to the material's forming surface, enabling not only large depth-of-cut grinding but also reducing the grinding force on the workpiece, avoiding damage to workpieces with hard and brittle characteristics, and obtaining a workpiece surface with less subsurface damage. Appropriately adjusting the angle or dressing the cup-shaped wheel can extend its service life and reduce the frequency of grinding wheel replacement. Attached Figure Description

[0040] The accompanying drawings, which form part of this application, are provided to further illustrate the invention.

[0041] Figure 1 is a schematic diagram of the overall structure of the hard and brittle pipe fitting assembled with the over-positioning grinding device.

[0042] Figure 2 is a schematic diagram showing the contact between the grinding wheel and the hard and brittle pipe during the machining of the pipe.

[0043] Figure 3 is a schematic diagram of the over-positioning fit of the grinding wheel, rigid mandrel, support plate and guide wheel during the machining of hard and brittle pipe fittings.

[0044] Figure 4 is a schematic diagram of the working principle of the over-positioning geometric layout during the grinding of hard and brittle pipe fittings.

[0045] Figure 5 shows the determination of the grinding angle based on the stability diagram.

[0046] Figure 6 shows a physical image of a hard and brittle pipe after over-positioning grinding. It shows the grinding of a one-meter silicon carbide pipe and the measurement of its wall thickness.

[0047] Figure 7 shows the roundness error of the processed hard and brittle pipe fitting. The actual object in the figure is a 100mm long silicon carbide pipe after measurement.

[0048] Explanation of reference numerals in the attached drawings: 1-rigid mandrel; 2-hard and brittle tubular component; 3-support plate; 4-guide wheel; 5-grinding wheel; 6-vibration damping device. Detailed Implementation

[0049] The invention will be described in detail below with reference to specific embodiments.

[0050] Referring to Figures 1 and 2, the over-positioning grinding method for a hard and brittle pipe with a large length-to-diameter ratio in this embodiment is implemented by using an over-positioning grinding device. Figure 1 shows a schematic diagram of the overall structure of the hard and brittle pipe and the over-positioning grinding device. The over-positioning grinding device includes a rigid mandrel 1, a vibration damping device 6, a support plate 3, a grinding wheel 5, and a guide wheel 4. The rigid mandrel 1 is horizontally set and used to support the hard and brittle pipe 2 with a large length-to-diameter ratio. Since the hard and brittle pipe 2 is a pipe with a large length-to-diameter ratio, and the rigid mandrel 1 passes through the inner hole of the rigid mandrel 1 and is used to support the hard and brittle pipe 2, the rigid mandrel 1 is also a support member with a large length-to-diameter ratio. The rigid mandrel 1 is prone to bending downwards, so when the rigid mandrel 1 supports the hard and brittle pipe 2, the two ends of the rigid mandrel 1 are tensioned by a tensioning device to keep the rigid mandrel 1 and the hard and brittle pipe 2 always horizontal. A support plate 3 is positioned below the rigid mandrel 1 and also supports the high aspect ratio hard and brittle pipe 2. The support provided by the rigid mandrel 1 and the support plate 3 ensures that the hard and brittle pipe 2 remains horizontal during processing. Two vibration damping devices 6 are provided, one at each end of the rigid mandrel 1 and used to support it. Since the hard and brittle pipe 2 vibrates during processing, the rigid mandrel 1 also vibrates due to inertia. The vibration damping devices 6 reduce the vibration amplitude and frequency of the rigid mandrel 1, thereby reducing the vibration frequency and amplitude of the hard and brittle pipe 2 and improving its processing accuracy. A guide wheel 4 is installed on one side of the rigid mandrel 1 and is used to rotate and advance the workpiece, ensuring smooth processing. A grinding wheel 5 is installed on the other side of the rigid mandrel 1 and is used to grind the outer diameter of the hard and brittle pipe 2.

[0051] The over-positioning grinding process of the hard and brittle pipe fitting 2 is as follows:

[0052] S1. Assembly and positioning of the hard and brittle tube: As shown in Figure 1, the rigid mandrel 1 passes through the inner hole of the hard and brittle tube 2 with a large length-to-diameter ratio and is clearance-fitted with the hard and brittle tube 2. The clearance between the rigid mandrel 1 and the hard and brittle tube 2 is in the range of 0.2 to 0.5 mm, which ensures that the hard and brittle tube 2 can move along the length direction of the rigid mandrel 1 and also realizes the positioning support of the hard and brittle tube 2, tensions the rigid mandrel 1 and keeps the hard and brittle tube 2 horizontal; each end of the rigid mandrel 1 and the position close to the hard and brittle tube 2 is supported by a vibration damping device 6 to reduce the vibration amplitude and frequency of the rigid mandrel 1 during the processing of the hard and brittle tube 2, thereby reducing the vibration frequency and amplitude of the hard and brittle tube 2 and improving the processing accuracy of the workpiece; the support plate 3 slightly contacts the outer tube surface of the hard and brittle tube 2 and supports the hard and brittle tube 2 at an angle. The support plate 3 is set close to the grinding wheel 5, and the supporting surface of the support plate 3 is a 30° inclined surface;

[0053] S2, Determine the grinding area: Arrange the grinding wheel 5 and the guide wheel 4 on both sides of the hard and brittle pipe 2 respectively, and keep the axes of the grinding wheel 5 and the guide wheel 4 at the same height. Adjust the height of the two so that the axes of the guide wheel 4 and the grinding wheel 5 are lower than the axis of the hard and brittle pipe 2. The grinding surface of the grinding wheel 5 and the guide support surface of the guide wheel 4 are directly opposite each other. The rigid mandrel 1, the grinding wheel 5, the guide wheel 4 and the support plate 3 form the grinding area of ​​the hard and brittle pipe 2 with over-positioning support.

[0054] S3, guide wheel positioning: move the hard and brittle tube 2 to the grinding area, and move the guide wheel 4 to the side of the hard and brittle tube 2 until the guide support surface of the guide wheel 4 contacts and squeezes the outer tube surface of the hard and brittle tube 2 so that there is a pre-pressure between the guide wheel 4 and the hard and brittle tube 2. The hard and brittle tube 2 moves out of the grinding area and keeps the guide wheel 4 in place.

[0055] S4, Tool setting: Drive the guide wheel 4 to rotate forward, and send the hard and brittle tube 2 with a large length-to-diameter ratio into the grinding area. The guide wheel 4 contacts and drives the hard and brittle tube 2 forward while rotating in the opposite direction. The grinding wheel 5 rotates in the opposite direction and feeds a small amount to the side of the hard and brittle tube 2 to achieve the tool setting operation.

[0056] S5, Grinding of Hard and Brittle Pipe Fittings: Set the rotational speed and feed rate of the guide wheel 4 and the rotational speed and feed rate of the grinding wheel 5, and set the grinding amount of the hard and brittle pipe fitting 2; drive the guide wheel 4 to rotate forward, with a working speed of 15 rpm / min to 20 rpm / min, feeding the hard and brittle pipe fitting 2 with a large length-to-diameter ratio into the grinding area. The guide wheel 4 contacts and drives the hard and brittle pipe fitting 2 forward while simultaneously rotating in the opposite direction. The grinding wheel 5 rotates in the opposite direction and feeds towards the hard and brittle pipe fitting 2. The linear velocity of the grinding wheel 5 is 30 m / s. When the outer diameter of the grinding wheel 5 is 400 mm, the rotational speed of the grinding wheel 5 is 1400 rpm / min. The grinding speed is from 1000 rpm to 1500 rpm. As the grinding wheel 5 grinds and feeds, the surface of the hard and brittle pipe 2 is gradually removed. The preload of the guide wheel 4 and the support plate 3 on the hard and brittle pipe 2 gradually decreases, which will affect the machining accuracy of the hard and brittle pipe 2. Therefore, as the hard and brittle pipe 2 is processed, in addition to the grinding wheel 5 gradually feeding, the guide wheel 4 and the support plate 3 also gradually feed to ensure that the preload of the hard and brittle pipe 2 is relatively constant. At the same time, the guide wheel 4, the support plate 3 and the rigid mandrel 1 always maintain the over-positioning support of the hard and brittle pipe 2. As the hard and brittle pipe 2 moves, the grinding of the hard and brittle pipe 2 with a large length-to-diameter ratio is realized.

[0057] As shown in Figures 3 and 4, since the support plate 3 is located on the side close to the grinding wheel 5 and provides oblique support to the surface of the hard and brittle tube 2, and the contact points between the guide wheel 4 and the grinding wheel 5 and the hard and brittle tube 2 are all lower than the axis of the hard and brittle tube 2, the guide wheel 4 and the grinding wheel 5 also play a supporting and positioning role for the hard and brittle tube 2 during grinding. However, the support plate 3, guide wheel 4, and grinding wheel 5 all provide upward support for the hard and brittle tube 2, forming the grinding area. The rigid mandrel 1 and the hard and brittle tube 2 are clearance-fitted, which not only ensures the rotation and forward movement of the hard and brittle tube 2, but also keeps the hard and brittle tube 2 horizontal when the rigid mandrel 1 is tensioned. That is, the hard and brittle tube 2 is pressed into the grinding area and is supported and positioned at multiple points during processing. This not only achieves stable support for the hard and brittle tube 2 through over-positioning, but also provides a positioning reference for the machining of the outer diameter of the workpiece. Under this over-positioning support, the grinding accuracy of the outer circle of the hard and brittle tube 2 is improved, and the coaxiality of the outer circle and inner circle of the hard and brittle tube 2 after grinding can be guaranteed. This achieves high-precision machining of the hard and brittle tube 2 with a large length-to-diameter ratio. As shown in Figure 3, the circular outline formed by the dashed lines is the outline of the hard and brittle tube 2 in the initial position, and the circular outline formed by the solid lines is the outline of the hard and brittle tube 2 after grinding. As can be seen from Figure 3, the two outlines before and after grinding are coaxial and coaxial with the inner circle, thus ensuring the coaxiality of the inner circle and outer circle of the workpiece after grinding.

[0058] In this embodiment, the guide wheel 4 adopts a single-leaf hyperboloid structure, which can not only drive the workpiece to rotate stably and achieve uniform machining of the outer cylindrical surface of the workpiece, but also drive the workpiece to move forward at a uniform speed, achieving uniform machining of the workpiece in the length direction. The grinding wheel 5 can be a parallel grinding wheel or a cup-shaped grinding wheel. When the grinding wheel 5 is a cup-shaped grinding wheel, the rotation axis of the cup-shaped grinding wheel is perpendicular to the direction of the feed speed, so that the grinding in the feed direction becomes outer cylindrical surface grinding instead of plane grinding, which can reduce the grinding force. The outer cylindrical surface of the grinding wheel removes material and has a smaller contact area, so more precise cutting control of the workpiece can be achieved. It is especially suitable for high-precision outer cylindrical grinding, which can achieve higher surface quality and dimensional accuracy. Meanwhile, the cup-shaped grinding wheel has a concentrated cutting area, resulting in lower force during grinding and reduced cutting force. The abrasive grain movement trajectory on the wheel end face is parallel to the material's forming surface, enabling large depth-of-cut grinding while reducing the grinding force on the workpiece. This avoids damage to workpieces with hard and brittle characteristics, resulting in a workpiece surface with less subsurface damage. Appropriate angle adjustments or dressing of the cup-shaped grinding wheel can extend its service life and reduce the frequency of tool replacement. Since the cup-shaped grinding wheel uses the annular grinding surface at the cup opening for material removal, if the axis of the cup-shaped grinding wheel is perpendicular to the axis of the workpiece, it would result in two grinding contact surfaces between the cup-shaped grinding wheel and the workpiece surface, leading to repeated grinding and affecting the workpiece's machining quality. Therefore, there is an angle between the grinding surface of the cup-shaped grinding wheel and the workpiece surface, with the angle θ > 0, to ensure point contact grinding with a small area, avoiding low-damage to the workpiece. In contrast, the parallel grinding wheel has only one grinding end face. Therefore, when using a parallel grinding wheel, it should be parallel to the hard and brittle pipe 2.

[0059] When the workpiece enters the grinding zone, the supporting surface of the support plate 3 makes slight contact with the workpiece surface to achieve the purpose of support. It should be noted that before the guide wheel 4 contacts the workpiece surface, the support plate 3 and the workpiece surface are only in slight contact. When the guide wheel 4 contacts and drives the workpiece to rotate and move forward, the contact area between the workpiece and the supporting surface of the support plate 3 changes from slight contact to full contact, increasing the contact area. The guide wheel 4, rigid spindle 1, and support plate 3 generate a suitable preload on the workpiece to ensure the machining accuracy of the workpiece surface. If the support plate 3 and the workpiece surface have a large-area contact support before the guide wheel 4 contacts the workpiece surface, the supporting force between the support plate 3 and the workpiece increases when the guide wheel 4 contacts and drives the workpiece to rotate and move forward, which can easily lead to a decrease in the machining accuracy of the workpiece. Furthermore, the inclination angle of the supporting surface of the support plate 3 is best at around 30°, as this angle range provides the greatest stability and the best rounding effect.

[0060] In actual processing, it is necessary to first determine the grinding angle of the grinding wheel for grinding. However, when adjusting the position of the guide wheel, grinding wheel and hard and brittle pipe, it is difficult to measure the grinding angle, which increases the difficulty of adjusting the position of the guide wheel, grinding wheel and hard and brittle pipe. Therefore, in this embodiment, the height difference h between the axis of the hard and brittle pipe and the axis of the grinding wheel is determined based on the grinding angle β, which makes it easier to adjust the position of the grinding wheel and the guide wheel.

[0061] Figure 4 shows a schematic diagram of the working principle of the over-positioning geometry during the grinding of hard and brittle pipes. The height difference h between the axis of the guide wheel and the grinding wheel and the axis of the hard and brittle pipe is obtained in the following way:

[0062] Let R be the outer radius of the rigid and brittle pipe fitting with a large length-to-diameter ratio. w The radius of the guide wheel is R. c The radius of the grinding wheel is R. g Let h be the height difference between the axis of the hard and brittle pipe and the axis of the grinding wheel; when the grinding wheel contacts the hard and brittle pipe, let A be the initial contact point between the grinding wheel and the hard and brittle pipe, and let l be the tangent at point A; when the guide wheel contacts the hard and brittle pipe, let B be the initial contact point between the guide wheel and the hard and brittle pipe; when the support plate contacts the hard and brittle pipe, let C be the initial contact point between the support plate and the hard and brittle pipe.

[0063] Let the axis of the rigid and brittle pipe be O, and the center of the guide wheel be O. c The center of the grinding wheel is O. g , ∠AOC=α, ∠BOC=φ, ∠AO g O c =β g ,∠O g O c B = β c β is the grinding angle of the grinding wheel, δ is the angle between OA and the horizontal line, and the inclination angle of the supporting surface of the support plate is γ, with O g Establish a rectangular coordinate system with the center of the circle, and let the point of tangency A lie in the coordinate system xO. g The coordinates in y are (x, y); when there is an offset angle θ between the axis of the grinding wheel and the axis of the hard and brittle pipe, the grinding wheel grinds at the offset angle θ. The projection of the profile of the grinding wheel in the section perpendicular to the feed speed direction is then in xO. g The equation of the elliptic curve in y can be expressed as:

[0064] Where y is the height difference between the tangent point A and the axis of the grinding wheel, and x is the horizontal distance from the tangent point A to the vertical axis y;

[0065] From formula (1), we obtain the following relationship: x = R g sinθcosβ g (2) y=Rg sinβ g (3)

[0066] The slope of the tangent line l passing through the point of tangency A on the elliptic curve can be expressed as:

[0067] Since the tangent of the slope of tangent l is the angle between tangent l and the x-axis, the angle δ between tangent l and the x-axis can be obtained from formula (4):

[0068] Based on geometric relationships, the following formula is obtained: β c ≈h / (R w +R c (6) h=y+R w sinδ (7) β=β c +δ=π-φ-α (8)

[0069] Let δ, y, β c Substituting into equations (7) and (8), we get:

[0070] In trigonometric functions, when the angle is small, the following simplification occurs: cot(β g )≈1 / β g (12)

[0071] Therefore, substituting formulas (11) and (12) into formulas (9) and (10) yields: h = R g β g +R w β g sinθ (14)

[0072] Combining formulas (13) and (14), we get:

[0073] In this embodiment, the process of obtaining the grinding angle β is as follows:

[0074] Based on geometric relationships, the following formula is obtained:

[0075] Stability growth coefficient A i The expression is:

[0076] Combining formulas (4)-(17), formula (18) can be transformed into a variable with only angles β and γ, and formula (18) becomes:

[0077] Based on the open-source software Python and the stability growth coefficient A i The stability plot is shown in Figure 5. When A i When the value is greater than 0, the region is stable. Based on the inclination angle γ of the support surface of the support plate, the range of values ​​for β within the stable region is selected.

[0078] In this embodiment, the height difference h between the axis of the grinding wheel (the axis of the guide wheel) and the axis of the hard and brittle pipe is determined based on the grinding angle β of the grinding wheel. After the position of the hard and brittle pipe is determined, the height of the grinding wheel and the guide wheel can be determined based on the height difference h, thereby reducing the installation difficulty of the grinding wheel and the guide wheel.

[0079] In addition, the height difference h determined by the grinding angle β of the grinding wheel can ensure the grinding accuracy of the outer circle of the hard and brittle tube. It can also prevent the guide wheel from being unable to drive the workpiece to rotate stably due to an excessively high height difference h, which would cause the workpiece to jump. Conversely, if the height difference h is too low, it will cause angularity on the surface of the hard and brittle tube. The height difference h determined by the grinding angle β can effectively ensure the stable rounding of the outer diameter of the hard and brittle tube with a large length-to-diameter ratio.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions created by the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions created by the present invention without departing from the essence and scope of the technical solutions created by the present invention.

Claims

1. A method for over-positioning grinding of hard and brittle tubular components with a large length-to-diameter ratio, characterized in that, The specific grinding process is as follows: S1, Assembly and positioning of hard and brittle pipe fittings: A rigid mandrel passes through the inner hole of a hard and brittle pipe fitting with a large length-to-diameter ratio and is clearance-fitted with the hard and brittle pipe fitting. The rigid mandrel is tensioned to keep the hard and brittle pipe fitting horizontal. Each end of the rigid mandrel and the position close to the hard and brittle pipe fitting is supported by a vibration damping device to reduce the vibration amplitude and frequency of the rigid mandrel during the processing of the hard and brittle pipe fitting. The support plate contacts the outer pipe surface of the hard and brittle pipe fitting and supports the hard and brittle pipe fitting. S2, Determine the grinding area: Arrange the grinding wheel and guide wheel on both sides of the hard and brittle pipe, and keep the axes of the grinding wheel and guide wheel at the same height. Adjust their height so that there is a height difference between the axes of the guide wheel and the grinding wheel and the axis of the hard and brittle pipe. The grinding surface of the grinding wheel and the guide support surface of the guide wheel face each other. The grinding wheel, guide wheel and support plate form the grinding area of ​​the hard and brittle pipe, and the rigid mandrel is used to provide over-positioning support for the hard and brittle pipe. S3, Guide Roller Positioning: Move the hard and brittle tube to the grinding area, and move the guide roller toward the hard and brittle tube until the guide support surface of the guide roller contacts and presses against the outer tube surface of the hard and brittle tube, so that there is a pre-pressure between the guide roller and the hard and brittle tube. The hard and brittle tube is moved out of the grinding area, and the guide roller is kept in place. S4, Tool setting: Drive the guide wheel to rotate forward, and feed the hard and brittle tube with a large length-to-diameter ratio into the grinding area. The guide wheel contacts and drives the hard and brittle tube forward while rotating in the opposite direction. The grinding wheel rotates in the opposite direction and feeds a small amount towards the hard and brittle tube side to achieve the tool setting operation. S5, Grinding of Hard and Brittle Pipes: Set the rotational speed and feed rate of the guide wheel and the rotational speed and feed rate of the grinding wheel, and set the grinding amount of the hard and brittle pipe. Drive the guide wheel to rotate forward, and feed the hard and brittle pipe with a large length-to-diameter ratio into the grinding area. The guide wheel contacts and drives the hard and brittle pipe forward while rotating in the opposite direction. The grinding wheel rotates in the opposite direction and feeds towards the hard and brittle pipe. As the grinding wheel grinds and feeds, the guide wheel and the support plate feed towards the hard and brittle pipe to always maintain the over-positioning support of the guide wheel, the support plate and the rigid mandrel on the hard and brittle pipe. As the hard and brittle pipe moves, the grinding of the hard and brittle pipe with a large length-to-diameter ratio is achieved.

2. The over-positioning grinding method for hard and brittle tubular components with a large length-to-diameter ratio according to claim 1, characterized in that, In S5, the linear velocity of the grinding wheel is 30 m / s.

3. The over-positioning grinding method for hard and brittle tubular components with a large aspect ratio according to claim 1, characterized in that, In S5, when the outer diameter of the grinding wheel is 400mm, the rotational speed of the grinding wheel is 1400rpm / min to 1500rpm / min.

4. The over-positioning grinding method for a hard and brittle tubular component with a large aspect ratio according to claim 1, characterized in that, In S5, the operating speed of the guide wheel is 15 rpm / min to 20 rpm / min.

5. The over-positioning grinding method for a hard and brittle tubular component with a large aspect ratio according to claim 1, characterized in that, The range of the clearance between the rigid mandrel and the hard and brittle tubular parts is 0.2 to 0.5 mm.

6. The over-positioning grinding method for a hard and brittle tubular component with a large length-to-diameter ratio according to claim 1, characterized in that, The support plate is positioned close to the grinding wheel and obliquely supports the hard and brittle pipe. The supporting surface of the support plate is inclined, with an inclination angle of 30°.

7. The over-positioning grinding method for hard and brittle tubular components with a large length-to-diameter ratio according to claim 1, characterized in that, The grinding wheel is a parallel grinding wheel.

8. The over-positioning grinding method for a hard and brittle tubular component with a large aspect ratio according to claim 1, characterized in that, The grinding wheel is a cup-shaped grinding wheel, and there is an offset angle θ between the axis of the cup-shaped grinding wheel and the axis of the hard and brittle pipe, where θ > 0.

9. The over-positioning grinding method for a hard and brittle tubular component with a large aspect ratio according to claim 8, characterized in that, In S2, the height difference between the axis of the guide wheel and the grinding wheel and the axis of the hard and brittle tube is obtained in the following way: Let R be the outer radius of the rigid and brittle pipe fitting with a large length-to-diameter ratio. w The radius of the guide wheel is R. c The radius of the grinding wheel is R. g Let h be the height difference between the axis of the hard and brittle pipe and the axis of the grinding wheel; when the grinding wheel contacts the hard and brittle pipe, let A be the initial contact point between the grinding wheel and the hard and brittle pipe, and let l be the tangent at point A; when the guide wheel contacts the hard and brittle pipe, let B be the initial contact point between the guide wheel and the hard and brittle pipe; when the support plate contacts the hard and brittle pipe, let C be the initial contact point between the support plate and the hard and brittle pipe. Let the axis of the rigid and brittle pipe be O, and the center of the guide wheel be O. c The center of the grinding wheel is O. g , ∠AOC=α, ∠BOC=φ, ∠AO g O c =β g ,∠O g O c B = β c β is the grinding angle of the grinding wheel, δ is the angle between OA and the horizontal line, and the inclination angle of the supporting surface of the support plate is γ, with O g Establish a rectangular coordinate system with the center of the circle, and let the point of tangency A lie in the coordinate system xO. g The coordinates in y are (x, y); when there is an offset angle θ between the axis of the grinding wheel and the axis of the hard and brittle pipe, the grinding wheel grinds at the offset angle θ. The projection of the profile of the grinding wheel in the section perpendicular to the feed speed direction is then in xO. g The equation of the elliptic curve in y can be expressed as: Where y is the height difference between the tangent point A and the axis of the grinding wheel, and x is the horizontal distance from the tangent point A to the vertical axis y; From formula (1), we obtain the following relationship: x=R g sinθcosβ g (2) y=R g sinβ g (3) The slope of the tangent line l passing through the point of tangency A on the elliptic curve can be expressed as: Since the tangent of the slope of tangent l is the angle between tangent l and the x-axis, the angle δ between tangent l and the x-axis can be obtained from formula (4): Based on geometric relationships, the following formula is obtained: b c ≈h / (R w +R c ) (6) h=y+R w sinδ (7) β=β c +δ=π-φ-α (8) δ, y, β c Substituting into equations (7) and (8), we get: In trigonometric functions, when the angle is small, the following simplification occurs: cot(b g )≈1 / β g (12) Therefore, substituting formulas (11) and (12) into formulas (9) and (10) yields: h=R g b g +R w b g sinth (14) Combining formulas (13) and (14) yields:

10. The over-positioning grinding method for a hard and brittle tubular component with a large aspect ratio according to claim 9, characterized in that, The process for obtaining the grinding angle β is as follows: Based on geometric relationships, the following formula is obtained: Stability growth coefficient A i The expression is: Combining formulas (4)-(17), formula (18) can be transformed into a variable with only angles β and γ, and formula (18) becomes: Based on the open-source software Python and the stability growth coefficient A i The stability plot is obtained when A i When the value is greater than 0, the region is stable. Based on the inclination angle γ of the support surface of the support plate, the range of values ​​for β within the stable region is selected.

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