Cathode Profile Design Method for Electrochemical Machining of the Stator of All-Metal Oil Screw Drill

Abstract

The present invention belongs to the technical field of electrochemical machining, and particularly relates to a design method for the cathode profile of an all-metal oil screw drill stator by electrochemical machining. The contour curve of the cathode profile is designed into a dot matrix according to unequal gaps, so as to obtain the control points, order and knot vector of the contour curve, construct operators, and use integral spline operators to control the global shape of the contour curve to achieve rough fitting of the cathode contour; when the square curvature of the cathode contour curve is the smallest relative to the integral of its arc length, the curvature of the curve is the most uniform. A fitting index for the cathode contour curve is constructed, and the discrete curvature at each point of the cathode contour curve is calculated in turn to achieve precise fitting of the cathode contour curve, and the error can be controlled within the accuracy range of 0.002 mm; the "B-τ" spline inner contour integration method is used to design the cathode profile of the all-metal oil screw drill stator. The present invention has the advantages of short cathode design cycle, high forming accuracy, and significantly reduced cathode manufacturing cost.

Description

Technical Field

[0001] The present invention provides a design method for the cathode profile of an all-metal oil screw drill stator by electrolytic machining, belonging to the technical field of electrolytic machining. Background Technique

[0002] Screw drills are widely used in directional wells, horizontal wells and other drilling operations due to their advantages such as large output torque, easy operation, and simple structure. They are one of the most widely used downhole power drills at present. With the development of deep well, ultra-deep well, and geothermal well drilling operations, the downhole temperature is generally 120 - 300 °C. Traditional rubber bushing screw drills cannot meet the actual production requirements due to disadvantages such as low bushing strength, small pressure resistance, uneven stress, and fast wear. The stator of an all-metal screw drill has far higher heat resistance than traditional screw drills and has broad application prospects. It is difficult to meet the requirements by traditional mechanical methods for machining the stator of an all-metal oil screw drill, and the service life of the stator and bushing is relatively short. Electrolytic machining is a special machining method that uses the principle of electrochemical reaction of metals in electrolytic solution to achieve one-time forming of workpieces. It has advantages such as good surface quality, high productivity, no tool loss, and no cutting stress. It is an indispensable technical means in advanced manufacturing and is widely used in fields such as oil drilling and production, aerospace, weaponry, automobile manufacturing, and medical devices.

[0003] The cathode profile of the all-metal oil screw drill stator by electrolytic machining is complex, and there is "anisotropy" in the electrochemical etching process. At present, regarding the cathode manufacturing methods for different existing workpieces, the design methods of cathodes are relatively limited. For example, the cosθ method has the disadvantage of a long cathode development cycle; the number of fitting iterations of the polynomial curve fitting method increases significantly, and the entire development process is extremely complex. These problems need to be solved urgently in practical applications. In response to this, this patent proposes a new design method for the cathode profile of the all-metal oil screw drill stator by electrolytic machining, effectively solving the above problems. Summary of the Invention

[0004] The present invention provides a design method for the cathode profile of an all-metal oil screw drill stator by electrolytic machining, aiming to solve the technical problems existing in the prior art, such as the long cathode development cycle of the cosθ method, and the relatively large number of fitting iterations and complex development process of the polynomial curve fitting.

[0005] To achieve the purpose of the present invention, the present invention provides the following technical solutions: A design method for the cathode profile of an all-metal oil screw drill stator by electrolytic machining, including the following steps

[0006] Step 1. According to the contour curve of the all-metal oil screw drill stator, determine its contour curve equation, and design the cathode for the electrolytic machining of the all-metal oil screw drill stator by using the reverse copying method;

[0007] Step 2. Determine the new contour curve model: Form a dot matrix by designing the contour curve of the cathode profile according to non-equal gaps, and select a set of control points of the contour curve Order r and knot vector Use the basis function Construct the r-th order S n operator; With the interpolation points of the piecewise linear function Make the j-th general component of the S n operator Through integral mean value substitution, obtain the integral spline operator R n , generate a new contour curve model;

[0008] Step 3. Globally rough fit the cathode contour curve: Through global transformation of the given set to obtain a new set of control points Generate a new contour curve model, introduce the shape parameter τ in the integral spline operator R n to globally rough fit the cathode contour curve;

[0009] Step 4. Locally refine the fit of the cathode contour curve: According to the fitting index G, sequentially calculate the discrete curvature of the points on the cathode contour curve to locally refine the fit of the cathode contour curve;

[0010] Step 5. Use the "B-τ" spline inner contour integration method to fit the cathode contour curve to construct a cathode profile model, and judge whether it meets the curve fitting requirements. If it meets the fitting requirements, proceed to the next step; otherwise, re-enter Step 4;

[0011] Step 6. According to the constructed cathode profile model, manufacture a cathode for electrochemical machining of the stator of a full-metal positive displacement motor for oil drilling

[0012] Further, the specific steps of Step 2 are as follows

[0013] (1) The r-th order S n operator:

[0014]

[0015] In the formula, S n represents the operator, is the control point of the contour curve, and v is the knot vector

[0016] Among them, the basis function is recursively defined as:

[0017]

[0018]

[0019]

[0020] where \(v\) i is the control point and the corresponding parameter value is denoted as the Schoenberg node, and there are

[0021]

[0022] is the general component, \(\mu\) j (\(j = 1, 2\)) are the interpolation points of the piecewise linear function

[0023] (2). Replace the \(j\)-th component of the \(S\) n operator through the integral average value, and there is

[0024]

[0025] to obtain the spline variation decreasing integral operator \(R\) n n The new contour curve model generated by the operator is expressed in matrix form;

[0026]

[0027]

[0028] wherein:

[0029]

[0030] Furthermore, the process of introducing the shape parameter \(\tau\) into the integral spline operator \(R\) n is as follows:

[0030] Introduce the shape parameter \(\tau\) into the spline variation decreasing integral operator, and replace the integral average value expression in equation (4) with:

[0031]

[0032] The operator \(R\) containing the shape parameter n is written in matrix form as:

[0033]

[0034] wherein:

[0035]

[0036]

[0037] Furthermore, in step (4)

[0038] First, determine the fitting index \(G\) as:

[0039]

[0040] Among them, K i is the discrete curvature at point , as shown in Figure 2 , and the specific calculation method is as follows:

[0041]

[0042] In the formula, H i and H i+1 are the moduli of the vectors respectively, and Δ i is the determinant value of the matrix .

[0043] Then, according to the fitting index G, calculate the discrete curvature of the points on the cathode contour curve in sequence, and perform appropriate correction to minimize the integral of the square curvature k 2 (s) of the cathode contour curve with respect to its arc length, and fit the cathode contour curve to achieve local fine fitting of the cathode contour curve.

[0044] Furthermore, in the fifth step, judge whether the curve meets the conditions according to the index G, fitting error, and the distribution of the curvature of the contour curve.

[0045] Compared with the prior art, the present invention has the following advantages and effects:

[0046] 1. The method of the present invention has a short cathode design cycle. The present invention adopts the B-τ spline inner contour integration method to design the cathode profile of the all-metal oil screw drill stator electrolytic machining. The global rough fitting of the cathode contour curve is realized by controlling the contour curve through the integral spline operator; calculate the discrete curvature at each point of the cathode contour curve to minimize the integral of the square curvature k 2 (s) of the cathode contour curve with respect to its arc length, and achieve fine fitting of the cathode contour curve. This process can complete the optimization of the cathode profile through one iteration, with a smooth and uniform surface, greatly shortening the number of iterations and reducing the development cycle.

[0047] 2. The present invention is based on a cathode design method for the all-metal oil screw drill stator electrolytic machining, with high forming accuracy. The B-τ spline inner contour integration method is used for cathode design, global rough fitting is carried out and continuously corrected. When the integral of the square curvature k 2 (s) of the cathode contour curve with respect to its arc length reaches the minimum, a new cathode contour curve is formed. At the same time, the curvature comb of the curve fitted by the B-τ spline inner contour integration method is significantly better than the initial cathode contour curve, and the fitting error of the cathode curve is only 0.002 mm.

[0048] 3. The method of the present invention can complete the optimization of the cathode profile through one iteration, reduce the number of cathode corrections, and significantly reduce the cathode manufacturing cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a flowchart of the cathode profile design method based on B-τ spline proposed by the present invention;

[0050] Figure 2 is a schematic diagram of discrete curvature calculation;

[0051] Figure 3 is the inner contour diagram of the stator of a full-metal positive displacement motor for oil drilling. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] The following further elaborates on the specific embodiments of the present invention with reference to the accompanying drawings of the specification.

[0053] The design concept of the present invention is as follows: The cathode profile curve is designed into a dot matrix according to unequal intervals to obtain the control points, order, and knot vector of the profile curve, construct an operator, and use the integral spline operator to control the global shape of the profile curve to achieve a rough fitting of the cathode profile; when the integral of the square curvature of the cathode profile curve with respect to its arc length is minimized, the curvature of the curve is the most uniform. Construct a fitting index for the cathode profile curve, and calculate the discrete curvature at each point of the cathode profile curve in turn to achieve an accurate fitting of the cathode profile curve.

[0054] As Figure 1 shown, the present invention proposes a design method for the cathode profile of the stator of a full-metal positive displacement motor for oil drilling. In the actual process, it specifically includes the following steps:

[0055] Step 001. According to the stator profile curve of the full-metal positive displacement motor for oil drilling, determine its stator profile curve equation, design the cathode for electrolytic machining of the stator of the full-metal positive displacement motor for oil drilling using the reverse copying method, and proceed to Step 002;

[0056] Step 002. Design the profile curve of the cathode surface into a dot matrix according to unequal intervals, and select a set of control points of the profile curve order r and knot vector Use the basis function to construct the rth order S n operator. With the interpolation points of the piecewise linear function the jth general component of the S n operator can be obtained by replacing with the integral average value to get the integral spline operator R n . Represent the new profile curve model generated by the R n operator in matrix form, and proceed to Step 003;

[0057] Step 002 specifically includes the following steps:

[0058] Step 00201. From the control points of the contour curve order r and the knot vector obtain the r-th order S operator constructed from the basis functions n Operator:

[0059]

[0060] where the basis functions are recursively defined as:

[0061]

[0062]

[0063]

[0064] where v i is the parameter value corresponding to the control point denoted as the Schoenberg knot, and there is

[0065]

[0066] is the general component, and μ j (j = 1, 2) are the interpolation points of the piecewise linear function and enter Step 00202;

[0067] Step 00202. Replace the j-th component of the S n operator by the integral average value, and there is

[0068]

[0069] to obtain the spline variation diminishing integral operator R n n , and represent the new contour curve model generated by the Roperator in matrix form

[0070]

[0071] where:

[0072]

[0073] Step 003. Obtain a new set of control points by performing a global transformation on the given set ​​​A new contour curve model is generated, which has the properties of B-spline and Markov chain N. In the integral spline operator R of the new contour curve n introduce the shape parameter τ. Use the integral spline operator to control the global shape of the contour curve, realize the global rough fitting of the cathode contour curve, and enter step 004;

[0074] The specific steps of step 003 are as follows:

[0075] Step 00301. Perform a global transformation on the given set to obtain a new control point set A new contour curve model with the properties of B-spline and Markov chain N is generated. When the new contour curve undergoes an affine transformation in the coordinate system, it will not change, and the entire curve will be located within the control polygon. In order to introduce the shape parameter τ into the spline variation diminishing integral operator, replace the integral average expression in equation (4) with:

[0076]

[0077] and enter step 00302;

[0078] Step 00302. Write the operator R containing the shape parameter n in matrix form as:

[0079]

[0080] where:

[0081]

[0082]

[0083] Using the integral spline operator can control the global situation of the contour curve and realize the global rough fitting of the cathode contour curve.

[0084] Step 004. According to the fitting index G, calculate the discrete curvature of the points on the cathode contour curve in turn, and perform appropriate correction to make the integral of the square curvature k 2 (s) with respect to its arc length is minimized. Under this condition, fit the cathode contour curve, and the error is only 0.002 mm, realizing the local fine fitting of the cathode contour curve, and enter step 005;

[0085] The specific steps of step 004 are as follows:

[0086] Step 00401. The fitting index G of the cathode contour curve is:

[0087]

[0088] Among them, K i is the discrete curvature at the point as shown in Figure 2 and the specific calculation method is as follows:

[0089]

[0090] In the formula, H i and H i+1 are the moduli of the vectors respectively, and Δ i is the determinant value of the matrix .

[0091] Step 00402. According to the fitting index G, calculate the discrete curvature of the points on the cathode contour curve in sequence, and perform appropriate correction to minimize the integral of the square curvature k 2 (s) of the cathode contour curve with respect to its arc length, and fit the cathode contour curve to achieve local fine fitting of the cathode contour curve.

[0092] In the said step 005, a cathode profile model is established based on the cathode contour curve fitted by the "B-τ" spline inner contour integration method. According to the index G, fitting error and the distribution of the contour curve curvature, it is judged whether the curve meets the conditions. If it meets the fitting requirements, go to step 006; otherwise, go to step 004.

[0093] In the said step 006, use the cathode profile model established in step 005 to manufacture the cathode for electrochemical machining of the stator of the all-metal positive displacement motor for oil drilling.

[0094] Referring to Figure 3 , it can be seen that the profile of the stator of the all-metal positive displacement motor for oil drilling is closely related to the cathode contour curve, and the cathode obtained by this method has good machining effect, greatly shortening the cathode manufacturing cycle.

[0095] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Based on the technical solutions of the present invention, any improvements and equivalent transformations made to the design method according to the principles of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A design method for the cathode profile of a stator in an all-metal positive displacement motor for oil drilling, characterized in that: Including the following steps Step 1. Determine the contour curve equation of the stator of the all-metal positive displacement motor for oil drilling according to its contour curve, and design the cathode for electrolytic machining of the stator of the all-metal positive displacement motor for oil drilling by the reverse copying method; Step 2. Determine the new contour curve model: form a dot matrix by designing the contour curve of the cathode profile with unequal gaps, and select a set of control points of the contour curve Order r and knot vector Use the basis function Construct the r-th order S n operator; with the interpolation points of the piecewise linear function Make the S n The j-th general component of the operator Through integral mean value substitution, obtain the integral spline operator R n , and generate a new contour curve model; Step 3. Globally and roughly fit the cathode contour curve: By performing a global transformation on the given set to obtain a new control point set generate a new contour curve model, introduce the shape parameter τ in the integral spline operator R n to globally and roughly fit the cathode contour curve; Step 4. Locally refine the fitting of the cathode contour curve: Calculate the discrete curvature of the points on the cathode contour curve in turn according to the fitting index G, and locally refine the fitting of the cathode contour curve; Step 5. Construct a cathode profile model with the cathode contour curve after fitting by the "B-τ" spline inner contour integration method, and judge whether it meets the curve fitting requirements. If it meets the fitting requirements, go to the next step; otherwise, re-enter Step 4; Step 6. Fabricate the cathode for electrolytic machining of the stator of the all-metal positive displacement motor for oil drilling according to the constructed cathode profile model.

2. A method for designing the cathode profile of an all-metal oil screw drill stator by electrolytic machining according to claim 1, characterized in that, The specific steps of step two include the following steps: (1) r-order S n operator: where S n represents an operator, is the control point of the contour curve, v is the knot vector, Among them, the basic function is recursively defined as: where v i is the control point and the corresponding parameter value is denoted as the Schoenberg node, and there is For General component, μ j (j = 1, 2) are the interpolation points of the piecewise linear function (2). Replace S n The j-th component of the operator By replacing with the integral average value, we have Obtain the spline variation diminishing integral operator R n , and represent R in matrix form n The new contour curve model generated by the operator; Wherein: 。 3. A method for designing the cathode profile of an all-metal oil screw drill stator by electrochemical machining according to claim 1 or 2, characterized in that In step 3, the process of introducing the shape parameter τ into the integral spline operator R n is as follows: Introduce the shape parameter τ into the spline variation diminishing integral operator, and replace the integral average expression in Equation (4) with: The operator R with shape parameters n is written in matrix form as: Wherein:

4. A method for designing the cathode profile of an electrolytic machining of the stator of an all-metal positive displacement motor for oil drilling, as claimed in claim 3, characterized in that In the said Step 4 First, determine the fitting index G as: where K i is the discrete curvature at the point , as shown in Figure 2, and the specific calculation method is as follows: Then, according to the fitting index G, the discrete curvature of the points on the cathode contour curve is calculated in sequence and appropriately corrected so that the integral of the square curvature k 2 (s) with respect to its arc length is minimized, and the cathode contour curve is fitted to achieve local fine fitting of the cathode contour curve.​ 5. The method for designing the cathode profile of the stator of an all-metal positive displacement motor for oil drilling according to claim 4, characterized in that, In the said Step 5, judge whether the curve meets the conditions according to the index G, the fitting error and the distribution of the contour curve curvature.

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