A method for mapping macro-parameters of an involute cylindrical gear

Abstract

This invention discloses a method for measuring the macroscopic parameters of involute cylindrical gears, comprising: S1, counting the number of gear teeth and measuring the gear tooth width, addendum circle diameter, and dedendum circle diameter; S2, using two sets of measuring rods of different diameters to measure the span between the rods; S3, measuring the axial tooth pitch; S4, measuring the total tooth height and rounding the results by 1 and 3 respectively; S5, measuring the helix angle and adding and subtracting 5° after rounding the results to integers; S6, using computer programming to iteratively calculate and find a combination of parameters such as normal module, normal pressure angle, and helix angle that matches the measured data; and S7, calculating other parameters of the gear based on the parameter combinations matched in S1 to S5. This invention utilizes computer programming to calculate the macroscopic parameters of gears, freeing surveyors from repetitive and tedious calculations and improving surveying efficiency.

Description

Technical Field

[0001] This invention relates to the field of involute cylindrical gear mapping technology, specifically to a method for mapping the macroscopic parameters of involute cylindrical gears. Background Technology

[0002] Gear parameter mapping helps to digest and absorb advanced technologies from home and abroad and repair failed gears. With the advancement of gear design technology, in many industries, gear parameter design has abandoned the design habit of "taking standard values". This has led to the fact that the traditional mapping method of "approaching standard values" is not suitable for non-standard gear designs, especially high-precision non-standard gear designs.

[0003] Traditional methods for measuring gears require measuring the length of the common normal, which has the following limitations:

[0004] 1. Not applicable to narrow helical gears;

[0005] 2. The accuracy of common normal measurement is limited. Taking a spur gear with a module of 2, 20 teeth, and a pressure angle of 20° as an example, when the tooth thickness changes by 0.01mm, the length of the common normal changes by only 0.0094mm, while the change in the span of the gear exceeds 0.02mm.

[0006] Of course, modern, advanced gear measuring instruments have the function of mapping unknown gears. However, such gear measuring instruments are expensive, and not all gear manufacturing plants have this type of equipment. Moreover, the results generated by such gear measuring instruments usually have many decimal places and cannot be used directly. Therefore, existing technologies, whether in terms of mapping methods or mapping equipment, have limitations. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method for measuring the macroscopic parameters of involute cylindrical gears.

[0008] The technical solutions to the above technical problems are as follows:

[0009] A method for measuring the macroscopic parameters of an involute cylindrical gear includes the following steps:

[0010] S1, count the number of teeth on the gear, and measure the tooth width, addendum circle diameter, and dedendum circle diameter of the gear;

[0011] S2, select two sets of measuring rods with different diameters, and record the diameters of the measuring rods as dp1 and dp2 respectively. Then use the two sets of measuring rods with different diameters to measure the gear span distance, and record the measurement results as M1 and M2.

[0012] S3. Measure the axial tooth pitch of the gear using a lathe or milling machine, and record the axial tooth pitch of the gear as px;

[0013] S4. Use a caliper to measure the total tooth height of the gear teeth. Divide the measurement results by 1 and 3 respectively and round them up to obtain the upper limit Mn_max and the lower limit Mn_min of the module. The rounding accuracy is the same as the first trial step size Mn_step. Use a protractor to measure the helix angle of the gear. After rounding the measurement result to an integer, add and subtract 5° respectively to obtain the upper limit beta_max and the lower limit beta_min of the helix angle. The rounding accuracy is the same as the second trial step size beta_step. The upper limit an_max of the pressure angle of the gear is 30°, and the lower limit an_min is 15°. The rounding accuracy is the same as the third trial step size an_step;

[0014] S5. Give the mapping tolerance eps_px of the axial pitch and the mapping tolerance eps_s of the tooth thickness. Denote the mapping tolerance of the axial pitch as eps_px and the mapping tolerance of the tooth thickness as eps_s;

[0015] S6. Use computer programming to trial-calculate the axial pitch px_cal and the tooth thickness corresponding to the over-pin distances M1 and M2 under various parameter combinations. Denote the tooth thickness corresponding to the over-pin distance M1 as s1_cal and the tooth thickness corresponding to the over-pin distance M2 as s2_cal;

[0016] S7. Calculate the absolute value Δpx of the difference between the axial pitch px_cal and the measured axial pitch px, and the absolute value Δs of the difference between the tooth thicknesses s1_cal and s2_cal. Output the parameter combinations that meet the condition "Δpx < eps_px and Δs < eps_s" as the qualified mapping results.

[0017] Furthermore, in S4, the first trial step size Mn_step takes a value of 0.01 mm or 0.05 mm, the second trial step size beta_step takes a value of 0.1° or 0.5°, and the third trial step size takes a value of 0.1° or 0.5°.

[0018] Furthermore, the specific calculation steps in S6 are as follows:

[0019] (1). Calculate the axial pitch px_cal using the trial-calculated module and the trial-calculated helix angle;

[0020] (2). Calculate the tooth thickness s1_cal corresponding to the over-pin distance M1 and the tooth thickness s2_cal corresponding to the over-pin distance M2 using the number of teeth, the measured over-pin distances M1 and M2, the trial-calculated module, the trial-calculated pressure angle, and the trial-calculated helix angle.

[0021] The beneficial effects of the present invention are:

[0022] 1. It breaks through the mapping habit of "relying on the standard value", and is suitable for the mapping of gears with non-standard parameters that are becoming more and more common;

[0023] 2. Using computer programming frees surveyors from repetitive and tedious calculations. The programming approach is simple and clear, requiring less programming skills from surveyors, while also improving surveying efficiency.

[0024] 3. The program is highly flexible. Depending on the surveying conditions, measurement accuracy, and surveying requirements, the program parameters can be easily adjusted to output the desired results. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method for measuring the macroscopic parameters of involute cylindrical gears according to the present invention;

[0026] Figure 2 This is a computer program flowchart of the present invention. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0028] like Figure 1 and Figure 2 As shown, a method for measuring the macroscopic parameters of an involute cylindrical gear includes the following steps:

[0029] S1, count the number of teeth on the gear, and measure the tooth width, addendum circle diameter, and dedendum circle diameter of the gear;

[0030] S2, select two sets of measuring rods with different diameters, and record the diameters of the measuring rods as dp1 and dp2 respectively. Then use the two sets of measuring rods with different diameters to measure the gear span distance, and record the measurement results as M1 and M2.

[0031] S3. Measure the axial tooth pitch of the gear using a lathe or milling machine, and record the axial tooth pitch of the gear as px;

[0032] S4. Measure the total tooth height using calipers, divide the measurement results by 1 and 3 respectively and round them up to obtain the upper limit Mn_max and lower limit Mn_min of the module. The rounding accuracy is consistent with the first trial calculation step Mn_step. Measure the gear helix angle using an angle gauge, round the measurement results to integers, and add and subtract 5° respectively to obtain the upper limit beta_max and lower limit beta_min of the helix angle. The rounding accuracy is consistent with the second trial calculation step beta_step. The upper limit an_max of the gear pressure angle is 30°, and the lower limit an_min is 15°. The rounding accuracy is consistent with the third trial calculation step an_step.

[0033] S5, give the measurement tolerance of axial tooth pitch eps_px and the measurement tolerance of tooth thickness eps_s, and denote the measurement tolerance of axial tooth pitch as eps_px and the measurement tolerance of tooth thickness as eps_s.

[0034] S6. Using computer programming, calculate the axial pitch \(p_{x\_cal}\) and the tooth thickness corresponding to the measurement over pins \(M1\) and \(M2\) under various parameter combinations. Denote the tooth thickness corresponding to the measurement over pins \(M1\) as \(s1\_cal\), and the tooth thickness corresponding to the measurement over pins \(M2\) as \(s2\_cal\).

[0035] S7. Calculate the absolute value \(\Delta p_x\) of the difference between the calculated axial pitch \(p_{x\_cal}\) and the measured axial pitch \(p_x\), and the absolute value \(\Delta s\) of the difference between the tooth thicknesses \(s1\_cal\) and \(s2\_cal\). Output the parameter combinations that satisfy the condition "\(\Delta p_x < eps\_px\) and \(\Delta s < eps\_s\)" as the qualified mapping results.

[0036] In S4, the first trial step size \(Mn\_step\) is taken as \(0.01\ mm\) or \(0.05\ mm\), the second trial step size \(beta\_step\) is taken as \(0.1°\) or \(0.5°\), and the third trial step size is taken as \(0.1°\) or \(0.5°\).

[0037] The specific calculation steps in S6 are as follows:

[0038] (1). Calculate the axial pitch \(p_{x\_cal}\) using the trial module and the trial helix angle.

[0039] (2). Calculate the tooth thickness \(s1\_cal\) corresponding to the measurement over pins \(M1\) and the tooth thickness \(s2\_cal\) corresponding to the measurement over pins \(M2\) using the number of teeth, the measured measurement over pins \(M1\) and \(M2\), the trial module, the trial pressure angle, and the trial helix angle.

[0040] Specifically, to reduce the influence of measurement errors, the diameter difference between \(dp1\) and \(dp2\) should be large.

[0041] Specifically, when the measurement accuracy of the axial pitch and the measurement over pins is high, the mapping tolerances \(eps\_px\) of the axial pitch and \(eps\_s\) of the tooth thickness are taken as smaller values; otherwise, larger values are taken. To reduce the number of low-quality alternative solutions, the measurement accuracy needs to be improved, so that smaller mapping tolerances can be set, thereby excluding calculation results with large deviations in the computer program.

[0042] Specifically, after mapping the parameters of the teeth, write a computer program, and map the macroscopic parameters of the cylindrical gear through the computer program. The computer program is as follows:

[0043] Specifically, the main body of the computer program has a three-layer loop structure. The outermost layer is the normal module, starting from Mn_min, with a step size of Mn_step, and looping until Mn_max. The middle layer is the normal pressure angle, starting from an_min, with a step size of an_step, and looping until an_max. The innermost layer is the helix angle, starting from beta_min, with a step size of beta_step, and looping until beta_max. It calculates the axial tooth pitch px_cal and the tooth thickness s1_cal and s2_cal corresponding to the span distances M1 and M2 under all combinations of the above loop variables. It calculates the absolute value of the difference between the axial tooth pitch px_cal and the measured axial tooth pitch px, and the absolute value of the difference between the tooth thickness s1_cal and s2_cal. The parameter combination whose absolute value of the above two differences is less than the corresponding tolerance is output as a qualified surveying result.

[0044] Specifically, after obtaining qualified surveying results, the surveyors select a set of parameter combinations from the qualified surveying results as the final parameter scheme. If the surveying work of paired gears is carried out in parallel, the selected parameter combinations must have the same normal module, normal pressure angle and helix angle.

[0045] Specifically, the final parameter scheme is used as the basis to calculate a complete set of gear parameters, including the addendum coefficient, clearance coefficient, and displacement coefficient.

[0046] Finally, it should be noted that the above-described embodiments are merely preferred embodiments of the present invention used to illustrate the technical solutions of the present invention, and are not intended to limit them, much less limit the scope of protection of the present invention; although the invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the scope of protection of the claims.

Claims

1. A method for measuring the macroscopic parameters of an involute cylindrical gear, characterized in that, It includes the following steps: S1. Count the number of teeth of the gear, and measure the tooth width, addendum circle diameter, and dedendum circle diameter of the gear; S2. Select two sets of measuring rods with different diameters, record the diameters of the measuring rods as dp1 and dp2 respectively, then use the two sets of measuring rods with different diameters to measure the over-pin distance of the gear, and record the measurement results as M1 and M2; S3. Use a lathe or a milling machine to measure the axial pitch of the gear, and record the axial pitch of the gear as px; S4. Use a caliper to measure the total tooth height of the tooth, divide the measurement results by 1 and divide by 3 respectively and round them to obtain the upper limit Mn_max and the lower limit Mn_min of the module. The rounding accuracy is the same as the first trial step size Mn_step. Use a protractor to measure the helix angle of the gear, round the measurement result to an integer and then add and subtract 5° respectively to obtain the upper limit beta_max and the lower limit beta_min of the helix angle. The rounding accuracy is the same as the second trial step size beta_step. The upper limit an_max of the pressure angle of the gear is taken as 30°, and the lower limit an_min is taken as 15°. The rounding accuracy is the same as the third trial step size an_step; S5. Give the mapping tolerance eps_px of the axial pitch and the mapping tolerance eps_s of the tooth thickness, and record the mapping tolerance of the axial pitch as eps_px and the mapping tolerance of the tooth thickness as eps_s; S6. Use computer programming to trial-calculate the axial pitch px_cal and the tooth thickness corresponding to the over-pin distances M1 and M2 under various parameter combinations. The tooth thickness corresponding to the over-pin distance M1 is recorded as s1_cal, and the tooth thickness corresponding to the over-pin distance M2 is recorded as s2_cal; S7. Calculate the absolute value Δpx of the difference between the axial pitch px_cal and the measured axial pitch px and the absolute value Δs of the difference between the tooth thicknesses s1_cal and s2_cal, and output the parameter combinations that meet the condition "Δpx < eps_px and Δs < eps_s" as the qualified mapping results.

2. The method for measuring the macroscopic parameters of an involute cylindrical gear according to claim 1, characterized in that, In S4, the first trial step size Mn_step takes a value of 0.01 mm or 0.05 mm, the second trial step size beta_step takes a value of 0. I° or 0.5°, and the third trial step size takes a value of 0.1° or 0.5°.

3. The method for measuring the macroscopic parameters of an involute cylindrical gear according to claim 1, characterized in that, The specific calculation steps in S6 are as follows: (1). Calculate the axial pitch px_cal using the trial-calculated module and the trial-calculated helix angle; (2). Calculate the tooth thickness s1_cal corresponding to the over-pin distance M1 and the tooth thickness s2_cal corresponding to the over-pin distance M2 using the number of teeth, the measured over-pin distances M1 and M2, the trial-calculated module, the trial-calculated pressure angle, and the trial-calculated helix angle.

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