A method for measuring the cumulative deviation of the tooth angle of a double gear

Abstract

This invention discloses a method for measuring the cumulative angular deviation of teeth in a double gear. It considers the initial tooth pair angular deviation, and the initial tooth pair can be selected arbitrarily without special requirements. No special marking is required before measurement. After measurement, the initial angular deviation δ can be recorded and the marking is performed before optimization calculation. This method enables rapid positioning of all tooth pairs in a double gear that meet the cumulative deviation requirements.

Description

Technical Field

[0001] This invention relates to the field of measurement methods, and specifically to a method for measuring the cumulative deviation of the tooth angle of a double gear. Background Technology

[0002] Currently, for double gears with angular requirements, post-machining measurement and acceptance is hampered by the difficulty in controlling the initial deviation of the calibrated gear pair and in locating other gear pairs that meet the cumulative deviation requirements. To provide a basis for product acceptance, individual measurements and comparisons are often required, which is inefficient and inconvenient. For some double gears without angular requirements, relying on manual observation or random measurements after machining and before assembly to provide a basis for machine preparation results in methods with poor stability and reliability, lacking rationality. Summary of the Invention

[0003] Purpose of the invention

[0004] To address the above problems, this invention provides a method for measuring the cumulative deviation of the tooth angle in a double gear.

[0005] Invention Technology Solutions

[0006] A method for measuring the cumulative deviation of the tooth angle of a double gear includes the following steps:

[0007] (1) Determine or calibrate the initial measurement tooth pair, and measure the initial angular deviation δ, where δ is the initial angular deviation of the controlled or selected tooth pair;

[0008] (2) Determine the upper deviation U of the cumulative angular deviation of the double gear. Error and lower deviation D Error ;

[0009] (3) Define the initial angular deviation δ and the cumulative angular deviation U. Error and lower deviation D Error The values ​​of the input gear teeth Zi and the output gear teeth Zo of the double gear shaft;

[0010] (4) Construct the input gear angle distribution matrix In and the output gear angle distribution matrix Out according to the following formulas;

[0011]

[0012] (5) Find the In(i) that meets the conditions according to the following formula, and return the corresponding i value or the matrix I composed of i values;

[0013] In(i)∈[Out-U Error Out+D Error ]

[0014] (6) According to the following formula, find Out(j) that meets the conditions and return the corresponding j value or the matrix J composed of j values;

[0015] Out(j)∈[In-U Error In+D Error ]

[0016] (7) Calculate the minimum cumulative deviation M according to the following formula. e (i, j).

[0017] M e (i, j) = Min[|In-Out|]

[0018] Preferably, the upper deviation U of the cumulative angular deviation of the double gears in step (2) Error and lower deviation D Error Determined based on acceptance standards or assembly requirements.

[0019] Preferably, in step (5), logic calculation software is used to find In(i) that meets the conditions.

[0020] Preferably, in step (6), logic calculation software is used to find Out(j) that meets the conditions.

[0021] Preferably, in step (7), In-Out is the subtraction of the elements of matrix In(i) and matrix Out(j).

[0022] Preferably, the logic computing software includes MATLAB, MathCad, Mathmatic, Maple, SciLab, MATRIXx, and VisSim.

[0023] Preferably, the logic computing software includes MATLAB, MathCad, Mathmatic, Maple, SciLab, MATRIXx, and VisSim.

[0024] Preferably, this method can be implemented using programming.

[0025] Advantages of this invention: This method considers the initial tooth pair angular deviation. The initial tooth pair can be selected arbitrarily without special requirements. No special marking is required before measurement. After measurement, the initial angular deviation δ can be marked and recorded before the optimization calculation. This enables rapid positioning of all tooth pairs of double gears that meet the cumulative deviation requirements, improves measurement efficiency, and saves ineffective measurement time. Attached Figure Description

[0026] Figure 1 The double gear described in the embodiment.

[0027] Figure 2The initial gear pair is used for calibration measurement of the double gear as described in the embodiment. Detailed Implementation

[0028] The present invention is achieved through the following technical solution.

[0029] A method for measuring the cumulative deviation of tooth angle in a double gear system, using the following set of double gears as an example, is implemented as follows:

[0030] Table 1 Input parameters for the double gear program

[0031]

[0032] Step 1: Calibrate the initial measurement tooth pair and measure the initial angular deviation δ = 2.1°.

[0033] Step two, assuming the upper deviation U of the cumulative angular deviation of the double gears according to the acceptance criteria or assembly requirements. Error =0 and lower deviation D Error =0.05.

[0034] Step 3: Input the double gear and output the number of gear teeth Z. i =199, Z o =131, initial angular deviation δ = 2.1°, cumulative angular deviation U according to acceptance criteria or assembly requirements Error =0 and lower deviation D Error =0.05.

[0035] Construct the input gear angle distribution matrix In(i) and the output gear angle distribution matrix Out(j) according to the formula;

[0036]

[0037] Step 4: Using the following formula, use logic calculation software to find In(i) that meets the conditions, and return the corresponding i value or the matrix I formed by it;

[0038] In(i)∈[Out-U Error Out+D Error ]

[0039] Step 5: Use logic calculation software such as MATLAB to find Out(j) that meets the conditions, and return the corresponding j value or the matrix J composed of it;

[0040] Out(j)∈[In-U Error In+D Error ]

[0041] Available logic computing software includes MATLAB, MathCad, Mathmatic, Maple, SciLab, MATRIXx, VisSim, etc.

[0042] Step 6: Calculate the minimum cumulative deviation M using the following formula. e(i，j) :

[0043] M e (i, j) = Min[|In-Out|]

[0044] Here, In-Out is the subtraction of the elements of matrix In(i) and Out(j).

[0045] This method can be implemented using programming. The pseudocode example of the double gear in this embodiment is as follows:

[0046]

[0047]

[0048] Running the program produces a double gear.

[0049] Input gear tooth matrix that meets cumulative deviation requirements

[0050] I = [12 91 132 170];

[0051] The output gear tooth matrix meets the cumulative deviation requirement.

[0052] J = [9 61 88 113];

[0053] The minimum cumulative deviation of the input tooth is indicated by the tooth index i = 132.

[0054] The minimum cumulative deviation of the output tooth is j = 88;

[0055] and minimum cumulative deviation M e = -9.5516 × 10 -4 .

[0056] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be used to limit the scope of protection of the present invention. All equivalent transformations or modifications made according to the spirit and essence of the present invention should be covered within the scope of protection of the present invention. The technologies, shapes, and structures not described in detail in this invention are all well-known technologies.

Claims

1. A method for measuring the cumulative deviation of the tooth angle in a double-gear assembly, characterized in that, Includes the following steps: (1) Determine or calibrate the initial measurement tooth pair and measure the initial angular deviation δ, where δ is the initial angular deviation of the controlled or selected tooth pair; (2) Determine the upper deviation of the cumulative angular deviation of the double gear. U Error and lower deviation D Error ; (3) Define the value of the initial angular deviation δ and the cumulative angular deviation. U Error and lower deviation D Error The numerical value, the number of input gear teeth of the double gear shaft Zi and the number of output gear teeth Zo ; (4) Construct the input gear angle distribution matrix according to the following formula. In and output gear angle distribution matrix Out ; (5) Find the matching conditions according to the following formula. In ( i ), and return the corresponding i value or i Matrix of values I ; (6) Find the matching conditions according to the following formula. Out ( j ), and return the corresponding j value or j Matrix of values J ; (7) Calculate the minimum cumulative deviation according to the following formula. M e (i, j); 。 2. The method for measuring the cumulative deviation of the tooth angle of a double gear as described in claim 1, characterized in that, The upper deviation of the cumulative angular deviation of the double gear in step (2) U Error and lower deviation D Error Determined based on acceptance standards or assembly requirements.

3. The method for measuring the cumulative deviation of the tooth angle of a double gear as described in claim 1, characterized in that, In step (5), logic calculation software is used to find those that meet the conditions. In ( i ).

4. The method for measuring the cumulative deviation of the tooth angle of a double gear as described in claim 1, characterized in that, In step (6), logic calculation software is used to find those that meet the conditions. Out ( j ).

5. The method for measuring the cumulative deviation of the tooth angle of a double gear as described in claim 1, characterized in that, In step (7) In - Out For matrix In ( i ) and matrix Out ( j Subtract the elements of ) by iterating through them.

6. The method for measuring the cumulative deviation of the tooth angle of a double gear as described in claim 3, characterized in that, Logical computation software includes MATLAB, MathCad, Mathmatic, Maple, SciLab, MATRIXx, and VisSim.

7. The method for measuring the cumulative deviation of the tooth angle of a double gear as described in claim 4, characterized in that, Logical computation software includes MATLAB, MathCad, Mathmatic, Maple, SciLab, MATRIXx, and VisSim.

8. A method for measuring the cumulative deviation of the tooth angle of a double gear as described in any one of claims 1 to 7, characterized in that, This method can be implemented using programming.

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