Gear design method based on DOE full factor
Through the DOE full-factor design method, the problems of cumbersome calculation of gear macro parameters and inability to obtain the optimal solution in one go were solved, the efficiency and accuracy of the gear design process were achieved, and the gear design with optimal parameters was ensured.
Patent Information
- Application Number
- CN202510426963.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-07
- Publication Date
- 2025-09-05
AI Technical Summary
The existing gear macro-parameter calculation method is cumbersome, unable to obtain the optimal solution in one go, and unable to consider all possibilities of input variables, resulting in low calculation efficiency.
The DOE full factor design method is adopted to screen out the optimal factor combination by setting the iteration range and step size of the gear macro parameters, and calculate the basic parameters of the gear pair, including the effective tooth top normal tooth thickness, slip rate, total overlap and end face overlap. Gear design is carried out only after ensuring that these parameters meet the requirements.
It realizes the one-time consideration of all factors in the gear design process, avoids multiple adjustments, ensures the optimality and computational efficiency of gear parameters, and can obtain the optimal solution when the iterative step size and factors are sufficient.
Smart Images
Figure CN120597428A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of gear design, and in particular to a gear design method based on DOE full factors. Background Art
[0002] The current mainstream methods for calculating gear macro parameters include the following: 1. Manual calculation methods based on traditional formulas. This method primarily relies on basic gear parameters (such as module, number of teeth, pressure angle, etc.) and geometric dimensions (such as pitch circle diameter, addendum diameter, and root diameter). 2. Software-based calculation methods, which utilize specialized gear design software (such as MASTA) to calculate and optimize gear macro parameters. These software programs automatically calculate gear geometry, meshing stiffness, transmission error, and other parameters based on the input design parameters, and then optimize the design. For example, in the design of a two-stage parallel-axis gear reducer for new energy, the software calculates the tooth width that minimizes the transmission error and checks whether the gear's boundary dimensions meet the design requirements. 3. Calculation methods based on empirical formulas. In some specific application scenarios, empirical formulas are also used to quickly estimate gear macro parameters. For example, in the design of large wind turbine gearboxes, gear parameters are initially determined based on existing empirical formulas and design specifications, and then adjusted through detailed calculations and optimization. 4. Calculation methods based on multi-objective optimization typically require simultaneous consideration of multiple objectives, such as improving power density and reducing vibration and noise. Therefore, multi-objective optimization methods are widely used in the calculation of gear macro parameters. For example, by establishing an optimization model that incorporates multiple objective functions, such as tooth root bending stress, tooth surface contact stress, and average mesh stiffness, weighting coefficients are used to balance the importance of different objectives.
[0003] All of the above methods are forward designs, requiring constant adjustment of basic input parameters to obtain a better solution. They all have the following problems:
[0004] 1. The calculation process is cumbersome, requiring continuous input of variables required to calculate the gear macro parameters and then obtain other parameters, making it impossible to obtain the optimal solution in one go; 2. It is impossible to consider all possibilities of the required input variables, and theoretically, it is impossible to obtain the optimal solution. Summary of the Invention
[0005] In order to solve the above-mentioned problems, the present invention provides a gear design method based on DOE full factor. This method obtains the optimal factor combination of gear macro parameters by screening the factor combination of all gear macro parameters, and designs the gear according to the factor combination.
[0006] The technical solution of the present invention is: a gear design method based on DOE full factor, comprising the following steps:
[0007] 1) Setting the iteration range and the iteration step of the gear macro parameters according to the DOE full factor, and dividing each gear macro parameter into multiple factors according to the iteration range and the iteration step of each gear macro parameter;
[0008] 2) Setting target parameters and their error ranges, wherein the target parameters include effective tooth tip normal thickness, slip ratio, total contact, and end face contact;
[0009] 3) Combine the factors of each gear macro parameter in sequence, and calculate the basic parameters of the gear pair based on each factor combination;
[0010] 4) Based on the basic parameters of the gear pair calculated for each factor combination in step 3), the gear axial contact and center distance of each factor combination are calculated respectively to determine whether the gear axial contact and center distance meet the requirements. If so, proceed to step 5); otherwise, eliminate the factor combination; if all factor combinations do not meet the requirements, adjust the target parameters and their error ranges, and return to step 3);
[0011] 5) Calculate the effective tooth tip normal tooth thickness, slip rate, end face overlap, and total overlap of the factor combination respectively, and determine whether the effective tooth tip normal tooth thickness, slip rate, end face overlap, and total overlap all meet the requirements. If so, save the factor combination; otherwise, screen out the factor combination; if all factor combinations do not meet the requirements, adjust the target parameters and their error ranges, and return to step 3); if the number of saved factor combinations is greater than 1, select the factor combination with the largest total overlap to design the gear.
[0012] Preferably, in step 1), the gear macro parameters include gear center distance, meshing tooth width, tooth ratio, involute gear pair module, helix angle, and involute gear pair normal pressure angle.
[0013] Preferably, in step 3), the basic parameters of the gear pair include the pitch circle of the driving gear, the pitch circle of the driven gear, the number of teeth of the driving gear, the number of teeth of the driven gear, the base pitch of the gear pair, the pitch circle of the driving gear, the pitch circle of the driven gear, the end face pressure angle, the top circle diameter of the driving gear, the top circle diameter of the driven gear, the root circle of the driving gear, and the root circle of the driven gear.
[0014] Preferably, in step 4), the calculation formula for the gear axial contact is:
[0015]
[0016] Where, ε β is the axial overlap of the gears, B is the meshing tooth width, Z is the number of teeth, d is the pitch circle, β is the helix angle, and π is pi.
[0017] Preferably, in step 4), the calculation formula of the gear center distance is:
[0018] a=0.5*M n (Z1+Z2) / cos(β)
[0019] Where a is the center distance, M n Involute gear pair module, Z1 is the number of teeth of the driving gear, Z2 is the number of teeth of the driven gear, and β is the helix angle.
[0020] Preferably, in step 5), the calculation formula of the effective tooth addendum normal tooth thickness is:
[0021] S n =S t *cosβ
[0022] Where S n is the effective tooth top normal thickness, S t is the end face tooth thickness, and β is the helix angle.
[0023] Preferably, in step 5), the slip ratio is calculated as follows:
[0024] λ=k a -(1-k a )
[0025] Where λ is the slip ratio, k a is the tooth tip slip coefficient.
[0026] Preferably, in step 5), the calculation formula for the end face overlap is:
[0027]
[0028] Where, ε α is the end face overlap, d ae1 is the top diameter of the driving gear, d ae2 is the addendum diameter of the driven gear, α ae1 is the pressure angle of the tooth tip circle of the driving gear, α ae2 is the pressure angle of the driven gear tooth tip circle, α t is the end face pressure angle, β is the helix angle, α 12 is the meshing angle, a is the gear center distance,
[0029] Preferably, in step 5), the calculation formula of the total overlap is:
[0030] ε=ε α +ε β
[0031] Where ε is the total overlap, ε α is the end face overlap, ε βis the gear axial contact ratio.
[0032] The advantages of the present invention are:
[0033] 1. The present invention uses DOE full-factor design to consider all factors of the variables required to calculate the gear macro parameters at one time, without the need to repeatedly adjust the input parameters, and all solutions can be obtained at one time.
[0034] 2. As long as the iteration step is small enough and the global factors are sufficient, the present invention can obtain the optimal solution of various macroscopic parameters of the gear.
[0035] Glossary
[0036] DOE: The full name is Design of Experiments. It is a mathematical and statistical method used to arrange experiments and analyze experimental data. It aims to obtain ideal experimental results and scientific conclusions through smaller experimental scales, shorter experimental cycles and lower experimental costs. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION
[0038] See also Figure 1 , a gear design method based on DOE full factor, including the following steps:
[0039] 1) The iteration range and the step size of the gear macro parameters are set according to the DOE full factor. The gear macro parameters include gear center distance, meshing tooth width, tooth ratio, involute gear pair module, helix angle, and involute gear pair normal pressure angle. According to the iteration range and the step size of each gear macro parameter, each gear macro parameter is divided into multiple factors. The results are shown in Table 1:
[0040]
[0041]
[0042] Table 1
[0043] 2) Set target parameters and their error ranges, including effective tooth top normal thickness, slip rate, total contact, and end face contact; see Table 2,
[0044]
[0045] Table 2
[0046] 3) The factors of the macroscopic parameters of each gear are combined in sequence, and the basic parameters of the gear pair are calculated according to the combination of each factor; the basic parameters of the gear pair include the pitch circle of the driving gear, the pitch circle of the driven gear, the number of teeth of the driving gear, the number of teeth of the driven gear, the base pitch of the gear pair, the pitch circle of the driving gear, the pitch circle of the driven gear, the end face pressure angle, the addendum diameter of the driving gear, the addendum diameter of the driven gear, the root circle of the driving gear, and the root circle of the driven gear.
[0047] Theoretical pitch circle of the driving gear The calculation formula is:
[0048]
[0049] Where, is the theoretical pitch circle of the driving gear, a is the gear center distance, and u is the gear ratio.
[0050] Theoretical pitch circle of the driving gear The calculation formula is:
[0051]
[0052] Where, is the pitch circle of the driven gear, a is the gear center distance, and u is the gear ratio.
[0053] The calculation formula for the number of teeth Z1 of the driving gear is:
[0054]
[0055] Where Z1 is the number of teeth on the driving gear, is the theoretical pitch circle of the driving gear, Mn is the module of the involute gear pair, β is the helix angle, and [] indicates rounding.
[0056] The calculation formula for the number of teeth Z2 of the driven gear is:
[0057]
[0058] Where Z2 is the number of teeth on the driven gear, u is the gear ratio, is the theoretical pitch circle of the driving gear, M n is the module of the involute gear pair, β is the helix angle, and [] indicates rounding.
[0059] The pitch circle d of the driving gear W1 The calculation formula is:
[0060]
[0061] Where, d W1is the pitch circle of the driving gear, Z1 is the number of teeth of the driving gear, Z2 is the number of teeth of the driven gear, and a is the center distance of the gears.
[0062] The pitch circle d of the driven gear W2 The calculation formula is:
[0063]
[0064] Where, d W2 Pitch circle of the driven gear, d W1 is the pitch circle of the driving gear, Z1 is the number of teeth of the driving gear, Z2 is the number of teeth of the driven gear, and a is the center distance of the gears.
[0065] The base pitch P of the gear pair bN The calculation formula is:
[0066] P bN =πM n cosα n
[0067] Where, P bN is the base pitch of the gear pair, π is the circumference of the circle, M n is the module of the involute gear pair, α n is the normal pressure angle of the involute gear pair.
[0068] The calculation formula of the pitch circle d1 of the driving gear is:
[0069]
[0070] Where d1 is the pitch circle of the driving gear, M n is the module of the involute gear pair, Z1 is the number of teeth of the driving gear, and β is the helix angle.
[0071] The calculation formula of the pitch circle d2 of the driven gear is:
[0072]
[0073] Where d2 is the pitch circle of the driven gear, M n is the module of the involute gear pair, Z2 is the number of teeth on the driven gear, and β is the helix angle.
[0074] The end face pressure angle α t The calculation formula is:
[0075]
[0076] Where, α t is the end pressure angle, α n is the normal pressure angle of the involute gear pair, and β is the helix angle.
[0077] The gear pair meshing angle α 12 The calculation formula is:
[0078]
[0079] Where, α 12 is the meshing angle of the gear pair, d1 is the pitch circle of the driving gear, d2 is the pitch circle of the driven gear, a is the gear center distance, α t is the end pressure angle.
[0080] According to the sum of the gear pair modification coefficients X, the normal modification coefficient x1 of the driving gear is determined according to the gear modification coefficient distribution method.
[0081]
[0082] Among them, x1 is the normal modification coefficient of the driving gear, x2 is the normal modification coefficient of the driven gear, Z1 is the number of teeth of the driving gear, Z2 is the number of teeth of the driven gear, β is the helix angle, α 12 is the meshing angle of the gear pair, α t is the end pressure angle, and inv is the involute function.
[0083] Select the modification coefficient distribution method x1. According to industry standards, after the sum of the modification coefficients of the gear pair x1+x2 is determined, there are four ways to distribute the normal modification coefficient x1 of the driving gear:
[0084] Method 1:
[0085] Method 2:
[0086] Method 3:
[0087] Method 4:
[0088] Where Z v1 =Z1sec 3 β
[0089] Among them, Z v1 is the equivalent number of teeth of the driving gear, β is the helix angle, u is the gear ratio, x1 is the normal modification coefficient of the driving gear, and x2 is the normal modification coefficient of the driven gear;
[0090] The driving gear tooth tip circle diameter d a1 The calculation formula is:
[0091] d a1 =d1+2(h * +x1)M n
[0092] Where, da1 is the diameter of the tooth top circle of the driving gear, d1 is the pitch circle of the driving gear, h * is the tooth top height coefficient, x1 is the normal displacement coefficient of the driving gear, M n is the module of the involute gear pair.
[0093] The driven gear tooth tip circle diameter d a2 The calculation formula is:
[0094] d a2 =d2+2(h * +x2)M n
[0095] Where, d a2 is the top diameter of the driven gear, d2 is the pitch circle of the driven gear, h * is the tooth top height coefficient, x2 is the normal displacement coefficient of the driven gear, M n is the module of the involute gear pair.
[0096] The root circle d of the driving gear f1 The calculation formula is:
[0097] d f1 =d1-2(h * +c * -x1)M n
[0098] Where, d f1 is the root circle of the driving gear, d1 is the pitch circle of the driving gear, h * is the tooth addendum coefficient, c * is the top clearance coefficient, x1 is the normal displacement coefficient of the driving gear, M n is the module of the involute gear pair.
[0099] The driven gear root circle d f2 The calculation formula is:
[0100] d f2 =d2-2(h * +c * -x2)M n
[0101] Where, d f2 is the root circle of the driven gear, d2 is the pitch circle of the driven gear, h * is the tooth addendum coefficient, c * is the top clearance coefficient, x2 is the normal displacement coefficient of the driven gear, M n is the module of the involute gear pair.
[0102] 4) Based on the basic parameters of the gear pair calculated for each factor combination in step 3), the gear axial contact and center distance of each factor combination are calculated respectively to determine whether the gear axial contact and center distance meet the requirements. If so, proceed to step 5); otherwise, eliminate the factor combination; if all factor combinations do not meet the requirements, adjust the target parameters and their error ranges, and return to step 3); after performing combination calculations based on the factors in Table 1, 1751 factor combinations remain that meet the requirements.
[0103] The calculation formula of the gear axial contact is:
[0104]
[0105] Where, ε β is the axial overlap of the gears, B is the meshing tooth width, Z is the number of teeth, d is the pitch circle, β is the helix angle, and π is pi.
[0106] The calculation formula of the gear center distance is:
[0107] a=0.5*M n (Z1+Z2) / cos(β)
[0108] Where a is the center distance, M n Involute gear pair module, Z1 is the number of teeth of the driving gear, Z2 is the number of teeth of the driven gear, and β is the helix angle.
[0109] 5) By calculating the effective tooth top normal tooth thickness, slip rate, end face overlap, and total overlap of the remaining 1751 factor combinations in step 4), it is determined whether their effective tooth top normal tooth thickness, slip rate, end face overlap, and total overlap all meet the requirements. After the calculation, the remaining 4 groups of factor combinations meet the requirements. According to the maximum overlap principle, the gear design scheme with the largest total overlap among the 4 groups of factor combinations is selected.
[0110] Derive the functional relationship between the tooth tip radius and the corresponding tooth tip thickness.
[0111] ① The relationship between the end face tooth thickness function and the radius of any circle is as follows:
[0112]
[0113] In the formula, inv(α 12x )=tan(α 12x )-α 12x
[0114] inv(α t )=tan(α t )-α t Among them, α t is the end pressure angle, R is the radius, R Xis the radius of any circle, r b is the base circle radius, S tx is the thickness of any round tooth on the end face, i represents the numbers 1 and 2, α 12 is the meshing angle, subscript 1 represents the driving gear parameter, subscript 2 represents the driven gear parameter, subscript 12 represents the gear pair, and subscript X represents an arbitrary circle;
[0115] ②Substituting the above formula into
[0116]
[0117] Among them, α t is the end pressure angle, R X is the radius of any circle, r b is the base circle radius,
[0118] S tx is the thickness of any round tooth on the end face, i represents the numbers 1 and 2, α 12 is the meshing angle, subscript 1 represents the driving gear parameter, subscript 2 represents the driven gear parameter, subscript 12 represents the gear pair, and subscript X represents an arbitrary circle;
[0119] The relationship between the normal tooth tip and the end tooth thickness corresponding to any tooth tip circle radius is:
[0120] S nx =S tx *cos(β x )
[0121] That is S nx *sec(β x )=S tx
[0122] By transformation we get:
[0123] Where β is the helix angle, β x is the helix angle of any circle, R1 is the radius of the driving gear, R X is the radius of any circle, S tx is the thickness of any round tooth on the end face, S nx It is the thickness of any round tooth on the normal surface;
[0124] ③Simplify the above formula to get
[0125]
[0126] Finally, the functional relationship between any tooth top circle radius and the corresponding tooth top thickness is obtained:
[0127]
[0128] Among them, α tis the end face pressure angle, β is the helix angle, R X is the radius of any circle, R is the radius, S tx is the thickness of any round tooth on the end face, S nx is the thickness of any round tooth on the normal surface, i represents the number 1, 2, α 12 is the meshing angle, subscript 1 represents the driving gear parameter, subscript 2 represents the driven gear parameter, subscript 12 represents the gear pair, and subscript x represents an arbitrary circle;
[0129] The calculation formula of the effective tooth addendum normal tooth thickness is:
[0130] S n =S t *cosβ
[0131] Where S n is the effective tooth top normal thickness, S t is the end face tooth thickness, and β is the helix angle.
[0132] The relationship between the tooth tip radius and the tooth tip end pressure angle is as follows:
[0133]
[0134] Among them, α at is the pressure angle at the tooth top surface, d b is the base circle, d a is the tooth addendum circle.
[0135] Tooth tip slip coefficient of driving gear
[0136]
[0137] Among them, α at is the pressure angle at the tooth tip, α t is the end pressure angle, k a is the tooth tip slip coefficient;
[0138] The calculation formula of the slip ratio is:
[0139] λ=k a -(1-k a )
[0140] Where λ is the slip ratio, k a is the tooth tip slip coefficient.
[0141] The slip ratio of the driving gear and the slip ratio of the driven gear are calculated in the same way.
[0142] The calculation formula of the end face overlap is:
[0143]
[0144] Where, ε α is the end face overlap, d ae1 is the top diameter of the driving gear, d ae2 is the addendum diameter of the driven gear, α ae1 is the pressure angle of the tooth tip circle of the driving gear, α ae2 is the pressure angle of the driven gear tooth tip circle, α t is the end face pressure angle, β is the helix angle, α 12 is the engagement angle, and a is the gear center distance.
[0145] The calculation formula of the total overlap is:
[0146] ε=ε α +ε β
[0147] Where ε is the total overlap, ε α is the end face overlap, ε β is the gear axial contact ratio.
[0148] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications made to the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the scope of protection of the present invention.
Claims
1. A gear design method based on DOE full factor, characterized by: The following steps are involved: 1) Setting the iteration range and the iteration step of the gear macro parameters according to the DOE full factor, and dividing each gear macro parameter into multiple factors according to the iteration range and the iteration step of each gear macro parameter; 2) Setting target parameters and their error ranges, wherein the target parameters include effective tooth tip normal thickness, slip ratio, total contact, and end face contact; 3) Combine the factors of each gear macro parameter in sequence, and calculate the basic parameters of the gear pair based on each factor combination; 4) Based on the basic parameters of the gear pair calculated for each factor combination in step 3), the gear axial contact and center distance of each factor combination are calculated respectively to determine whether the gear axial contact and center distance meet the requirements. If so, proceed to step 5); otherwise, eliminate the factor combination; if all factor combinations do not meet the requirements, adjust the target parameters and their error ranges, and return to step 3); 5) Calculate the effective tooth tip normal tooth thickness, slip rate, end face overlap, and total overlap of the factor combination respectively, and determine whether the effective tooth tip normal tooth thickness, slip rate, end face overlap, and total overlap all meet the requirements. If so, save the factor combination; otherwise, screen out the factor combination; if all factor combinations do not meet the requirements, adjust the target parameters and their error ranges, and return to step 3); if the number of saved factor combinations is greater than 1, select the factor combination with the largest total overlap to design the gear.
2. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 1), the gear macro parameters include gear center distance, meshing tooth width, tooth ratio, involute gear pair module, helix angle, and involute gear pair normal pressure angle.
3. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 3), the basic parameters of the gear pair include the pitch circle of the driving gear, the pitch circle of the driven gear, the number of teeth of the driving gear, the number of teeth of the driven gear, the base pitch of the gear pair, the pitch circle of the driving gear, the pitch circle of the driven gear, the end face pressure angle, the top circle diameter of the driving gear, the top circle diameter of the driven gear, the root circle of the driving gear, and the root circle of the driven gear.
4. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 4), the calculation formula of the gear axial contact is: Where, ε β is the axial overlap of the gears, B is the meshing tooth width, Z is the number of teeth, d is the pitch circle, β is the helix angle, and π is pi.
5. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 4), the calculation formula of the gear center distance is: a=0.5*M n (Z1+Z2) / cos(β) Where a is the center distance, M n Involute gear pair module, Z1 is the number of teeth of the driving gear, Z2 is the number of teeth of the driven gear, and β is the helix angle.
6. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 5), the calculation formula of the effective tooth addendum normal tooth thickness is: S n =S t *cosβ Where S n is the effective tooth top normal thickness, S t is the end face tooth thickness, and β is the helix angle.
7. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 5), the slip ratio is calculated as follows: λ=k a -(1-k a ) Where λ is the slip ratio, k a is the tooth tip slip coefficient.
8. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 5), the calculation formula of the end face overlap is: Where, ε α is the end face overlap, d ae1 is the top diameter of the driving gear, d ae2 is the top circle diameter of the driven gear, α ae1 is the pressure angle of the tooth tip circle of the driving gear, α ae2 is the pressure angle of the driven gear tooth tip circle, α t is the end face pressure angle, β is the helix angle, α 12 is the engagement angle, and a is the gear center distance.
9. The gear design method based on DOE full factor according to claim 1, characterized in that: In step 5), the calculation formula of the total overlap is: e=e α +e β Where ε is the total overlap, ε α is the end face overlap, ε β is the gear axial contact ratio.