Method for calculating actual contact ratio of thermoplastic resin gear, method for deriving coefficient of friction of thermoplastic resin gear, method for predicting tooth root temperature of thermoplastic resin gear, and method for predicting service life of thermoplastic resin gear

Abstract

This method for calculating an actual contact ratio of a thermoplastic resin gear includes: a step 1 for measuring a temperature distribution of a pair of gears; a step 2 for employing CAE structural analysis to calculate a temperature distribution of a structural analysis model A having the same shape as the pair of gears; a step 3 for preparing temperature dependency data of a modulus of elasticity a of a thermoplastic resin; a step 4 for performing, in any order, a step 4a for correcting the modulus of elasticity a in accordance with a strain rate dependency, and a step 4b for correcting the modulus of elasticity a in accordance with an actual amount of deformation of the gears; a step 5 for using a modulus of elasticity a' after correction to calculate a contact stress distribution by means of CAE structural analysis; a step 6 for calculating an angular difference from a start point to an end point of meshing of the pair of gears on the basis of the contact stress distribution; and a step 7 for calculating the actual contact ratio of the pair of gears from the angular difference.

Description

Method for calculating the actual contact ratio of thermoplastic resin gears, method for deriving the friction coefficient of thermoplastic resin gears, method for predicting the root temperature of thermoplastic resin gears, and method for predicting the life of thermoplastic resin gears

[0001] The present invention relates to a method for calculating the actual contact ratio of thermoplastic resin gears, a method for deriving the friction coefficient of thermoplastic resin gears, a method for predicting the root temperature of thermoplastic resin gears, and a method for predicting the life of thermoplastic resin gears.

[0002] Gears made of thermoplastic resins such as polyamide resins and polyacetal resins are lightweight, have high vibration absorption properties, and are self-lubricating. Therefore, they can be used without lubrication and can be easily produced by injection molding or other methods, and are therefore used in a wide range of fields in place of metal gears. As the applications of resin gears expand, there are increasingly strict requirements for miniaturization, noise reduction, high heat resistance for high-speed use, and long-term durability (fatigue fracture life) (see Patent Document 1).

[0003] In Europe, the gear fatigue characteristics of plastic gears (VDI 2736 Blatt 2) are estimated using root temperature calculated from the gear profile, operating conditions, and other factors. The calculation of the root temperature, which is required for the estimation, is significantly affected by the friction coefficient of the plastic gear. The pin-on-disk method, ring-on-ring method, and ball-on-disk method are commonly used to measure the friction coefficient for plastic gears. However, these methods significantly differ from the sliding behavior of actual gears, resulting in inconsistencies in the friction coefficient of the actual gears. Furthermore, the contact ratio also significantly affects the calculation of root temperature. However, the calculation formula for root temperature does not take into account the contact ratio (actual contact ratio) that takes into account the root temperature rise and tooth deformation of plastic gears. As a result, the accuracy of predicting root temperature using the friction coefficient measured using conventional methods and the contact ratio that takes into account tooth deformation is low, which ultimately makes it difficult to accurately evaluate the gear fatigue characteristics of plastic gears.

[0004] Japanese Patent Application Laid-Open No. 2017-62017

[0005] The present invention has been made in consideration of the above-mentioned problems of the conventional technology, and an object of the present invention is to provide a method for calculating the contact ratio (actual contact ratio) of thermoplastic resin gears taking into account tooth temperature and tooth deformation, a method for more accurately deriving the friction coefficient of thermoplastic resin gears, a method for predicting the root temperature of thermoplastic resin gears with high accuracy, and a method for predicting the fatigue life of thermoplastic resin gears with high accuracy.

[0006] One aspect of the present invention that solves the above problem is as follows: (1) A method for calculating an actual contact ratio of a pair of gears, at least one of which is made of a thermoplastic resin, comprising: Step 1: rotating the pair of gears, at least one of which is made of a thermoplastic resin, at a predetermined rotation speed while meshing with each other and measuring the temperature distribution of the pair of gears; Step 2: creating a structural analysis model A having the same shape as the pair of gears by CAE, inputting the temperatures obtained from the temperature distribution of the pair of gears measured in Step 1 into the structural analysis model A, and calculating the temperature distribution of the structural analysis model A by CAE structural analysis; Step 3: preparing temperature dependency data of the elastic modulus a of the thermoplastic resin that constitutes the pair of gears; Step 4, which performs the following steps in any order: Step 4a, in which a location where maximum tensile strain occurs in a strain distribution at the base of the meshing teeth when the pair of gears are meshed is calculated by CAE structural analysis from the temperature distribution of structural analysis model A calculated in Step 2 and the temperature dependency data of elastic modulus a prepared in Step 3, and corrects said elastic modulus a or the elastic modulus obtained in Step 4b below based on the strain rate dependency of the elastic modulus of the gears in structural analysis model A calculated from the location where maximum tensile strain occurs in the strain distribution; and Step 4b, in which actual deformation amounts of the pair of gears are measured, an amount of deformation by CAE structural analysis is calculated using CAE structural analysis model B which has the same shape as the pair of gears and is created to reflect said actual deformation amounts, and then a ratio X between said actual deformation amount and the deformation amount obtained by CAE structural analysis is found, and the elastic modulus a or the elastic modulus obtained in Step 4a is corrected based on said ratio X. Step 5: calculating a contact stress distribution by CAE structural analysis using the corrected elastic modulus a' obtained in Step 4 when a predetermined torque is applied to the driving gear of the pair of gears; Step 6: calculating an angular difference from the meshing start point to the meshing end point of the pair of gears based on the contact stress distribution calculated in Step 5; and Step 7: calculating an actual contact ratio of the pair of gears by dividing the angular difference calculated in Step 6 by an angle (360° / number of teeth) corresponding to the circular pitch of the pair of gears.

[0007] (2) A method for deriving the friction coefficient of thermoplastic resin gears, comprising a step 8 of measuring a transmission efficiency η of torque transmitted from a drive gear to a driven gear of a pair of gears, and deriving the friction coefficient of the thermoplastic resin gears using a gear transmission loss equation from the actual contact ratio calculated by the method for calculating the actual contact ratio of thermoplastic resin gears described in (1) above and the torque transmission efficiency η measured in the step 8.

[0008] (3) The method for deriving the friction coefficient of a thermoplastic resin gear according to (2) above, wherein the friction coefficient of the thermoplastic resin gear is derive by substituting the actual contact ratio into one of the following formulas 1 to 3:

[0009] [In formulas 1 to 3, ε α is the face-to-face contact ratio, η is the torque transmission efficiency, μ is the friction coefficient of the thermoplastic resin gear, and u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth in the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in the pair of gears, ε １ is the approach contact ratio, ε ２ indicates the far contact ratio.]

[0010] (4) A method for predicting the root temperature of a thermoplastic resin gear, comprising substituting the actual contact ratio calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear as set forth in (1) above and the friction coefficient μ calculated by any method (excluding the method for deriving the friction coefficient of a thermoplastic resin gear as set forth in (2) above) into the following formula 4 and any of the following formulas 5 to 7:

[0011] [In formula 4, θ Ｆｕβ is the root temperature (℃), θ ０ is the ambient temperature (°C), P is the nominal output (2π x rotation speed x torque) (W), μ is the friction coefficient of the thermoplastic resin gear, k θ，Ｆｕβ is the heat storage factor, and is the heat transfer coefficient (K·(m / s)) defined in VDI 2736 Blatt 2 for a pair of gears, at least one of which is made of thermoplastic resin. ｃ ・mm１．７５ / W), b is the tooth width (mm), m ｎ is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), v is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), ｔ ｃ The term is the heat dissipation factor, v ｔ is the pitch circumference speed (m / s), c is a constant between 0.05 and 0.70, R λ，Ｇ is the housing thermal resistance (K m 2 / W), A Ｇ is the housing heat dissipation area (m ２ ), ED is the relative meshing time per 10 minutes, H ｖ indicates the loss factor calculated by the following formulas 5 to 7 according to the value of the actual contact ratio.]

[0012] [In formulas 5 to 7, ε α is the front contact ratio, u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth in the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in the pair of gears, ε １ is the approach contact ratio, ε ２ indicates the far contact ratio.]

[0013] (5) A method for predicting the root temperature of a thermoplastic resin gear, which predicts the root temperature of a thermoplastic resin gear by substituting the contact ratio taking deformation into account and the friction coefficient μ calculated by the method for deriving a friction coefficient of a thermoplastic resin gear described in (2) above into the following equations 4 and 5 to 7:

[0014] [In formula 4, θ Ｆｕβ is the root temperature (℃), θ ０ is the ambient temperature (°C), P is the nominal output (2π x rotation speed x torque) (W), μ is the friction coefficient of the thermoplastic resin gear, k θ，Ｆｕβ is the heat storage factor, and is the heat transfer coefficient (K·(m / s)) defined in VDI 2736 Blatt 2 for a pair of gears, at least one of which is made of thermoplastic resin. ｃ ・mm １．７５ / W), b is the tooth width (mm), mｎ is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), v is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), ｔ ｃ The term is the heat dissipation factor, v ｔ is the pitch circumference speed (m / s), c is a constant between 0.05 and 0.70, R λ，Ｇ is the housing thermal resistance (K m 2 / W), A Ｇ is the housing heat dissipation area (m ２ ), ED is the relative meshing time per 10 minutes, H ｖ indicates the loss factor calculated by the following formulas 5 to 7 according to the value of the actual contact ratio.]

[0015] [In formulas 5 to 7, ε α is the front contact ratio, u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth in the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in the pair of gears, ε １ is the approach contact ratio, ε ２ indicates the far contact ratio.]

[0016] (6) A method for predicting the root temperature of a thermoplastic resin gear, comprising substituting the actual contact ratio calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear according to (1) above and the friction coefficient μ calculated by the method for deriving the friction coefficient of a thermoplastic resin gear according to (2) above into the following equations 4 and 5 to 7:

[0017] [In formula 4, θ Ｆｕβ is the root temperature (℃), θ ０ is the ambient temperature (°C), P is the nominal output (2π x rotation speed x torque) (W), μ is the friction coefficient of the thermoplastic resin gear, k θ，Ｆｕβ is the heat storage factor, and is the heat transfer coefficient (K·(m / s)) defined in VDI 2736 Blatt 2 for a pair of gears, at least one of which is made of thermoplastic resin. ｃ ・mm １．７５ / W), b is the tooth width (mm), mｎ is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), v is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), ｔ ｃ The term is the heat dissipation factor, v ｔ is the pitch circumference speed (m / s), c is a constant between 0.05 and 0.70, R λ，Ｇ is the housing thermal resistance (K m 2 / W), A Ｇ is the housing heat dissipation area (m ２ ), ED is the relative meshing time per 10 minutes, H ｖ indicates the loss factor calculated by the following formulas 5 to 7 according to the value of the actual contact ratio.]

[0018] [In formulas 5 to 7, ε α is the front contact ratio, u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth in the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in the pair of gears, ε １ is the approach contact ratio, ε ２ indicates the far contact ratio.]

[0019] (7) When the pair of gears is a combination of thermoplastic resin gears, the number of teeth z in the formula 4 is the total number of teeth of the pair of gears (however, when the entire circumference does not mesh, only the number of teeth in the meshing range is counted), c in the formula 4 is set to 0.10 to 0.60, and k in the formula 4 is set to θ，Ｆｕβ (A) is set to A⋅ln(b)+B) to (A⋅ln(b)+C) (where b is the face width (mm), A is 1130 to 3610, B is −1.782A+3286, and C is −1.728A+5291).

[0020] (8) When the pair of gears is a combination of a thermoplastic resin gear and a metal gear, the number of teeth z in the formula 4 is the total number of teeth of the pair of gears (however, when the entire circumference does not mesh, only the number of teeth in the meshing range is counted), c in the formula 4 is set to 0.10 to 0.60, and k in the formula 4 is set to θ，Ｆｕβ The method for predicting the root temperature of a thermoplastic resin gear according to any one of claims 4 to 6, wherein at least one of the following is carried out: (A ln(b) + B) to (A ln(b) + C) (where b is the face width (mm), A is 100 to 2000, B is -2.284A + 1424, and C is -2.316A + 3637).

[0021] (9) A method for predicting a lifespan of a thermoplastic resin gear, comprising a step 9 of preparing an S-N curve of the thermoplastic resin gear for each temperature of the teeth of the thermoplastic resin gear, and predicting a lifespan of the thermoplastic resin gear based on the S-N curve corresponding to the root temperature obtained by the method for predicting the root temperature of a thermoplastic resin gear according to any one of (4) to (8).

[0022] The present invention provides a method for calculating the contact ratio (actual contact ratio) of thermoplastic resin gears that takes into account tooth temperature and tooth deformation, a method for more accurately deriving the friction coefficient of thermoplastic resin gears, a method for predicting the root temperature of thermoplastic resin gears with high accuracy, and a method for predicting the fatigue life of thermoplastic resin gears with high accuracy.

[0023] 1 is a diagram showing a pair of gears in mesh and explaining the contact ratio. FIG. 2 is a graph showing the relationship between temperature distribution and the distance in the face width direction of the gears. FIG. 3 is a top view of a CAE analysis model A of a resin gear. FIG. 4 is a diagram showing the tooth root strain distribution in CAE analysis. FIG. 5 is a graph showing the relationship between the tooth root strain and the gear division number in CAE analysis. FIG. 6 is a graph showing the relationship between the elastic modulus and the strain rate of a tensile test specimen. (A) A top view and (B) a front view of a device for measuring the deformation amount of gear teeth. FIG. 7 is a graph showing the relationship between the gear load (torque) and the rotation angle of the rotating gear (actually measured values ​​and CAE analysis values). FIG. 8 is a graph showing the ratio of the actual measured values ​​to the CAE analysis values ​​for the relationship between the gear load (torque) and the rotation angle of the rotating gear. FIG. 9 is a graph showing the gear load (torque) and the rotation angle of the rotating gear with a corrected elastic modulus. FIG. 10 is a graph showing the relationship between the gear load (torque) and the rotation angle of the rotating gear with a corrected elastic modulus. FIG. 11 is a graph showing the relationship between the temperature and the contact ratio. 1 is a graph showing the relationship between the maximum tooth temperature and the coefficient of friction for gear pairs 1 to 8 (without grease). 2 is a graph showing the relationship between the maximum tooth temperature and the coefficient of friction for gear pairs 1', 3', 5', and 6' (with grease). 3 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 1 to 7 (without grease) using the tooth root temperature prediction method of this embodiment. 4 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 1', 3', 5', and 6' (with grease) using the tooth root temperature prediction method of this embodiment. 5 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 8 to 11 (without grease) using the tooth root temperature prediction method of this embodiment. 6 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 8 to 11 using the tooth root temperature prediction method of this embodiment. 7 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 8 to 11 using the tooth root temperature prediction method of this embodiment. 8 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 8 to 11 using the tooth root temperature prediction method of this embodiment. 9 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 8 to 11 using the tooth root temperature prediction method of this embodiment. 10 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 8 to 11 using the tooth root temperature prediction method of this embodiment. 11 is a graph showing the relationship between the predicted temperature and the measured temperature for gear pairs 8 to 11 using the tooth root temperature prediction method of this embodiment. 1A and 1B are graphs showing the relationship between the predicted temperature and the actually measured temperature by the tooth root temperature prediction method of the present embodiment. 1B are graphs showing the relationship between the predicted temperature and the actually measured temperature by the tooth root temperature prediction method of the present embodiment. 1C are (a) a cross-sectional view and (b) a side view of a resin gear with 54 teeth used in various evaluations.(a) A cross-sectional view and (b) a side view of a resin gear with 23 teeth used in various evaluations. (a) A cross-sectional view and (b) a side view of a resin gear with 14 teeth used in various evaluations. (a) A cross-sectional view and (b) a side view of a metal gear with 18 teeth used in various evaluations. (b) A side view of a metal gear with 14 teeth used in various evaluations. (c) A cross-sectional view of a metal gear with 35 teeth used in various evaluations. (d) A cross-sectional view of a metal gear with 54 teeth used in various evaluations.

[0024] <Method for Calculating Actual Contact Ratio of Thermoplastic Resin Gears> The method for calculating the actual contact ratio of thermoplastic resin gears (hereinafter simply referred to as "resin gears") according to this embodiment is a method for calculating the actual contact ratio of a pair of gears, at least one of which is made of thermoplastic resin. The method includes the following steps 1 to 7. Step 1: A pair of gears, at least one of which is made of thermoplastic resin, is rotated at a predetermined rotation speed while meshing with each other, and the temperature distribution of the pair of gears is measured. Step 2: A structural analysis model A having the same shape as the pair of gears is created using CAE, and the temperatures obtained from the temperature distribution of the pair of gears measured in step 1 are input into the structural analysis model A, and the temperature distribution of the structural analysis model A is calculated by CAE structural analysis. Step 3: Data on the temperature dependence of the elastic modulus a of the thermoplastic resin constituting the pair of gears is prepared. Step 4: Using the temperature distribution of structural analysis model A calculated in Step 2 and the temperature dependency data of elastic modulus a prepared in Step 3, the location of maximum tensile strain in the strain distribution at the base of the meshing teeth of the pair of gears is calculated by CAE structural analysis, and the elastic modulus a or the elastic modulus obtained in Step 4b below is corrected using the strain rate dependency of the elastic modulus of the gears in structural analysis model A calculated from the location of maximum tensile strain in the strain distribution. Step 4a is performed in any order, and the actual deformation of the pair of gears is measured, and a CAE structural analysis model B having the same shape as the pair of gears is created to reflect the actual deformation, and the deformation amount obtained by CAE structural analysis is calculated. Then, a ratio X between the actual deformation and the deformation obtained by CAE structural analysis is determined, and the elastic modulus a or the elastic modulus obtained in Step 4a is corrected using the ratio X. Step 5: Using the corrected elastic modulus a' obtained in Step 4, calculate the contact stress distribution when a predetermined torque is applied to the driving gear of the pair of gears through CAE structural analysis. Step 6: Calculate the angular difference between the meshing start point and meshing end point of the pair of gears based on the contact stress distribution calculated in Step 5. Step 7: Calculate the actual contact ratio of the pair of gears by dividing the angular difference calculated in Step 6 by the angle equivalent to the circular pitch (360° / number of teeth).

[0025] First, let us explain the "actual contact ratio" with reference to FIG. 1. FIG. 1 shows the meshed state between teeth 12 of gear 10 and teeth 22 of gear 20 (see FIG. 1(D)). FIGS. 1(A) to 1(C) show enlarged views of the meshed portions of the gears. In addition, in FIGS. 1(A) to 1(C), black dots indicate the points where the teeth of each gear contact each other. In FIG. 1(A), the teeth of each gear contact one location, in FIG. 1(B), two locations, and in FIG. 1(C), one location. Thus, when a pair of gears rotates in mesh, the number of teeth in contact varies depending on the rotation angle. The "actual contact ratio" is the value obtained by dividing the angle corresponding to the meshing length when a pair of thermoplastic resin gears rotates in mesh with each other by the angle corresponding to the circular pitch of the pair of gears (360° / number of teeth). Unlike metal gears, thermoplastic resin gears deform significantly, causing the meshed teeth to bend. Therefore, the meshing ratio cannot be considered the same as that of metal gears. When gears are made of metal, their elastic modulus is extremely high and changes little with temperature, resulting in little deformation, and the contact ratio remains essentially unchanged even when deformation is taken into account. On the other hand, in the case of plastic gears, their elastic modulus is low and varies greatly with temperature, so the contact ratio also varies depending on operating conditions (tooth temperature and load). Therefore, in this embodiment of the present invention, which relates to plastic gears, a contact ratio that takes deformation into account is not used, but an "actual contact ratio" that takes into account tooth deflection specific to thermoplastic resin gears is calculated. Steps 1 to 7 for calculating the actual contact ratio are explained below. Note that the following explanation shows various evaluation results, which were evaluated using the following measuring instruments.23 インチ ホイールが、ホイールセットまで、ホイールセットまで、ホイールセットまで、カードセットまで、カードセットまで、カードセットまで、カードセットまで、カードセットをホイールします。 24 18-tooth metal gear (see Figure 25) 14-tooth metal gear (see Figure 26) 35-tooth metal gear (see Figure 27) 54-tooth metal gear (see Figure 28) The numbers in Figures 22 to 28 indicate the dimensions (mm) of each element. 25 and 26, a metal gear 30 is formed by connecting a gear 34 to a shaft 32.

[0026] [Step 1] In Step 1, a pair of gears, at least one of which is made of a thermoplastic resin, is rotated at a predetermined rotational speed while meshing with each other, and the temperature distribution of the pair of gears is measured. That is, the temperature distribution is measured while the pair of gears is rotating. The temperature distribution can be measured using a non-contact thermometer, such as a radiation thermometer, a thermograph, or an infrared camera. The predetermined rotational speed can be set arbitrarily. For example, as described below, when predicting the root temperature of a gear, the rotational speed of the gear set for predicting the root temperature can be used. The temperature distribution of the gear can be measured in the tooth width direction and the rim. The gear fixing jig used to mount the gear in the miniature gear fatigue testing machine can be made of either metal or resin, but resin is preferred because it does not absorb heat from the tooth surface.

[0027] At least one of the pair of gears may be made of a thermoplastic resin, and both may be made of thermoplastic resin, or one may be made of a thermoplastic resin and the other a metal gear. When both gears are made of thermoplastic resin, the thermoplastic resins may be the same or different. Furthermore, the thermoplastic resin of one or both of the thermoplastic resin gears may be filled with a fibrous or other inorganic filler. Furthermore, the pair of gears may have the same shape, or may have different numbers of teeth and / or different face widths.

[0028] [Step 2] In Step 2, a structural analysis model A having the same shape as the pair of gears is created using CAE (Computer Aided Engineering), the temperatures obtained from the temperature distribution of the pair of gears measured in Step 1 are input into the structural analysis model A, and the temperature distribution of the structural analysis model A is calculated by CAE structural analysis. It is also conceivable to use the elastic modulus obtained from the measured temperature distribution by thermography to perform CAE structural analysis to calculate the actual contact ratio. However, problems with thermography include the fact that it can only measure the temperature distribution on the surface of the molded product and that it takes a long time to obtain the measured temperature distribution. Therefore, in Step 2, the temperature distribution obtained by CAE structural analysis (the measured temperature distribution is reflected in CAE) is used.

[0029] In step 2, the temperature distribution measured in step 1, such as the tooth width center temperature and the rim average temperature, is input as temperature conditions into CAE structural analysis software, and a heat conduction analysis is performed to calculate the temperature distribution obtained by CAE analysis. Figure 2 shows the measured temperature distribution (black circles) and the temperature distribution obtained by CAE heat conduction analysis (white circles). Note that the mesh model used for the CAE structural analysis can be, for example, the structural analysis model A shown in Figure 3.

[0030] [Step 3] In step 3, data on the temperature dependence of the elastic modulus a of the thermoplastic resin constituting the pair of gears is prepared. That is, in step 3, data on the elastic modulus a versus temperature is prepared for the thermoplastic resin constituting the pair of gears. This data may be obtained by actual measurement, or existing data such as values ​​published by the manufacturer may be used. Note that step 3 may be performed before the start of step 4, or may be performed before the start of step 1 or step 2.

[0031] [Step 4] Step 4 includes step 4a: calculating, by CAE structural analysis, the location of maximum tensile strain in the strain distribution at the base of the meshed teeth of the pair of gears when the gears are meshed, based on the temperature distribution of structural analysis model A calculated in step 2 and the temperature dependency data of elastic modulus a prepared in step 3; and correcting elastic modulus a or the elastic modulus obtained in step 4b below, based on the strain rate dependency of the gear elastic modulus in structural analysis model A calculated from the location of maximum tensile strain in the strain distribution. Also included is step 4b: measuring the actual deformation of the pair of gears, calculating the deformation by CAE structural analysis using CAE structural analysis model B, which has the same shape as the pair of gears and reflects the actual deformation, and then calculating the ratio X between the actual deformation and the deformation by CAE structural analysis, and correcting elastic modulus a or the elastic modulus obtained in step 4a using the ratio X. Steps 4a and 4b can be performed in any order. That is, either step 4a or step 4b can be performed first. Steps 4a and 4b will now be described.

[0032] (Step 4a) In short, step 4a is a step of correcting the elastic modulus a prepared in step 3 (or the elastic modulus after correction of the elastic modulus a in step 4b) in consideration of the strain rate dependency calculated from the strain distribution.

[0033] Figure 4 shows the strain distribution calculated by CAE structural analysis. Figure 4 shows the strain distribution when the drive-side gear 10 and the driven-side gear 20 are rotated at a rotation speed of 100 rpm and a torque of 9 N m. The dimensions and other specifications of the drive-side gear 10 and the driven-side gear 20 are as follows: Gear shape (drive side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) Gear shape (driven side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) The strain is greatest within circle 24 in Figure 4, i.e., at the location where the maximum tensile strain occurs in the strain distribution at the base of the tooth of the driven-side gear 20, which is in contact with the tooth of the drive-side gear 10.

[0034] Strain rate dependency refers to the change in properties of a material depending on the strain rate when a load is applied to it, and as the strain rate (e.g., tensile speed) increases in resin materials, the material strength and elastic modulus tend to increase. Therefore, in resin gears, calculations must take into account the strain rate dependency of the elastic modulus that occurs due to differences in operating conditions (rotational speed).

[0035] First, the temperature dependence of the elastic modulus of each part of the gear is calculated from the temperature distribution of structural analysis model A calculated in step 2. A deformation analysis is performed by CAE analysis using the calculated data on the temperature dependence of the elastic modulus to calculate the strain rate at the location where the maximum tensile strain occurs in the strain distribution at the base of the meshing teeth when the resin gears are actually meshed. Next, the strain rate of the elastic modulus is calculated, for example, as follows. The following example uses a drive gear and a driven gear with the following shapes, with a rotation speed of 100 rpm and a torque of 9 N m. Gear shape (drive side): spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) Gear shape (driven side): spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) a) Define the CAE analysis time (s / section) and angular velocity (rad / s) per section in the CAE analysis (for example, 0.02 s / section and 0.175 rad / s). b) Convert to the gear rotation angle (° / section) per section in the CAE analysis. c) Calculate the rotation angle (°) by multiplying the gear rotation angle per section in the CAE analysis obtained in b) by the number of sections from the start of strain to its peak. d) Calculate the time (s) required to rotate the rotation angle calculated in c) (for example, 0.008 s). This is the number of divisions (CAE) converted into time (s) e) Strain rate ( / s) = strain / time required for analysis (s) = (0.02 (maximum strain point) - 0.005 (start of strain point)) / 0.008 s = 1.86 ( / s). In other words, if you calculate the time from the point where strain occurs to the maximum strain point and the time it takes to reach that point, you can calculate the strain rate of the elastic modulus as 1.86 ( / s).

[0036] Fig. 5 is a graph showing the relationship between the division number and the strain at the tooth base in the CAE analysis. In Fig. 5, the horizontal axis shows the division number, but by converting the division number to time, the slope of the graph (straight line) in the part surrounded by the dashed line in Fig. 5 becomes the strain rate.

[0037] Next, the elastic modulus of the resin gear for CAE analysis is corrected to match the actual measured value (elastic modulus obtained by a tensile test using an ISO tensile test piece). The measured values ​​of the elastic modulus are shown in the graph of FIG.

[0038] As shown in Figure 6, the elastic modulus at a strain rate of 1.86 ( / s) is approximately 2800 MPa. The ratio of this to the reference elastic modulus of 1940 MPa (reference conditions: tensile speed 1 (mm / s), strain rate 0.01 ( / s)) is 2800 / 1940 = 1.45. Therefore, the elastic modulus that takes into account the strain rate dependency of a plastic gear obtained by CAE analysis can be calculated by multiplying the reference elastic modulus by 1.45. This allows for correction of the elastic modulus due to differences in rotation speed based on the strain rate. While it is desirable to use data on the temperature dependency of the elastic modulus corresponding to the actual gear conditions (strain rate), it is also possible to measure the strain rate dependency of the elastic modulus in advance, calculate the elastic modulus corresponding to the actual gear strain rate, and then calculate the elastic modulus at each temperature from the previously obtained temperature dependency of the elastic modulus.

[0039] (Step 4b) In short, step 4b is a step of correcting the elastic modulus a prepared in step 3 (or the elastic modulus after correcting the elastic modulus a in step 4a) in consideration of the actual deformation amount.

[0040] First, an example of measuring the actual deformation of a gear is shown. FIG. 7 shows an example of a testing machine used to measure the actual deformation of a gear. In the testing machine 30 shown in FIG. 7, gear 10 and gear 20 are in mesh with each other. Gear 10 is set to rotate around shaft 32, while gear 20 is fixed so as not to rotate. A load application lever 34 is attached to shaft 32 behind gear 10. When load application lever 34 is pressed downward, gear 10 swings clockwise in FIG. 7. Since gear 10 is meshed with fixed gear 20, rotation is restricted, resulting in slight displacement of the teeth of gears 10 and 20. In the testing machine 30 shown in FIG. 7, a load (torque) is applied to gear 10 by pressing load application lever 34 downward. This allows the relationship between the displacement of load application lever 34 and torque in response to tooth deformation to be determined. In other words, the displacement of load application lever 34 relative to a given torque can be converted into an axial rotation angle. In other words, the rotation angle of the gear is calculated indirectly from the deformation amount of the teeth.

[0041] The equipment and conditions for measuring the actual deformation of a gear are shown below, but these are merely examples and the present embodiment is not limited to these. Testing machine: Universal testing machine UTA-50KN-RTC manufactured by A&D Co., Ltd. Gear material: DURACON (registered trademark), POM M90-44 (unfilled), manufactured by Polyplastics Co., Ltd. Gear shape (rotating side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) Gear shape (fixed side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) Torque: 1, 3, 5, 7, 9 N m (the upper limit can be set to the allowable stress (MPa) depending on the material) Test speed at the force point: Can be set appropriately taking into account strain rate dependency and stress relaxation. For example, a speed of 5 mm / min. Horizontal distance to the force point: 65 mm Lubrication: Oil lubrication (TRUSCO Nakayama Corporation, industrial gear oil, viscosity ISO VG 100) *Helps prevent instability of load transmission due to stick-slip phenomenon (grease or other lubricants are also acceptable) Ambient temperature: 23°C Radial play ｒ : 0.2 mm

[0042] Next, CAE creates a CAE analysis model B that reflects the gear shape from the actual measurement test. Then, deformation analysis is performed to calculate the shaft rotation angle from the tooth displacement amount. In the deformation analysis using CAE, the shaft rotation angle is calculated from the tooth displacement amount that is not affected by deformation due to load (torque) application.

[0043] Figures 8 and 9 show the results of comparing the measured values ​​of the gear rotation angle with the CAE analysis values. Figure 8 shows the measured values ​​(open graph) and the CAE analysis values ​​(hatched graph) for the relationship between the gear load (torque) and the gear rotation angle. Figure 9 shows the ratio of the measured values ​​to the CAE analysis values ​​for the relationship between the gear load (torque) and the gear rotation angle. Because the CAE analysis values ​​are lower than the measured values ​​for all loads (torques), it is possible to make the elastic modulus calculated by CAE analysis appear to match the measured deformation by correcting it to reduce it.

[0044] Table 1 below shows the corrected elastic modulus obtained by dividing the uncorrected elastic modulus (2500 MPa) at 23°C for each torque by the "measured / CAE ratio." For example, in the case of a torque of 9 N m, the "measured / CAE ratio" is 1.51, so the elastic modulus corrected for the measured-CAE deviation is: = uncorrected elastic modulus (2500 MPa) × 1 / 1.51 = uncorrected elastic modulus (2500 MPa) × 0.66 = 1.7 × 10 ３ MPa. The relationship between the torque and the rotation angle using this corrected elastic modulus is compared between the CAE analysis results and the actual measurement results, as shown in Figure 10. In Figure 10, white circles indicate CAE analysis values, and black circles indicate actual measurement values.

[0045]

[0046] From FIG. 10, it can be seen that the measured values ​​of the rotation angle and the CAE calculated values ​​are generally in agreement, which indicates that the above-mentioned correction of the elastic modulus is appropriate.

[0047] An example of the case where the elastic modulus is corrected by the above steps 4a and 4b is shown in Table 2 below.

[0048]

[0049] The elastic modulus a' used in step 5 (the table on the right) is the elastic modulus a corrected by steps 4a and 4b.

[0050] As described above, by correcting the elastic modulus in steps 4a and 4b, the elastic modulus for CAE analysis can be corrected to an elastic modulus corresponding to the actual measurement. Also, as described above, steps 4a and 4b can be performed in any order, and either step can be performed first.

[0051] [Step 5] Step 5 is a step in which the corrected elastic modulus a' obtained in Step 4 is used to calculate the contact stress distribution when a predetermined torque is applied to the driving gear of the pair of gears through CAE structural analysis. The corrected elastic modulus a' calculated in Step 4 and the measurement conditions (torque) are input into CAE structural analysis software, and deformation analysis (contact analysis) is performed to calculate the contact stress distribution when a predetermined torque is applied to the driving gear. A mesh model similar to the structural analysis model A shown in Figure 3 can be used for the CAE structural analysis.

[0052] [Step 6] Step 6 is a step for calculating the angular difference between the meshing start point and the meshing end point of a pair of gears based on the contact stress distribution calculated in Step 5. From the contact stress distribution calculated in Step 5, the "angle difference between the meshing start point and the meshing end point" (θ ｅｎｄ -θ ｓｔａｒｔ ) is calculated.

[0053] [Step 7] Step 7 is a step for calculating the actual contact ratio of the pair of gears by dividing the angle difference calculated in Step 6 by the angle equivalent to the circular pitch (360° / number of teeth). ｅｎｄ -θ ｓｔａｒｔ ) to θ ｐｉｔｃｈ (the angle equivalent to the circular pitch (360° / number of teeth)) to calculate the actual contact ratio of the resin gear according to the measurement conditions (contact ratio = (θ ｅｎｄ -θ ｓｔａｒｔ ) / θ ｐｉｔｃｈ ).

[0054] As explained above, the method for calculating the actual contact ratio of a thermoplastic resin gear according to this embodiment makes it possible to calculate the actual contact ratio taking into account the temperature and deformation of the teeth. The calculated actual contact ratio can be applied to the following methods for deriving the friction coefficient of a thermoplastic resin gear according to this embodiment, as well as the methods for predicting the root temperature of a thermoplastic resin gear and the lifespan of a thermoplastic resin gear, which will be described later. However, the present invention is not limited to these methods.

[0055] <Method of Deriving Friction Coefficient of Thermoplastic Resin Gears> The method of deriving the friction coefficient of thermoplastic resin gears of this embodiment includes step 8 of measuring the transmission efficiency η of torque transmitted from the drive gear to the driven gear of a pair of gears, and deriving the friction coefficient of the thermoplastic resin gears using a gear transmission loss equation from the actual contact ratio calculated by the above-mentioned method of calculating the actual contact ratio of thermoplastic resin gears of this embodiment and the torque transmission efficiency η measured in step 8.

[0056] In the method for deriving the friction coefficient of a thermoplastic resin gear according to this embodiment, the friction coefficient is calculated from the actual contact ratio calculated by the above-described method for calculating the actual contact ratio of a thermoplastic resin gear according to this embodiment and a measured value of the transmission efficiency η of torque transmitted from the drive gear to the driven gear of a pair of gears. In other words, in this embodiment, the friction coefficient is calculated taking into account the actual contact ratio of the pair of gears, so that the friction coefficient is derived in accordance with the actual sliding behavior of the gears. Therefore, unlike when using friction coefficients derived by the pin-on-disk method, ring-on-ring method, or ball-on-disk method, the accuracy of predicting the tooth root temperature (described later) is improved.

[0057] In step 8, the transmission efficiency of torque transmitted from the drive gear to the driven gear of the pair of gears is measured. The torque transmission efficiency can be calculated by measuring the torque of the driven gear and the torque of the drive gear and using the formula: torque of driven gear × (number of teeth of drive gear / number of teeth of driven gear) / torque of drive gear. For example, if the torque value of the drive gear is 2.47, the torque value of the driven gear is 2.37, the number of teeth of the drive gear is 54, and the number of teeth of the driven gear is 54, the transmission efficiency η = 2.37 × (54 / 54) / 2.47 = 0.96.

[0058] Next, the friction coefficient of the thermoplastic resin gear is calculated using a gear transmission loss equation based on the actual contact ratio calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear according to this embodiment and the torque transmission efficiency η calculated in step 8. Examples of gear transmission loss equations include the Niemann equation, the Buckingham equation, and the Merritt equation. The Niemann equation will be explained below.

[0059] The friction coefficient μ of the thermoplastic resin gear is calculated by substituting the actual contact ratio calculated by the method for calculating the actual contact ratio of the thermoplastic resin gear of the present embodiment into one of the following equations 1 to 3.

[0060] [In formulas 1 to 3, ε α is the face-to-face contact ratio, η is the torque transmission efficiency, μ is the friction coefficient of the thermoplastic resin gear, and u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth in the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in the pair of gears, ε １ is the approach contact ratio, ε ２ indicates the far contact ratio.]

[0061] Front contact ratio ε α is 1<ε α < 2, apply Equation 1, and α is 2<ε α < 3, apply Equation 2, and α is 3<ε α If <4, then apply Equation 3.

[0062] In formulas 1 to 3, the approach contact ratio ε １ is calculated from the angle between the meshing start point and the meshing pitch point (the intersection of the meshing pitch circle and the line connecting the center points of both gears). ２ is calculated from the angle between the meshing pitch point (the intersection of the meshing pitch circle and the line connecting the center points of both gears) and the meshing end point. α is the approach contact ratio ε１ Contact ratio ε ２ The sum of ε α =ε1+ε2.

[0063] In formulas 1 to 3, z １ is the number of teeth of the gear with the fewer teeth in the pair of gears, z ２ indicates the number of teeth of the gear with the larger number of teeth of the pair of gears.

[0064] Table 3 below shows the actual contact ratio (transverse contact ratio) calculated using the method for calculating the actual contact ratio of thermoplastic resin gears according to this embodiment, and the friction coefficient μ calculated using Niemann's formula (formulas 2 and 3 above) based on the actual contact ratio. It also shows the rotation speed, torque, and maximum tooth temperature values ​​for eight examples (gear pairs 1 to 8). Here, the "rotation speed" and "torque" are values ​​for the drive gear. The dimensions and other specifications of the gear pairs used are listed below. Gear profile (drive side): spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) Gear profile (driven side): spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) Gear pairs 1 to 8 use different gear materials, as follows: Gear pair 1: Drive side: Thermoplastic resin 1, Driven side: Thermoplastic resin 1 Gear pair 2: Drive side: Thermoplastic resin 2, Driven side: Thermoplastic resin 2 Gear pair 3: Drive side: Thermoplastic resin 3, Driven side: Thermoplastic resin 3 Gear pair 4: Drive side: Thermoplastic resin 4, Driven side: Thermoplastic resin 4 Gear pair 5: Drive side: Thermoplastic resin 5, Driven side: Thermoplastic resin 5 Gear pair 6: Drive side: Thermoplastic resin 6, Driven side: Thermoplastic resin 6 Gear pair 7: Drive side: Thermoplastic resin 1, Driven side: Thermoplastic resin 5 Gear pair 8: Drive side: Metal gear 1, Driven side: Thermoplastic resin 1 In gear pair 8, the metal gear 1 used on the drive side is as follows. Metal gear 1: SG1S 18L-1010 (spur gear (module 1.0 mm, number of teeth 18, face width 10 mm, pressure angle 20°, addendum modification coefficient 0)) manufactured by Kyoiku Gears Co., Ltd.

[0065] The materials (thermoplastic resins) constituting the gears used in gear pairs 1 to 8 are as follows: Thermoplastic resin 1: DURACON (registered trademark) POM M90-44 (unfilled), manufactured by Polyplastics Co., Ltd. Thermoplastic resin 2: DURACON (registered trademark) POM NW-02, manufactured by Polyplastics Co., Ltd. Thermoplastic resin 3: DURACON (registered trademark) POM YF-10, manufactured by Polyplastics Co., Ltd. Thermoplastic resin 4: DURACON (registered trademark) POM M25-44, manufactured by Polyplastics Co., Ltd. Thermoplastic resin 5: DURANEX (registered trademark) PBT 2002, manufactured by Polyplastics Co., Ltd. Thermoplastic resin 6: PA66-based resin Leona 1300G (filled with fibrous filler), manufactured by Asahi Kasei Corporation

[0066] On the other hand, Figure 11 is a graph showing the relationship between the maximum tooth temperature and the contact ratio. The solid line shows the contact ratio taking deformation into account, and the dashed line shows the actual contact ratio calculated using the method for calculating the actual contact ratio of thermoplastic resin gears of this embodiment (see Table 3). Figure 11 reveals that the contact ratio taking deformation into account is constant over a given temperature range, whereas the actual contact ratio changes depending on the maximum tooth temperature. Figure 12 is a graph showing the relationship between the maximum tooth temperature and the friction coefficient μ for gear pairs 1 to 8. The solid line shows the friction coefficient μ calculated using Niemann's equation based on the contact ratio taking deformation into account. The dashed lines also show the friction coefficient μ (see Table 3) calculated using Niemann's equation (Equations 2 and 3) based on the actual contact ratio calculated using the method for calculating the actual contact ratio of thermoplastic resin gears of this embodiment (see Table 3). 12, it can be seen that the friction coefficient μ calculated based on the contact ratio taking deformation into account changes depending on the maximum tooth temperature, whereas the friction coefficient μ calculated based on the actual contact ratio and applying Niemann's equation (the above equations 2 and 3) for gear pairs 1 to 8 is almost constant within a given temperature range. Furthermore, since the friction coefficient μ is almost constant for all gear pairs 1 to 8, it can be seen that the friction coefficient μ is almost constant not only between the same thermoplastic resins, but also between combinations of different thermoplastic resins, combinations of thermoplastic resins filled with fibrous or other fillers, and combinations of thermoplastic resin and metal.

[0067]

[0068] Next, we will explain examples of gear pairs 1, 3, 5, and 6 (gear pairs 1', 3', 5', and 6', respectively) in which grease was applied to the gears. As with gear pairs 1 to 8, the actual contact ratios of gear pairs 1', 3', 5', and 6' were calculated using the method for calculating the actual contact ratio of thermoplastic resin gears of this embodiment, and the friction coefficient μ was derived based on the actual contact ratios using Niemann's equation (Equations 2 and 3 above). The actual contact ratios and friction coefficient μ are shown in Table 4. The relationship between the maximum tooth temperature and the friction coefficient μ for gear pairs 1', 3', 5', and 6' is shown in the graph in Figure 13. 13, it can be seen that the friction coefficient μ calculated based on the contact ratio taking deformation into account changes depending on the maximum tooth temperature, whereas the friction coefficient μ calculated using Niemann's equation (Equations 2 and 3 above) based on the actual contact ratio for gear pairs 1', 3', 5', and 6' is almost constant within a given temperature range. It can also be seen that applying grease to the gears reduces the friction coefficient compared to the same gear pairs without grease.

[0069]

[0070] In the method of deriving the friction coefficient of a thermoplastic resin gear according to this embodiment, the friction coefficient of the resin gear can be derived as described above. The friction coefficient of the resin gear derived in this embodiment takes into account the actual sliding behavior of the gears, and therefore is equal to or close to the actual friction coefficient of the gears.

[0071] <Method for Predicting Root Temperature of Thermoplastic Resin Gear> The method for predicting the root temperature of a thermoplastic resin gear of this embodiment has three forms, form 1 to form 3. In all of the forms, the root temperature of the thermoplastic resin gear is predicted by substituting the actual contact ratio of the thermoplastic resin gear and the friction coefficient μ of the thermoplastic resin gear into either of the following formulas 4 and 5 to 7.

[0072] [In formula 4, θＦｕβ is the root temperature (℃), θ ０ is the ambient temperature (°C), P is the nominal output (2π x rotation speed x torque) (W), μ is the friction coefficient of the thermoplastic resin gear, k θ，Ｆｕβ is the heat storage factor, and is the heat transfer coefficient (K·(m / s)) defined in VDI 2736 Blatt 2 for a pair of gears, at least one of which is made of thermoplastic resin. ｃ ・mm １．７５ / W), b is the tooth width (mm), m ｎ is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), v is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), ｔ ｃ The term is the heat dissipation factor, v ｔ is the pitch circumference speed (m / s), c is a constant between 0.05 and 0.70, R λ，Ｇ is the housing thermal resistance (K m 2 / W), A Ｇ is the housing heat dissipation area (m ２ ), ED is the relative meshing time per 10 minutes, H ｖ indicates the loss factor calculated by the following formulas 5 to 7 according to the value of the actual contact ratio.]

[0073] [In formulas 5 to 7, ε α is the front contact ratio, u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth in the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in the pair of gears, ε １ is the approach contact ratio, ε ２ indicates the far contact ratio.]

[0074] In formula 4, H ｖ : The loss factor defined in VDI 2736 Blatt 2 is the face-to-face contact ratio ε α The transverse contact ratio ε α is 1<ε α < 2, apply Equation 5, and α is 2<ε α < 3, apply Equation 6, andα is 3<ε α If <4, then apply Equation 7.

[0075] In Formulas 5 to 7, z １ , z ２ , ε １ , ε ２ is z in Formulas 1 to 3 １ , z ２ , ε １ , ε ２ This is the same as above, and the explanations given in equations 1 to 3 apply as is.

[0076] In the first embodiment, the actual contact ratio of the thermoplastic resin gear is calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear according to the present embodiment, and the friction coefficient μ of the thermoplastic resin gear is calculated by any method (excluding the method for deriving a friction coefficient specified in the method for deriving a friction coefficient of a thermoplastic resin gear according to the present embodiment). In the second embodiment, the actual contact ratio of the thermoplastic resin gear is calculated by the contact ratio not taking deformation into account, and the friction coefficient μ of the thermoplastic resin gear is calculated by the method for deriving a friction coefficient of a thermoplastic resin gear according to the present embodiment. In the third embodiment, the actual contact ratio of the thermoplastic resin gear is calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear according to the present embodiment, and the friction coefficient μ of the thermoplastic resin gear is calculated by the method for deriving a friction coefficient of a thermoplastic resin gear according to the present embodiment.

[0077] In the first embodiment, the coefficient of friction μ of a thermoplastic resin gear is calculated by any measurement method, including the pin-on-disk method, ring-on-ring method, ball-on-disk method, etc., except for the friction coefficient measurement method specified in the method for deriving the friction coefficient of a thermoplastic resin gear of this embodiment described above. In the first embodiment, the actual contact ratio of a thermoplastic resin gear is calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear of this embodiment described above, which is a contact ratio that takes into account the temperature and deformation of the teeth (actual contact ratio), and therefore the accuracy of predicting the root temperature of a resin gear can be improved.

[0078] In the second embodiment, the contact ratio of the thermoplastic resin gears is a contact ratio that takes deformation into account. In the second embodiment, the friction coefficient μ derived by the method for deriving the friction coefficient of a thermoplastic resin gear according to the present embodiment is used, and therefore the friction coefficient is the same as or close to the actual friction coefficient of the gears, improving the accuracy of predicting the root temperature of the resin gears.

[0079] In the third embodiment, the actual contact ratio and the friction coefficient μ of the thermoplastic resin gear are calculated or derived in the above-described embodiment. That is, the "actual contact ratio" and "friction coefficient μ" of the resin gear according to the measurement conditions are substituted into the tooth root temperature prediction formula shown in Equation 4. Therefore, the third embodiment provides the highest accuracy in predicting the tooth root temperature of a resin gear.

[0080] Figure 14 shows the relationship between the predicted and measured temperatures at the root of a resin gear to which the third embodiment is applied. Each plot in Figure 14 shows the relationship between the predicted and measured temperatures at the root when the same gear pairs as those described above for gear pairs 1 to 7 are used. The dashed line indicates the case where the predicted and measured temperatures are equal. As shown in Figure 14, the predicted and measured temperatures for the root temperatures are almost identical for all gear pairs.

[0081] Next, we will explain an example of evaluating the dedendum temperature prediction for the gear pairs 1', 3', 5', and 6' in which grease is applied to the gears. Figure 15 shows the relationship between the predicted and measured dedendum temperatures of resin gears to which the third embodiment is applied, similar to Figure 14 above. As shown in Figure 15, in all examples, the predicted and measured dedendum temperatures are almost identical. This means that it is possible to predict the dedendum temperature of gears even when grease is applied to the gears.

[0082] FIG. 16 shows the relationship between the predicted and measured temperatures at the roots of gear pairs 8 to 11. Gear pairs 8 to 11 are all combinations of plastic gears and metal gears. Gear pair 8 has been described above, but will be described again below. Gear pairs 9 to 11 are the following combinations. Gear pair 8: Drive side: Metal gear 1, Driven side: Thermoplastic resin 1 Gear pair 9: Drive side: Metal gear 2, Driven side: Thermoplastic resin 1 Gear pair 10: Drive side: Metal gear 3, Driven side: Thermoplastic resin 1 Gear pair 11: Drive side: Metal gear 4, Driven side: Thermoplastic resin 1 Metal gear 1: Kyoiku Gears Co., Ltd., SG1S 18L-1010 (spur gear (module 1.0 mm, number of teeth 18, face width 10 mm, pressure angle 20°, addendum modification coefficient 0)) Metal gear 2: Kyoiku Gears Co., Ltd., SG1S 54B-1012 (spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum modification coefficient 0)) Metal gear 3: Kyoiku Gears Co., Ltd., SG1S 35B-1010 (spur gear (module 1.0 mm, number of teeth 35, face width 10 mm, pressure angle 20°, addendum modification coefficient 0)) Metal gear 4: SG1S 14L-1008 (spur gear (module 1.0 mm, number of teeth 14, face width 10 mm, pressure angle 20°, addendum modification coefficient 0) manufactured by Kyoiku Gears Co., Ltd.) Metal gear 2 is machined to have a keyway. Metal gear 3 is machined to have a keyway and an inner diameter of 12 mm. Figure 16 shows that even when a plastic gear and a metal gear are combined, the predicted and measured temperatures for the root temperature are nearly identical.

[0083] As described above, for all of gear pairs 1 to 11, the predicted and measured root temperatures are almost identical. This shows that the root temperatures can be accurately predicted by using the friction coefficient of the resin gear derived in this embodiment, not only for the same thermoplastic resins, but also for combinations of different thermoplastic resins, combinations of thermoplastic resins filled with fibrous or other fillers, and combinations of thermoplastic resin and metal.

[0084] On the other hand, Figure 17 shows the relationship between the predicted temperature (solid line) and the actually measured temperature (dashed line) of the tooth base of a resin gear when the second embodiment is applied. A slight discrepancy is observed between the predicted temperature and the actually measured temperature. From the results of Figures 14 to 17, it can be seen that the third embodiment shown in Figures 14 to 16 has higher prediction accuracy.

[0085] In the case of a combination of plastic gears, in order to further improve the prediction accuracy of the tooth root temperature of the plastic gears, the number of teeth z in Equation 4 should be the total number of teeth of the pair of gears, c in Equation 4 should be set to 0.10 to 0.60, and k in Equation 4 should be set to θ，Ｆｕβ is set to (A·ln(b)+B) to (A·ln(b)+C) (where b is the face width (mm), A is 1130 to 3610, B is -1.782A+3286, and C is -1.728A+5291). In order to further improve the prediction accuracy of the tooth root temperature, it is preferable that A is set to 1770 to 2890, B is set to -1.907A+3943, and C is set to -2.154A+5647. On the other hand, in the case of a combination of a resin gear and a metal gear, the number of teeth z in the above formula 4 should be set to the total number of teeth of the pair of gears (however, if the entire circumferences do not mesh, only the number of teeth in the meshing range is counted), c in the above formula 4 should be set to 0.10 to 0.60, and k θ，Ｆｕβ is preferably set to (A ln(b) + B) to (A ln(b) + C) (where b is the tooth width (mm), A is 100 to 2000, B is -2.284A + 1424, and C is -2.316A + 3637), and to further improve the accuracy of tooth root temperature prediction, it is preferable that A is 550 to 1550, B is -2.300A + 1981, and C is -2.300A + 3111. Each of these is explained below.

[0086] FIG. 18 shows the third embodiment, in which the number of teeth z in Equation 4 is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing range is counted) (i.e., z = z １ +z ２) shows the relationship between the predicted temperature at the base of the tooth of the resin gear and the actually measured temperature. In addition, in FIG. 18, four types of pairs of gears are shown (represented by plots of black circles, squares, black triangles, and white triangles), and each pair of gears has a different number of teeth. The plots of black circles show the z １ = 54, z ２ = 54, and the square plot is z １ = 23, z ２ = 23, and the plot shown by the black triangles is z １ = 23, z ２ = 54, and the plot shown by the white triangles is z １ = 14, z ２ As shown in Fig. 18, it can be seen that the predicted temperature and the actually measured temperature of the root temperature of each pair of gears are almost the same. On the other hand, Fig. 19 shows that in the first form, when the number of teeth z in Equation 4 is set to the number of teeth z of the gear with the fewer number of teeth, １ (i.e., z = z １ ) shows the relationship between the predicted and measured temperatures at the root of a resin gear. The plots of black circles, squares, black triangles, and white triangles in Figure 19 are the same as those in Figure 18. That is, the same pair of gears are measured in Figures 18 and 19. As can be seen from Figure 19, there is a partial discrepancy between the predicted and measured temperatures at the root. Therefore, when the number of teeth z in Equation 4 is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth within the meshing range is counted), the prediction accuracy of the root temperature improves. This is thought to be because the area through which heat is transferred to the root can be accurately reflected even for combinations with different numbers of teeth. For example, doubling the number of teeth (however, if the entire circumference does not mesh, only the number of teeth within the meshing range is counted) doubles the area through which heat flows, and the temperature rise is halved. However, if the number of teeth z is used for only one of the gears, such a temperature rise is not reflected.

[0087] On the other hand, by optimizing the heat dissipation factor, which indicates the degree of influence of heat dissipation in Equation 4, it is possible to make the predicted and measured values ​​of the tooth root temperature almost coincide with each other over the entire temperature range, regardless of the rotation speed. ｔ ｃ The constant c is 0.05 to 0.70, but in order to optimize the heat dissipation factor and improve the prediction accuracy of the tooth root temperature, it is preferably set to 0.10 to 0.60, and more preferably 0.15 to 0.55.

[0088] Furthermore, by optimizing the heat storage factor, which indicates the degree of influence of heat storage, it is possible to make the predicted value of the tooth root temperature almost coincide with the actual measured value. Regarding the influence of heat storage due to the tooth width of the gear, the larger the tooth width, the greater the temperature rise due to heat storage. The heat storage factor is expressed as k in Equation 4. θ，Ｆｕβ By making this a function of the face width b, the heat accumulation factor can be optimized. In this embodiment, when resin gears are combined, the heat accumulation factor due to the difference in face width is taken into consideration and the function k θ，Ｆｕβ is preferably (A·ln(b)+B) to (A·ln(b)+C) (where b is the face width (mm), A is 1130 to 3610, B is -1.782A+3286, and C is -1.728A+5291), and to further improve the accuracy of tooth root temperature prediction, it is more preferable that A is 1770 to 2890, B is -1.907A+3943, and C is -2.154A+5647. On the other hand, when a resin gear and a metal gear are combined, k in formula 4 θ，Ｆｕβ is preferably set to (A·ln(b)+B) to (A·ln(b)+C) (where b is the tooth width (mm), A is 100 to 2000, B is -2.284A+1424, and C is -2.316A+3637), and in order to further improve the accuracy of tooth root temperature prediction, it is preferable that A is 550 to 1550, B is -2.300A+1981, and C is -2.300A+3111. By setting them in this way, it is possible to improve the accuracy of tooth root temperature prediction even when the tooth width is changed.

[0089] Fig. 20 shows the predicted and measured temperatures of the tooth root temperature when the heat storage factor is optimized in the third embodiment. θ，Ｆｕβ In this case, k θ，Ｆｕβ = 475b + 1417 (where b is the face width (mm)). In Figure 20, the plots indicated by black circles, squares, black triangles, and open triangles represent the cases of face widths of 3 mm, 5 mm, 7.5 mm, and 10 mm, respectively. It can be seen that in all cases, the predicted and measured temperatures closely match. Meanwhile, Figure 21 shows the predicted and measured root temperatures for the third embodiment when the heat storage factor is not optimized. Figure 21 differs from Figure 20 only in that the heat storage factor is not optimized; the resin gears measured are the same, and are plotted in the same way as Figure 20. As can be seen from Figure 21, there is some discrepancy between the predicted and measured root temperatures. From the above, it can be seen that by optimizing the heat storage factor, it is possible to make the predicted and measured root temperatures closely match, even when the gear face widths are different.

[0090] <Method for Predicting Life of Thermoplastic Resin Gear> The method for predicting life of a thermoplastic resin gear of this embodiment includes step 9 of preparing an S-N curve for the thermoplastic resin gear for each tooth temperature of the thermoplastic resin gear. Then, the life of the thermoplastic resin gear is predicted based on the S-N curve corresponding to the root temperature obtained by the method for predicting root temperature of a thermoplastic resin gear of this embodiment described above.

[0091] In the method for predicting the life of a thermoplastic resin gear according to this embodiment, an S-N curve for the resin gear is prepared in advance for each temperature of the gear teeth (Step 9). Then, the life is predicted based on the S-N curve corresponding to the root temperature obtained by the method for predicting the root temperature of a thermoplastic resin gear according to this embodiment. Because the root temperature obtained by this method for predicting the root temperature is highly accurate, the accuracy of the life prediction can also be improved.

[0092] In step 9, an S-N curve for the thermoplastic resin gear is prepared for each temperature of the gear teeth. The S-N curve, also known as a fatigue life curve, shows the relationship between the tooth root bending stress of a resin gear and its life (the number of meshings until fracture). More specifically, the S-N curve is used to determine the fatigue strength of a resin gear through fatigue testing. It is a logarithmic representation of the number of stress cycles applied to a number of resin gears until fracture at each constant tooth root bending stress. The graph is plotted with the number of stress cycles on the horizontal axis and the logarithm of the stress amplitude on the vertical axis, resulting in a downward-sloping curve. Then, in step 9, an S-N curve is prepared for each temperature of the gear teeth. For example, an S-N curve is prepared for each temperature, such as 30°C, 40°C, 50°C, etc.

[0093] In this embodiment, the tooth root temperature obtained by the method for predicting the tooth root temperature of a thermoplastic resin gear according to the present embodiment is used. An S-N curve corresponding to the obtained tooth root temperature is selected, but if there is no S-N curve for a temperature that matches the tooth root temperature, the life of the resin gear can be predicted based on an estimated S-N curve at the tooth root temperature obtained by extrapolation or interpolation.

[0094] 10 20 Gear 12 22 Teeth 30 Testing machine 32 Shaft 34 Load application lever

Claims

1. A method for calculating an actual contact ratio of a pair of gears, at least one of which is made of a thermoplastic resin, comprising the steps of: Step 1: rotating a pair of gears, at least one of which is made of a thermoplastic resin, at a predetermined rotation speed while meshing with each other, and measuring a temperature distribution of the pair of gears; Step 2: creating a structural analysis model A having the same shape as the pair of gears by CAE, inputting the temperatures obtained from the temperature distribution of the pair of gears measured in step 1 into the structural analysis model A, and calculating the temperature distribution of the structural analysis model A by CAE structural analysis; Step 3: preparing temperature dependency data of elastic modulus a of the thermoplastic resin constituting the pair of gears; Step 4, in which a location where a maximum tensile strain occurs in a strain distribution at the base of the meshed teeth when the pair of gears are meshed is calculated by CAE structural analysis from the temperature distribution of the structural analysis model A calculated in Step 2 and the temperature dependency data of the elastic modulus a prepared in Step 3, and the elastic modulus a or the elastic modulus obtained in Step 4b below is corrected based on the strain rate dependency of the elastic modulus of the gears in the structural analysis model A calculated from the location where the maximum tensile strain occurs in the strain distribution; and Step 4b, in which an actual deformation amount of the pair of gears is measured, an amount of deformation by CAE structural analysis is calculated using a CAE structural analysis model B having the same shape as the pair of gears and created to reflect the actual deformation amount, and then a ratio X between the actual deformation amount and the deformation amount by CAE structural analysis is obtained, and the elastic modulus a or the elastic modulus obtained in Step 4a is corrected based on the ratio X. Step 5: calculating a contact stress distribution when a predetermined torque is applied to the driving gear of the pair of gears by CAE structural analysis using the corrected elastic modulus a′ obtained in step 4; A step 6 of calculating an angle difference between a meshing start point and a meshing end point of the pair of gears based on the contact stress distribution calculated in the step 5; and Step 7: calculating an actual contact ratio of the pair of gears by dividing the angle difference calculated in step 6 by an angle (360° / number of teeth) corresponding to the circular pitch of the pair of gears; A method for calculating an actual contact ratio of a thermoplastic resin gear, comprising:

2. 13. A method for deriving the friction coefficient of thermoplastic resin gears, comprising a step 8 of measuring a transmission efficiency η of torque transmitted from a drive gear to a driven gear of a pair of gears, and deriving the friction coefficient of the thermoplastic resin gears from the actual contact ratio calculated by the method for calculating an actual contact ratio of thermoplastic resin gears according to claim 1 and the torque transmission efficiency η measured in step 8, using a gear transmission loss equation.

3. 3. The method for deriving the friction coefficient of a thermoplastic resin gear according to claim 2, further comprising the step of substituting the actual contact ratio into any one of the following formulas 1 to 3 to derive the friction coefficient of the thermoplastic resin gear: [0010] [In formulas 1 to 3, ε α is the contact ratio, η is the torque transmission efficiency, μ is the friction coefficient of the thermoplastic resin gear, and u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth of the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in a pair of gears, ε １ is the approach contact ratio, ε ２ indicates the contact ratio.]

4. A method for predicting a root temperature of a thermoplastic resin gear, comprising substituting an actual contact ratio calculated by the method for calculating an actual contact ratio of a thermoplastic resin gear as set forth in claim 1 and a friction coefficient μ derived by any derivation method (excluding the method for derivation of a friction coefficient of a thermoplastic resin gear as set forth in claim 2) into the following formula 4 and any of the following formulas 5 to 7 to predict a root temperature of the thermoplastic resin gear. [0025] [In formula 4, θ Ｆｕβ is the tooth root temperature (℃), θ ０ is the environmental temperature (℃), P is the nominal output (2π x rotation speed x torque) (W), μ is the friction coefficient of the thermoplastic resin gear, k θ，Ｆｕβ is the heat storage factor, and is the heat transfer coefficient (K·(m / s)) defined in VDI 2736 Blatt 2 for a pair of gears, at least one of which is made of thermoplastic resin. ｃ ・mm １．７５ / W), b is the tooth width (mm), m ｎ is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), and v is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), ｔ ｃ The term is the heat dissipation factor, v ｔ is the pitch circumference speed (m / s), c is a constant between 0.05 and 0.70, R λ，Ｇ is the housing thermal resistance (K m 2 / W), A Ｇ is the housing heat dissipation area (m ２ ), ED is the relative meshing time per 10 minutes, H ｖ indicates a loss factor calculated by the following formulas 5 to 7 according to the actual contact ratio. [0030] [In formulas 5 to 7, ε α is the front contact ratio, u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth of the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in a pair of gears, ε １ is the approach contact ratio, ε ２ indicates the contact ratio.]

5. A method for predicting the root temperature of a thermoplastic resin gear, comprising substituting the contact ratio not taking deformation into consideration and the friction coefficient μ calculated by the method for deriving a friction coefficient of a thermoplastic resin gear as set forth in claim 2 into the following equations 4 and 5 to 7. [0045] [In formula 4, θ Ｆｕβ is the tooth root temperature (℃), θ ０ is the environmental temperature (℃), P is the nominal output (2π x rotation speed x torque) (W), μ is the friction coefficient of the thermoplastic resin gear, k θ，Ｆｕβ is the heat storage factor, and is the heat transfer coefficient (K·(m / s)) defined in VDI 2736 Blatt 2 for a pair of gears, at least one of which is made of thermoplastic resin. ｃ ・mm １．７５ / W), b is the tooth width (mm), m ｎ is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), v is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), ｔ ｃ The term is the heat dissipation factor, v ｔ is the pitch circumference speed (m / s), c is a constant between 0.05 and 0.70, R λ，Ｇ is the housing thermal resistance (K m 2 / W), A Ｇ is the housing heat dissipation area (m ２ ), ED is the relative meshing time per 10 minutes, H ｖ indicates a loss factor calculated by the following formulas 5 to 7 according to the actual contact ratio. [0050] [In formulas 5 to 7, ε α is the front contact ratio, u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth of the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in a pair of gears, ε １ is the approach contact ratio, ε ２ indicates the contact ratio.]

6. A method for predicting a root temperature of a thermoplastic resin gear, comprising substituting the actual contact ratio calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear according to claim 1 and the friction coefficient μ calculated by the method for deriving a friction coefficient of a thermoplastic resin gear according to claim 2 into the following equations 4 and 5 to 7. [006] [In formula 4, θ Ｆｕβ is the tooth root temperature (℃), θ ０ is the environmental temperature (℃), P is the nominal output (2π x rotation speed x torque) (W), μ is the friction coefficient of the thermoplastic resin gear, k θ，Ｆｕβ is the heat storage factor, and is the heat transfer coefficient (K·(m / s)) defined in VDI 2736 Blatt 2 for a pair of gears, at least one of which is made of thermoplastic resin. ｃ ・mm １．７５ / W), b is the tooth width (mm), m ｎ is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), v is the normal module (mm), z is the total number of teeth of a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing area is counted), ｔ ｃ The term is the heat dissipation factor, v ｔ is the pitch circumference speed (m / s), c is a constant between 0.05 and 0.70, R λ，Ｇ is the housing thermal resistance (K m 2 / W), A Ｇ is the housing heat dissipation area (m ２ ), ED is the relative meshing time per 10 minutes, H ｖ indicates a loss factor calculated by the following formulas 5 to 7 according to the actual contact ratio. [0070] [In formulas 5 to 7, ε α is the front contact ratio, u is the gear ratio z ２ / z １ , β b is the twist angle of the base cylinder, z １ is the number of teeth of the gear with the fewer teeth of the pair of gears, z ２ is the number of teeth of the gear with the larger number of teeth in a pair of gears, ε １ is the approach contact ratio, ε ２ indicates the contact ratio.]

7. In the case where the pair of gears is a combination of thermoplastic resin gears, the number of teeth z in the formula 4 is the total number of teeth of the pair of gears (however, when the entire circumference does not mesh, only the number of teeth in the meshing range is counted), c in the formula 4 is 0.10 to 0.60, and k in the formula 4 is θ，Ｆｕβ The method for predicting the root temperature of a thermoplastic resin gear according to any one of claims 4 to 6, wherein at least one of the following is carried out: (A x ln(b) + B) to (A x ln(b) + C) (where b is the face width (mm), A is 1130 to 3610, B is -1.782A + 3286, and C is -1.728A + 5291).

8. In the case where the pair of gears is a combination of a thermoplastic resin gear and a metal gear, the number of teeth z in the formula 4 is the total number of teeth of the pair of gears (however, when the entire circumference does not mesh, only the number of teeth in the meshing range is counted), c in the formula 4 is 0.10 to 0.60, and k in the formula 4 is θ，Ｆｕβ The method for predicting the root temperature of a thermoplastic resin gear according to any one of claims 4 to 6, wherein at least one of the following is carried out: (A · ln(b) + B) to (A · ln(b) + C) (where b is the face width (mm), A is 100 to 2000, B is -2.284A + 1424, and C is -2.316A + 3637).

9. Step 9 includes preparing an S-N curve for a thermoplastic gear for each temperature of the teeth of the thermoplastic gear; A method for predicting a life of a thermoplastic resin gear, comprising: predicting a life of the thermoplastic resin gear on the basis of the S-N curve corresponding to the root temperature obtained by the method for predicting a root temperature of a thermoplastic resin gear according to any one of claims 4 to 6.

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