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

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

[Technical Field]

[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. [Background technology]

[0002] Gears made from thermoplastic resins such as polyamide resins or 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, so they are being 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 geometry, 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, ring-on-ring, and ball-on-disk methods 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 has a significant effect on 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. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2017-62017 Summary of the Invention [Problem to be solved by the invention]

[0005] The present invention has been made in consideration of the above-mentioned problems of the conventional technology, and its object 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. [Means for solving the problem]

[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 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 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 constituting 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 the strain distribution at the root 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 corrects said elastic modulus a or the elastic modulus obtained in Step 4a using said 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; Step 6: calculating an angle difference between the meshing start point and the meshing end point of the pair of gears based on the contact stress distribution calculated in step 5; and Step 7: calculating the 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 the actual contact ratio of a thermoplastic resin gear, including:

[0007] (2) A method for deriving the friction coefficient of thermoplastic resin gears, comprising 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 method for calculating the actual contact ratio of thermoplastic resin gears described in (1) above and the torque transmission efficiency η measured in step 8.

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

[0009]

number

[0010] (4) 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 actual contact ratio calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear described in (1) above and the friction coefficient μ derived by any derivation method (excluding the method for deriving the friction coefficient of a thermoplastic resin gear described in (2) above) into the following formula 4 and any of the following formulas 5 to 7:

[0011]

number

[0012]

number

[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 the friction coefficient of a thermoplastic resin gear described in (2) above into the following equations 4 and 5 to 7:

[0014]

number

[0015]

number

[0016] (6) 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 actual contact ratio calculated by the method for calculating the actual contact ratio of a thermoplastic resin gear described in (1) above and the friction coefficient μ derived by the method for deriving the friction coefficient of a thermoplastic resin gear described in (2) above into the following equations 4 and 5 to 7:

[0017]

number

[0018]

number

[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 The method for predicting the root temperature of a gear made of thermoplastic resin according to any one of (4) to (6), wherein at least one of the following is carried out: (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,FuβThe 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 step 9 includes preparing an SN curve of a thermoplastic resin gear for each temperature of the teeth of the thermoplastic resin gear; A method for predicting a life of a thermoplastic resin gear, comprising predicting a life of the thermoplastic resin gear based on the SN 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). [Effects of the Invention]

[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. [Brief explanation of the drawings]

[0023] [Figure 1] FIG. 10 is a diagram illustrating a state in which a pair of gears are meshed, and is used to explain the contact ratio. [Figure 2] 1 is a graph showing the relationship between temperature distribution and distance in the tooth width direction of a gear. [Figure 3] FIG. 2 is a top view showing a CAE analysis model A of a plastic gear. [Figure 4] FIG. 10 is a diagram showing the tooth root strain distribution in CAE analysis. [Figure 5] 1 is a graph showing the relationship between gear division number and tooth root strain in CAE analysis. [Figure 6] 1 is a graph showing the relationship between the elastic modulus and the strain rate of a tensile test piece. [Figure 7]1A and 1B are top and front views, respectively, of a device for measuring the deformation of gear teeth. [Figure 8] 1 is a graph showing the relationship (measured values ​​and CAE analysis values) of the rotation angle of the rotating gear with respect to the load (torque) on the gear. [Figure 9] 1 is a graph showing the ratio of the actual measurement value to the CAE analysis value regarding the relationship between the load (torque) on the gear and the rotation angle of the rotating gear. [Figure 10] 10 is a graph showing the rotation angle of the rotating gear relative to the load (torque) on the gear with the corrected elastic modulus. [Figure 11] 10 is a graph showing the relationship between temperature and contact ratio. [Figure 12] 10 is a graph showing the relationship between the maximum tooth temperature and the coefficient of friction for gear pairs 1 to 8 (without grease). [Figure 13] 1 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). [Figure 14] 10 is a graph showing the relationship between predicted temperatures and actually measured temperatures for gear pairs 1 to 7 (without grease) according to the tooth root temperature prediction method of the present embodiment. [Figure 15] 10 is a graph showing the relationship between predicted temperatures and actually measured temperatures for gear pairs 1′, 3′, 5′, and 6′ (with grease) according to the tooth root temperature prediction method of the present embodiment. [Figure 16] 10 is a graph showing the relationship between predicted temperatures and actually measured temperatures for gear pairs 8 to 11 (without grease) according to the tooth root temperature prediction method of the present embodiment. [Figure 17] 1 is a graph showing the relationship between the predicted temperature and the actually measured temperature according to the tooth root temperature prediction method of the present embodiment. [Figure 18] 1 is a graph showing the relationship between the predicted temperature and the actually measured temperature according to the tooth root temperature prediction method of the present embodiment. [Figure 19] 1 is a graph showing the relationship between the predicted temperature and the actually measured temperature according to the tooth root temperature prediction method of the present embodiment. [Figure 20]1 is a graph showing the relationship between the predicted temperature and the actually measured temperature according to the tooth root temperature prediction method of the present embodiment. [Figure 21] 1 is a graph showing the relationship between the predicted temperature and the actually measured temperature according to the tooth root temperature prediction method of the present embodiment. [Figure 22] FIG. 1 shows (a) a cross-sectional view and (b) a side view of a resin gear with 54 teeth used in various evaluations. [Figure 23] FIG. 1 shows (a) a cross-sectional view and (b) a side view of a resin gear with 23 teeth used in various evaluations. [Figure 24] FIG. 1 shows (a) a cross-sectional view and (b) a side view of a resin gear with 14 teeth used in various evaluations. [Figure 25] FIG. 1 is a side view of a metal gear with 18 teeth used in various evaluations. [Figure 26] FIG. 1 is a side view of a metal gear with 14 teeth used in various evaluations. [Figure 27] FIG. 1 is a cross-sectional view of a metal gear with 35 teeth used in various evaluations. [Figure 28] This is a cross-sectional view of a metal gear with 54 teeth used in various evaluations. DETAILED DESCRIPTION OF THE INVENTION

[0024] <Calculation method for 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 a thermoplastic resin gear, and includes the following steps 1 to 7. Step 1: A pair of gears, at least one of which is made of thermoplastic resin, are 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 structural analysis model A, and the temperature distribution of structural analysis model A is calculated using CAE structural analysis. Step 3: Prepare data on the temperature dependence of the elastic modulus a of the thermoplastic resin that constitutes the pair of gears. Step 4: Using the temperature distribution in structural analysis model A calculated in Step 2 and the temperature dependency data on elastic modulus a prepared in Step 3, the location of maximum tensile strain in the strain distribution at the base of the meshing teeth when the pair of gears are meshed 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 gear elastic modulus in structural analysis model A calculated from the location of maximum tensile strain in the strain distribution (Step 4a). The actual deformation of the pair of gears is measured, and a CAE structural analysis model B with the same shape as the pair of gears is created to reflect the actual deformation. Then, the 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. These steps are performed in any order. 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: Based on the contact stress distribution calculated in Step 5, the angle difference between the meshing start point and meshing end point of the pair of gears is calculated. Step 7: The angular difference calculated in Step 6 is divided by the angle equivalent to the circular pitch (360° / number of teeth) to calculate the actual contact ratio of the pair of gears.

[0025] First, the "actual contact ratio" will be explained with reference to FIG. 1. FIG. 1 shows the meshed state between tooth 12 of gear 10 and tooth 22 of gear 20 (see FIG. 1(D)), and 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 rotate 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, when gears are made of plastic, 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 invention, which concerns plastic gears, the contact ratio that takes deformation into account is not used, but rather the "actual contact ratio" that takes into account tooth deflection specific to thermoplastic resins is calculated. Steps 1 to 7 for calculating the actual contact ratio will be described below. In the following description, various evaluation results are shown, and the evaluations were performed using the following measuring instruments. Actual temperature distribution measurement: Thermovision CPA-7800 thermography, manufactured by Chino Corporation Structural analysis software: ADVENTURECluster 2020, manufactured by Allied Engineering Co., Ltd. Actual deformation measurement: Strength testing machine (Tensilon UTA-50KN) Torque transmission efficiency measurement: Small gear fatigue testing machine (Ono Sokki Co., Ltd.) Gear molding shape Shape of a gear molded with 54 teeth (see Figure 22) Shape of a gear molded with 23 teeth (see Figure 23) Shape of a gear molded with 14 teeth (see Figure 24) Metal gear of gear 18 (see Figure 25) Metal gear with 14 teeth (see Figure 26) A metal gear with 35 teeth (see Figure 27) A metal gear with 54 teeth (see Figure 28) 22 to 28 indicate the dimensions (mm) of each element. Metal gear 30 shown in Figures 25 and 26 has a shape in which gear 34 is connected to 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, thermography, or 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 in 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 structural analysis model A, and the temperature distribution of structural analysis model A is calculated using CAE structural analysis. Here, it is possible 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 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 CAE structural analysis can be, for example, structural analysis model A shown in Figure 3.

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

[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 but reflects the actual deformation, 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. In other words, either step 4a or step 4b can be performed first. Steps 4a and 4b are described below.

[0032] (Step 4a) In short, step 4a is a step of correcting the elastic modulus a prepared in step 3 (or the corrected elastic modulus obtained by correcting the elastic modulus a in step 4b) taking into account 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 gear 10 and the driven 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 gear 10 and the driven gear 20 are shown below. Gear shape (drive side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum shift coefficient 0) Gear shape (driven side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum shift coefficient 0) The strain is greatest within circle 24 in FIG. 4, that is, 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 that is in contact with the tooth of the driving-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, and in resin materials, as the strain rate (for example, tensile speed) increases, 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. By performing a deformation analysis using CAE analysis using the calculated data on the temperature dependence of the elastic modulus, the strain rate at the location where maximum tensile strain occurs in the strain distribution at the base of the meshing teeth when the plastic gears are actually meshed is calculated. Next, the strain rate of the elastic modulus is calculated, for example, as follows. The following example uses drive and driven gears with the following shapes, with a rotation speed of 100 rpm and 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 shift coefficient 0) Gear shape (driven side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum shift coefficient 0) a) Define the time (s / section) and angular velocity (rad / s) per section in the CAE analysis (e.g., 0.02 s / section and 0.175 rad / s). b) CAE analysis: Convert into gear rotation angle per division (° / division). c) The rotation angle (°) of the gear per division obtained from the CAE analysis in b) is multiplied by the number of divisions 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 to time (s). e) Strain rate ( / s) = strain / time required for analysis (s) = (0.02 (maximum strain) - 0.005 (start of strain)) / 0.008 s = 1.86 ( / s). In other words, by calculating the time from the point where strain occurs to the point where maximum strain occurs and the time it takes to reach that point, the strain rate of the elastic modulus is calculated to be 1.86 ( / s).

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

[0037] Next, the elastic modulus for the resin gear CAE analysis is corrected to match the actual measured value (elastic modulus obtained by tensile testing using an ISO tensile test piece). The measured values ​​of the elastic modulus are shown in the graph in Figure 6.

[0038] From Figure 6, the elastic modulus at a strain rate of 1.86 ( / s) is approximately 2800 MPa. The ratio to the standard elastic modulus of 1940 MPa (standard 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 plastic gears using CAE analysis can be found by multiplying the standard elastic modulus by 1.45. In other words, it is possible to correct the elastic modulus that occurs due to differences in rotation speed using strain rate. It is desirable to use data on the temperature dependency of the elastic modulus according to the actual gear conditions (strain rate). However, 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 temperature dependency of the elastic modulus obtained in advance.

[0039] (Step 4b) Step 4b is, in short, 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. At this time, because gear 10 is meshed with fixed gear 20, rotation is restricted, and the teeth of gears 10 and 20 are slightly displaced. 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 the shaft rotation angle. In other words, the rotation angle of the gear is calculated indirectly from the deformation amount of the teeth.

[0041] Here, the equipment and conditions for measuring the actual deformation amount of the gear are shown below, but these are only examples and the present embodiment is not limited to these. Testing machine: A&D Co., Ltd. universal testing machine UTA-50KN-RTC Gear material: Polyplastics Co., Ltd., Duracon (registered trademark), POM M90-44 (unfilled) Gear shape (rotating side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum shift coefficient 0) Gear shape (fixed side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum shift coefficient 0) Torque: 1, 3, 5, 7, 9 N·m (can be set to the allowable stress (MPa) depending on the material) Test speed at the point of force: Can be set appropriately taking into consideration 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 in load transmission due to stick-slip phenomenon (grease or other lubricants are also acceptable) Ambient temperature: 23℃ Radial play j r :0.2mm

[0042] Next, CAE analysis model B is created using CAE, which reflects the gear shape from the actual measurement test. Then, deformation analysis is used to calculate the shaft rotation angle from the tooth displacement amount. In CAE deformation analysis, 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 also 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 apparent deformation amount match the measured value by correcting the elastic modulus calculated by CAE analysis in a direction that decreases it.

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

[0045] [Table 1]

[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 valid.

[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] [Table 2]

[0049] The elastic modulus a' used in step 5 (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. As mentioned above, step 4a and step 4b may be performed in any order, and either may 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 a deformation analysis (contact analysis) is performed to calculate the contact stress distribution when a specified torque is applied to the drive gear. A mesh model similar to structural analysis model A shown in Figure 3 can be used for the CAE structural analysis.

[0052] [Step 6] Step 6 is a step of calculating the angular difference between the meshing start point and the meshing end point of the 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 from the start point of meshing to the end point of meshing" (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). The angle difference (θ 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 plastic 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 for deriving the friction coefficient of thermoplastic resin gears> The method for 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 the gear transmission loss equation from the actual contact ratio calculated by the above-mentioned method for 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 described above into one of the following formulas 1 to 3.

[0060]

number

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

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

[0063] In formulas 1 to 3, z1 represents the number of teeth of the gear with the fewer number of teeth of the pair of gears, and z2 represents the number of teeth of the gear with the greater 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 of this embodiment, and the friction coefficient μ calculated using Niemann's equation (Equations 2 and 3 above) based on the actual contact ratio, along with 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 also shown below. Gear shape (drive side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum shift coefficient 0) Gear shape (driven side): Spur gear (module 1.0 mm, number of teeth 54, face width 10 mm, pressure angle 20°, addendum shift coefficient 0) The gear pairs 1 to 8 differ in the materials used for the gears 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 the gear pair 8, the metal gear 1 used on the drive side is as follows. 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 shift coefficient 0))

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

[0066] FIG. 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). It can be seen from FIG. 11 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. FIG. 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 the Niemann equation based on the contact ratio taking deformation into account. The dashed lines also show the friction coefficient μ (see Table 3) calculated using the Niemann equation (the above-mentioned 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] [Table 3]

[0068] Next, we will explain examples of gear pairs 1, 3, 5, and 6 in which grease was applied to the gears and evaluated (gear pairs 1', 3', 5', and 6', respectively). 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 of FIG. 13. Figure 13 shows 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 for gear pairs 1', 3', 5', and 6' calculated using Niemann's equation (Equations 2 and 3 above) based on the actual contact ratio remains almost constant within a specified 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] [Table 4]

[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 gears> The method for predicting the root temperature of a thermoplastic resin gear of this embodiment has three forms, namely, Form 1 to Form 3. In all 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 the following formula 4 or any of the following formulas 5 to 7.

[0072]

number

[0073]

number

[0074] In Equation 4, H v The loss factor defined in VDI 2736 Blatt 2 is the transverse contact ratio ε α The transverse contact ratio ε α is 1<ε αIf <2, apply Equation 5 and calculate the transverse contact ratio ε α is 2<ε α If <3, apply Equation 6 and calculate the transverse contact ratio ε α is 3<ε α If <4, apply Equation 7.

[0075] In equations 5 to 7, z1, z2, ε1, and ε2 are the same as z1, z2, ε1, and ε2 in equations 1 to 3, and the explanations given for 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 above-described method for calculating an actual contact ratio of a thermoplastic resin gear of this 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 above-described method for deriving a friction coefficient of a thermoplastic resin gear of this embodiment). In the second embodiment, the actual contact ratio of the thermoplastic resin gear is the contact ratio that takes deformation into consideration, and the friction coefficient μ of the thermoplastic resin gear is the friction coefficient μ derived by the method for deriving the friction coefficient of a thermoplastic resin gear of this embodiment described above. In the third embodiment, the actual contact ratio of the thermoplastic resin gear is calculated by the method for calculating an actual contact ratio of a thermoplastic resin gear of the present embodiment described above, 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 of the present embodiment described above.

[0077] In the first embodiment, the friction coefficient μ of a thermoplastic resin gear is calculated by any measurement method. Examples of such methods include the pin-on-disk method, the ring-on-ring method, the ball-on-disk method, and the like, in addition to the friction coefficient measurement method specified in the method for deriving the friction coefficient of a thermoplastic resin gear of this embodiment. 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 the thermoplastic resin gear of the present embodiment described above, and is a contact ratio that takes into account the tooth temperature and tooth deformation (actual contact ratio), so that the prediction accuracy of the tooth root temperature of the 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 consideration. In the second embodiment, the friction coefficient μ derived by the method for deriving a friction coefficient of a thermoplastic resin gear according to the present embodiment is used. Therefore, the friction coefficient is equal to or close to the actual friction coefficient of the gear, thereby improving the accuracy of predicting the root temperature of the resin gear.

[0079] In the third embodiment, the actual contact ratio of the thermoplastic resin gear 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 temperature and the measured temperature at the root of a resin gear to which the third embodiment is applied. In Figure 14, each plot shows the relationship between the predicted temperature and the measured temperature (each plot) at the root when the same gear pairs as gear pairs 1 to 7 described above are used. The dashed line indicates the case where the predicted temperature and the measured temperature are equal. As shown in Figure 14, it can be seen that the predicted temperature and the measured temperature at the root of the gear are almost the same for all gear pairs.

[0081] Next, we will explain an example of evaluating the tooth root 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 temperatures at the tooth root of a resin gear to which the third embodiment is applied, similar to Figure 14 above. As shown in Figure 15, in all examples, the predicted and measured temperatures for the tooth root temperature are almost identical. In other words, it is clear that the tooth root temperature of a gear can be predicted even when grease is applied to the gears.

[0082] FIG. 16 shows the relationship between the predicted temperature and the measured temperature at the root of the gears for 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: driving side: metal gear 3, driven side: thermoplastic resin 1 Gear pair 11: driving 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 shift 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 shift 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 shift coefficient 0)) Metal Gear 4: Kyoiku Gears Co., Ltd., SG1S 14L-1008 (spur gear (module 1.0 mm, number of teeth 14, face width 10 mm, pressure angle 20°, addendum shift coefficient 0)) The metal gear 2 is provided with a keyway. The metal gear 3 is provided with a keyway and has an inner diameter of 12 mm. From FIG. 16, it can be seen that the predicted and measured temperatures at the root of the teeth are almost identical even when the resin gear and metal gear are combined.

[0083] As described above, for all of gear pairs 1 to 11, the predicted and measured temperatures for the tooth root temperatures are almost identical. This shows that the tooth 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 It is preferable to set at least one of the following: (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). To further improve the accuracy of tooth root temperature prediction, it is preferable to set A to 1770 to 2890, B to -1.907A+3943, and C 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 the total number of teeth of the pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshing range should be counted), c in the above formula 4 should be 0.10 to 0.60, and k θ,Fuβis preferably set to (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), and to further improve the accuracy of prediction of the tooth root temperature, it is preferable that A is 550 to 1550, B is -2.300A+1981, and C is -2.300A+3111. Each of these will be explained below.

[0086] FIG. 18 shows the relationship between the predicted and measured temperatures at the root of a resin gear in the third form, where the number of teeth z in Equation 4 is the total number of teeth of the pair of gears (however, if the entire circumference does not mesh, only the number of teeth within the meshed range is counted) (i.e., z = z1 + z2). FIG. 18 also shows four types of pairs of gears (represented by black circles, squares, black triangles, and open triangles), and each pair of gears has a different number of teeth. The black circle plots show z1 = 54, z2 = 54, the square plots show z1 = 23, z2 = 23, the black triangle plots show z1 = 23, z2 = 54, and the open triangle plots show z1 = 14, z2 = 23. As shown in FIG. 18, the predicted and measured root temperatures for each pair of gears are nearly identical. On the other hand, Fig. 19 shows the relationship between the predicted and measured temperatures at the root of a resin gear in the first form when the number of teeth z in Equation 4 is set to z1, the number of teeth of the gear with the fewer teeth (i.e., z = z1). The plots of black circles, squares, black triangles, and white triangles in Fig. 19 are the same as those in Fig. 18. In other words, the pair of gears being measured is the same in Fig. 18 and Fig. 19. As Fig. 19 shows, there is a partial discrepancy between the predicted and measured root temperatures. From the above, if the number of teeth z in Equation 4 is taken to be the total number of teeth on a pair of gears (however, if the entire circumference does not mesh, only the number of teeth in the meshed area is counted), the prediction accuracy for the tooth root temperature improves. This is thought to be because it allows the area through which heat is transferred to the tooth root to be correctly reflected even for combinations of different numbers of teeth. For example, if the number of teeth (however, if the entire circumference does not mesh, only the number of teeth in the meshed area is counted) is doubled, the area through which heat flows in also doubles, and the temperature rise is halved. However, if the number of teeth z is taken to be the total number of teeth on one of the gears, this temperature rise will not be reflected.

[0087] On the other hand, by optimizing the heat dissipation factor in Equation 4, which indicates the degree of influence of heat dissipation, it is possible to make the predicted and measured values ​​of the tooth root temperature almost coincide with each other across the entire temperature range, regardless of the rotation speed. The heat dissipation factor is expressed as v t c The constant c is 0.05 to 0.70, but 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 gear face width, the larger the face width, the greater the temperature rise due to heat storage. The heat storage factor is expressed in Equation 4 as k 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 differences 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 tooth 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, in the case of a combination of a plastic gear and a metal gear, k in the above formula 4 θ,Fuβ is preferably set to (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), 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. By setting them in this way, it is possible to improve the accuracy of tooth root temperature prediction even when the face width changes.

[0089] FIG. 20 shows the predicted and measured temperatures of the tooth root when the heat storage factor is optimized in the third embodiment. θ,Fuβ In 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 in Figure 21, there is some discrepancy between the predicted and measured root temperatures. It can be seen that by optimizing the heat storage factor, the predicted and measured root temperatures can be made to closely match, even when the gear face widths are different.

[0090] <Life Prediction Method for Thermoplastic Resin Gears> The method for predicting a lifespan of a thermoplastic resin gear of this embodiment includes Step 9 of preparing an SN curve of the thermoplastic resin gear for each tooth temperature of the thermoplastic resin gear. Then, the lifespan of the thermoplastic resin gear is predicted based on the SN curve corresponding to the root temperature obtained by the method for predicting a 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 of this embodiment, an SN 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 SN curve corresponding to the root temperature obtained by the method for predicting the root temperature of a thermoplastic resin gear of this embodiment. Because the root temperature obtained by the method for predicting the root temperature of this embodiment is highly accurate, the accuracy of the life prediction can also be improved.

[0092] In step 9, an SN curve for the thermoplastic resin gear is prepared for each temperature of the thermoplastic resin gear teeth. The SN curve, also known as a fatigue life curve, shows the relationship between the tooth root bending stress of a resin gear and its lifespan (the number of meshings until fracture). More specifically, the SN 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 horizontal axis represents the number of stress cycles, and the vertical axis represents the logarithm of the amplitude of stress, forming a downward-sloping curve. Then, in step 9, an SN curve is prepared for each temperature of the gear teeth. For each temperature, for example, an SN 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 SN curve corresponding to the obtained tooth root temperature is selected. However, if there is no SN curve for a temperature that matches the tooth root temperature, the life of the resin gear can be predicted based on an estimated SN curve for the tooth root temperature obtained by extrapolation or interpolation. [Explanation of symbols]

[0094] 10 20 Gears 12 22 teeth 30 Testing Machine 32 axes 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: 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 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 constituting 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 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; Step 6: calculating an angle difference between the meshing start point and 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 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 the actual contact ratio of a thermoplastic resin gear, including:

2. A method for deriving the friction coefficient of thermoplastic resin gears, comprising step 8 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 an actual contact ratio of thermoplastic resin gears according to claim 1 and the torque transmission efficiency η measured in step 8.

3. 3. The method for deriving the friction coefficient of a thermoplastic resin gear according to claim 2, wherein the friction coefficient of the thermoplastic resin gear is derive by substituting the actual contact ratio into one of the following equations 1 to 3: [Equation 1] [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.]

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 according to claim 1 and the friction coefficient μ calculated by any method (excluding the method for deriving a friction coefficient of a thermoplastic resin gear according to claim 2) into the following formula 4 and any of the following formulas 5 to 7. [Equation 2] [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), 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.] [Equation 3] [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.]

5. A method for predicting the root temperature of a thermoplastic resin gear, comprising 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 as set forth in claim 2 into the following equations 4 and 5 to 7: [Equation 4] [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), 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.] [Equation 5] [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.]

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 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: [Equation 6] [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), 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.] [Equation 7] [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.]

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, if 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 1130 to 3610, B is -1.782A + 3286, and C is -1.728A + 5291).

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, if 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).

9. Step 9 includes preparing an S-N curve of a thermoplastic resin gear for each temperature of the teeth of the thermoplastic resin gear; A method for predicting a life of a thermoplastic resin gear, comprising: predicting a life 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 claims 4 to 6.

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