Method for calculating actual contact ratio of thermoplastic resin gear, method for deriving friction coefficient 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

A method for calculating the actual contact ratio of gears made of thermoplastic resin comprises: a step 1 in which the temperature distribution of a pair of gears is measured; step 2, calculating the temperature distribution of a structure analysis model A having the same shape as the pair of gears by using CAE structure analysis; a step 3 for preparing temperature dependency data of the elastic modulus a of the thermoplastic resin; a step (4) in which a step (4a) for calibrating the elastic modulus (a) by means of strain rate dependency and a step (4b) for calibrating the elastic modulus (a) by means of the actual deformation amount of the gear are carried out regardless of the order; 5, the calibrated elastic modulus a'is used, and CAE structural analysis is used for calculating contact stress distribution; a step 6 of calculating an angular difference from a start point to an end point of meshing in the pair of gears on the basis of the contact stress distribution; and step 7, calculating the actual overlap ratio of the pair of gears through the angle difference.

Description

Technical Field

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

[0002] Gears made of thermoplastic resins such as polyamide resins or polyacetal resins are lightweight, highly absorbing vibrations, and self-lubricating. Therefore, they can be used even without adding oil, and can be easily produced by injection molding, etc. From this point of view, they are used in a wide range of fields instead of metal gears. As the use of resin gears expands, requirements for miniaturization, noise reduction, high heat resistance for use at high speeds, and long-term durability (fatigue failure life) have become stricter (see Patent Document 1).

[0003] In Europe, the gear fatigue characteristics of resin gears (VDI 2736 Blatt 2) are estimated using the tooth root temperature calculated based on the gear shape, operating conditions, etc. The friction coefficient of the resin gear has a great influence on the calculation of the tooth root temperature required for the estimation. Generally, as a method for measuring the friction coefficient used in the calculation of resin gears, the pin-on-disk method, the ring-on-ring method, and the ball-on-disk method can be used. However, the sliding form of the resins in these methods is very different from the actual sliding form of the gears, so there is a problem of inconsistency with the actual friction coefficient of the gears. In addition, the overlap degree also has a great influence in the calculation formula for calculating the tooth root temperature. However, in the calculation formula for calculating the tooth root temperature, the overlap degree (actual overlap degree) that takes into account the increase in the tooth root temperature of the resin gear and the deformation of the teeth is not taken into account. Therefore, the prediction accuracy of the tooth root temperature predicted by the friction coefficient measured by the conventional technique and the contact ratio without considering the deformation of the tooth is low, and the gear fatigue characteristics of the resin gear cannot be evaluated with high accuracy.

[0004] Prior art literature

[0005] Patent Literature

[0006] Patent Document 1: Japanese Patent Application Publication No. 2017-62017 Summary of the invention

[0007] Problems to be solved by the invention

[0008] The present invention has been completed in view of the above-mentioned existing problems, and its subject is to provide a method for calculating the overlap (actual overlap) taking into account the temperature of the teeth and the deformation of the teeth in a thermoplastic resin gear, a method for more accurately deriving the friction coefficient of the thermoplastic resin gear, a method for predicting the root temperature of the thermoplastic resin gear with high precision, and a method for predicting the fatigue life of the thermoplastic resin gear with high precision.

[0009] Technical solutions to solve problems

[0010] One aspect of the present invention for solving the above-mentioned problems is as follows.

[0011] (1) A method for calculating the actual contact ratio of a pair of gears, at least one of which is a thermoplastic resin gear, comprising:

[0012] Step 1: rotating a pair of gears, at least one of which is a thermoplastic resin gear, at a predetermined rotation speed in a mutually meshing state, and measuring the temperature distribution of the pair of gears;

[0013] Step 2, using CAE to create a structural analysis model A having the same shape as the pair of gears, inputting the temperature 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 using CAE structural analysis;

[0014] Step 3: preparing temperature dependency data of elastic modulus a of the thermoplastic resin constituting the pair of gears;

[0015] Step 4: Step 4a and Step 4b are performed in no particular order, wherein Step 4a calculates the position of the maximum tensile strain in the strain distribution of the tooth root of the meshing teeth when the pair of gears are meshed, using CAE structural analysis, based on the temperature distribution of the structural analysis model A calculated in Step 2 and the temperature dependence data of the elastic modulus a prepared in Step 3, and calibrates the elastic modulus a or the elastic modulus obtained in the following Step 4b by the strain rate dependence of the elastic modulus of the gear in the structural analysis model A calculated based on the position of the maximum tensile strain in the strain distribution, wherein Step 4b measures the actual deformation of the pair of gears, and calculates the deformation based on the CAE structural analysis using a CAE structural analysis model B created to reflect the actual deformation and having the same shape as the pair of gears, and then calculates the ratio X between the actual deformation and the deformation based on the CAE structural analysis, and calibrates the elastic modulus a or the elastic modulus obtained in Step 4a by the ratio X;

[0016] Step 5: using the calibrated elastic modulus a' obtained in step 4, and using CAE structural analysis, calculating the contact stress distribution when a predetermined torque is applied to the transmission-side gear of the pair of gears;

[0017] Step 6: calculating the angle difference from the meshing start point to the meshing end point in the pair of gears based on the contact stress distribution calculated in step 5; and

[0018] Step 7: The actual overlap of the pair of gears is calculated by dividing the angle difference calculated in step 6 by an angle equivalent to the circumferential pitch of the pair of gears (360° / number of teeth).

[0019] (2) A method for deriving the friction coefficient of a thermoplastic resin gear, comprising: step 8 of measuring the transmission efficiency η of the torque transmitted from the driving gear of a pair of gears to the driven gear, and deriving the friction coefficient of the thermoplastic resin gear using a gear transmission loss formula based on the actual overlap calculated by the actual overlap calculation method of the thermoplastic resin gear described in (1) and the torque transmission efficiency η measured in step 8.

[0020] (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 derived by substituting the numerical value of the actual contact ratio into any one of the following equations 1 to 3.

[0021] [Mathematical expression 1]

[0022]

[0023]

[0024]

[0025] [In formulas 1 to 3, ε α represents the end surface overlap, η represents the torque transmission efficiency, μ represents the friction coefficient of the thermoplastic resin gear, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.]

[0026] (4) A method for predicting the tooth root temperature of a thermoplastic resin gear, which predicts the tooth root temperature of the thermoplastic resin gear by substituting the actual overlap calculated by the method for calculating the actual overlap of the thermoplastic resin gear described in (1) above and the friction coefficient μ derived by any derivation method (except the method for deriving the friction coefficient of the thermoplastic resin gear described in (2) above) into the following formula 4 and any one of the following formulas 5 to 7.

[0027] [Mathematical expression 2]

[0028]

[0029] [In Formula 4, θ Fuβ represents the tooth root temperature (°C), θ0 represents the ambient temperature (°C), P represents the rated power (2π×speed×torque) (W), μ represents the friction coefficient of the thermoplastic resin gear, and k θ，Fuβ represents the heat storage coefficient and the heat transfer coefficient (K·(m / s) c mm 1.75 / W) is defined by VDI 2736 Blatt 2 of a pair of gears, at least one of which is a thermoplastic resin gear. b represents the tooth width (mm), m n represents the normal module (mm), z represents the total number of teeth of a pair of gears (wherein, in the case of non-meshing throughout the cycle, only the number of teeth in the meshing range is counted), v t c One term represents the heat dissipation coefficient, v t represents the circumferential speed of the pitch circle (m / s), c represents a constant of 0.05 to 0.70, R λ，G Indicates the thermal resistance of the shell (K·m 2 / W), A G Indicates the heat dissipation area of ​​the shell (m 2 ), ED represents the relative meshing time per 10 minutes, H v It represents the loss coefficient obtained by the following equations 5 to 7 based on the actual overlap value.

[0030] [Mathematical expression 3]

[0031]

[0032]

[0033]

[0034] [In formulas 5 to 7, ε α represents the end face overlap, u represents the gear ratio z2 / z1, β brepresents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.]

[0035] (5) A method for predicting the tooth root temperature of a thermoplastic resin gear, which predicts the tooth root temperature of the thermoplastic resin gear by substituting the overlap without considering deformation and the friction coefficient μ derived by the method for deriving the friction coefficient of the thermoplastic resin gear described in (2) into the following equations 4 and 5 to 7.

[0036] [Mathematical expression 4]

[0037]

[0038] [In Formula 4, θ Fuβ represents the tooth root temperature (°C), θ0 represents the ambient temperature (°C), P represents the rated power (2π×speed×torque) (W), μ represents the friction coefficient of the thermoplastic resin gear, and k θ，Fuβ represents the heat storage coefficient and the heat transfer coefficient (K·(m / s) c mm 1.75 / W) is defined by VDI 2736 Blatt 2 of a pair of gears, at least one of which is a thermoplastic resin gear. b represents the tooth width (mm), m n represents the normal module (mm), z represents the total number of teeth of a pair of gears (wherein, in the case of non-meshing throughout the cycle, only the number of teeth in the meshing range is counted), v t c One term represents the heat dissipation coefficient, v t represents the circumferential speed of the pitch circle (m / s), c represents a constant of 0.05 to 0.70, R λ，G Indicates the thermal resistance of the shell (K·m 2 / W), A G Indicates the heat dissipation area of ​​the shell (m 2 ), ED represents the relative meshing time per 10 minutes, H v It represents the loss coefficient obtained by the following equations 5 to 7 based on the actual overlap value.

[0039] [Mathematical expression 5]

[0040]

[0041]

[0042]

[0043] [In formulas 5 to 7, ε αrepresents the end face overlap, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.]

[0044] (6) A method for predicting the tooth root temperature of a thermoplastic resin gear, which predicts the tooth root temperature of the thermoplastic resin gear by substituting the actual overlap calculated by the method for calculating the actual overlap of the thermoplastic resin gear described in (1) above and the friction coefficient μ derived by the method for deriving the friction coefficient of the thermoplastic resin gear described in (2) above into the following equations 4 and 5 to 7.

[0045] [Mathematical expression 6]

[0046]

[0047] [In Formula 4, θ Fuβ represents the tooth root temperature (°C), θ0 represents the ambient temperature (°C), P represents the rated power (2π×speed×torque) (W), μ represents the friction coefficient of the thermoplastic resin gear, and k θ，Fuβ represents the heat storage coefficient and the heat transfer coefficient (K·(m / s) c mm 1.75 / W) is defined by VDI 2736 Blatt 2 of a pair of gears, at least one of which is a thermoplastic resin gear. b represents the tooth width (mm), m n represents the normal module (mm), z represents the total number of teeth of a pair of gears (wherein, in the case of non-meshing throughout the cycle, only the number of teeth in the meshing range is counted), v t c One term represents the heat dissipation coefficient, v t represents the circumferential speed of the pitch circle (m / s), c represents a constant of 0.05 to 0.70, R λ，G Indicates the thermal resistance of the shell (K·m 2 / W), A G Indicates the heat dissipation area of ​​the shell (m 2 ), ED represents the relative meshing time per 10 minutes, H v It represents the loss coefficient obtained by the following equations 5 to 7 based on the actual overlap value.

[0048] [Mathematical expression 7]

[0049]

[0050]

[0051]

[0052] [In formulas 5 to 7, ε α represents the end face overlap, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.]

[0053] (7) A method for predicting the tooth root temperature of a thermoplastic resin gear according to any one of (4) to (6) above, wherein, when the pair of gears is a combination of thermoplastic resin gears, at least one of the following is performed: the number of teeth z in the equation 4 is set to the total number of teeth of the pair of gears (wherein, when there is no meshing throughout the entire cycle, only the number of teeth in the range where meshing occurs is counted); c in the equation 4 is set to 0.10 to 0.60; and k in the equation 4 is set to θ，Fuβ Suppose it is A·ln(b)+B)~(A·ln(b)+C) (wherein b is the tooth width (mm), A is 1130~3610, B is -1.782A+3286, and C is -1.728A+5291).

[0054] (8) A method for predicting the tooth root temperature of a thermoplastic resin gear according to any one of (4) to (6) above, wherein, when the pair of gears is a combination of a thermoplastic resin gear and a metal gear, at least one of the following is performed: the number of teeth z in the equation 4 is set to the total number of teeth of the pair of gears (wherein, when there is no meshing throughout the entire cycle, only the number of teeth in the range where meshing occurs is counted); c in the equation 4 is set to 0.10 to 0.60; and k in the equation 4 is set to θ，Fuβ Suppose it is (A·ln(b)+B)~(A·ln(b)+C) (wherein b is the tooth width (mm), A is 100~2000, B is -2.284A+1424, and C is -2.316A+3637).

[0055] (9) A method for predicting the life of a thermoplastic resin gear, comprising: preparing an SN curve of the thermoplastic resin gear for each temperature of a tooth of the thermoplastic resin gear;

[0056] The life of the thermoplastic resin gear is predicted based on the SN curve corresponding to the tooth root temperature obtained by the method for predicting the tooth root temperature of the thermoplastic resin gear according to any one of (4) to (8).

[0057] Effects of the Invention

[0058] According to the present invention, there can be provided a method for calculating the degree of overlap (actual degree of overlap) in a thermoplastic resin gear taking into account the temperature of the teeth and the deformation of the teeth, a method for more accurately deriving the friction coefficient of the thermoplastic resin gear, a method for predicting the tooth root temperature of the thermoplastic resin gear with high accuracy, and a method for predicting the fatigue life of the thermoplastic resin gear with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 The diagram shows a state in which a pair of gears are meshed, and is used to explain the degree of overlap.

[0060] Figure 2 This is a graph showing the relationship between the distance in the tooth width direction of a gear and the temperature distribution.

[0061] Figure 3 A top view showing a CAE analysis model A of a resin gear.

[0062] Figure 4 A diagram showing the strain distribution at the tooth root in CAE analysis.

[0063] Figure 5 This is a graph showing the relationship between the gear division number and the strain at the tooth root in CAE analysis.

[0064] Figure 6 This is a graph showing the relationship between the strain rate and the elastic modulus of a tensile test specimen.

[0065] Figure 7 (A) Top view and (B) front view of a device for measuring the deformation amount of gear teeth.

[0066] Figure 8 A graph showing the relationship between the load (torque) of the gear and the rotation angle of the rotating side gear (actually measured values ​​and CAE analysis values).

[0067] Fig. 9 Regarding the relationship between the load (torque) of the gear and the rotation angle of the rotating side gear, a graph showing the ratio of the actually measured value to the CAE analysis value is shown.

[0068] Fig.10 A graph showing the load (torque) of the gear and the rotation angle of the rotating side gear in the calibrated elastic modulus.

[0069] Fig.11 A graph showing the relationship between temperature and coincidence.

[0070] Fig.12 A graph showing the relationship between the maximum temperature of the teeth and the friction coefficient in gear pairs 1 to 8 (without lubricating oil).

[0071] Fig.13Graph showing the relationship between the maximum temperature of the teeth and the friction coefficient in the gear pairs 1', 3', 5' and 6' (with lubricant).

[0072] Fig.14 A graph showing the relationship between the predicted temperature and the actually measured temperature in the gear pairs 1 to 7 (without lubricating oil) obtained by the tooth root temperature prediction method according to the present embodiment.

[0073] Fig.15 A graph showing the relationship between the predicted temperature and the actually measured temperature in the gear pairs 1', 3', 5', and 6' (with lubricating oil) obtained by the tooth root temperature prediction method according to the present embodiment.

[0074] Fig.16 A graph showing the relationship between the predicted temperature and the actually measured temperature in the gear pairs 8 to 11 (without lubricating oil) obtained by the tooth root temperature prediction method according to the present embodiment.

[0075] Fig.17 A graph showing the relationship between the predicted temperature and the actually measured temperature obtained by the tooth root temperature prediction method according to the present embodiment.

[0076] Fig.18 A graph showing the relationship between the predicted temperature and the actually measured temperature obtained by the tooth root temperature prediction method according to the present embodiment.

[0077] Fig.19 A graph showing the relationship between the predicted temperature and the actually measured temperature obtained by the tooth root temperature prediction method according to the present embodiment.

[0078] Fig. 20 A graph showing the relationship between the predicted temperature and the actually measured temperature obtained by the tooth root temperature prediction method according to the present embodiment.

[0079] Fig.21 A graph showing the relationship between the predicted temperature and the actually measured temperature obtained by the tooth root temperature prediction method according to the present embodiment.

[0080] Fig. 22 (a) is a cross-sectional view and (b) is a side view of a resin gear having 54 teeth used for various evaluations.

[0081] Fig.23 (a) is a cross-sectional view and (b) is a side view of a resin gear having 23 teeth used for various evaluations.

[0082] Fig.24 (a) is a cross-sectional view and (b) is a side view of a resin gear having 14 teeth used for various evaluations.

[0083] Fig.25 This is a side view of a metal gear with 18 teeth used for various evaluations.

[0084] Fig.26 This is a side view of a metal gear with 14 teeth used for various evaluations.

[0085] Fig. 27 This is a cross-sectional view of a metal gear with 35 teeth used for various evaluations.

[0086] Fig.28 It is a cross-sectional view of a metal gear having 54 teeth used for various evaluations. DETAILED DESCRIPTION

[0087] <Calculation method of actual contact ratio of thermoplastic resin gears>

[0088] The method for calculating the actual contact ratio of thermoplastic resin gears (hereinafter also referred to as "resin gears") of the present 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.

[0089] Step 1: A pair of gears, at least one of which is a gear made of a thermoplastic resin, is rotated at a predetermined rotation speed in a state where the gears are meshed with each other, and the temperature distribution of the pair of gears is measured.

[0090] Step 2: Use CAE to create a structural analysis model A having the same shape as a pair of gears, input the temperature obtained from the temperature distribution of the pair of gears measured in step 1 into the structural analysis model A, and use CAE structural analysis to calculate the temperature distribution of the structural analysis model A.

[0091] Step 3: Prepare data on the temperature dependency of the elastic modulus a of the thermoplastic resin constituting the pair of gears.

[0092] Step 4: Perform step 4a and step 4b in no particular order, wherein step 4a calculates the position of the maximum tensile strain in the strain distribution of the tooth root of the meshing teeth when a pair of gears are meshed using CAE structural analysis based on the temperature distribution of the structural analysis model A calculated in step 2 and the temperature dependence data of the elastic modulus a prepared in step 3, and calibrates the elastic modulus a or the elastic modulus obtained in the following step 4b by the strain rate dependence of the elastic modulus of the gear in the structural analysis model A calculated based on the position of the maximum tensile strain in the strain distribution, wherein step 4b measures the actual deformation of the pair of gears, and calculates the deformation based on the CAE structural analysis using a CAE structural analysis model B created to reflect the actual deformation and having the same shape as the pair of gears, and then calculates the ratio X between the actual deformation and the deformation based on the CAE structural analysis, and calibrates the elastic modulus a or the elastic modulus obtained in step 4a by the ratio X.

[0093] Step 5: Using the calibrated elastic modulus a' obtained in step 4, CAE structural analysis is used to calculate the contact stress distribution when a predetermined torque is applied to the transmission-side gear of the pair of gears.

[0094] Step 6: Based on the contact stress distribution calculated in step 5, calculate the angle difference from the meshing start point to the meshing end point in a pair of gears. And

[0095] Step 7: Calculate the actual overlap of a pair of gears by dividing the angle difference calculated in step 6 by the angle equivalent to the circular pitch (360° / number of teeth).

[0096] First, regarding the “actual overlap” reference Figure 1 to explain. Figure 1 The state in which the teeth 12 of the gear 10 and the teeth 22 of the gear 20 are meshed is shown (see Figure 1 (D)), Figure 1 (A) to (C) of FIG. 1 show the meshing parts of the teeth of each gear. Figure 1 In (A) to (C) of FIG. 1 , the points where the teeth of the gears are in contact with each other are indicated by black dots. Figure 1 (A) is 1 place, (B) is 2 places, and (C) is 1 place, and the teeth of each gear are in contact. In this way, when a pair of gears rotate in a meshing state, the number of teeth in contact varies depending on the rotation angle. "Actual overlap" refers to the value obtained by dividing the angle equivalent to the meshing length of a pair of gears made of thermoplastic resin during rotation in a meshing state by the angle equivalent to the circumferential pitch of the pair of gears (360° / number of teeth). As a thermoplastic resin gear, unlike a metal gear, the overlap cannot be considered in the same way as a metal gear due to large deformation and bending of the meshing teeth. In the case of a gear made of metal, the deformation is small due to the extremely high elastic modulus and small temperature change, and the overlap does not substantially change even if the deformation is taken into account. On the other hand, in the case of a resin gear, because the elastic modulus is low and the elastic modulus varies greatly with temperature, the overlap also varies according to the operating conditions (tooth temperature and load). Therefore, in the present embodiment concerning the resin gear, the "actual contact ratio" is calculated taking into account the deflection of the teeth peculiar to thermoplastic resin gears, and the contact ratio which does not take deformation into account is not used.

[0097] Hereinafter, steps 1 to 7 for calculating the actual overlap will be described. In the following description, various evaluation results are shown, and the evaluation was performed using the following measuring instruments and the like.

[0098] ·Measurement of actual temperature distribution: CHINO Co., Ltd., thermal imager CPA-7800

[0099] Structural analysis software: Allied Engineering Corporation, ADVENTURECluster2020

[0100] Actual deformation measurement: strength testing machine (TENSILON UTA-50KN)

[0101] · Torque transmission efficiency measurement: Small gear fatigue testing machine (manufactured by Ono Sakuki Co., Ltd.)

[0102] Shape of gear molding

[0103] Gear molded product shape with 54 teeth (refer to Fig. 22 )

[0104] Gear molded product shape with 23 teeth (refer to Fig.23 )

[0105] Gear molded product shape with 14 teeth (refer to Fig.24 )

[0106] The metal gear of the gear 18 (see Fig.25 )

[0107] Metal gear with 14 teeth (refer to Fig.26 )

[0108] Metal gear with 35 teeth (refer to Fig. 27 )

[0109] Metal gear with 54 teeth (refer to Fig.28 )

[0110] also, Figures 22 to 28 The numerical value in each of represents the size (mm) of each element. Fig.25 and 26 The metal gear 30 shown is a shape in which a shaft 32 and a gear 34 are connected.

[0111] [Step 1]

[0112] In step 1, a pair of gears, at least one of which is a thermoplastic resin gear, is rotated at a prescribed rotational speed in a state of mutual meshing, and the temperature distribution of the pair of gears is measured. That is, the temperature distribution is measured while the pair of gears are rotated. The temperature distribution can be measured by a non-contact thermometer, such as a radiation thermometer, thermal imaging, an infrared camera, etc. In addition, the prescribed rotational speed can be set arbitrarily. For example, as described later, in the case of wanting to predict the root temperature of a gear, the rotational speed of the gear set when predicting the root temperature can be used. In addition, the temperature distribution of the gear can be measured in the width direction of the tooth and the gear edge. The material of the gear fixing fixture used to mount the gear on the small gear fatigue testing machine can be metal or resin, but it is preferably made of resin that does not deprive the tooth surface of heat.

[0113] It is sufficient that at least one of the pair of gears is a thermoplastic resin gear, and both gears may be thermoplastic resin gears, or one gear may be a thermoplastic resin gear and the other gear may be a metal gear. In addition, when both gears are thermoplastic resin gears, the thermoplastic resins may be the same or different. Furthermore, inorganic fillers such as fibrous fillers may be filled in the thermoplastic resin of one or both thermoplastic resin gears. Furthermore, the pair of gears may have the same shape or may have different numbers of teeth and / or tooth widths.

[0114] [Step 2]

[0115] In step 2, CAE (Computer Aided Engineering) is used to create a structural analysis model A having the same shape as a pair of gears, the temperature obtained from the temperature distribution of the pair of gears measured in step 1 is input into the structural analysis model A, and the temperature distribution of the structural analysis model A is calculated using CAE structural analysis.

[0116] Here, it is also possible to use the elastic modulus obtained from the measured temperature distribution of thermal imaging to perform CAE structural analysis for calculating the actual overlap. However, in thermal imaging, there are problems such as only being able to measure the temperature distribution on the surface of the molded product and taking a long time to obtain the measured temperature distribution. Therefore, in step 2, the temperature distribution based on CAE structural analysis is used (the measured temperature distribution is reflected in CAE).

[0117] In step 2, the temperature distribution measured in step 1 is input into the CAE structural analysis software as temperature conditions, such as the center temperature of the tooth width and the average temperature of the gear rim, and the temperature distribution based on CAE analysis is calculated by performing heat conduction analysis. Figure 2 The measured temperature distribution (black circles) and the temperature distribution based on CAE heat conduction analysis (white circles) are shown in FIG. In addition, the mesh model used for CAE structural analysis, for example, can be used Figure 3 Structural analysis model A shown.

[0118] [Step 3]

[0119] In step 3, data on the temperature dependency of the elastic modulus a of the thermoplastic resin constituting the pair of gears is prepared.

[0120] That is, in step 3, data of elastic modulus a relative to 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 manufacturers may be used.

[0121] In addition, step 3 may be performed before step 4, or before step 1 or step 2.

[0122] [Step 4]

[0123] In step 4, step 4a is included, which uses CAE structural analysis to calculate the position of the maximum tensile strain in the strain distribution of the tooth root of the meshing teeth when a pair of gears are meshed, based on the temperature distribution of the structural analysis model A calculated in step 2 and the temperature dependence data of the elastic modulus a prepared in step 3, and calibrates the elastic modulus a or the elastic modulus obtained in the following step 4b by the strain rate dependence of the elastic modulus of the gear in the structural analysis model A calculated based on the position of the maximum tensile strain in the strain distribution. In addition, step 4b is included, which measures the actual deformation of the pair of gears, calculates the deformation based on the CAE structural analysis using the CAE structural analysis model B created to reflect the actual deformation and composed of the same shape as the pair of gears, and then calculates the ratio X between the actual deformation and the deformation based on the CAE structural analysis, and calibrates the elastic modulus a or the elastic modulus obtained in step 4a by the ratio X. Moreover, step 4a and step 4b are performed in no particular order. That is, either step 4a or step 4b can be performed first. Next, step 4a and step 4b are described.

[0124] (Step 4a)

[0125] In short, step 4a is a step of calibrating the elastic modulus a prepared in step 3 (or the calibrated elastic modulus in which the elastic modulus a is calibrated in step 4b) in consideration of the strain rate dependency calculated from the strain distribution.

[0126] Figure 4 2 shows the strain distribution calculated by CAE structural analysis. Figure 4The strain distribution when the transmission side gear 10 and the driven side gear 20 are rotated at a speed of 100 rpm and a torque of 9 N·m is shown. Here, the specifications such as the dimensions of the transmission side gear 10 and the driven side gear 20 are shown below.

[0127] Gear shape (transmission side): spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, tooth addendum correction coefficient 0)

[0128] Gear shape (driven side): spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, tooth addendum correction coefficient 0)

[0129] In with Figure 4 The strain distribution of the maximum tensile strain at the position where the maximum tensile strain occurs is within the circle 24 in FIG. 1 , that is, at the tooth root of the tooth of the driven side gear 20 which contacts the tooth of the driving side gear 10 .

[0130] Strain rate dependence means that when a load is applied to a material, the properties change according to the strain rate. When the strain rate (e.g., stretching speed) in a resin material increases, the material strength and elastic modulus tend to increase. Therefore, in resin gears, it is necessary to consider the calculation of the strain rate dependence of the elastic modulus caused by different operating conditions (rotation speed).

[0131] First, the temperature dependence of the elastic modulus of each part of the gear is calculated based on the temperature distribution of the structural analysis model A calculated in step 2. By using the calculated temperature dependence data of the elastic modulus to perform deformation analysis based on CAE analysis, the strain rate of the position where the maximum tensile strain occurs in the strain distribution of the tooth root of the meshing tooth when the resin gear is actually meshed is calculated. Next, for example, the strain rate of the elastic modulus is calculated in the following manner. The following example uses the following shape of the transmission side gear and the driven side gear, the rotation speed: 100rpm, the torque: 9N·m.

[0132] Gear shape (transmission side): spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, tooth addendum correction coefficient 0)

[0133] Gear shape (driven side): spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, tooth addendum correction coefficient 0)

[0134] a) Define the time (s / partition) and angular velocity (rad / s) for each partition in the CAE analysis (for example, 0.02 s / partition and 0.175 rad / s).

[0135] b) Convert to the rotation angle of the gear per partition for CAE analysis (° / partition).

[0136] c) The rotation angle (°) is calculated by multiplying the rotation angle of the gear per section obtained by CAE analysis in b) by the number of sections from the start to the peak of the strain.

[0137] d) Calculate the time (s) required to rotate the angle calculated in c) (e.g., 0.008s). This is the form of converting the number of partitions (CAE) into time (s)

[0138] e) Strain rate ( / s) = strain / time required for analysis (s) = (0.02 (maximum strain moment) - 0.005 (starting strain moment)) / 0.008s = 1.86 ( / s).

[0139] That is, when the strain rate of the elastic modulus is calculated based on the location where the strain occurs, the time of maximum strain and the time until then are calculated, the result is 1.86 ( / s).

[0140] Figure 5 This is a graph showing the relationship between the partition number and the strain of the tooth root in CAE analysis. Figure 5 In the example, the horizontal axis represents the partition number. However, by converting the partition number into time, Figure 5 The slope of the graph (straight line) of the portion surrounded by the one-dot chain line is the strain rate.

[0141] Next, the elastic modulus of the resin gear used for CAE analysis was calibrated to match the actual measured value (elastic modulus based on a tensile test using an ISO tensile test piece). The actual measured value of the elastic modulus is shown in Figure 6 of charts.

[0142] according to Figure 6 , the elastic modulus at a strain rate of 1.86 ( / s) is about 2800MPa. When the ratio to the benchmark elastic modulus of 1940MPa (baseline conditions; tensile speed 1 (mm / s), strain rate 0.01 ( / s)) is calculated, 2800 / 1940=1.45. Therefore, the elastic modulus taking into account the strain rate dependence of the resin gear based on CAE analysis is calculated by multiplying the benchmark elastic modulus by 1.45. That is, calibration can be performed based on the strain rate of the elastic modulus generated by different rotation speeds.

[0143] In addition, it is preferred to use temperature dependence data of the elastic modulus corresponding to the actual gear condition (strain rate), but it is also possible to pre-measure the strain rate dependence of the elastic modulus, calculate the elastic modulus corresponding to the actual strain rate of the gear, and calculate the elastic modulus at each temperature based on the temperature dependence of the elastic modulus obtained in advance.

[0144] (Step 4b)

[0145] In short, step 4b is a step of calibrating the elastic modulus a prepared in step 3 (or the calibrated elastic modulus in which the elastic modulus a is calibrated in step 4a) in consideration of the actual deformation amount.

[0146] First, an example of measuring the actual deformation amount of a gear is shown. Figure 7 An example of a testing machine used to measure the actual deformation of a gear is shown below. Figure 7 In the test machine 30 shown, the gear 10 and the gear 20 are in meshing state, the gear 10 is set to rotate around the shaft 32, and the gear 20 is fixed in a non-rotating manner. In addition, an additional load rod 34 is provided on the shaft 32 behind the gear 10. When the additional load rod 34 is pressed downward, the gear 10 Figure 7 At this time, the gear 10 is meshed with the fixed gear 20, so the rotation is restricted, and the teeth of the gear 10 and the gear 20 will be slightly displaced. Figure 7 In the test machine 30 shown, by pressing the additional load rod 34 downward to apply a load (torque) to the gear 10, the relationship between the displacement of the additional load rod 34 and the torque corresponding to the deformation of the teeth can be obtained. That is, the displacement of the additional load rod 34 with respect to an arbitrary torque can be converted into the shaft rotation angle. In other words, the rotation angle of the gear can be indirectly calculated based on the deformation of the teeth.

[0147] Here, the types of equipment and conditions for measuring the actual deformation amount of the gear are shown below, but the following is an example and the present embodiment is not limited to the following.

[0148] Testing machine: Universal testing machine UTA-50KN-RTC manufactured by A&D Co., Ltd.

[0149] Gear material: Polyplastics Co., Ltd., DURACON (registered trademark), POM M90-44 (no filler)

[0150] Gear shape (rotating side): Spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, addendum correction coefficient 0)

[0151] Gear shape (fixed side): Spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, addendum correction coefficient 0)

[0152] Torque: 1, 3, 5, 7, 9 N·m (The upper limit can be set to the allowable stress (MPa) corresponding to the material)

[0153] Test speed at the force point: It can be appropriately set by considering the strain rate dependency and stress relaxation. For example, the speed is 5 mm / min.

[0154] Horizontal distance to force point: 65mm

[0155] Lubrication: Oil lubrication (TRUSCO Nakayama Co., Ltd., industrial gear oil viscosity ISO VG 100)

[0156] ※The function of suppressing the instability of load transfer caused by stick-slip phenomenon (lubricant oil and other lubricants are acceptable)

[0157] Ambient temperature: 23°C

[0158] Radial clearance j r :0.2mm

[0159] Next, CAE is used to create a CAE analysis model B that reflects the gear shape of the actual test. Then, the shaft rotation angle is calculated based on the displacement of the teeth through deformation analysis. In the CAE-based deformation analysis, the shaft rotation angle is calculated based on the displacement of the teeth that are not affected by the deformation caused by the load (torque).

[0160] The results of comparing the measured values ​​of the gear rotation angle with the CAE analysis values ​​are shown in Figure 8 , 9 . Figure 8 The relationship between the load (torque) of the gear and the rotation angle of the gear is shown with the measured values ​​(blank graph) and the CAE analysis values ​​(shaded graph). Fig. 9 The relationship between the load (torque) on the gear and the rotation angle of the gear is shown as the ratio of the measured value to the CAE analysis value. Under any load (torque), the CAE analysis value is lower than the measured value, so calibration is performed to reduce the directionality of the elastic modulus calculated by CAE analysis, so that the deformation amount can be consistent with the measured value in appearance.

[0161] Table 1 below shows the calibrated elastic modulus obtained by dividing the uncalibrated elastic modulus (2500 MPa) at 23°C at 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 of the measured-CAE deviation is calibrated.

[0162] = Uncalibrated elastic modulus (2500MPa) × 1 / 1.51

[0163] = Uncalibrated elastic modulus (2500MPa) × 0.66

[0164] =1.7×10 3 MPa

[0165] In addition, the relationship between torque and rotation angle using the calibrated elastic modulus is shown in the table below, comparing the results of CAE analysis with those of actual measurement. Fig.10 .exist Fig.10 In the figure, white circles represent CAE analysis values, and black circles represent measured values.

[0166] [Table 1]

[0167]

[0168] according to Fig.10 It can be seen that the measured value of the rotation angle is roughly consistent with the CAE calculated value, so the above-mentioned calibration of the elastic modulus is appropriate.

[0169] An example of the case where the elastic modulus is calibrated through the above steps 4a and 4b is shown in Table 2 below.

[0170] [Table 2]

[0171]

[0172] The elastic modulus a calibrated through steps 4a and 4b is the elastic modulus a′ used in step 5 (the table on the right side).

[0173] As described above, by calibrating the elastic modulus through step 4a and step 4b, the elastic modulus used for CAE analysis can be calibrated to an elastic modulus corresponding to actual measurement.

[0174] In addition, as mentioned above, there is no particular order between the above steps 4a and 4b, and either step can be performed first.

[0175] [Step 5]

[0176] Step 5 is a step of calculating the contact stress distribution when a predetermined torque is applied to the transmission-side gear of the pair of gears by CAE structural analysis using the calibrated elastic modulus a' obtained in step 4.

[0177] The calibrated elastic modulus a' and the measurement conditions (torque) calculated in step 4 are input into the CAE structural analysis software to perform deformation analysis (contact analysis) to calculate the contact stress distribution when a specified torque is applied to the gear on the transmission side. The mesh model used for CAE structural analysis can be used with Figure 3 The same model as shown in Structural Analysis Model A.

[0178] [Step 6]

[0179] Step 6 is a step of calculating the angular difference from the meshing start point to the meshing end point in a pair of gears based on the contact stress distribution calculated in step 5.

[0180] Based on the contact stress distribution calculated in step 5, calculate the "angle difference from the meshing start point to the meshing end point" (θ end -θ start ).

[0181] [Step 7]

[0182] Step 7 is a step of calculating the actual overlap of a pair of gears by dividing the angle difference calculated in step 6 by the angle equivalent to the circumferential pitch (360° / number of teeth).

[0183] The angle difference (θ) from the meshing start point to the meshing end point calculated in step 6 is end -θ start ) divided by θ pitch (corresponding to the angle of the circumferential pitch (360° / number of teeth)), calculate the actual contact ratio of the resin gear corresponding to the measurement conditions (contact ratio = (θ end -θ start ) / θ pitch ).

[0184] As described above, the actual contact ratio of the thermoplastic resin gear of the present embodiment can be calculated by the calculation method of the actual contact ratio of the thermoplastic resin gear of the present embodiment, taking into account the temperature of the tooth and the deformation of the tooth. Moreover, the calculated actual contact ratio can be applied to the method for deriving the friction coefficient of the thermoplastic resin gear of the present embodiment shown below, and the method for predicting the root temperature of the thermoplastic resin gear of the present embodiment and the method for predicting the life of the thermoplastic resin gear described later. However, it is not limited to these.

[0185] <Method for deriving the friction coefficient of thermoplastic resin gears>

[0186] The method for deriving the friction coefficient of the thermoplastic resin gear of the present embodiment includes: step 8 of measuring the transmission efficiency η of the torque transmitted from the driving gear of a pair of gears to the driven gear, and deriving the friction coefficient of the thermoplastic resin gear using the transmission loss formula of the gear based on the actual overlap calculated by the actual overlap calculation method of the thermoplastic resin gear of the present embodiment and the torque transmission efficiency η measured in step 8.

[0187] In the method for deriving the friction coefficient of the thermoplastic resin gear of the present embodiment, the friction coefficient is derived based on the actual contact calculated by the method for calculating the actual contact of the thermoplastic resin gear of the present embodiment described above and the measured value of the transmission efficiency η of the torque transmitted from the driving gear of a pair of gears to the driven gear. That is, in the present embodiment, the friction coefficient is derived taking into account the actual contact of the pair of gears, so the friction coefficient that matches the actual sliding form between the gears is derived. Therefore, unlike the case of using the friction coefficient derived by the pin-disk method, the ring-disk method, and the ball-disk method, the prediction accuracy of the tooth root temperature described later is improved.

[0188] In step 8, the transmission efficiency of the torque transmitted to the driven gear is determined based on the transmission gear of a pair of gears. The torque transmission efficiency can be calculated by measuring the torque of the driven side gear and the torque of the transmission side gear, and by the formula of torque of the driven side gear×(number of teeth of the transmission side gear / number of teeth of the driven side gear) / torque of the transmission side gear. For example, when the torque value of the transmission side gear is 2.47, the torque value of the driven side gear is 2.37, the number of teeth of the transmission side gear is 54, and the number of teeth of the driven side gear is 54, the transmission efficiency η=2.37×(54 / 54) / 2.47=0.96.

[0189] Next, the friction coefficient of the thermoplastic resin gear is derived using the transmission loss formula of the gear, based on the actual contact calculated by the calculation method of the actual contact of the thermoplastic resin gear of the present embodiment described above and the torque transmission efficiency η calculated in step 8. As the transmission loss formula of the gear, Niemann formula, Buckingham formula, Merritt formula, etc. can be listed. The Niemann formula is explained below.

[0190] The friction coefficient μ of the thermoplastic resin gear is derived by substituting the numerical value of the actual contact ratio calculated by the method for calculating the actual contact ratio of the thermoplastic resin gear according to the present embodiment into any one of the following equations 1 to 3.

[0191] [Mathematical expression 8]

[0192]

[0193]

[0194]

[0195] [In formulas 1 to 3, ε α represents the end surface overlap, η represents the torque transmission efficiency, μ represents the friction coefficient of the thermoplastic resin gear, u represents the gear ratio z2 / z1, β brepresents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.]

[0196] The end face overlap ε α 1<ε α <2, using formula 1, the end face overlap ε α 2<ε α When <3, use formula 2, and the end face overlap ε α 3<ε α When <4, use formula 3.

[0197] In equations 1 to 3, the meshing overlap ε1 is obtained from the angle between the meshing start point and the meshing node (the intersection of the line connecting the center points of the two gears and the meshing pitch circle). In addition, the meshing overlap ε2 is obtained from the angle between the meshing node (the intersection of the line connecting the center points of the two gears and the meshing pitch circle) and the meshing end point. α is the sum of the meshing overlap ε1 and the meshing overlap ε2, that is, ε α =ε1+ε2.

[0198] In Formulas 1 to 3, z1 represents the number of teeth of the gear with the smaller number of teeth among the pair of gears, and z2 represents the number of teeth of the gear with the larger number of teeth among the pair of gears.

[0199] In the following Table 3, the actual contact (end face contact) calculated by the calculation method of the actual contact of the thermoplastic resin gear of the present embodiment and the friction coefficient μ derived by the Niemann formula (the above formulas 2 and 3) based on the actual contact are shown together with the numerical values ​​of the rotation speed, torque and maximum temperature of the teeth for 8 examples (gear pairs 1 to 8). Here, "rotation speed" and "torque" are numerical values ​​of the gear on the transmission side. In addition, the specifications (specifications) such as the size of the gear pair used are shown below.

[0200] Gear shape (transmission side): spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, tooth addendum correction coefficient 0)

[0201] Gear shape (driven side): spur gear (module 1.0mm, number of teeth 54, tooth width 10mm, pressure angle 20°, tooth addendum correction coefficient 0)

[0202] In addition, in the gear pairs 1 to 8, the materials of the gears used are different as shown below.

[0203] Gear pair 1: Transmission side: Thermoplastic resin 1, Driven side: Thermoplastic resin 1

[0204] Gear pair 2: Transmission side: Thermoplastic resin 2, Driven side: Thermoplastic resin 2

[0205] Gear pair 3: Transmission side: Thermoplastic resin 3, Driven side: Thermoplastic resin 3

[0206] Gear pair 4: Transmission side: Thermoplastic resin 4, Driven side: Thermoplastic resin 4

[0207] Gear pair 5: Transmission side: Thermoplastic resin 5, Driven side: Thermoplastic resin 5

[0208] Gear pair 6: Transmission side: Thermoplastic resin 6, Driven side: Thermoplastic resin 6

[0209] Gear pair 7: Transmission side: Thermoplastic resin 1, Driven side: Thermoplastic resin 5

[0210] Gear pair 8: Transmission side: Metal gear 1, Driven side: Thermoplastic resin 1

[0211] In the gear pair 8, the metal gear 1 used for the transmission side is as follows.

[0212] Metal gear 1: SG1S18L-1010 (spur gear (module 1.0 mm, number of teeth 18, tooth width 10 mm, pressure angle 20°, tooth addendum correction coefficient 0) manufactured by Kyoyuk Gear Industry Co., Ltd.)

[0213] The materials (thermoplastic resins) constituting the gears used in the gear pairs 1 to 8 are shown below.

[0214] Thermoplastic resin 1: Polyplastics Co., Ltd., DURACON (registered trademark) POM M90-44 (no filler)

[0215] Thermoplastic resin 2: Polyplastics Co., Ltd., DURACON (registered trademark) PОMNW-02

[0216] Thermoplastic resin 3: Polyplastics Co., Ltd., DURACON (registered trademark) PОM YF-10

[0217] Thermoplastic resin 4: Polyplastics Co., Ltd., DURACON (registered trademark) PОMM25-44

[0218] Thermoplastic resin 5: Polyplastics Co., Ltd., DURANEX (registered trademark) PBT 2002

[0219] Thermoplastic resin 6: PA66-based resin LEONA1300G (filled with fibrous filler) manufactured by Asahi Kasei Corporation

[0220] on the other hand, Fig.11The graph shows the relationship between the maximum temperature of the teeth and the contact ratio. The solid line shows the contact ratio without considering the deformation, and the dotted line shows the actual contact ratio calculated by the above-mentioned calculation method of the actual contact ratio of the thermoplastic resin gear of the present embodiment (see Table 3). Fig.11 It can be seen that the overlap without considering deformation is constant in a specified temperature range, while the actual overlap varies according to the maximum temperature of the tooth. Fig.12 This is a graph showing the relationship between the maximum temperature of the teeth and the friction coefficient μ in gear pairs 1 to 8. The solid line represents the friction coefficient μ derived using the Niemann formula based on the contact without considering deformation. In addition, each dotted line represents the friction coefficient μ derived using the Niemann formula (the above-mentioned formulas 2 and 3) based on the actual contact calculated by the calculation method of the actual contact of the thermoplastic resin gears of the present embodiment in gear pairs 1 to 8 (see Table 3). Fig.12 It can be seen that the friction coefficient μ derived based on the contact ratio without considering deformation changes according to the maximum temperature of the teeth, while the friction coefficient μ in the gear pairs 1 to 8 derived based on the actual contact ratio using the Niemann formula (the above formulas 2 and 3) is approximately constant in a predetermined temperature range. In addition, it can be seen that the friction coefficient μ is approximately constant in any of the gear pairs 1 to 8, so the friction coefficient μ is approximately constant in the combination of different thermoplastic resins, the combination of thermoplastic resins filled with fibrous fillers, and the combination of thermoplastic resins and metals, not to mention the same thermoplastic resins.

[0221] [Table 3]

[0222]

[0223] Next, an example of evaluating the gear lubricant applied to the gear pairs 1, 3, 5, and 6 (gear pairs 1', 3', 5', and 6', respectively) will be described. In the gear pairs 1', 3', 5', and 6', the actual overlap is calculated by the calculation method of the actual overlap of the thermoplastic resin gears of the present embodiment, as in the case of the gear pairs 1 to 8, and the friction coefficient μ is derived based on the actual overlap using the Niemann formula (the above-mentioned formulas 2 and 3). The actual overlap and the friction coefficient μ are shown in Table 4, respectively. In addition, the relationship between the maximum temperature of the teeth and the friction coefficient μ in the gear pairs 1', 3', 5', and 6' is shown in Table 4. Fig.13 of charts.

[0224] according to Fig.13It can be seen that the friction coefficient μ derived based on the contact ratio without considering deformation changes according to the maximum temperature of the tooth, while the friction coefficient μ in the gear pairs 1', 3', 5' and 6' derived based on the actual contact ratio using the Niemann formula (the above formulas 2 and 3) is approximately constant in the specified temperature range. In addition, it can be confirmed that by applying lubricating oil to the gears, the friction coefficient becomes smaller compared with the same gear pair without lubricating oil.

[0225] [Table 4]

[0226]

[0227] In the method for deriving the friction coefficient of the thermoplastic resin gear of the present embodiment, the friction coefficient of the resin gear can be derived by adopting the above method. Moreover, the friction coefficient of the resin gear derived in the present embodiment is a coefficient that takes into account the actual sliding form between the gears, and thus becomes a value that is consistent with or close to the friction coefficient of the actual gear.

[0228] <Prediction method of tooth root temperature of thermoplastic resin gear>

[0229] The method for predicting the tooth root temperature of a thermoplastic resin gear in this embodiment has three methods, namely the first method to the third method. Any method is to substitute the actual overlap degree of the thermoplastic resin gear and the friction coefficient μ of the thermoplastic resin gear into the following formula 4 and any one of the following formulas 5 to 7 to predict the tooth root temperature of the thermoplastic resin gear.

[0230] [Mathematical expression 9]

[0231]

[0232] [In Formula 4, θ Fuβ represents the tooth root temperature (°C), θ0 represents the ambient temperature (°C), P represents the rated power (2π×speed×torque) (W), μ represents the friction coefficient of the thermoplastic resin gear, and k θ，Fuβ represents the heat storage coefficient and the heat transfer coefficient (K·(m / s) c mm 1.75 / W) is defined by VDI 2736 Blatt 2 of a pair of gears, at least one of which is a thermoplastic resin gear. b represents the tooth width (mm), m n represents the normal module (mm), z represents the total number of teeth of a pair of gears (wherein, in the case of non-meshing throughout the cycle, only the number of teeth in the meshing range is counted), v t c One term represents the heat dissipation coefficient, v t represents the circumferential speed of the pitch circle (m / s), c represents a constant of 0.05 to 0.70, Rλ，G Indicates the thermal resistance of the shell (K·m 2 / W), A G Indicates the heat dissipation area of ​​the shell (m 2 ), ED represents the relative meshing time per 10 minutes, H v It represents the loss coefficient obtained by the following equations 5 to 7 based on the actual overlap value.

[0233] [Mathematical expression 10]

[0234]

[0235]

[0236]

[0237] [In formulas 5 to 7, ε α represents the end face overlap, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.]

[0238] In formula 4, H v : Loss coefficient defined by VDI 2736 Blatt 2, based on the end face overlap ε α Different from the end face overlap ε α 1<ε α <2, using formula 5, the end face overlap ε α 2<ε α When <3, use formula 6, and the end face overlap ε α 3<ε α When <4, use formula 7.

[0239] z1, z2, ε1, ε2 in Formulas 5 to 7 are the same as z1, z2, ε1, ε2 in Formulas 1 to 3, and the description in Formulas 1 to 3 is directly applicable.

[0240] Moreover, in the first embodiment, as the actual overlap of the thermoplastic resin gears, the actual overlap calculated by the method for calculating the actual overlap of the thermoplastic resin gears in the present embodiment described above is used, and as the friction coefficient μ of the thermoplastic resin gears, the friction coefficient μ calculated by an arbitrary derivation method (but except the friction coefficient derivation method specified in the method for deriving the friction coefficient of the thermoplastic resin gears in the present embodiment described above) is used.

[0241] In the second embodiment, the contact without considering deformation is used as the actual contact of the thermoplastic resin gear, and the friction coefficient μ derived by the method for deriving the friction coefficient of the thermoplastic resin gear of the present embodiment is used as the friction coefficient μ of the thermoplastic resin gear.

[0242] In the third method, as the actual overlap of the thermoplastic resin gears, the actual overlap calculated by the method for calculating the actual overlap of the thermoplastic resin gears in the present embodiment described above is used, and as the friction coefficient μ of the thermoplastic resin gears, the friction coefficient μ derived by the method for deriving the friction coefficient of the thermoplastic resin gears in the present embodiment described above is used.

[0243] In the first method, the friction coefficient μ of the thermoplastic resin gear is calculated by an arbitrary measurement method, but as an arbitrary measurement method, in addition to the friction coefficient measurement method specified in the method for deriving the friction coefficient of the thermoplastic resin gear in the above-mentioned embodiment, the pin-disc method, the ring-disc method, the ball-disc method, etc. can be listed.

[0244] In the first method, the actual overlap of the thermoplastic resin gear is calculated by the calculation method of the actual overlap of the thermoplastic resin gear of the present embodiment described above, which is an overlap (actual overlap) that takes into account the temperature of the teeth and the deformation of the teeth. Therefore, the prediction accuracy of the tooth root temperature of the resin gear can be improved.

[0245] In the second aspect, as the contact ratio of the thermoplastic resin gear, the contact ratio without considering the deformation is used.

[0246] In the second embodiment, since the friction coefficient μ derived by the above-mentioned method for deriving the friction coefficient of the thermoplastic resin gear of this embodiment is used as the friction coefficient, it becomes a value consistent with or close to the actual friction coefficient of the gear, which can improve the prediction accuracy of the tooth root temperature of the resin gear.

[0247] In the third method, the actual contact ratio of the thermoplastic resin gear and the friction coefficient μ of the thermoplastic resin gear are both calculated or derived in the present embodiment described above. That is, the "actual contact ratio" and "friction coefficient μ" of the resin gear corresponding to the measurement conditions are substituted into the tooth root temperature prediction formula represented by the above formula 4. Therefore, the third method has the highest prediction accuracy of the tooth root temperature of the resin gear.

[0248] Fig.14 The relationship between the predicted temperature and the measured temperature of the tooth root of a resin gear using the third embodiment is shown. Fig.14In FIG. 1 , each plotted point represents the relationship between the predicted temperature of the tooth root and the measured temperature (each plotted point) when the same gear pair as the above-mentioned gear pairs 1 to 7 is used. The dotted line represents the case where the predicted temperature is equal to the measured temperature. Fig.14 As shown, it can be seen that for the tooth root temperature in any gear pair, the predicted temperature is roughly consistent with the measured temperature.

[0249] On the other hand, an example in which the prediction of the tooth root temperature is evaluated for the gear pairs 1 ′, 3 ′, 5 ′, and 6 ′ to which the gear lubricant is applied will be described. Fig.15 The relationship between the predicted temperature and the measured temperature of the tooth root of the resin gear using the third method is similar to the above Fig.14 The same is shown. Fig.15 As shown, it can be seen that the predicted temperature and the measured temperature are substantially consistent with each other in any example. That is, it can be seen that the gear root temperature can be predicted even when the gear lubricant is applied.

[0250] also, Fig.16 The relationship between the predicted temperature and the measured temperature of the tooth root is shown in relation to gear pairs 8 to 11. Gear pairs 8 to 11 are all combinations of resin gears and metal gears. Although gear pair 8 is described above, it will be described again below. In addition, gear pairs 9 to 11 are the following combinations.

[0251] Gear pair 8: Transmission side: Metal gear 1, Driven side: Thermoplastic resin 1

[0252] Gear pair 9: Transmission side: Metal gear 2, Driven side: Thermoplastic resin 1

[0253] Gear pair 10: Transmission side: Metal gear 3, Driven side: Thermoplastic resin 1

[0254] Gear pair 11: Transmission side: Metal gear 4, Driven side: Thermoplastic resin 1

[0255] Metal gear 1: SG1S18L-1010 (spur gear (module 1.0 mm, number of teeth 18, tooth width 10 mm, pressure angle 20°, tooth addendum correction coefficient 0) manufactured by Kyoyuk Gear Industry Co., Ltd.)

[0256] Metal gear 2: SG1S 54B-1012 (spur gear (module 1.0 mm, number of teeth 54, tooth width 10 mm, pressure angle 20°, tooth addendum correction coefficient 0) manufactured by Kyoyuk Gear Industry Co., Ltd.)

[0257] Metal gear 3: SG1S 35B-1010 (spur gear (module 1.0 mm, number of teeth 35, tooth width 10 mm, pressure angle 20°, tooth addendum correction coefficient 0) manufactured by Kyoyuk Gear Industry Co., Ltd.

[0258] Metal gear 4: SG1S14L-1008 (spur gear (module 1.0 mm, number of teeth 14, tooth width 10 mm, pressure angle 20°, tooth addendum correction coefficient 0) manufactured by Kyoyuk Gear Industry Co., Ltd.

[0259] Furthermore, key groove processing was performed on the metal gear 2. Furthermore, key groove processing was performed on the metal gear 3 and the inner diameter of the gear was processed to 12 mm.

[0260] according to Fig.16 It can be seen that, also in the combination of the resin gear and the metal gear, regarding the tooth root temperature, the predicted temperature and the actually measured temperature are substantially consistent.

[0261] From the above content, it can be seen that regarding the tooth root temperature in any one of the gear pairs 1 to 11, since the predicted temperature is almost the same as the measured temperature, the tooth root temperature can be predicted with high accuracy 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 resins and metals by using the friction coefficient of the resin gear derived in this embodiment.

[0262] on the other hand, Fig.17 The relationship between the predicted temperature (solid line) and the measured temperature (dashed line) of the tooth root of the resin gear to which the second method is applied is shown. It is found that the predicted temperature and the measured temperature are slightly different. Figure 14 to Figure 17 The results show that, Figure 14 to Figure 16 The third formula shown has a higher prediction accuracy.

[0263] In the case of a combination of resin gears, in order to further improve the prediction accuracy of the tooth root temperature of the resin gear, it is preferred to perform at least one of the following: the number of teeth z in equation 4 is set to the total number of teeth of a pair of gears; c in equation 4 is set to 0.10 to 0.60; and k in equation 4 is set to θ，Fuβ Set to (A·ln(b)+B)~(A·ln(b)+C) (where b is the tooth width (mm), A is 1130~3610, 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 preferred that A is set to 1770~2890, B is set to -1.907A+3943, and C is set to -2.154A+5647.

[0264] On the other hand, in the case of a combination of a resin gear and a metal gear, it is preferable to set the number of teeth z in the above formula 4 to the total number of teeth of a pair of gears (wherein, when there is no meshing throughout the entire cycle, only the number of teeth in the range where meshing occurs is counted), set c in the above formula 4 to 0.10 to 0.60, and set k to θ，FuβSet to (A·ln(b)+B)~(A·ln(b)+C) (wherein b is the tooth width (mm), A is 100~2000, B is -2.284A+1424, and C is -2.316A+3637). In order to further improve the prediction accuracy of the tooth root temperature, it is preferred that A is set to 550~1550, B is set to -2.300A+1981, and C is set to -2.300A+3111.

[0265] The following explains them respectively.

[0266] Fig.18 In the third embodiment, the relationship between the predicted temperature and the measured temperature of the tooth root of the resin gear is shown, in which the number of teeth z in Formula 4 is set to the total number of teeth of a pair of gears (wherein, when there is no meshing throughout the entire cycle, only the number of teeth in the range where meshing occurs is counted) (i.e., z=z1+z2). Fig.18 In the figure, four types of gears are shown as a pair (represented by black circles, squares, black triangles, and white triangles), and the number of teeth of each gear in any pair of gears is different. The black circle points represent z1=54, z2=54, the square points represent z1=23, z2=23, the black triangle points represent z1=23, z2=54, and the white triangle points represent z1=14, z2=23. Fig.18 As shown, the predicted temperature and the measured temperature are almost the same for the tooth root temperature of any pair of gears. Fig.19 Regarding the case where the number of teeth z in Expression 4 is set to the number of teeth z1 of the gear with the smaller number of teeth (ie, z=z1) in the first embodiment, the relationship between the predicted temperature and the measured temperature of the tooth root of the resin gear is shown. Fig.19 The black circle, square, black triangle and white triangle of each plot point and Fig.18 The same. That is, Fig.18 and Fig.19 In the example, the pair of gears to be measured are identical. Fig.19 As shown, regarding the tooth root temperature, the predicted temperature and the actually measured temperature partially disagree.

[0267] According to the above, when the number of teeth z in Formula 4 is set to the total number of teeth of a pair of gears (wherein, in the case of non-meshing for a whole cycle, only the number of teeth in the range where meshing occurs is counted), the prediction accuracy of the tooth root temperature is improved. It is believed that this is because the area of ​​heat transfer to the tooth root can be accurately reflected even in a combination with different numbers of teeth. For example, when the number of teeth (wherein, in the case of non-meshing for a whole cycle, only the number of teeth in the range where meshing occurs is counted) is doubled, the area of ​​heat inflow is also doubled, and the temperature rise is also 1 / 2, but when it is set to the number of teeth of either gear, such a temperature rise is not reflected.

[0268] On the other hand, in Formula 4, by rationalizing the heat dissipation coefficient that indicates the influence of heat dissipation, the predicted value of the tooth root temperature can be made substantially consistent with the measured value in the entire temperature range regardless of the rotation speed. The heat dissipation coefficient in Formula 4 is v t c Furthermore, although the constant c is 0.05 to 0.70, it is preferably set to 0.10 to 0.60, and more preferably set to 0.15 to 0.55, in order to optimize the heat dissipation coefficient and improve the prediction accuracy of the tooth root temperature.

[0269] Furthermore, by rationalizing the heat storage coefficient, which indicates the influence of heat storage, the predicted value of the tooth root temperature can be made almost consistent with the measured value. Regarding the influence of the tooth width of the gear on heat storage, the larger the tooth width, the greater the temperature rise due to heat storage. The heat storage coefficient is k in formula 4. θ，Fuβ By making it a function of the tooth width b, the heat storage coefficient can be optimized. In the present embodiment, in the case of a combination of resin gears, k is a function that takes into account the heat storage factor based on the different tooth widths. θ，Fuβ It is preferably (A·ln(b)+B)~(A·ln(b)+C) (wherein b is the tooth width (mm), A is 1130~3610, 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 more preferable that A is set to 1770~2890, B is set to -1.907A+3943, and C is set to -2.154A+5647.

[0270] On the other hand, in the case of a combination of a resin gear and a metal gear, it is preferable to replace k in the above formula (4) with θ，Fuβ Set to (A·ln(b)+B)~(A·ln(b)+C) (where b is the tooth width (mm), A is 100~2000, B is -2.284A+1424, and C is -2.316A+3637). In order to further improve the prediction accuracy of the tooth root temperature, it is preferred that A is set to 550~1550, B is set to -2.300A+1981, and C is set to -2.300A+3111. By setting in this way, the prediction accuracy of the tooth root temperature can be improved even when the tooth width changes.

[0271] Fig. 20 The predicted temperature and the actual temperature of the tooth root temperature when the heat storage coefficient is optimized in the third embodiment are shown. θ，Fuβ Set k θ，Fuβ =475b+1417 (where b is the tooth width (mm)). Fig. 20In the figure, the black circle, square, black triangle, and white triangle plot points represent the cases of tooth width: 3mm, tooth width: 5mm, tooth width: 7.5mm, and tooth width: 10mm, respectively. It can be seen that the predicted temperature and the measured temperature are roughly consistent in any case. On the other hand, Fig.21 The predicted temperature and the actually measured temperature of the tooth root temperature when the heat storage coefficient is not optimized in the third embodiment are shown. Fig.21 The only difference between the two is that the heat storage coefficient is not rationalized. Fig. 20 The resin gears to be measured are the same as Fig. 20 The same plot points are used to represent the Fig.21 As shown, the predicted temperature and the measured temperature partially disagree with each other regarding the tooth root temperature. As can be seen from the above, by optimizing the heat storage coefficient, the predicted value of the tooth root temperature can be made substantially consistent with the measured value even when the tooth width of the gear is different.

[0272] <Life prediction method for thermoplastic resin gears>

[0273] The life prediction method of the thermoplastic resin gear of the present embodiment includes: step 9 of preparing an SN curve of the thermoplastic resin gear for each temperature of the teeth of the thermoplastic resin gear. And based on the SN curve corresponding to the tooth root temperature obtained by the above-mentioned method for predicting the tooth root temperature of the thermoplastic resin gear of the present embodiment, the life of the thermoplastic resin gear is predicted.

[0274] In the life prediction method of the thermoplastic resin gear of the present embodiment, the SN curve of the resin gear is prepared in advance for each temperature of the gear teeth (step 9). And the life is predicted based on the SN curve corresponding to the root temperature obtained by the method for predicting the root temperature of the thermoplastic resin gear of the present embodiment described above. The root temperature obtained by the method for predicting the root temperature of the present embodiment has high accuracy, so the accuracy of life prediction can also be improved.

[0275] In step 9, the SN curve of the thermoplastic resin gear is obtained for each temperature of the teeth of the thermoplastic resin gear. The SN curve is also called a fatigue life curve, which shows the relationship between the root bending stress and the life (number of meshing times until fracture) of the resin gear. More specifically, the SN curve is a curve for obtaining the fatigue strength of the resin gear through fatigue testing, and the number of stress repetitions until the multiple resin gears are broken is represented by logarithms, and the horizontal axis is the stress repetition number and the vertical axis is the logarithm of the amplitude stress, and the SN curve is a graph, and it is the lower right curve.

[0276] Then, in step 9, an SN curve is prepared for each temperature of the gear teeth. For example, each temperature is 30°C, 40°C, 50°C, and so on, and an SN curve for each temperature is prepared.

[0277] In this embodiment, the tooth root temperature obtained by the above-mentioned method for predicting the tooth root temperature of the thermoplastic resin gear of this embodiment is used. Although the SN curve corresponding to the obtained tooth root temperature is selected, if there is no SN curve with a temperature consistent with the tooth root temperature, the life of the resin gear can be predicted based on the estimated SN curve at the tooth root temperature obtained by extrapolation or interpolation.

[0278] Description of symbols

[0279] 10 20 Gear

[0280] 12 22 teeth

[0281] 30 Testing Machine

[0282] 32 Axis

[0283] 34 Additional load bar.

Claims

1. A method for calculating the actual contact ratio of a pair of gears, at least one of which is a thermoplastic resin gear, characterized in that: include: Step 1: rotating a pair of gears, at least one of which is a thermoplastic resin gear, at a predetermined rotation speed in a mutually meshing state, and measuring the temperature distribution of the pair of gears; Step 2: using CAE to create a structural analysis model A having the same shape as the pair of gears, and inputting the temperature 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 using CAE structural analysis; Step 3: preparing temperature dependency data of elastic modulus a of the thermoplastic resin constituting the pair of gears; Step 4: Step 4a and Step 4b are performed in no particular order, wherein Step 4a calculates the position of the maximum tensile strain in the strain distribution of the tooth root of the meshing teeth when the pair of gears are meshed using CAE structural analysis based on the temperature distribution of the structural analysis model A calculated in Step 2 and the temperature dependence data of the elastic modulus a prepared in Step 3, and calibrates the elastic modulus a or the elastic modulus obtained in the following Step 4b by the strain rate dependence of the elastic modulus of the gear in the structural analysis model A calculated based on the position of the maximum tensile strain in the strain distribution, wherein Step 4b measures the actual deformation of the pair of gears, and calculates the deformation based on the CAE structural analysis using a CAE structural analysis model B created to reflect the actual deformation and having the same shape as the pair of gears, and then calculates the ratio X between the actual deformation and the deformation based on the CAE structural analysis, and calibrates the elastic modulus a or the elastic modulus obtained in Step 4a by the ratio X; Step 5: using the calibrated elastic modulus a' obtained in step 4, and using CAE structural analysis, calculating the contact stress distribution when a predetermined torque is applied to the transmission-side gear of the pair of gears; Step 6: calculating the angle difference from the meshing start point to the meshing end point in the pair of gears based on the contact stress distribution calculated in step 5; and Step 7: The actual overlap of the pair of gears is calculated by dividing the angle difference calculated in step 6 by an angle equivalent to the circumferential pitch of the pair of gears (360° / number of teeth).

2. A method for deriving a friction coefficient of a thermoplastic resin gear, characterized in that: The method comprises the steps of measuring the transmission efficiency η of the torque transmitted from the driving gear of a pair of gears to the driven gear, and deriving the friction coefficient of the thermoplastic resin gear using the transmission loss formula of the gear based on the actual overlap calculated by the calculation method of the actual overlap of the thermoplastic resin gear according to claim 1 and the torque transmission efficiency η measured in the step 8.

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 derived by substituting the actual contact ratio value into any one of the following equations 1 to 3: [Mathematical expression 1] In formulas 1 to 3, ε α represents the end surface overlap, η represents the torque transmission efficiency, μ represents the friction coefficient of the thermoplastic resin gear, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.

4. A method for predicting the tooth root temperature of a thermoplastic resin gear, characterized in that: Substituting the actual contact calculated by the method for calculating the actual contact of the thermoplastic resin gear according to claim 1 and the friction coefficient μ derived by any derivation method other than the method for deriving the friction coefficient of the thermoplastic resin gear according to claim 2 into the following equation 4 and any one of the following equations 5 to 7, the tooth root temperature of the thermoplastic resin gear is predicted. [Mathematical expression 2] In formula 4, θ Fuβ represents the tooth root temperature (°C), θ0 represents the ambient temperature (°C), P represents the rated power (2π×speed×torque) (W), μ represents the friction coefficient of the thermoplastic resin gear, and k θ，Fuβ represents the heat storage coefficient and the heat transfer coefficient (K·(m / s) c mm 1.75 / W) is defined by VDI 2736 Blatt 2 of a pair of gears, at least one of which is a thermoplastic resin gear. b represents the tooth width (mm), m n represents the normal module (mm), z represents the total number of teeth of a pair of gears, where only the number of teeth in the meshing range is counted when there is no meshing in the whole circle, and v t c One term represents the heat dissipation coefficient, v t represents the circumferential speed of the pitch circle (m / s), c represents a constant of 0.05 to 0.70, R λ，G Indicates the thermal resistance of the shell (K·m 2 / W), A G Indicates the heat dissipation area of ​​the shell (m 2 ), ED represents the relative meshing time per 10 minutes, H v represents the loss coefficient obtained according to the numerical value of the actual overlap according to the following equations 5 to 7, [Mathematical expression 3] In formulas 5 to 7, ε α represents the end face overlap, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.

5. A method for predicting the tooth root temperature of a thermoplastic resin gear, characterized in that: The tooth root temperature of the thermoplastic resin gear is predicted by substituting the overlap without considering deformation and the friction coefficient μ derived by the method for deriving the friction coefficient of the thermoplastic resin gear according to claim 2 into the following equations 4 and 5 to 7. [Mathematical expression 4] In formula 4, θ Fuβ represents the tooth root temperature (°C), θ0 represents the ambient temperature (°C), P represents the rated power (2π×speed×torque) (W), μ represents the friction coefficient of the thermoplastic resin gear, and k θ，Fuβ represents the heat storage coefficient and the heat transfer coefficient (K·(m / s) c mm 1.75 / W) is defined by VDI 2736 Blatt 2 of a pair of gears, at least one of which is a thermoplastic resin gear. b represents the tooth width (mm), m n represents the normal module (mm), z represents the total number of teeth of a pair of gears, where only the number of teeth in the meshing range is counted when there is no meshing in the whole circle, and v t c One term represents the heat dissipation coefficient, v t represents the circumferential speed of the pitch circle (m / s), c represents a constant of 0.05 to 0.70, R λ，G Indicates the thermal resistance of the shell (K·m 2 / W), A G Indicates the heat dissipation area of ​​the shell (m 2 ), ED represents the relative meshing time per 10 minutes, H v represents the loss coefficient obtained according to the numerical value of the actual overlap according to the following equations 5 to 7, [Mathematical expression 5] In formulas 5 to 7, ε α represents the end face overlap, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.

6. A method for predicting the tooth root temperature of a thermoplastic resin gear, characterized in that: The actual contact ratio calculated by the method for calculating the actual contact ratio of the thermoplastic resin gear according to claim 1 and the friction coefficient μ derived by the method for deriving the friction coefficient of the thermoplastic resin gear according to claim 2 are substituted into the following equations 4 and 5 to 7 to predict the tooth root temperature of the thermoplastic resin gear. [Mathematical expression 6] In formula 4, θ Fuβ represents the tooth root temperature (°C), θ0 represents the ambient temperature (°C), P represents the rated power (2π×speed×torque) (W), μ represents the friction coefficient of the thermoplastic resin gear, and k θ，Fuβ is the heat storage coefficient, and the heat transfer coefficient (K·(m / s) c mm 1.75 / W) is defined by VDI 2736 Blatt 2 of a pair of gears, at least one of which is a thermoplastic resin gear. b represents the tooth width (mm), m n represents the normal module (mm), z represents the total number of teeth of a pair of gears, where only the number of teeth in the meshing range is counted when there is no meshing in the whole circle, and v t c One term represents the heat dissipation coefficient, v t represents the circumferential speed of the pitch circle (m / s), c represents a constant of 0.05 to 0.70, R λ，G Indicates the thermal resistance of the shell (K·m 2 / W), A G Indicates the heat dissipation area of ​​the shell (m 2 ), ED represents the relative meshing time per 10 minutes, H v represents the loss coefficient obtained according to the numerical value of the actual overlap according to the following equations 5 to 7, [Mathematical expression 7] In formulas 5 to 7, ε α represents the end face overlap, u represents the gear ratio z2 / z1, β b represents the base circle helix angle, z1 represents the number of teeth of the gear with fewer teeth in a pair of gears, z2 represents the number of teeth of the gear with more teeth in a pair of gears, ε1 represents the meshing overlap, and ε2 represents the meshing overlap.

7. The method for predicting the tooth root temperature of a thermoplastic resin gear according to any one of claims 4 to 6, characterized in that: When the pair of gears are a combination of gears made of thermoplastic resin, at least one of the following is performed: The number of teeth z in the formula 4 is set to the total number of teeth of a pair of gears, wherein only the number of teeth in the range where meshing occurs is counted when there is no meshing for a whole cycle; The c in the formula 4 is set to 0.10 to 0.60; and The k in the formula 4 is θ，Fuβ Set as (A·ln(b)+B)~(A·ln(b)+C), where b is the tooth width (mm), A is 1130~3610, B is -1.782A+3286, and C is -1.728A+5291.

8. The method for predicting the tooth root temperature of a thermoplastic resin gear according to any one of claims 4 to 6, characterized in that: When the pair of gears is a combination of a thermoplastic resin gear and a metal gear, at least one of the following is performed: The number of teeth z in the formula 4 is set to the total number of teeth of a pair of gears, wherein only the number of teeth in the range where meshing occurs is counted when there is no meshing for a whole cycle; The c in the formula 4 is set to 0.10 to 0.60; and The k in the formula 4 is θ，Fuβ Set as (A·ln(b)+B)~(A·ln(b)+C), where b is the tooth width (mm), A is 100~2000, B is -2.284A+1424, and C is -2.316A+3637.

9. A method for predicting the life of a thermoplastic resin gear, characterized in that: include: Step 9 of preparing an SN curve of the thermoplastic resin gear for each temperature of the teeth of the thermoplastic resin gear, The life of the thermoplastic resin gear is predicted based on the SN curve corresponding to the tooth root temperature obtained by the method for predicting the tooth root temperature of the thermoplastic resin gear according to any one of claims 4 to 8.

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