Method for calculating a predicted value of the jump torque of a toothed belt

Abstract

The value of the overall correction coefficient (K) and the value of the meshing correction coefficient (Kmn) of the driven pulley, which are determined in advance so that the average of the difference between the calculated value of the jump torque (Tq) when the product (ES) of the longitudinal modulus of elasticity (E) and the sectional area (S) of the toothed belt (1), the tooth height (h), the pitch circle radius (Rr) of the driving pulley, the pitch circle radius (Rn) of the driven pulley, the initial tension (T0), the span length (Lt) on the tension side, the span length (Ls) on the slack side, the wrap angle (θr), and the wrap angle (θn) are substituted in the equations (1) to (3) and the measured value of the jump torque (Tq) are compared, is the smallest, are stored in the storage section (12). The jump torque (Tq) of the toothed belt (1) wound around the driving pulley (DR) and the driven pulley (DN) is calculated by substituting the values of the various parameters, the value of the overall correction coefficient (K), and the value of the meshing correction coefficient (Kmn) stored in the equations (1) to (3).

Description

Technical Field

[0001] This invention relates to a method for calculating and controlling the predicted value of the jumping torque of a toothed belt. Background Technology

[0002] In addition to gears and chains, drive belts are also widely used as power transmission mechanisms. Drive belts are broadly classified into friction drive belts, which transmit power through friction with pulleys, and meshing drive belts, which transmit power through mechanical engagement with pulleys. Meshing drive belts include toothed belts, which have teeth only on their inner circumferential surface that mesh with the pulley grooves, and double-sided toothed belts, which have teeth on both their inner and outer circumferential surfaces.

[0003] Friction belts transmit power while allowing some slippage between the pulleys and the belt, so the rotation of the driving pulley and the driven pulley may not be synchronized. In contrast, as seen in meshing belts, also known as synchronous belts, there is no slippage between the pulleys and the belt, and the rotation of the driving and driven pulleys is essentially synchronized. Therefore, when it is necessary to accurately maintain the speed ratio between the driving and driven pulleys, friction belts are not used; instead, meshing belts are employed.

[0004] One point to note when using meshing drive belts is the phenomenon known as "tooth skipping" or "jumping," where the teeth of the meshing drive belt move beyond the tooth grooves of the pulleys and towards adjacent grooves. If this jump occurs, not only will the speed ratio between the driving and driven pulleys be unreliable, but the excessive force acting on the belt and pulley shafts will also damage the entire power transmission mechanism. Therefore, when using meshing drive belts, a design that prevents jumping is essential.

[0005] Existing technical documents

[0006] Non-patent literature

[0007] Non-Patent Literature 1: Tomio Koyama, Weiming Zhang, Asahiko Nishiguchi, Masanori Kagoya, Research on skipped teeth of 123 toothed belt (skipped tooth generation mechanism), Proceedings of the Second Seminar on Lubrication Design of Mechanical Elements of the Japan Society of Mechanical Engineers [No. 02-12], 2002, Vol. 2, pp. 107-110 Summary of the Invention

[0008] The problem that the invention aims to solve

[0009] Regarding this point, research related to the skipping of toothed belts can be cited in the paper by Koyama et al. (see Non-Patent Literature 1). According to this paper, in the case of a two-shaft layout with pulleys of the same diameter, skipping occurs at the beginning of engagement of the driven pulley (the slack side of the belt) by the belt teeth contacting the pulley teeth. Moreover, the skipping torque (the maximum transmitted torque before the belt teeth are fully contacting the pulley teeth) is affected by various factors such as tooth shape, belt properties, belt length, the difference in distance between the belt and pulley, coefficient of friction, pulley layout, number of pulley teeth, operating conditions, and installation tension, and is therefore considered difficult to predict. Therefore, in the past, skipping torque could only be measured by installing a toothed belt on an actual machine, which required significant cost and time.

[0010] Therefore, the object of the present invention is to calculate the predicted value of the jump torque of the toothed belt with high accuracy without actually measuring the jump torque, thereby easily indicating to the user the optimal meshing drive belt that does not produce jump.

[0011] Technical solutions for solving the problem

[0012] This invention relates to a calculation and control method for predicting the jump torque Tq, where Tq is the jump torque of a toothed belt, the toothed belt being wound around a layout including a drive pulley and a driven pulley. The calculation and control method executes the following steps (1a), (1b), and (1c) via a control device: (1a) storing the following values ​​in a storage device: the force-strain relationship value ES of the toothed belt in a tensile test, calculated using the product of the equivalent longitudinal elastic modulus E along the belt length direction and the cross-sectional area S of the toothed belt; the tooth height h; the pitch circle radius Rr of the drive pulley; and the pitch circle radius Rn of the driven pulley; the values ​​of various parameters including the force-strain relationship ES of the toothed belt in a tensile test, calculated using the product of the equivalent longitudinal elastic modulus E along the belt length direction and the cross-sectional area S of the toothed belt; and the values ​​of the pitch circle radius Rn of the drive pulley and the driven pulley. The values ​​of various parameters, including the initial tension T0 when the toothed belt is wound between the belts, the tension side span length Lt, the slack side span length Ls, the winding angle θr of the toothed belt on the drive pulley, and the winding angle θn of the toothed belt on the driven pulley; the value of the overall correction coefficient K and the value of the meshing correction coefficient Kmn of the driven pulley; (b) Substituting the values ​​of the various parameters, the value of the overall correction coefficient K, and the value of the meshing correction coefficient Kmn stored in step (1a) into equations (1) to (3), calculate the predicted value of the jump torque Tq; (c) Output the predicted value of the jump torque Tq calculated in step (1b). The value of the overall correction coefficient K and the value of the meshing correction coefficient Kmn of the driven pulley are predetermined as follows: the calculated value of the jump torque Tq when the values ​​of the above parameters are substituted into equations (1) to (3) is compared with the measured value of the jump torque Tq, and the average difference is minimized.

[0013]

Mathematical Formula 1

[0014]

[0015]

[0016]

[0017] Based on the above method, except for cases where the toothed belt has special specifications or the toothed belt travels at a high speed, a predicted value of the jump torque Tq that is close to the measured value can be calculated.

[0018] Furthermore, this invention provides a method for calculating and controlling the predicted value of a jump torque Tq, where Tq is the jump torque of a toothed belt wound around a layout including a drive pulley and a driven pulley. The calculation and control method executes the following steps (2a), (2b), and (2c) via a control device: (2a) storing the following values ​​in a storage device: the force-strain relationship ES of the toothed belt in a tensile test, calculated using the product of the equivalent longitudinal elastic modulus E along the belt length direction and the cross-sectional area S of the toothed belt; the tooth height h; the pitch circle radius Rr of the drive pulley and the pitch circle radius Rn of the driven pulley; the initial tension T0 when the toothed belt is wound between the drive pulley and the driven pulley; the tension side span length Lt; the slack side span length Ls; the winding angle θr of the toothed belt on the drive pulley; and the... The values ​​of various parameters, such as the winding angle θn of the toothed belt; the values ​​of various parameters, such as the centrifugal tension Tc calculated based on the layout, the linear density m of the toothed belt, the travel speed V of the toothed belt, the centrifugal force correction coefficient Kc corrected based on the centrifugal force corresponding to the mass and travel speed of the toothed belt traveling in the layout, and the belt correction coefficient Kb corrected for the difference in hardness and friction coefficient of the teeth of the toothed belt; and the values ​​of the overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley; (2b) Substituting the values ​​of the various parameters, the overall correction coefficient K and the meshing correction coefficient Kmn stored in step (2a) into equations (2) to (5), the predicted value of the jump torque Tq is calculated; (2c) The predicted value of the jump torque Tq calculated in step (2b) is output. The value of the overall correction coefficient K and the value of the meshing correction coefficient Kmn of the driven pulley are predetermined as follows: the calculated value of the jump torque Tq when the values ​​of the above parameters are substituted into equations (1) to (3) is compared with the measured value of the jump torque Tq, and the average difference is minimized.

[0019]

Mathematical Formula 2

[0020]

[0021]

[0022]

[0023]

[0024] T = mV2

[0025] Formula (5)

[0026] In the above method, a predicted value of the jump torque Tq can be calculated considering the following coefficients: a centrifugal force correction coefficient Kc, which is corrected for the centrifugal force corresponding to the mass and travel speed of the toothed belt traveling in a layout including a drive pulley and a driven pulley; and a belt correction coefficient Kb, which corrects for differences in the hardness and friction coefficient of the toothed belt teeth. Therefore, even when the toothed belt has special specifications and the travel speed of the toothed belt is high, the accuracy of the predicted value of the jump torque Tq can be improved.

[0027] Furthermore, the present invention is a calculation and control method for the predicted value of the jump torque Tq described above, wherein the calculation and control method may further perform the following steps (2d), (2e), (2f), (2g), and (2h): (2d) calculate the effective tension Ten according to equation (6), wherein equation (6) represents the relationship between the predicted value Tqn of the jump torque Tq on the driven pulley calculated by step (2b) and the effective tension Ten, which is the difference between the tension on the tension side and the slack side related to the driven pulley; (2e) further store the value of the meshing correction coefficient Kmr of the drive pulley, which is predetermined by the same method as the value of the meshing correction coefficient Kmn of the driven pulley, in the storage device; (2f) further calculate the effective tension Ten according to equation (7). The effective tension Ter, the equation (7) represents the relationship between the predicted value Tqr of the jump torque Tq of the drive pulley calculated by substituting the value of the meshing correction coefficient Kmr stored in step (2e) into equation (7) and the difference between the tension on the tension side and the slack side tension related to the drive pulley, i.e., the effective tension Ter; (2g) compare the magnitude of the effective tension Ten with the effective tension Ter, and if Ten≤Ter, determine the predicted value Tqn as the predicted value of the jump torque Tq of the entire layout, and if Ten>Ter, determine the predicted value Tqr as the predicted value of the jump torque Tq of the entire layout; and (2h) output the predicted value of the jump torque Tq determined in step (2g).

[0028]

Mathematical Expression 3

[0029]

[0030]

[0031] For example, in a 2-axis layout, if the number of teeth of the driven pulley and the driving pulley are the same, a jump will inevitably occur on the driven pulley. Therefore, by outputting the predicted value of the jump torque Tq on the driven pulley based on equation (4), the predicted value of the overall jump torque Tq of the layout can be calculated.

[0032] However, when the number of teeth on the driven pulley is significantly larger than that on the drive pulley (large reduction ratio), or when the winding angle of the toothed belt on the drive pulley is small in layouts with three or more shafts, skipping may sometimes occur on the drive pulley. In such cases, even if only the skipping torque on the driven pulley is calculated, the skipping torque on the drive pulley will be lower than the calculated skipping torque, therefore it cannot be said that the skipping torque for the entire layout has been calculated.

[0033] Therefore, by calculating the jump torque on each of the driven and driving pulleys, and using the jump torque of the pulley with the lower effective tension as the overall jump torque of the layout, the accuracy of the predicted jump torque can be further improved.

[0034] Invention Effects

[0035] By accurately calculating the predicted value of the skip torque of the toothed belt without actually measuring the skip torque, the user can be easily advised to select the optimal meshing drive belt that will not skip. Attached Figure Description

[0036] Figure 1 This is an explanatory diagram of a power transmission mechanism according to this embodiment, in which a toothed belt is wound between the drive pulley and the driven pulley.

[0037] Figure 2 This is an illustration of a partial cut-off section of the toothed belt that is wrapped around the drive pulley.

[0038] Figure 3 This is a diagram illustrating the mechanism by which the jump occurs.

[0039] Figure 4 This is an explanatory diagram related to the lifting of the toothed belt on the driven pulley during a jump.

[0040] Figure 5 This is a graph showing the relationship between the tension T and the effective tension Te of the toothed belt in the driving state of the power transmission mechanism.

[0041] Figure 6 This is a schematic diagram illustrating an information processing device.

[0042] Figure 7 This is a simplified illustration of layouts 1-4.

[0043] Figure 8 (A) is a graph representing the test results of test examples 1 to 3. Figure 8 (B) is a graph showing the experimental results of test examples 4 to 8.

[0044] Figure 9 (A) is a graph representing the relationship between B / A in equation (13) and the overall correction coefficient K. Figure 9 (B) is a graph showing the relationship between the number of meshing teeth Zmn on the driven pulley and the meshing correction coefficient Kmn of the driven pulley in equation (14).

[0045] Figure 10 (A) is a graph showing the test results of test examples 9 to 13. Figure 10 (B) is a graph showing the test results of test examples 14-16.

[0046] Figure 11 This is a graph showing the relationship between the value of (Hs / (100-Hs)·μ) and the correction coefficient Kb when the values ​​in Table 5 are substituted into Equation (16).

[0047] Figure 12 (A) is a graph representing the test results of test examples 17-19. Figure 12 (B) is a graph showing the test results of test examples 20-25.

[0048] Figure 13 It is a graph showing the relationship between B / A and the centrifugal force correction coefficient Kc in equation (17).

[0049] Figure 14 (A) is a chart summarizing the conditions under which jumps occur at the drive pulley (tooth profile S8M of the toothed belt). Figure 14 (B) is a chart summarizing the conditions under which jumps occur on the driven pulley (tooth profile S8M of the toothed belt).

[0050] Figure 15 (A) is a chart summarizing the conditions under which jumps occur at the drive pulley (tooth profile S3M of the toothed belt). Figure 15 (B) is a chart summarizing the conditions under which jumps occur at the driven pulley (tooth profile S3M of the toothed belt). Detailed Implementation

[0051] (Implementation Method)

[0052] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0053] First, the toothed belt 1 (meshing transmission belt), the drive pulley DR and the driven pulley DN that wrap around the toothed belt 1 will be explained.

[0054] (Power transmission mechanism)

[0055] like Figure 1 As shown, the toothed belt 1 is used to wrap around the drive pulley DR, which is connected to the drive rotating shaft, and the driven pulley DN, which is connected to the driven rotating shaft. Thus, when the drive rotating shaft rotates, the drive pulley DR rotates, and its rotational motion is transmitted to the driven pulley DN via the toothed belt 1, thereby causing the driven rotating shaft to rotate and transmitting power.

[0056] (toothed band 1)

[0057] The toothed band 1 is made of a rubber-like elastomer, such as... Figure 1 and Figure 2 As shown, the convex teeth 2 are arranged on the inner circumferential surface along the length of the belt at a certain tooth pitch. Additionally, as... Figure 2 As shown, the distance from the front end of tooth 2 to the bottom surface of tooth 2 in the thickness direction is the tooth height h of tooth 2.

[0058] On the back of the toothed belt 1, the core wire is embedded in a spiral shape wound along the length of the belt and arranged at specified intervals in a cross-sectional view in the width direction of the belt.

[0059] The rubber-like elastomer constituting the toothed belt 1 is composed of rubber, elastomer, or synthetic resin, etc. The rubber-like elastomer preferably contains rubber (cross-linked rubber). Furthermore, the JISA hardness of the rubber-like elastomer is preferably 70 degrees or higher. The core wire is a highly elastic and high-strength cord. The core wire is formed, for example, from carbon fiber, aramid fiber, glass fiber, etc. Additionally, to improve adhesion to the rubber-like elastomer, the core wire may be bonded. Furthermore, the toothed surface (inner circumferential surface) of the toothed belt 1 may also be covered with toothed cloth.

[0060] (Drive pulley DR)

[0061] The drive pulley DR is made of synthetic resins such as polyacetal, nylon, and polypropylene, or metal. For example... Figure 1 and Figure 2 As shown, multiple teeth DR1 are formed circumferentially at certain intervals on the outer peripheral surface of the drive pulley DR. Furthermore, the teeth 2 of the toothed belt 1 mesh with the grooves DR2 formed between the teeth DR1. In this embodiment, the radius Rr (pulley pitch circle radius of the drive pulley DR) refers to the distance from the center of the drive pulley DR to the pulley pitch circle PP (e.g., ...). Figure 2As shown, the radius Rr of the drive pulley DR is the distance from the center of the core wire when the toothed belt 1 is wrapped around the drive pulley DR (the distance Rr is the distance a from the center of the drive pulley DR to the front end of the toothed section DR1) to the distance PLD (Pitch Line Differential) from the front end of the toothed section DR1 to the circumference PP (center of the core wire) of the pulley pitch.

[0062] The groove depth h2 of the drive pulley DR2 (refer to) Figure 2 It is preferable that the tooth height h of tooth part 2 is larger, but it can also be approximately the same as the tooth height h of tooth part 2.

[0063] In addition, such as Figure 2 As shown, in the driving state of the power transmission mechanism, the belt travel direction of the toothed part DR1 and the toothed part 2 of the drive pulley DR is ( Figure 2 A portion of the face on the opposite side (in the direction of the arrow) makes surface contact. Additionally, as... Figure 1 As shown, in the driving state, the angle at which the toothed belt 1 on the outer periphery of the drive pulley DR contacts the drive pulley DR is set as the winding angle θr (rad).

[0064] (Driven pulley DN)

[0065] Both the driven pulley DN and the driving pulley DR are made of synthetic resins such as polyacetal, nylon, and polypropylene, or metal. Figure 1 and Figure 2 As shown, a plurality of teeth DN1 are formed circumferentially at certain intervals on the outer peripheral surface of the driven pulley DN. Furthermore, the teeth 2 of the toothed belt 1 mesh with the grooves DN2 formed between the teeth DN1. In this embodiment, the radius Rn (pulley pitch circle radius of the driven pulley DN) refers to the distance from the center of the driven pulley DN to the pulley pitch circle PP. In other words, the radius Rn of the driven pulley DN is the value obtained by adding the distance b from the center of the driven pulley DN to the tip of the teeth DN1 to the distance PLD from the tip of the teeth DN1 to the pulley pitch circle PP (the center of the core wire).

[0066] The groove depth h3 (not shown) of the groove portion DN2 of the driven pulley DN is preferably greater than the tooth height h of the tooth portion 2, but it can also be approximately the same as the tooth height h of the tooth portion 2.

[0067] In addition, such as Figure 1 As shown, in the driving state of the power transmission mechanism, the belt travel direction of the driven pulley DN's teeth DN1 and DN2 is ( Figure 1 The face of the surface in the direction of the arrow is in contact with a portion of the surface. Additionally, as... Figure 1As shown, in the driving state, the angle at which the toothed belt 1 on the outer periphery of the driven pulley DN contacts the driven pulley DN is set as the winding angle θn (rad).

[0068] Here, under the driving state of the power transmission mechanism, the toothed belt 1 elongates due to the increased tension on the tension side span. It is assumed that this elongation of the toothed belt 1 on the tension side span is absorbed by the toothed belt 1 floating (tilting outwards) on the driven pulley DN. Furthermore, if the transmitted power increases, it is assumed that the elongation of the toothed belt 1 on the tension side span cannot be completely absorbed by the elongation equivalent to the floating of the toothed belt 1 on the driven pulley DN, resulting in a jump where the teeth 2 of the toothed belt 1 move past the teeth DN1 of the driven pulley DN towards the adjacent groove DN2 (see reference). Figure 3 In this embodiment, the maximum transmitted torque before the tooth 2 of the toothed belt 1 is about to fully engage with the tooth DN1 of the driven pulley DN (before the jump occurs) is defined as the jump torque Tq.

[0069] (Information processing device 10)

[0070] like Figure 6 As shown, the information processing device 10 is a general-purpose computer used to calculate the jump torque Tq. Through user operation, it can input various data and requests, store and save data, and perform calculations. The information processing device 10 of this embodiment includes a control unit 11 (control device), a storage unit 12 (storage device), an input unit 13, and a display unit 14 (display device).

[0071] The control unit 11 is the part that performs computer control (CPU, etc.) in the information processing device 10.

[0072] The storage unit 12 consists of ROM (Read Only Memory) storing the system program, RAM (Random Access Memory) which is a rewritable storage area, flash memory, etc.

[0073] The input unit 13 is an operating device used by users to input various data, requests, and commands, such as a keyboard or mouse.

[0074] Display unit 14 displays information based on instructions from control unit 11, etc.

[0075] In this embodiment, the storage unit 12 stores an information table containing the values ​​of various parameters used in the calculation of the jump torque Tq (described later) and a program containing the algorithm used in the calculation of the jump torque Tq.

[0076] Specifically, in the information table of the storage unit 12, the following values ​​are stored through input from the input unit 13: the equivalent longitudinal elastic modulus E of the toothed belt 1 in the belt length direction, the cross-sectional area S of the toothed belt 1, the value (ES) obtained by multiplying the longitudinal elastic modulus E by the cross-sectional area S according to the relationship between force and strain in the tensile test of the toothed belt 1, the tooth height h of the toothed belt 1, and the values ​​of various parameters such as the radius Rr (pitch circle radius of the drive pulley DR) and the radius Rn (pitch circle radius of the driven pulley DN); the initial tension T0 when the toothed belt 1 is wound between the drive pulley DR and the driven pulley DN, and the tension side span length Lt (refer to...). Figure 1 ), Relaxed side span length Ls (refer to) Figure 1 The values ​​of various parameters include the winding angle θr (rad) of the toothed belt 1 on the outer periphery of the drive pulley DR in contact with the drive pulley DR, and the winding angle θn (rad) of the toothed belt 1 on the outer periphery of the driven pulley DN in contact with the driven pulley DN. In addition, the overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley are stored. These overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley are predetermined values ​​that are calculated by comparing the jump torque calculated by substituting the values ​​of the above various parameters into the following equations (1) to (3) with the measured value of the jump torque, and the average of the difference is minimized. Details will be described later. Furthermore, the values ​​of various parameters are stored, including the centrifugal tension Tc calculated based on the layout of the drive pulley DR and driven pulley DN, which is the tension generated by the centrifugal force of the toothed belt 1; the linear density m of the toothed belt 1 (mass per unit length of the toothed belt 1, maintained within the program); the traveling speed V of the toothed belt 1; the centrifugal force correction coefficient Kc, which is corrected based on the centrifugal force corresponding to the mass and traveling speed V of the toothed belt 1 traveling in the layout; the belt correction coefficient Kb, which corrects for the difference in hardness and friction coefficient of the teeth 2 of the toothed belt 1; and the meshing correction coefficient Kmr of the drive pulley. These values ​​will be described in detail later. Here, the tension side span length Lt is the distance between the contact points of the toothed belt and the pulley on the side where the toothed belt begins to mesh with the drive pulley, and the slack side span length Ls is the distance between the contact points of the toothed belt and the pulley on the side where the meshing of the toothed belt with the drive pulley is released. The ES value is calculated as follows: with the annular toothed belt wound around a pair of pulleys, a load is applied in the direction of tension of the toothed belt, and the difference in belt tension at two specified points (e.g., a load equivalent to the belt's installation tension and the maximum effective tension applied during a jump) is divided by the rate of change of the belt length, multiplied by 100. The initial tension T0 can be determined using known methods such as an acoustic tension meter.

[0077] In addition, in the storage unit 12, as an algorithm used in the calculation of the jump torque Tq, there is a program that reads in various parameters stored in the information table and calculates the predicted value of the jump torque Tq, and is programmed with the following formulas (1) to (7).

[0078] Furthermore, in the power transmission mechanism, the measured values ​​of the tension distribution on the driven pulley DN, especially the tension distribution just before the jump, are not constant. They also change continuously in the form of a near-quadratic curve from the slack side to the tension side in both the drive pulley DR and the driven pulley DN. Therefore, the effective span length "A" on the tension side and the effective span length "B" on the slack side of the toothed belt 1 are calculated using equations (2) and (3), with the center of the winding portion of each of the drive pulley DR and the driven pulley DN as the distance between them.

[0079] (Simplified correction method)

[0080]

Mathematical Expression 4

[0081]

[0082]

[0083]

[0084] (Final Correction Formula)

[0085]

Mathematical Expression 5

[0086]

[0087] T c =mV 2 ...Formula (5)

[0088] (The jump torque in the event of a jump on the drive pulley is also taken into account.)

[0089]

Mathematical Expression 6

[0090]

[0091]

[0092] (Explanation of the simplified correction formula)

[0093] The calculation process of the above equation (1) will be explained. In the power transmission mechanism, when the drive shaft is stationary, the tension of the tension side span length Lt and the slack side span length Ls, which are not in contact with the drive pulley DR and the driven pulley DN, is equal (initial tension: T0). When the drive shaft starts to rotate, the tension of the tension side span entering the drive pulley DR (tension side tension: Tt) increases, and the tension of the slack side span exiting the drive pulley DR (slack side tension: Ts) decreases. The driven pulley DN is rotated by this tension difference (effective tension: Te = Tt - Ts). As the transmitted power increases, Tt increases (Tt = T0 + (B / A + B)Te), and Ts decreases (Ts = T0 - (A / A + B)Te). Furthermore, the tension side tension when Ts = 0 is calculated as Tt* = (A + B)T0 / A and (Tt = Tt*) (refer to...). Figure 5 Furthermore, when Tt > Tt*, Tt = Te.

[0094] As described above, in the driving state of the power transmission mechanism, the toothed belt 1 elongates due to the increased tension in the tension side span. It is assumed that this elongation of the toothed belt 1 in the tension side span is absorbed by the toothed belt 1 floating (tilting outwards) on the driven pulley DN. Furthermore, if the transmitted power increases, it is assumed that the elongation x of the toothed belt 1 in the tension side span (referring to (Equation 8): Tt>Tt*, Tt=Te) cannot be completely absorbed by the elongation y equivalent to the floating (float amount r) of the toothed belt 1 on the driven pulley DN, resulting in a jump. The maximum transmitted torque T before this jump is about to occur is set as the jump torque Tq. Figure 3 As shown, the main reason why the belt lifts off the slack side of the pulley winding is that the tension on the slack side is 0 and the belt pressing force is 0. The influence of the bending moment caused by the tooth load when the belt teeth mesh with the pulley teeth, as well as the right-angle component of the normal force and friction force caused by the tooth load, i.e., the belt pushing force, is significantly manifested.

[0095]

Mathematical Expression 7

[0096]

[0097] Here, the tension Tt in equation (2) is theoretically Tt = Te as described above, but in reality, the slack tension Ts is not 0, especially near the jump, the slack tension Ts tends to increase along with the load. Therefore, if we consider the experimentally derived correction coefficient K (≤1) and calculate it as Te = KTt, then the belt elongation x of the toothed belt 1 on the tension side span at the jump replaces equation (8) and becomes equation (9).

[0098]

Mathematical Expression 8

[0099]

[0100] On the other hand, such as Figure 4 As shown, assuming that during a jump, the buoyancy r is the same as the tooth height h of the toothed belt 1 (r = h), and the angle α (rad) of the buoyancy portion of the toothed belt 1 on the driven pulley DN corresponds to the winding angle θn at which the toothed belt 1 and the driven pulley DN come into contact (α = θn). Furthermore, since the belt elongation x of the tension side span is equal to the belt elongation y (y = (Rn + r)α - Rnα = rα) corresponding to the buoyancy (buoyancy r) of the toothed belt 1 on the driven pulley DN, equation (10) is derived.

[0101]

Mathematical Expression 9

[0102] x = y = hθ n ...(Equation 10)

[0103] However, the actual effective tooth height during the jump is presumed to be different from the tooth height h of tooth profile 1 for the following reasons.

[0104] (a) Due to the deformation of the teeth, the effective tooth height is reduced.

[0105] (b) During the jump, the meshing teeth of the wound portion of the toothed band 1 may not all float up evenly.

[0106] (c) The lifting of the wound portion caused by the belt elongation of the tension side span is not caused by either the driven pulley DN or the driving pulley DR, but by the pulleys of both with different lifting amounts.

[0107] (d) In the jump on the drive pulley DR, all teeth 2 need to cross teeth DR1, but on the driven pulley DN, a jump will occur even if all teeth 2 do not cross teeth DN1.

[0108] Based on the above reasons, instead of equation (10), the belt elongation y of the winding part during the jump is calculated by equation (11), and the meshing correction coefficient Kmn of the driven pulley DN is obtained experimentally in the same way as the correction coefficient K.

[0109]

Mathematical Formula 10

[0110] x = y = K m ·hθ n ...Formula (11)

[0111] Furthermore, when Te is derived from equations (9) and (11), it becomes equation (12).

[0112]

Mathematical Expression 11

[0113]

[0114] Then, when the maximum transmitted torque before the jump is about to occur, i.e. the jump torque Tq (Tq = Te·Rn), is derived, it becomes the initial equation (1).

[0115] (Explanation of the final correction formula)

[0116] Compared with the simplified correction formula (1), the final correction formula of the above formula (4) calculates the predicted value of the jump torque Tq with higher accuracy.

[0117] Specifically, the final correction formula of Equation (4) is based on Equation (1), further considering the centrifugal force correction coefficient Kc, which is corrected based on the centrifugal tension Tc corresponding to the mass m (linear density m of the toothed belt 1) and travel speed V of the toothed belt 1 traveling in the layout including the drive pulley DR and the driven pulley DN, and the belt correction coefficient Kb, which is corrected for the difference in hardness and friction coefficient of the toothed belt, to calculate the predicted value of the jump torque Tq. Therefore, even when the toothed belt 1 has a special specification and the travel speed V of the toothed belt 1 is large, the accuracy of the predicted value of the jump torque Tq can be improved. Here, the linear density m is the mass per unit length of the toothed belt 1, which is maintained in the program. The travel speed V is calculated based on the input layout. The centrifugal tension Tc is the tension generated by the centrifugal force of the toothed belt 1, which is calculated based on the input layout. The correction coefficients are described below.

[0118] Conversely, equation (1) is simply an expression in equation (4) with Kb = 1 and Kc = 0. Kb = 1 is the value used for standard specification belts (our company's over-torque G), and Kc = 0 means that the correction based on centrifugal tension Tc can be ignored when the travel speed V of the toothed belt is small. That is, when using a standard specification belt at low speed, both equation (1) and equation (4) provide approximately the same result.

[0119] (The calculation of the jump torque in the case of jumping on the drive pulley is also taken into account.)

[0120] In a 2-axis layout, when the number of teeth of the driven pulley DN and the driving pulley DR are the same, a jump will inevitably occur on the driven pulley DN. Therefore, the jump torque on the driven pulley DN can be calculated based on equation (4), so that the overall jump torque Tq of the layout can be calculated.

[0121] However, when the number of teeth on the driven pulley DN is much larger than the number of teeth on the drive pulley DR (large reduction ratio), or when the winding angle θr of the toothed belt 1 on the drive pulley DR is small in a layout with more than 3 shafts, skipping sometimes occurs on the drive pulley DR.

[0122] In this case, even if only the jump torque on the driven pulley DN is calculated, the jump torque of the entire layout cannot be said to have been calculated because the jump occurs on the drive pulley DR with a lower torque than the jump torque obtained by calculation.

[0123] Therefore, by calculating the jump torque Tqn on the driven pulley DN and the jump torque Tqr on the driving pulley DR, and using the jump torque of the one with lower effective tension as the overall jump torque Tq of the layout, the prediction accuracy can be further improved.

[0124] Specifically, after calculating the jump torque using equation (6) for calculating the jump torque Tqn on the driven pulley DN and equation (7) for calculating the jump torque Tqr on the drive pulley DR, the effective tension Ten (the difference between the tension on the tension side and the slack side on the driven pulley DN) and the effective tension Ter (the difference between the tension on the tension side and the slack side on the drive pulley DR) in each calculation are compared. If Ten ≤ Ter, the jump torque Tqn is used as the overall jump torque Tq for this layout; if Ten > Ter, the jump torque Tqr is used as the overall jump torque Tq for this layout. Furthermore, the magnitudes of the jump torques Tqn and Tqr are not compared.

[0125] Furthermore, Equation (6) only adds a subscript to Equation (4) to indicate the driven pulley DN, and is essentially no different from Equation (4). In order to calculate the jump torque Tqn on the drive pulley DR, Equation (7) changes the winding angle θr corresponding to the drive pulley DR, the radius Rr (pulley pitch circle radius of the drive pulley DR), and the meshing correction coefficient Kmr of the drive pulley DR in Equation (4), but the overall correction coefficient K, the centrifugal force correction coefficient Kc, and the belt correction coefficient Kb use the coefficients shared with Equation (4).

[0126] (Method for determining each correction factor)

[0127] The correction coefficients of the overall correction coefficient K, centrifugal force correction coefficient Kc, belt correction coefficient Kb, driven pulley meshing correction coefficient Kmn, and driving pulley meshing correction coefficient Kmr shown in equations (1) to (12) above are calculated in a way that the calculated value is approximately the same as the measured jump torque Tq.

[0128] Below is an example of how to determine each correction factor. However, the formulas and values ​​below are for toothed belts of a specific specification and tooth shape. If it is a toothed belt of other tooth shapes and specifications, the values ​​are determined accordingly. Therefore, the methods for determining each correction factor are not limited to the examples below.

[0129] (Determination of the overall correction factor K and the meshing correction factor Km)

[0130] The actual measured value of the jump torque in the testing machine configured as shown in layouts 1 to 4 described below is compared with the calculated value of the jump torque obtained by the calculation formula. The overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley are determined relative to the measured value of the jump torque in a way that makes equation (4) a good approximation.

[0131] The determination of the measured value of the jump torque using the testing machine was carried out in Figure 7 The tests were conducted under the conditions shown in Table 2 for layouts (A) to (D) and layouts 1 to 4 shown in Table 1.

[0132] Specifically, the drive pulley is rotated at a constant speed, and its rotation is transmitted to the driven pulley via a toothed belt. The load on the driven pulley is increased at a constant speed, and the torque at which a jump occurs is recorded as the jump torque. The test belt (toothed belt) is a "Super Torque G" (tooth profile: S8M, tooth pitch: 8mm, tooth height (h): 3.05mm, tooth hardness (Hs): 75 degrees, coefficient of friction (μ): 0.32) manufactured by Mitsubishi Belt Co., Ltd. For belts of low friction and high rigidity specifications described later, this specification is referred to as the standard specification. In addition, in this application, the tooth hardness refers to the JIS-A hardness measured by a type A hardness tester according to JIS-K6253-3 (2012). In Equation (4), the belt correction coefficient Kb is included as a coefficient used to correct the difference between the tooth hardness and the coefficient of friction, but in the case of using the standard specification used in this test, it is set to Kb = 1. Furthermore, this experiment was conducted at a relatively low speed of 500 rpm, so the maximum centrifugal tension Tc was approximately 0.53 N, which is sufficiently small relative to the initial tension T0. Therefore, the centrifugal force correction coefficient Kc can be considered to be 0. Thus, by setting Kb = 1 and Kc = 0 in equation (4), the overall correction coefficient K and the meshing correction coefficient Km can be determined with high precision.

[0133] Furthermore, in this experiment, all the jumps occurred on the driven pulley, so the calculated correction coefficient Km became the meshing correction coefficient Kmn of the driven pulley.

[0134] Additionally, in Table 1, the span length L represents the span length between the pulley and the next numbered pulley.

[0135] For example, in a 3-axis layout, the span length L of pulley number 1 represents the straight-line distance from the closest contact point between the pulley and belt on pulley number 1 and pulley number 2 to the closest contact point between the pulley and belt on pulley number 2 and pulley number 1. Similarly, the span length L of pulley number 2 represents the straight-line distance from the closest contact point between the pulley and belt on pulley number 2 and pulley number 3 to the closest contact point between the pulley and belt on pulley number 3 and pulley number 2. Furthermore, the span length L of pulley number 3 represents the straight-line distance from the closest contact point between the pulley and belt on pulley number 3 and pulley number 1 to the closest contact point between the pulley and belt on pulley number 1 and pulley number 3.

[0136] Additionally, in Table 1, which shows the layout, the center-to-center distance of the pulleys indicates the center-to-center distance between the pulley and the next pulley in the sequence.

[0137] For example, in a 3-axis layout, the center-to-center distance of pulley number 1 represents the straight-line distance from the center of pulley number 1 to the center of pulley number 2. Similarly, the center-to-center distance of pulley number 2 represents the straight-line distance from the center of pulley number 2 to the center of pulley number 3. Furthermore, the center-to-center distance of pulley number 3 represents the straight-line distance from the center of pulley number 3 to the center of pulley number 1. In addition, in the test conditions of Table 2, the rotation direction is the rotation direction of the driving pulleys and toothed belt. Figure 7 In the top view, CW represents clockwise, and CCW represents counterclockwise.

[0138] Table 1

[0139]

[0140] (Experimental conditions)

[0141] Table 2

[0142] Table 2

[0143]

[0144] (Experimental Results)

[0145] Figure 8 The results of test examples 1-3 are shown in (A). Figure 8 The results of experiments 4–8 are shown in (B). Figure 8 In the diagram, circles, rhombuses, and quadrilaterals represent the measured values ​​of the jump torque, while solid lines and dashed lines represent the calculated values ​​of the jump torque based on equation (4).

[0146] These test results show that the jump torque is proportional to the initial tension and increases with the belt width, in other words, with the belt's ES value.

[0147] Furthermore, when the span lengths on the tension side and the slack side are different, the jump torque increases in the rotation direction where the span length on the tension side is shorter (CW in this case), thus confirming the appropriateness of equation (4).

[0148] Next, the determination of the overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley will be explained in detail. The overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley are determined by comparing the measured value of the jump torque under the above test conditions with the calculated value of the jump torque when Kb=1 and Kc=0 in equation (4), and the average of their differences is minimized. More specifically, they are determined according to the steps in [1] to [4] below.

[0149] [1] such as Figure 8 (A) Figure 8 As shown in (B), the measured values ​​of the jump torque are plotted in a graph where the vertical axis is set to the jump torque and the horizontal axis is set to the initial tension.

[0150] [2] In addition, the calculated values ​​of the jump torque with appropriate initial values ​​for K and Km (specifically, K = 0.5 and Km = 0.5) are added to the above chart.

[0151] [3] The value of K was corrected by making the gradient of the calculated value of the jump torque close to the gradient of the measured value of the jump torque, so that the calculated value of the jump torque relative to the corrected value of K was close to the measured value.

[0152] [4] Repeating [2] and [3] above, K and Km are determined in a way that minimizes the average of the differences between all measured and calculated values.

[0153] The overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley, obtained through the above steps, are shown in equations (13) and (14) below. Furthermore, Zmn is the number of meshing teeth on the driven pulley. Additionally, in Figure 9 The graph in (A) shows the relationship between B / A in expression (13) and the overall correction coefficient K. Additionally, in Figure 9 In (B), a graph is shown showing the relationship between the number of meshing teeth Zmn on the driven pulley and the meshing correction coefficient Kmn of the driven pulley in expression (14).

[0154]

Mathematical Expression 12

[0155]

[0156] When B / A < 1, a = 0.290

[0157] When B / A > 1, a = 0.120

[0158]

[0159] The above describes the method for determining the meshing correction coefficient Kmn of the driven pulley under the condition that jump occurs in the driven pulley. However, by increasing the reduction ratio by using a driven pulley with more teeth, the same experiment can be performed under the condition that jump occurs in the driving pulley to determine the meshing correction coefficient Kmr of the driving pulley. The actually determined Kmr is given by the following formula. In the following formula, Zmr is the number of meshing teeth on the driving pulley.

[0160]

Mathematical Expression 13

[0161]

[0162] (Determination with correction factor Kb)

[0163] Next, the determination of the belt correction factor Kb will be explained. The belt correction factor Kb is a factor that corrects for the influence of the difference in hardness of the toothed belt teeth and the friction coefficient between the toothed belt and the toothed pulley on the jump torque. That is, when the hardness of the teeth is high, tooth deformation is suppressed, and the situation where the teeth of the toothed belt rest on the teeth of the pulley is suppressed, so the jump torque is considered to be larger.

[0164] Furthermore, when the coefficient of friction is low, the teeth of the toothed belt tend to slip off the inclined surface of the pulley groove. Therefore, it is assumed that the situation where the teeth of the toothed belt rest on the teeth of the pulley is suppressed, resulting in a larger jump torque. Thus, based on the assumption that the belt correction coefficient Kb is determined by the hardness of the toothed belt teeth and the coefficient of friction between the toothed belt and the toothed pulley, it was experimentally determined. The experiment was conducted under the following two conditions.

[0165] (Experimental Condition A)

[0166] The test layout for test condition A was the same as when determining the overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley, using layouts 2 to 4. The test belt (toothed belt) used was a belt with a reduced coefficient of friction (μ) of 0.26 achieved by coating the tooth surface of the same belt as described above, namely, the "Super Torque G" (tooth profile: S8M, tooth pitch: 8mm, tooth height (h): 3.05mm, tooth hardness Hs: 75 degrees) manufactured by Mitsubishi Belt Co., Ltd. This belt was referred to as the low-friction specification. The initial tension for layout 2 was set to three conditions: 125, 250, and 500 N; the initial tension for layouts 3 and 4 was set to one condition: 125 N. The speed of the drive pulley was set to 500 rpm. The test conditions are summarized in Table 3.

[0167] Table 3

[0168] Table 3

[0169]

[0170] (Experimental Condition B)

[0171] Test condition B uses the same simple 2-axis layout as layout 2 described above, but the number of teeth on both the driving and driven pulleys is set to 22. The test belt (toothed belt) used is the "GIGA Torque GX" (tooth profile: G8M, tooth pitch: 8mm, tooth height (h): 3.50mm, tooth hardness (Hs): 98 degrees, coefficient of friction (μ): 0.24) manufactured by Mitsubishi Belt Co., Ltd. This belt is referred to as a high-rigidity specification. The test conditions are summarized in Table 4.

[0172] Table 4

[0173] Table 4

[0174]

[0175] (Experimental Results)

[0176] Figure 10 The results of test examples 9-13 are shown in (A). Figure 10 The results of test examples 14–16 are shown in (B). Figure 10 In the diagram, circles, rhombuses, and quadrilaterals represent the measured values ​​of the jump torque, while solid lines and dashed lines represent the calculated values ​​of the jump torque based on equation (4).

[0177] Will Figure 10 (A) and Figure 8 Compared to (B), in the low-friction specification belt, it can be confirmed that the jump torque is greater than that in the standard specification belt.

[0178] Next, the determination of the belt correction coefficient Kb will be explained. In equation (4), it is assumed that the influence caused by centrifugal tension can be ignored in this experiment, so Kc is set to 0. K and Kmn are calculated using equations (13) and (14) above. Similar to when K and Kmn are determined, an appropriate initial value is input for Kb to calculate the jump torque, and the value of Kb is obtained in a way that makes the calculated value consistent with the measured value. The belt correction coefficient Kb is expressed by the following equation (16). In addition, Table 5 summarizes the hardness Hs of the toothed belt teeth, the friction coefficient μ between the toothed belt and the toothed pulley, and the belt correction coefficient Kb for each belt specification of the toothed belt. Figure 11 This is a graph showing the relationship between the value of (Hs / (100-Hs)·μ) and the correction coefficient Kb when the values ​​in Table 5 are substituted into Equation (16).

[0179]

Mathematical Expression 14

[0180]

[0181] Table 5

[0182] Table 5

[0183]

[0184] (Determination of the centrifugal force correction factor Kc)

[0185] Next, the determination of the centrifugal force correction factor Kc will be explained. When the toothed belt rotates, a centrifugal force is generated corresponding to its mass and travel speed. This centrifugal force acts as the force of the toothed belt resting on the teeth of the pulley; therefore, it is assumed that the jump torque decreases when the pulley's rotational speed is higher. In the experiments so far, since the drive pulley's rotational speed is as low as 500 rpm and the toothed belt's travel speed is also low, the influence of centrifugal force on the jump torque can be ignored, and Kc is set to 0. However, in actual use of toothed belts, they are sometimes used at much higher rotational speeds. By using centrifugal force-based correction, the prediction accuracy of the jump torque can be further improved.

[0186] (Experimental conditions)

[0187] First, for the 2-axis layout, tests were conducted with the same test belt, layout, and test conditions as in Test Example 4, except for the speed of the drive pulley. The drive pulley speeds were 500 rpm, 1000 rpm, 2000 rpm, and 3000 rpm. Specifically, the drive pulley speeds at an initial tension of 250 N were 500 rpm and 3000 rpm. Second, for the 3-axis layout, tests were conducted with the same test belt, layout, and test conditions as in Test Examples 7 and 8, except for the speed of the drive pulley. The drive pulley speeds were 500 rpm and 3000 rpm. The test conditions are summarized in Table 6.

[0188] Table 6

[0189] Table 6

[0190] Table 6

[0191]

[0192] (Experimental Results)

[0193] Figure 12 The results of test examples 17-19 are shown in (A). Figure 12 The results of test examples 20–25 are shown in (B). Figure 12In the diagram, circles, rhombuses, and quadrilaterals represent the measured values ​​of the jump torque, while solid lines and dashed lines represent the calculated values ​​of the jump torque based on equation (4).

[0194] When observing them, the jump torque decreases roughly in a quadratic curve as the rotational speed increases, which confirms the appropriateness of equation (4).

[0195] The method for determining the centrifugal force correction coefficient Kc is the same as the method for determining the correction coefficient Kb. That is, in equation (4), K, Kmn, and Kb are calculated using the values ​​obtained from equations (13), (14), and (16). An appropriate initial value is input to Kc to calculate the jump torque, so that the calculated value is consistent with the measured value. The obtained centrifugal force correction coefficient Kc is shown in the following equation (17). Furthermore, in Figure 13 The figure shows the relationship between B / A and centrifugal force correction coefficient Kc in expression (17).

[0196]

Mathematical Expression 15

[0197]

[0198] The methods for determining the various correction coefficients have been described above, but these correction coefficients sometimes vary depending on the belt specifications, tooth profile (especially tooth pitch), and other conditions. Therefore, the invention of this application is not limited to the form of the formulas for the correction coefficients or the values ​​of the coefficients described in this embodiment.

[0199] (Verification of prediction accuracy 1)

[0200] Based on the test conditions shown in the above test example, the matching between the jump torque measured by the inventors and the jump torque calculated using formula (4) was verified.

[0201] Figure 14 (A) summarizes the conditions under which a jump occurred at the drive pulley. Figure 14 (B) summarizes the conditions under which a jump occurred on the driven pulley.

[0202] Figure 14 (A) contains 37 conditions, with an average error of 5.3%, a maximum error of 12.4%, and a standard deviation of 2.7 Nm. Figure 14 (B) contains 56 conditions, with an average error of 10.2%, a maximum error of 39.5%, and a standard deviation of 4.2 Nm. Based on the above results, the calculation formula of this application can be considered to have relatively high prediction accuracy.

[0203] (Verification of prediction accuracy 2)

[0204] In the above test examples, the tooth profile of the test tape (toothed tape) was S8M, but verification was also conducted with a smaller pitch S3M tooth profile. The following shows the test conditions when the tooth profile of the test tape (toothed tape) was S3M, the test results of calculating the tape correction coefficient Kb, and the verification of the prediction accuracy.

[0205] (Experimental conditions)

[0206] Test belt (toothed belt) and pulley tooth profile: S3M

[0207] Layout: 2-axis layout (Layout 2) and 3-axis layout (Layout 1)

[0208] Pulley tooth count: Select from 24, 48, and 72 teeth pulleys, and combine them with initial tensions T0 of 25 N, 51 N, and 101 N.

[0209] Width: 10mm

[0210] Belt length: 600mm

[0211] Available in three specifications: standard, high-strength, and high-modulus (see Table 7).

[0212] (with specifications)

[0213] Table 7

[0214] Table 7

[0215] Table 7

[0216]

[0217] (Experimental Results)

[0218] Even when the test belt (toothed belt) has an S3M tooth profile, the jump torque is calculated by inputting an appropriate initial value for Kb, similar to the S8M tooth profile case, in a way that ensures the calculated value is consistent with the measured value. The Kb values ​​for each belt specification with the S3M tooth profile are shown in Table 8. Furthermore, if the measured and calculated jump torque values ​​are summarized in a chart, it becomes as follows... Figure 15 Even with the S3M tooth profile, the measured values ​​and calculated values ​​are well consistent, indicating that the calculation control method of this application can calculate the jump torque with high accuracy even with different tooth profiles.

[0219] Table 8

[0220] Table 8

[0221] Specifications With correction factor Kb Standard Specifications 1.55 High strength specifications 1.26 High elastic modulus specifications 0.84

[0222] (Calculation and processing of the predicted value of jump torque Tq)

[0223] Next, the calculation process for the predicted value of the jump torque Tq using the information processing device 10 will be explained.

[0224] First, the user inputs the equivalent longitudinal elastic modulus E of the toothed belt 1 in the belt length direction, the cross-sectional area S of the toothed belt 1, the value obtained by multiplying the longitudinal elastic modulus E by the cross-sectional area S (ES), the tooth height h of the toothed belt 1, and the radius Rr (pitch circle radius of the drive pulley DR) and the radius Rn (pitch circle radius of the driven pulley DN) of the driven pulley DN through the input section 13 of the information processing device 10. The values ​​of various parameters, such as initial tension T0, tension side span length Lt, slack side span length Ls, winding angle θr (rad), winding angle θn (rad), overall correction coefficient K, driven pulley meshing correction coefficient Kmn, centrifugal tension Tc, linear density m of toothed belt 1, traveling speed V of toothed belt 1, centrifugal force correction coefficient Kc, belt correction coefficient Kb, and drive pulley meshing correction coefficient Kmr, are stored in the information table of storage unit 12 (steps 1a and 1e).

[0225] Next, the user can choose Mode A, which uses a simplified correction formula (1) to calculate the predicted value of the jump torque Tq; Mode B, which uses a final correction formula (4) to calculate the predicted value of the jump torque Tq; and Mode C, which uses formulas (6) and (7) to calculate the predicted value of the jump torque Tq, taking into account the jump that occurs on the drive pulley. Furthermore, since the values ​​of various parameters obtained in each of Modes A to C are different, in step 1a above, the input unit 13 only needs to store the values ​​of the various parameters required for convenience in the storage unit 12.

[0226] (Mode A: Using simplified correction formula (1) etc.)

[0227] The control unit 11 of the information processing device 10 reads equations (1) to (3) from the program, reads the values ​​of various parameters required by equations (1) to (3) stored in the information table of the storage unit 12, and calculates the predicted value of the jump torque Tq (step 1b).

[0228] Then, the control unit 11 displays the predicted value of the calculated jump torque Tq on the display unit 14 (step 1c).

[0229] Based on the above method, except for cases where the toothed belt 1 has special specifications or the traveling speed of the toothed belt 1 is high, a predicted value of the jump torque Tq that is close to the measured value can be calculated.

[0230] (Mode B: Using the final corrective formula (4) etc.)

[0231] The control unit 11 of the information processing device 10 reads equations (2) to (5) from the program, reads the values ​​of various parameters required by equations (2) to (5) stored in the information table of the storage unit 12, and calculates the predicted value of the jump torque Tq (step 1b).

[0232] Then, the control unit 11 displays the predicted value of the calculated jump torque Tq on the display unit 14 (step 1c).

[0233] In the above method, a predicted value for the jump torque Tq can be calculated, taking into account the centrifugal force correction coefficient Kc, which is corrected for the centrifugal force corresponding to the mass and travel speed V of the toothed belt 1 traveling in the layout including the drive pulley DR and the driven pulley DN, and the belt correction coefficient Kb, which is corrected for the differences in hardness and friction coefficient of the teeth 2 of the toothed belt 1. Therefore, even when the toothed belt 1 has special specifications and the travel speed V of the toothed belt 1 is large, the accuracy of the predicted value of the jump torque Tq can be improved.

[0234] (Mode C: Using formulas (6) and (7), etc.)

[0235] The control unit 11 of the information processing device 10 calculates the effective tension Ten according to equation (6), which represents the relationship between the predicted value Tqn of the jump torque Tq on the driven pulley DN and the difference between the tension on the tension side and the tension on the slack side of the driven pulley DN, i.e., the effective tension Ten. The predicted value Tqn of the jump torque Tq on the driven pulley DN is calculated by reading the values ​​of various parameters required by equations (2) to (5) from the program and reading them into the information table stored in the storage unit 12 (step 1d).

[0236] Calculate the effective tension Ter according to equation (7), where equation (7) represents the relationship between the predicted value Tqr of the jump torque Tq on the drive pulley DR calculated by substituting the value of the meshing correction coefficient Kmr of the drive pulley stored in step 1e above into equation (7) and the difference between the tension on the tension side and the slack side of the drive pulley DR, i.e., the effective tension Ter (step 1f).

[0237] Next, the control unit 11 compares the calculated effective tension Ten with the effective tension Ter. If Ten ≤ Ter, the predicted value Tqn is determined as the predicted value of the overall jump torque Tq of the layout. If Ten > Ter, the predicted value Tqr is determined as the predicted value of the overall jump torque Tq of the layout (step 1g).

[0238] Then, the control unit 11 displays the predicted value of the jump torque Tq determined in step 1g above on the display unit 14 (step 1h).

[0239] According to the above method, as described above, the jump torque Tqn on the driven pulley DN and the jump torque Tqr on the drive pulley DR are calculated. The jump torque of the pulley with the lower effective tension is used as the overall jump torque Tq of the layout, thereby further improving the prediction accuracy.

[0240] (Other implementation methods)

[0241] The process of calculating the jump torque Tq, performed in the above embodiments, can also be executed as software (program, data) installed in information processing devices exemplified such as smartphones, portable computers, laptops, notebook computers, tablets, handheld personal computers, and PDAs (Personal Data Assistants). In this case, the software can also be downloaded from a server or the like via a communication unit and stored in a storage device (flash memory, etc.) within the portable information device. Furthermore, the communication unit can be a transmission line capable of two-way communication, such as the Internet or cable television, or a broadcast system that transmits information in only one direction.

[0242] In addition, the software that performs the calculation of the jump torque Tq can also be stored in storage media such as CD-ROM, DVD-ROM, MO (optical disk), hard disk, flash memory, etc., and can be read from the storage media and installed into the storage unit 12 of the information processing device 10 as needed.

[0243] In addition, the descriptions in the above embodiments can also be implemented as a service executed between an information terminal (input of various parameters) such as a smartphone or PC and an information processing device 10 (calculation of jump torque Tq) via the Internet (communication line).

[0244] Alternatively, the processing performed in the above embodiments can also be a program installed on a smartphone or PC. Furthermore, the program can also be stored on a storage medium.

[0245] Alternatively, the processing performed in the above embodiments can also be implemented as a calculation and control device that uses the jump torque Tq of the information processing device 10.

[0246] The embodiments of the present invention have been described above, but these are merely illustrative examples and do not specifically limit the present invention. The specific structure of each unit, etc., can be appropriately designed and modified. Furthermore, the effects described in the embodiments of the present invention are merely examples of the most preferred effects produced by the present invention, and the effects of the present invention are not limited to the effects described in the embodiments of the present invention.

[0247] This application is based on Japanese Patent Application No. 2021-109639, filed on June 30, 2021, and Japanese Patent Application No. 2022-097983, filed on June 17, 2022, the contents of which are incorporated herein by reference.

[0248] Label Explanation

[0249] 1. Toothed belt

[0250] 2. Teeth

[0251] 10. Information processing device

[0252] 11 Control Department

[0253] 12 Storage Department

[0254] 13 Input Section

[0255] 14 Display Section

[0256] DR drive pulley

[0257] DN driven pulley

[0258] Tq is the jump torque.

Claims

1. A method for calculating and controlling the predicted value of a jump torque Tq, wherein the jump torque Tq is the jump torque of a toothed belt, the toothed belt being wound around a layout including a drive pulley and a driven pulley, wherein... The computational control method executes the following steps (1a), (1b) and (1c) through a control device: (1a) Store the following values ​​in the storage device: The values ​​of various parameters, such as the force-strain relationship ES, tooth height h, pitch circle radius Rr of the driving pulley, and pitch circle radius Rn of the driven pulley, are obtained by using the product of the equivalent longitudinal elastic modulus E along the belt length direction and the cross-sectional area S of the toothed belt. The values ​​of various parameters are as follows: initial tension T0, tension side span length Lt, slack side span length Ls, winding angle θr of the toothed belt on the drive pulley, and winding angle θn of the toothed belt on the driven pulley when the toothed belt is wound between the drive pulley and the driven pulley. and The value of the overall correction coefficient K and the value of the meshing correction coefficient Kmn of the driven pulley; (1b) Substituting the values ​​of the various parameters stored in step (1a), the value of the overall correction coefficient K, and the value of the meshing correction coefficient Kmn stored in equations (1) to (3), calculate the predicted value of the jump torque Tq; and (1c) Output the predicted value of the jump torque Tq calculated in step (1b). The values ​​of the overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley are predetermined as follows: the calculated value of the jump torque Tq when the values ​​of the above parameters are substituted into equations (1) to (3) is compared with the measured value of the jump torque Tq, and the average difference between the two values ​​is minimized. 【Mathematical Formula 1】 2. A method for calculating and controlling the predicted value of a jump torque Tq, wherein the jump torque Tq is the jump torque of a toothed belt, the toothed belt being wound around a layout including a drive pulley and a driven pulley, wherein... The computational control method executes the following steps (2a), (2b) and (2c) through a control device: (2a) Store the following values ​​in the storage device: The values ​​of various parameters, such as the force-strain relationship ES, tooth height h, pitch circle radius Rr of the driving pulley, and pitch circle radius Rn of the driven pulley, are obtained by using the product of the equivalent longitudinal elastic modulus E along the belt length direction and the cross-sectional area S of the toothed belt. The values ​​of various parameters are as follows: initial tension T0, tension side span length Lt, slack side span length Ls, winding angle θr of the toothed belt on the drive pulley, and winding angle θn of the toothed belt on the driven pulley when the toothed belt is wound between the drive pulley and the driven pulley. The values ​​of various parameters include: centrifugal tension Tc calculated based on the layout, the linear density m of the toothed belt, the traveling speed V of the toothed belt, the centrifugal force correction coefficient Kc, which is corrected based on the centrifugal force corresponding to the mass and traveling speed of the toothed belt traveling in the layout, and the belt correction coefficient Kb, which corrects for differences in the hardness and friction coefficient of the teeth of the toothed belt; and The value of the overall correction coefficient K and the value of the meshing correction coefficient Kmn of the driven pulley; (2b) Substituting the values ​​of the various parameters stored in step (2a), the value of the overall correction coefficient K, and the value of the meshing correction coefficient Kmn stored in equations (2) to (5), calculate the predicted value of the jump torque Tq; and (2c) Output the predicted value of the jump torque Tq calculated in step (2b). The values ​​of the overall correction coefficient K and the meshing correction coefficient Kmn of the driven pulley are predetermined as follows: the calculated value of the jump torque Tq when the values ​​of the above parameters are substituted into equations (1) to (3) is compared with the measured value of the jump torque Tq, and the average difference between the two values ​​is minimized. 【Mathematical Formula 2】 T c =mV 2 …Formula (5).

3. The method for calculating and controlling the predicted value of the jump torque Tq according to claim 2, wherein, The computational control method also performs the following steps (2d), (2e), (2f), (2g) and (2h): (2d) Calculate the effective tension Ten according to Equation (6), which represents the relationship between the predicted value Tqn of the jump torque Tq on the driven pulley calculated by step (2b) and the effective tension Ten, which is the difference between the tension on the tension side and the slack side related to the driven pulley. (2e) Further, the value of the meshing correction coefficient Kmr of the drive pulley, which is predetermined by the same method as the value of the meshing correction coefficient Kmn of the driven pulley, is stored in the storage device; (2f) Further calculate the effective tension Ter according to Equation (7), which represents the relationship between the predicted value Tqr of the jump torque Tq of the drive pulley calculated by substituting the value of the meshing correction coefficient Kmr stored in step (2e) into Equation (7) and the effective tension Ter, which is the difference between the tension side tension and the slack side tension related to the drive pulley. (2g) Compare the effective tension Ten with the effective tension Ter. If Ten ≤ Ter, determine the predicted value Tqn as the predicted value of the overall jump torque Tq of the layout. If Ten > Ter, determine the predicted value Tqr as the predicted value of the overall jump torque Tq of the layout. (2h) Output the predicted value of the jump torque Tq determined in step (2g). 【Mathematical Expression 3】

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