JPH07332443A - Load share prediction method, life prediction method and life prediction device for belt - Google Patents

Abstract

PURPOSE:To improve prediction of the load share characteristics of a transmission belt, such as a toothed belt, and to perform prediction of a belt life based on load sharing characteristics. CONSTITUTION:In a multishaft transmission analyzing model to perform transmission in such a state that a toothed belt 3 is run around and between a plurality of toothed pulleys 1 and 1, geometric data containing at least the diameter and the central position of each pulley 1, the numbers of teeth, the pitches of tooth, and the tooth shape sizes of the pulleys 1 and the belt 3, material data containing elastic modulus of the tension member 4 of the belt 3, the elastic modulus of a tooth part 8, and a friction factor, and external data containing load torque, an angular velocity, and a shaft load are inputted and load share characteristics exerted on the belt 3 are predicted through analysis of a finite element. Further, the tooth part reaction distribution characteristics thereof are collated and compared with an S-N curve wherein durability life characteristics are preset according to tooth part reaction analysis distribution to predict a life for the actually working belt 3.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of predicting a load sharing characteristic of a belt during transmission, a method of predicting a belt life based on the characteristic, and a life predicting apparatus.

[0002]

2. Description of the Related Art Generally, a toothed belt has excellent features such as weight reduction, a large axial distance, no need for lubrication, and relatively good efficiency. Is widely used from large industrial machines to small office machines. In recent years, toothed belts have been used for driving camshafts of automobile engines, and their performance and reliability are required to be improved.

As a theory for elucidating the transmission mechanism of such a toothed belt, conventionally, for example, “Journal of the Japan Society of Mechanical Engineers, 4”
Vol. 2, No. 359 "(1976), pages 2233 to 22.
Page 41, "Proceedings of the Japan Society of Mechanical Engineers, Vol. 44, No. 387" (1
(1978) pp. 3913 to 3922, "Journa
l of Mechanical Design paper no, 77-DET-100 ”(19
1978), pages 208 to 215.

[0004]

However, it cannot be said that the above-mentioned conventional techniques have achieved sufficient results. That is, according to the well-known Coulomb friction law, if the friction force is F, the friction coefficient is μ, and the vertical force is N,
The frictional state has two states, a fixed state where F <μN and a sliding state where F = μN. The frictional state and the direction are the states in which the belt and the pulley are actually driven to rotate. Determined from mechanical behavior.

However, in the conventional transmission technology theory, this is known, and the frictional force, which is one of the power transmissions, is always treated as a sliding state. For this reason, although it is a meshing transmission, the history dependency of the frictional force, which has a high ratio in the transmission force, is ignored, and it is difficult to favorably predict the load sharing characteristic of the belt.

These points are not limited to toothed belts, and the same applies to other general transmission belts such as flat belts and V belts.

The present invention has been made in view of the above problems, and an object of the present invention is to improve the method of analyzing a belt transmission mechanism so as to share the load of a transmission belt such as a toothed belt or a flat belt. This is to make it possible to predict the characteristics well and to predict the life of the belt based on the load sharing characteristics.

[0008]

In order to achieve the above object, according to the present invention, a part of the belt transmission mechanism located below the core of the belt and in contact with the pulley is incorporated into the model of the belt transmission mechanism, and the pulley rotates. It was decided to analyze the belt transmission mechanism using the nonlinear finite element method under the condition that the belt is given a motion similar to the actual rotation of the belt.

That is, the invention of claims 1 to 6 is a method for predicting the load sharing of a belt. According to the invention of claim 1, a transmission analysis model for transmitting the belt by winding the belt around a pulley is prepared. On the other hand, the geometrical data, the material data and the external force data are input, and the load sharing characteristic applied to the belt is predicted by the finite element analysis.

In the second aspect of the present invention, the transmission analysis model is a multi-axis transmission model in which a belt is stretched between a plurality of pulleys for transmission.

In the invention of claim 3, the pulley is a toothed pulley and the belt is a toothed belt.

According to a fourth aspect of the present invention, in the belt load sharing prediction method according to the third aspect, the geometric data includes at least the diameter and center position of the pulley, the number of teeth of the pulley and the belt, the pitch of the teeth, and the tooth profile. The material data is at least the core elastic modulus of the belt, the tooth elastic modulus,
The data including the friction coefficient is used, and the external force data is data including at least the load torque, the angular velocity, and the shaft load.

According to the invention of claim 5, the pulley is a flat pulley and the belt is a flat belt. Further, in the invention of claim 6, the pulley is a V-pulley and the belt is a V-belt.

The invention of claim 7 is a method of predicting the life of a belt, and the method of the invention is characterized in that the characteristic of the load sharing of the belt predicted by the method of predicting the load sharing of the belt according to claim 1 or 2 is It is characterized by predicting the life of the belt actually used by comparing it with the life characteristics required according to the load sharing.

According to an eighth aspect of the invention, in the belt life predicting method of the seventh aspect, the pulley is a toothed pulley and the belt is a toothed belt. Further, in the invention of claim 9, the pulley is a flat pulley and the belt is a flat belt. In the invention of claim 10, the pulley is a V-pulley and the belt is a V-belt.

The invention of claims 11 to 14 is an apparatus for predicting the life of a belt. In the invention of claim 11, geometrical data, material data, and geometric data of a transmission analysis model in which a belt is wound around a pulley and transmitted. Data input means for inputting external force data, load sharing prediction means for predicting load sharing characteristics applied to the belt by finite element analysis based on the data input by this data input means, and load sharing prediction means The load sharing characteristic of the belt is compared with the life characteristic previously obtained according to the load sharing, and a life predicting means for predicting the life of the belt actually used is provided. .

According to a twelfth aspect of the invention, in the belt life predicting apparatus according to the eleventh aspect, the transmission analysis model is a multi-axis transmission model in which the belt is laid over a plurality of pulleys for transmission.

In the invention of claim 13, claim 11 or 1
In the belt life prediction device of No. 2, the pulley is a toothed pulley and the belt is a toothed belt.

According to a fourteenth aspect of the present invention, in the belt life predicting apparatus of the thirteenth aspect, the geometric data includes at least the diameter and center position of the pulley, the number of teeth of the pulley and the belt, the pitch of the teeth, and the tooth profile. The material data is at least the core body elastic modulus of the belt, the tooth elastic modulus,
The external force data is data including at least a load torque, an angular velocity, and an axial load.

[0020]

With the above structure, in the invention of claim 1, geometric data, material data and external force data are input to a transmission analysis model in which a belt is wound around a pulley and transmitted, and the finite element is based on these data. The load sharing characteristics applied to the belt are predicted by analysis. The load sharing characteristic of the belt obtained by the finite element analysis is substantially in agreement with the actual characteristic, so that the load sharing characteristic can be properly predicted.

According to the second aspect of the present invention, since the transmission analysis model is a multi-axis transmission model in which a belt is stretched between a plurality of pulleys, it is possible to predict the load sharing characteristic of the belt used in the multi-axis transmission system. You can

According to the third aspect of the present invention, the load sharing characteristic of the toothed belt can be predicted.

According to the fourth aspect of the present invention, when predicting the load sharing characteristic of the toothed belt, at least the diameter and center position of the pulley, the number of teeth of the pulley and the belt, the pitch of the tooth, and the tooth profile are used as geometric data. Input the data including, the material data is the data including at least the core body elastic modulus of the belt, the tooth elastic modulus, and the friction coefficient, and the external force data is
Since the data includes at least the load torque, the angular velocity, and the axial load, the data necessary for predicting the load sharing characteristic of the toothed belt can be properly obtained, and the prediction accuracy can be improved.

According to the invention of claim 5, the load sharing characteristic of the flat belt can be predicted, and in the invention of claim 6, the load sharing characteristic of the V belt can be predicted.

According to the invention of claim 7, the characteristic of the load sharing of the belt predicted by the method of predicting the load sharing of the belt according to claim 1 or 2 is compared with the life characteristic previously obtained according to the load sharing. This predicts the life of the belt actually used. Therefore, the life of the belt can be predicted.

According to the invention of claim 8 or 13, the life of the toothed belt, the life of the flat belt of the invention of claim 9 and the life of the V belt of the invention of claim 10 can be predicted.

In the eleventh aspect of the invention, the data input means inputs the geometric data, the material data and the external force data to the transmission analysis model in which the belt is wound around the pulley and is transmitted. Based on the data input by the data input means, the load sharing characteristic applied to the belt is predicted by the finite element analysis. Then, by the life predicting means, the characteristics of the load sharing of the belt predicted by the load sharing predicting means are compared with the life characteristics obtained in advance according to the load sharing, and the life of the belt actually used is predicted. To be done. Therefore, even in this case,
Similar to the invention of claim 7, the life of the belt can be predicted.

According to the twelfth aspect of the present invention, the life of the belt used in the multi-shaft transmission system can be predicted.

According to the fourteenth aspect of the invention, when predicting the life of the toothed belt, at least the diameter and center position of the pulley and the number of teeth of the pulley and the belt are used as the geometric data, similarly to the fourth aspect of the invention. Enter the data including the tooth pitch and tooth profile dimensions, the material data is data including at least the core body elastic modulus of the belt, the tooth elastic modulus, the friction coefficient,
Since the external force data is data including at least the load torque, the angular velocity, and the axial load, the data necessary for predicting the life of the toothed belt is properly obtained, and the prediction accuracy is improved.

[0030]

Embodiments of the present invention will be described below with reference to the drawings. (Embodiment 1) FIG. 3 schematically shows a belt transmission mechanism according to Embodiment 1 of the present invention.
A toothed pulley 3 having two, ... Is a toothed belt that is meshed with and wound around the toothed pulleys 1, 1, and this toothed belt 3 has a core body as shown in enlarged detail in FIG. An adhesive rubber layer 5 in which 4 is embedded, a back rubber layer 6 (cover rubber layer) integrally attached to the belt back surface side of the adhesive rubber layer 5, and an adhesive rubber layer 5 integrally attached to the belt bottom surface side, A large number of tooth portions 8, which mesh with the tooth portions 2, 2, ...
.. is formed, and a tooth cloth 9 (rubber canvas layer) that covers the surface of the tooth portion 8 of the tooth rubber layer 7.

Each tooth 8 of the belt 3 has a trapezoidal tooth profile as shown in FIG. 5A or an arc tooth profile such as S8M as shown in FIG. 5B. In the case of the trapezoidal tooth profile of the former, the tooth part reaction force Q acting from each tooth part 2 of the pulley 1 to each tooth part 8 of the belt 3 and the frictional force Fb between the tooth bottom surface of the belt 3 and the tooth top surface of the pulley 1 Transmission is carried out by two of. On the other hand, in the case of the latter arcuate tooth profile, transmission is performed by a total of three, which is the tooth reaction force Q and the friction force Fb, plus the friction force Ft between the tooth crest surface of the belt 3 and the tooth bottom surface of the pulley 1. Is done
The transmission mechanism becomes a little complicated.

FIG. 2 schematically shows the construction of a predicting device for predicting the life of the toothed belt by means of a transmission analysis model, and 11 is a belt 3 which is extended between a plurality of pulleys 1 and 1 for transmission. A data input unit for inputting geometric data, material data, and external force data for a multi-axis transmission analysis model. The geometric data includes at least the diameter and center position of each pulley 1, the number of teeth of the pulley 1 and the belt 3,
Includes tooth pitch and tooth profile dimensions. Further, the material data includes at least the elastic modulus of the core body 4 of the belt 3, the elastic modulus of the tooth portion 8, and the friction coefficient. Further, the external force data includes at least load torque, angular velocity and shaft load.

Reference numeral 12 is a load sharing prediction unit for predicting a load sharing characteristic applied to the belt 3 by finite element analysis based on the data input by the data input unit 11.
As the load sharing characteristics, the characteristics of the tooth reaction force distribution, the frictional force distribution, and the tension distribution are specifically predicted.

Further, reference numeral 13 is a life predicting section for predicting the life of the belt 3, and the life predicting section 13 is one of the characteristics of the load sharing of the belt 3 predicted by the load sharing predicting section 12 mentioned above. For the force distribution characteristics, an SN curve (teeth reaction force-
The life of the toothed belt 3 to be actually used is predicted by collating and comparing with the durable life characteristic curve) and referring to the compound rule or the minor rule.

In this embodiment, a concrete processing procedure for estimating the life of the toothed belt 3 by the transmission analysis model will be described with reference to FIG. 1. In the first step S1, the diameter of the pulley 1, the number of teeth, Its center position, pitch,
Geometrical data such as tooth profile is input to the meshing transmission analysis model. In the next step S2, material data such as the elastic modulus of the core body 4 of the belt 3, the elastic modulus of the tooth portion 8 and the friction coefficient are input, and in step S3, fluctuations in load torque, changes in angular velocity, axial load, etc. Input the external force data of.

FIG. 6 exemplifies the main part of the meshing transmission analysis model by the toothed belt 3. In this model, pitch 8
It has a circular arc tooth profile (S8M type) of 8 mm and a width of 1
A back rubber layer which is a drive system of a toothed belt 3 of 9.1 mm and two toothed pulleys 1, 1 with 24 grooves around which the toothed belt 3 is wound, and which hardly contributes to transmission in the belt 3. Modeling of 6 (cover rubber layer) is omitted. Further, in the modeled belt portion, the portion of the core body 4 is a 2-node beam element, and the tooth cloth 9 on the lower side of the core body 4 is
The (rubber canvas layer) and the tooth portion 8 are each represented by a quadrilateral 4-node planar element.

Since the pulley 1 is much harder than the belt 3, it is regarded as a rigid body, and only the outer peripheral shape is represented by a rigid body surface. In addition, one node is provided at the center of the pulley 1 to represent the movement of the pulley 1.

Further, a joining element is provided on a square element surface corresponding to the outer surfaces of the tooth cloth 9 and the tooth portion 8 which may come into contact with the pulley 1 in the belt 3, whereby the belt 3 and the pulley 1 come into contact with each other. , Consider friction and flaking. Friction is assumed to be according to Coulomb's law and the coefficient of friction is assumed to be constant for all analyses.

In step S4 after step S3, the initial arrangement of the meshing transmission analysis model is determined. Figure 7
(A) is an initial arrangement of a biaxial meshing transmission analysis model by the above-mentioned toothed belt, in which two pulleys 1 and 1 represented by a rigid surface are arranged side by side in the horizontal direction as close as possible, A model of a belt 3 is arranged in a circular shape so as to surround these pulleys 1 and 1. The belt 3 connected in a circular shape has an original natural appearance in a free state. In order to reduce the calculation cost, it is preferable to select a circle having a diameter as small as possible within the range in which it does not contact the pulley 1.
All the degrees of freedom are constrained for the drive pulley 1 on the left side in the figure, and the degrees of freedom for the driven pulley 1 on the right side are constrained in directions other than the horizontal direction.

Next, in step S5, a mesh for dividing the transmission analysis model into finite elements is generated, and then in step S6, analysis by the finite element method is executed. First, as shown in FIG. 7B, a load is applied to the rotation shaft of the driven pulley 1 and the belt 3 stretched between the drive and driven pulleys 1 and 1 is rotated with respect to the model in the initial arrangement. It is in a state of being stretched by the load W. Next, as shown in FIG. 7 (c), after the restraint of the rotation of the driven pulley 1 is released, a concentrated moment in a clockwise direction is applied to the driven pulley 1 in a diagram corresponding to the load torque Tr to start the driven state. To do. From this state, as shown in FIG. 7D, the drive pulley 1 is forcibly given a rotational angle displacement in the counterclockwise direction to obtain a final target steady state. The rotational angle displacement required to obtain this steady state must be at least the contact angle of the belt 3 with the pulley 1.

Then, in step S7, the belts 3 are respectively processed in the process from the initial arrangement to the steady state.
Load distribution, that is, the reaction force distribution of the tooth portion, the frictional force distribution, the strain distribution of the core body, the tension distribution, etc. are output.

Next, in step S8, the tooth reaction force distribution of the output load distribution is collated with the SN curve in which the endurance life characteristic is set in advance according to the tooth reaction force distribution. After that, in step S9, it is determined whether or not there are a plurality of tooth portion reaction force cycles during one round of the belt. When the determination is NO, the process directly proceeds to step S11. When the determination is YES, the fatigue degree per one round of the belt is calculated by the compound rule (or the minor rule) at step S10, and then the process proceeds to step S11. This step S
At 11, the estimated life of the belt 3 is output.

Therefore, in this embodiment, when predicting the life of the toothed belt 3, first, a multi-axis transmission analysis model in which the toothed belt 3 is bridged between a plurality of pulleys 1 and 1 is used. Geometrical data including the diameter and center position of each pulley 1, the number of teeth of the pulley 1 and the belt 3, the pitch of the teeth and the tooth profile, the elastic modulus of the core body 4 of the belt 3, the elastic modulus of the tooth portion 8, and the friction coefficient. The material data including the above and the external force data including the load torque, the angular velocity and the axial load are input. Then, based on these data, the load sharing characteristic applied to the toothed belt 3 by the finite element analysis is the tooth reaction force distribution,
It is predicted as each characteristic of the frictional force distribution and the tension distribution. Thereafter, among the characteristics of the load sharing of the toothed belt 3 thus predicted, the tooth reaction force distribution characteristic is an SN curve in which the endurance life characteristic is set in advance according to the tooth portion reaction force distribution. The collation and comparison are performed, and the compound rule or the minor rule is referred to, whereby the life of the toothed belt 3 actually used is predicted.

At this time, the load sharing characteristic of the toothed belt 3 obtained by the above finite element analysis substantially matches the actual characteristic,
The load sharing characteristic can be properly predicted. Therefore, the life of the toothed belt 3 used for the multi-axis transmission system can be predicted.

Further, the geometric data input to the multi-axis transmission analysis model is data including the diameter and center position of each pulley 1, the number of teeth of the pulley 1 and the belt 3, the pitch of the teeth, and the tooth profile dimension, and the material The data is data including the elastic modulus of the core body 4 of the belt 3, the elastic modulus of the tooth portion 8, and the friction coefficient,
Since the external force data is data including load torque, angular velocity, and axial load, data necessary for predicting the life of the toothed belt 3 can be properly obtained, and the prediction accuracy can be improved.

The present inventor conducted an experiment for verifying the tooth portion reaction force distribution of the load sharing of the toothed belt obtained by the finite element analysis as described above. 8 and 9 show a transmission force distribution measuring device for verifying the tooth part reaction force distribution of the load sharing of the above toothed belt, 21 is a base installed on the floor, 22 is a base 21 A fixed shaft rotatably supported at the right end of the upper surface and extending in the front-rear direction. A toothed pulley 18 having a radius R1 is provided at the front end of the fixed shaft 22, and a load drum 23 having a radius R2 is provided at the rear end. It is attached integrally with the rotation. The pole 2 is on the right floor of the base 21.
4 is erected, and a pulley 25 having a horizontal longitudinal axis is rotatably supported at the upper end of the pole 24.
The wire 25 is attached to the pulley 25 at the upper end of the pole 24.
Of the wire 26, one end of the wire 26 is connected to the load drum 23, and the load weight W2 is hung at the other end. The weight W2 hangs the toothed pulley 18
Is applied with a predetermined load torque Tr.

On the other hand, guide rails 28, 28 extending in the left-right direction are attached to the left half of the upper surface of the base 21, and a movable base 29 is movable on the guide rails 28, 28 in the left-right direction, that is, the fixed shaft 22. It is placed so that it can be moved toward and away from. A movable shaft 30 extending in the front-rear direction is rotatably supported on the right end of the movable base 29. A torque meter 31 is arranged on the front side of the intermediate portion of the movable shaft 30 and a gear box 32 is arranged on the rear side thereof. Has been done. In addition, the movable shaft 30
A toothed pulley 19 having a radius R1 is rotatably attached to the front end of the toothed pulley 19 with the toothed pulley 19 and the fixed shaft 22.
Toothed belt 20 for testing between the toothed pulley 18 at the front end
Is wrapped around. The rear end of the movable shaft 30 is drivingly connected to a motor 34 via a pulley mechanism 33, and the driving of the motor 34 causes the toothed pulley 19 to rotate.

A pulley 35 having a horizontal longitudinal axis is supported on the front end of the left side surface of the base 21.
The intermediate portion of the wire 36 is wound around the
One end of 5 is the load cell 3 on the left side of the front end of the movable table 30.
It is connected via 7. On the other hand, a weight W1 for initial tension is suspended at the other end of the wire 35.
A predetermined initial tension T0 is applied to the test belt 18 by setting 1.

At this time, if the tension T1 of the tension side span of the belt 18 and the tension T2 of the tension side of the slack side are T1 + T2 = 2.multidot.T0 = W1 (T1-T2) .R1 = Tr = W2.R2 Therefore, T1 = (W1 + W2.R2 / R1) / 2 T2 = (W1-W2.R2 / R1) / 2.

The toothed pulley 18 on the fixed shaft 22 side is used as a power transmission measuring pulley. That is, as shown in FIG. 10, a pair of slit portions L formed by cutting the pulley 18 from the outer peripheral edge toward the center of the pulley 18 on the fixed shaft 22 side.
Three sets of slits, which are a set of 1, L1, L2, L2, L3, and L3, are provided, and the root portions of the slit portions L1 to L3 are each 1 in correspondence with the rotation direction of the pulley 18.
Paired strain gauges 38, 38, ... Are attached.
The strain gauges 38 and 38 of the slit portions L1 and L1 show the tooth reaction force and the tooth tip friction force, the strain gauges 38 and 38 of the slit portions L2 and L2 give the tooth tip friction force, and further, the slit portion L3 and L3. The strain gauges 38, 38 are adapted to detect the root-bottom frictional force, respectively.
The tooth reaction force can be calculated by subtracting the detection data of the slit portions L2 and L2 from the detection data of L1.

The toothed belt 20 is an S8M type toothed belt for automobiles, the core body of which is glass fiber, the back rubber layer and the tooth rubber layer are hydrogenated SBR (styrene butadiene rubber), and the tooth cloth is further provided. Are made of nylon (registered trademark) canvas. On the other hand, the toothed pulleys 18, 19
Is a steel S8M type pulley having 24 grooves. Then, the belt 20 is tested under two kinds of tension conditions, and when the belt 20 is initially tensioned, its tooth pitch becomes larger or smaller than the tooth pitch of the pulleys 18, 19.
Testing was performed on different types of belts. The main specifications of the toothed pulleys 18 and 19 and the toothed belt 20 are shown in Table 1 below.

[0052]

[Table 1]

11 to 13 show experimental values (indicated by solid lines) of the transmission force distributions of the belt and pulley in a steady state by these experiments in comparison with calculated values (indicated by broken lines). In each figure, (a) shows the driving side and (b) shows the driven side. FIG. 11 shows that the pitch difference between the belt and the pulley (difference between the tooth pitch of the belt and the tooth pitch of the pulley) at the time of no tension is +0.002 mm, the tension on the tension side of the belt is 588N, and the tension on the slack side is 196N. It is the data under the tension condition. FIG. 12 shows data under tension conditions in which the tension on the belt is 490 N and the tension on the slack side is 294 N, with the same pitch difference. Further, in FIG. 13, the pitch difference is -0.038.
mm, the tension on the tension side of the belt is 588 N, and the tension on the slack side is 196 N.

In these drawings, the signs of the tooth reaction force Q, the tooth tip friction force Ft, and the tooth bottom friction force Fb are positive in the directions contributing to the transmission. Further, the horizontal axis represents the tooth number indicating the position of the meshing area between the belt and the pulley, and the vertical axis represents the magnitude of the load. Regarding the above tooth number, the meshing entrance where the belt enters the pulley is "0. Is defined as the number of teeth counted in the meshing exit direction from which the belt comes out. Therefore, the tension number on the drive side and the slack side on the driven side are “0”.

The experimental result of the transmission distribution is shown in FIG.
1 to 13, there is a big difference between the driving side and the driven side. That is, due to the static force balance, the driving side and the driven side have substantially the same transmission force distribution at the time of startup.
FIG. 14 shows the transmission load at the time of start-up ((a) in the figure shows the driving side, and (b) shows the driven side). However,
Focusing on one tooth, the drive side receives a friction history due to the tension change from the tension side to the slack side in the process in which the pulley rotates from the start-up to a steady state, and the driven side moves in the opposite direction. Along with the change in tension, the friction history is different from that on the drive side. Therefore, it is considered that the transmission force distribution at the time of startup changed so much that a large difference between the driving side and the driven side occurs in the steady state.

Comparing the characteristics shown in FIGS. 11 and 13, it can be seen that the positive and negative pitch differences also cause a large difference in the transmission force distribution. In particular, the places where the maximum value of the tooth reaction force is generated are opposite in both figures. That is, FIG. 15A shows the meshing state on the drive side in the steady rotation state, assuming that the pitch difference is 0 and the belt 3 does not expand or contract.
(B) schematically shows the meshing state on the driven side. Further, FIG. 15C schematically shows the meshing state when the belt 3 is simply wound around the pulley 1 when the pitch difference is positive, and FIG. 15D shows the meshing state when the pitch difference is negative. Therefore, when there is a pitch difference, the meshing state at the time of steady rotation is as shown in FIG. 15 (a) or (b).
It is an image in which the meshing state of (c) or (d) is overlapped. At this time, it is considered that the tooth reaction force is promoted at a position where the meshing surfaces of the belt 3 and the pulley 1 coincide with each other. When the pitch difference is positive, the driving side is the meshing inlet and the driven side is the meshing outlet. The meshing surfaces are coincident with each other, and on the other hand, when the pitch difference is negative, the opposite is where the meshing surfaces coincide. This coincides with the place where the maximum value of the tooth reaction force in FIGS. 11 and 13 occurs. ing.

Focusing on the root friction force on the drive side in FIG. 13, the root friction force continuously changes from negative to positive in accordance with the rotation direction. That is, the direction of the frictional force changes on the way, and the magnitude of the frictional force becomes 0 at that transition. This phenomenon is, as mentioned in the case of trapezoidal teeth,
Although it cannot be explained by the conventional transmission theory that the frictional state is always assumed to be the sliding state, according to the calculation result of the model according to the present invention considering two frictional states of sticking and sliding and the history dissimilarity of the direction. It can be successfully reproduced.

11 to 13, the tooth tip frictional force, which is a characteristic of the S8M type, has a small value in general,
The degree of that change is also low. The amount of tooth tip compression in the belt and pulley according to the experiment (belt tooth height-pulley groove depth = 0.
At 10 mm), the surface pressure is small, and the contact surface is located away from the core body 4 via the tooth portion 8. Therefore, it is considered that the followability to the movement of the core body 4 is reduced.

Comparing the calculation results of the transmission analysis model according to the present invention with the experimental results, both are qualitatively matched on the driving side and the driven side, and particularly, the tooth reaction force is also quantitatively matched. It can be seen that the transmission analysis according to the present invention is effective.

However, in the transmission analysis, the remarkable peak seen at the meshing outlet is not reproduced. It is considered that this peak is due to the addition of frictional resistance when the tooth portion 8 of the belt 3 comes out of the pulley 1, but it is considered that the above-mentioned frictional resistance could not be expressed due to the coarse division of elements in the analytical model. To be

Further, the degree of matching of the frictional force is slightly worse than the reaction force of the tooth portion, because the above element division is rough and the measurement error due to the small slit width at the tooth top portion of the measurement pulley, and as described above. The difference in the shear deformation of the rubber / cloth layer, which is directly connected to the root friction force, is considered. Since the actual toothed belt has a three-layer structure of a core, rubber and canvas (see Fig. 4), there is shear deformation that causes refraction in the middle, but in the analysis model it has a one-layer structure as shown in Fig. 6. Therefore, the shear deformation is simple, and due to this, the matching degree of the frictional force is reduced.

As described above, according to the transmission analysis of the present invention, although there is a point of the element roughness, the prediction accuracy of the tooth reaction force involved in the tooth shear fatigue is high, and therefore the number of axes is increased and the actual value is increased. It can be seen that the shear fatigue life of the tooth can be accurately predicted by approaching the layout and considering the torque fluctuation.

Next, the inventor of the present invention examined the influence of each specification of the transmission system on the transmission force distribution characteristic by using the finite element analysis model according to the present invention. The factors are the pitch difference Δp, where a large influence is observed in the case of the trapezoidal tooth profile, and the tooth tip compression amount Δc which is a characteristic of the S8M type belt. Further, the number of pulley teeth is 28, the tension on the belt tension side is 588 N,
The slack side tension was set to 196 N, and other specifications were in accordance with Table 1.

FIG. 16 shows the calculation results when the pitch difference Δp is changed, and FIG. 18 shows the calculation results when the tooth tip compression amount Δc is changed. In each figure, (a) shows the drive side and (b) shows the driven side. Are shown respectively. The solid line represents the tooth reaction force Q, and the broken line represents the tooth bottom friction force Fb.

The numerical values in FIG. 16 are pitch difference values. According to FIG. 16, it can be seen that the transmission force distribution greatly changes due to the pitch difference, as in the case of the trapezoidal tooth profile. That is, the peak position of the tooth reaction force moves according to the change in the pitch difference, and the direction of the friction force changes.

Generally, in a toothed belt installed in an automobile engine, it is considered that the load transmission on the drive pulley as the crank pulley is the most severe, so that FIG.
FIG. 17 shows the characteristics of the maximum tooth reaction force with respect to each pitch difference, focusing on the maximum tooth reaction force on the driving side shown in FIG. In FIG. 17, the maximum tooth part reaction force is minimum when the pitch difference is -0.014 mm.

Under the tension condition that the tension on the belt tension side is 588 N and the tension on the slack side is 196 N, 392 (= 5
88-196) N is considered to have an average tension, the belt has 0.11 (= 392 ÷ 343000 × 10).
Since it is stretched by 0)%, for a nominal pitch of 8 mm,
When the pitch difference defined in the state of no tension is -0.009 mm, the pitch difference is substantially zero. The pitch difference that minimizes the maximum tooth reaction force is on the negative side of -0.009 mm above.
Since it is 0.014 mm, the case where the pitch difference is negative is more advantageous for the tooth shear fatigue than the case where the pitch difference is positive.

On the other hand, regarding the tooth tip compression amount shown in FIG. 18, the pitch difference is −0.022 mm, and the alternate long and short dash line in the figure represents the tooth tip friction force Ft. The numerical value is the value of the tooth tip compression amount Δc. According to FIG. 18, the surface pressure of the tooth tip increases and the surface pressure of the tooth bottom decreases in accordance with the increase of the tooth tip compression amount Δc, so that the frictional force is greatly affected, but the tooth part reaction force is increased. It can be seen that is also affected. Especially on the drive side, the frictional force acts in the direction that maintains the positional relationship between the tooth portion of the belt and the pulley groove at the time of biting, so the tooth tip frictional force is in the negative direction. In terms of balance, the tooth reaction force also increases. FIG. 19 shows the tooth tip compression amount Δc.
FIG. 19 shows the characteristics of the maximum tooth part reaction force with respect to the above. In FIG. 19, an increase in the tooth tip compression amount causes an increase in the tooth tip friction force and an increase in the maximum tooth part reaction force. That is, considering only the shear fatigue of the tooth portion, the tip compression, which is a characteristic of the S8M type, works disadvantageously, and it is advantageous that there is no tip compression like the trapezoidal tooth profile. However, since the tip compression has the effect of relaxing the surface pressure at the bottom of the tooth with a small contact area and relaxing the polygonal winding of the core, it cannot be said that it should be absolutely eliminated.

(Embodiment 2) FIGS. 20 to 31 show Embodiment 2 (note that the same parts as those in FIGS. 5 and 7 are designated by the same reference numerals and detailed description thereof is omitted), and a flat belt is used. It is applied.

FIG. 20 shows a flat belt transmission mechanism, which is composed of flat pulleys 41, 41 and a flat belt 42 wound around them. As shown in FIG. 21, for example, the flat belt 42 includes an adhesive rubber layer 44 in which a core body 43 is embedded, an upper rubber layer 45 integrally bonded to the belt back side of the adhesive rubber layer 44, and an adhesive rubber layer 44. And a lower cover layer 46 (lower rubber layer) integrally bonded to the bottom surface side of the belt.

FIG. 22 schematically shows a transmission analysis model using a flat belt, and FIG. 22 (a) shows the initial arrangement state.
Further, FIG. 3B shows the final steady state. In this model, the core body 43 involved in the transmission in the flat belt is
And the lower cover layer 46 are modeled, and the core body 43
For the lower cover layer 46, and a 4-node plane stress element for the lower cover layer 46. Further, the pulley 41 is defined by a circular rigid surface having a predetermined outer diameter, and a joining element is arranged on the side of the lower cover layer 46 of the belt 42 that comes into contact with the pulley 41. With this joining element, the belt 42 and the pulley 4 are provided.
Consider contact, friction and delamination between 1's. Regarding friction, the friction force is F, the friction coefficient is μ (= constant), and the normal force is N.
Then, if F <μN, the state is fixed and F = μN
If so, apply the general Coulomb's law, which assumes a finite slip state.

FIG. 23 shows a biaxial transmission analysis model using a flat belt, and this model simulates the behavior during friction transmission between the belt and the pulley. First, as shown in FIG. 23A, the initial arrangement of the transmission analysis model is determined. That is, two flat pulleys 41, 41 represented by a rigid surface are arranged side by side in the horizontal direction as closely as possible, and a model of a flat belt 42 arranged in a circular shape is arranged so as to surround these pulleys 41, 41. is doing. The left drive pulley 41 is constrained in all the degrees of freedom to be completely fixed, and the right driven pulley 41 is constrained in degrees other than horizontal to be fixed in the vertical direction.

Next, analysis by the finite element method is executed. As shown in FIG. 23B, a load is applied to the rotation shaft of the driven pulley 41 with respect to the model in the initial arrangement,
The belt 42 stretched between the drive and driven pulleys 41, 41 is tensioned by the axial load W, and tension T1 and tension T2 on the tension side are applied to the belt 42. next,
As shown in FIG. 23C, while keeping the magnitude and direction of the tension in the same state, the constraint of the rotation of the driven pulley 41 is released, and a clock corresponding to the load torque Tr is applied to the driven pulley 41. A concentrated moment in the turning direction is applied to activate the system. From this state, as shown in FIG.
The drive pulley 41 is forcibly given a rotational angle displacement in the counterclockwise direction to obtain a final target steady state.

In this way, in the process from the initial arrangement to the steady state, the load sharing of the belt 42, that is, the frictional force distribution, the tension distribution of the core body 43, etc. are obtained. Thereafter, similarly to the first embodiment, the output load sharing characteristics are
Flat belt 4 in accordance with preset durability life characteristics
The estimated life of 2 is output.

Therefore, also in this embodiment, the same operational effect as that of the above-described first embodiment can be obtained.

FIG. 24 shows an experimental apparatus for verifying the load distribution friction force distribution of the flat belt obtained by the finite element analysis as described above, and 51 is a fixed body (not shown).
The first horizontal shaft rotatably supported by
A first flat pulley 52 is attached to the front end of the above, and a first wire sheave 53 is attached to the rear end thereof so as to rotate together. A second horizontal shaft 54 is arranged below the first horizontal shaft 51 so as to be able to move up and down, and a second flat pulley 55 having the same diameter as the first flat pulley 52 is provided at the front end of the second horizontal shaft 54. A second wire sheave 56 having the same diameter as that of the first wire sheave 53 is attached to the rear end thereof so as to rotate together, and a test flat belt 57 is wound between the first and second flat pulleys 52 and 55.

A weight W1 for initial tension is suspended at the front-rear intermediate portion of the second horizontal shaft 54, and a predetermined initial tension T0 is applied to the flat belt 57 for test by this weight W1. ing.

On the other hand, the first wire sheave 53 is wound around and connected to one end of a wire 58 whose intermediate portion hangs below the initial tension weight W1.
The other end of 8 is wound and connected to the second wire sheave 56 on the side opposite to the wire connection side to the first wire sheave 53. A third wire sheave 59 is wound around and suspended in the middle of the wire 58, and a load weight W2 is suspended on the shaft portion of the third wire sheave 59.
A predetermined load torque is applied to both flat pulleys 52 and 55 by this weight W2.

Further, the first flat pulley 52 is a power transmission measuring pulley. That is, as shown in FIG.
The first flat pulley 52 is processed with a pair of slit portions L, L, and the pulley 5 is provided at the root of the slit portions L, L.
One pair of strain gauges 3 corresponding to the two rotation directions
8 and 38 are attached, and this strain gauge 38,
The frictional force is detected by 38.

Further, a potentiometer 60 for detecting the angular displacement of the first flat pulley 52 is attached to the first horizontal shaft 51.

The core of the test flat belt 57 is made of aramid fiber, and the lower cover layer thereof is made of CR (chloroprene rubber). The flat pulleys 52 and 55 are made of steel. The main specifications of the flat pulleys 52, 55 and the flat belt 57 are shown in Table 2 below.

[0082]

[Table 2]

26 and 27, the experimental values (indicated by the solid line) of the frictional force distribution in the steady state of the belt and the pulley in these experiments are compared with the calculated values (indicated by the broken line and the alternate long and short dash line). (A) of each figure shows the drive side,
Further, (b) shows the driven side, respectively. FIG. 26 shows data under tension conditions in which the tension on the flat belt side is 196 N and the tension on the loose side is 98 N, and FIG. It is data under the conditions. In FIG. 26, the broken line indicates the calculated value when the friction coefficient μ is μ = 0.5.
The calculated values when = 0.7 are shown by the alternate long and short dash lines. Further, in FIG. 27, the friction coefficient μ on the driving side is μ =
Calculated value when 0.7, μ = 0.5 for driven side
The calculated values are shown respectively.

In FIGS. 26 and 27, in order to show the position at the contact portion on the abscissa, the position where the tension side of the belt comes into contact with the pulley is set to 0 °, and measurement is performed in the loosening direction around the central axis of the pulley. Indicates the angle. The vertical axis represents the magnitude of the load, and the direction of the frictional force is positive in the direction from the tension side to the slack side.

As is clear from FIGS. 26 and 27, the calculation results qualitatively agree with the experimental results. Quantitatively, when the friction coefficient μ on the driving side is μ = 0.7, and when the driven side is μ = 0.5, they are in agreement.
Therefore, according to the present embodiment, by appropriately setting the friction coefficient for the finite element model of the flat belt, the frictional force distribution can be accurately predicted, and the life of the flat belt is predicted. be able to. In particular, it is even more advantageous if the friction coefficient is different on the driving side and the driven side.

Further, referring to FIGS. 26 and 27,
It can be seen that in both the calculated value and the experimental value, the distribution of the frictional force is greatly different between the driving side and the driven side, and the direction of the frictional force on the driving side changes from negative to positive. That is,
As shown in FIG. 28, in the flat belt 42 in contact with the pulley 41, assuming that the virtual cross section of the lower cover layer 46 is at the position aa ′ at the initial stage, the pulley 41 rotates clockwise. Accordingly, as long as the contact portion does not slip, the movement of the core body 43 is delayed from the movement of the contact portion due to the curvature difference due to the thickness t of the lower cover layer 46, and the virtual cross section of the lower cover layer 46 is b.
-B ′ changes, and shear deformation δ occurs. On the drive side, this shear deformation δ forces the frictional force to move in the positive direction, and therefore, in the initial region of contact, the opposite direction, that is, the negative frictional force acts, in order to balance the forces.

This frictional force distribution on the driving side has a significant effect on the tension distribution of the core body 43. That is, from the balance of the lower cover layer 46 shown in FIG. 28, the tension increases from the tension side to the slack side in the negative region, while it decreases in the positive region, and therefore the tension at the contact portion with the pulley 41 is lower than the tension side. There is also a high tension range. For example, FIG. 29 shows a tension distribution calculation result on the drive side under a tension condition in which the tension on the tension side of the flat belt is 196 N and the tension on the slack side is 98 N.
A maximum tension of 40% higher than the tension on the tension side is observed.
The maximum tension is the tension on the tension side plus the sum of the negative frictional forces.

Next, paying attention to the frictional state of the contact portion, FIGS. 26 and 27 show the frictional state determined from the calculation result as the fixed state "ST" or the sliding state "SL". On the driving side, the area from the start of contact (tension side) to the point where the maximum positive frictional force is generated is the fixed area, and the area thereafter is the sliding area. That is, in the fixed area, as shown in FIG.
It is considered that the shear deformation of the lower cover layer 46 as shown in FIG. 8 occurs and the contact portion is slipping when it reaches the limit on the right side of the figure. Euler's theory holds in this sliding region.

On the other hand, on the driven side, most of the area except for both ends of contact is in a fixed state, and due to shear deformation of the lower cover layer 46 due to change in tension of the core body 43 in the rotational direction and difference in curvature. It is considered that the direction of the shear deformation that occurs is opposite, and the shear deformation that combines them is not reaching the slip limit.

Considering the belt life, the lower cover layer 4
Since the wear of No. 6 progresses in the sliding region, the sliding region should be as small as possible, and regarding the body fatigue, the maximum tension generated at the contact portion should be small, in other words, the total of the negative frictional force should be small. desirable. All of these are related to the driving side, and by comparing the frictional force distributions on the driving side, it is possible to qualitatively evaluate the belt life.

In order to obtain the guideline for improving the belt life, the influence of each factor in the belt on the frictional force distribution on the driving side was examined by using the analytical model of the present invention. The properties shown were obtained. The above-mentioned factors are the thickness t of the lower cover layer 46 and the elastic modulus E, and other conditions are the same as those in Table 2.

From these figures, the smaller the thickness t and the elastic modulus E of the lower cover layer 46, the smaller the sliding area, and the smaller the total negative friction force. It can be seen that the belt life is extended with respect to wear and fatigue of the core body 43. In addition to this, fatigue of the lower cover layer 46 itself can be taken into consideration.

(Embodiment 3) FIGS. 32 to 38 show Embodiment 3 (note that the same parts as those in FIGS. 5 and 7 are designated by the same reference numerals and their detailed description will be omitted). It is applied to a kind of block belt for high load transmission.

FIG. 32 shows a block belt transmission mechanism. This transmission mechanism comprises a pair of V pulleys 61, 61 and a block belt 62 wound between these V pulleys 61, 61. FIG. 33 shows the structure of the block belt 62. The belt 62 includes a pair of left and right endless tension bands 65, 65 made of rubber or the like in which a plurality of core bodies 64, 64, ... , Notch-shaped fitting grooves 68, 6 into which the respective tension bands 65 are detachably fitted in the left and right outer portions in the width direction
8. A large number of blocks 69, 6 having the right and left side surfaces capable of abutting on the side surface of the V-shaped belt groove of the V pulley 61.
9 and so on, and the fitting grooves 68, 68 of each block 69
The tension bands 65, 65 are fitted to the respective blocks, and a large number of blocks 69, 69, ... Are continuously fixed in the belt longitudinal direction.

That is, in this belt 62, on the upper surface of each tension band 65, upper concave grooves 66, which correspond to each block 69 and extend in the width direction thereof, as engaging portions of a constant pitch,
, And lower recessed grooves 67, 67, ... Corresponding to each of the recessed grooves 66, which are engaging portions of a constant pitch extending in the width direction of the tension body 65 are formed. on the other hand,
The tension band 65 is provided on the upper wall surface of the fitting groove 68 of each block 69.
The ridges 7 as locking portions that fit into the upper concave grooves 66 on the upper surface
No. 0 is provided on the lower wall surface of the fitting groove 68, and the ridges 71 are formed as locking portions to be fitted into the respective lower concave grooves 67 on the lower surface of the tension band 65. , 71
Are engaged with the concave grooves 66 and 67 of the tension band 65 to lock and fix the block 69 in the belt longitudinal direction.

FIG. 34 schematically shows a uniaxial transmission analysis model using the block belt 62. FIG. 34 (a) shows the initial arrangement state, and FIG. 34 (b) shows the final steady state. Show. Belt 62 and pulley 6 by this model
The behavior at the time of friction transmission between 1 is simulated. That is, a belt model having twice or more the contact length with the pulley 61 is prepared, and first, as shown in FIG. 34A (the figure shows the case where the contact angle is 180 °), the belt 62 travels. With respect to the direction, the front half is formed into an arc shape around which the pulley 61 is wound, and the second half is linearly arranged in the tangential direction at the end of winding,
Determine the initial placement of the transmission analysis model. Then, an analysis by the finite element method is executed. Specifically, with respect to the model in the initial arrangement, tension on the tension side and tension on the slack side are applied to both ends of the belt 62 in the tangential direction while the rotation of the drive pulley 61 is restrained to converge the equilibrium state at the time of starting. calculate. Although the drawing assumes a drive-side pulley, the tension-side tension and the loose-side tension may be reversed with respect to the driven-side pulley.

Next, while maintaining the magnitude and direction of the tension, the rotation angle is given by forced displacement with respect to the center of the pulley 61, the pulley 61 is rotated little by little in consideration of large deformation, and the convergence calculation is repeated. The analysis is ended when the steady running state is reached when the variation of the solution becomes small. At that time, the deformed state shown in FIG. 34B is obtained, and the total sum of the applied rotation angles is at least the contact angle or more (for example, 216 °).

In this way, in the process from the initial arrangement to the steady state, the load sharing of the belt 62, that is, the frictional force distribution, the tension distribution of the core bodies 64, 64, ...
Thereafter, as in the case of the first embodiment, the output characteristic of the load sharing is collated with the preset durability life characteristic, and the estimated life of the belt 62 is output.

Therefore, also in this embodiment, the same operational effect as that of the first embodiment can be obtained.

35 to 38 show calculated values of respective distributions of the transmission force and the vertical force in the steady state of the block belt 62 and the pulley in comparison with the experimental values, and the solid line in each figure shows the experimental values. , And the two-dot chain line shows the calculated value. The experimental load torque Tr is Tr = 9.8 Nm. The V angle of the block belt 62 is 26 °, and the V groove angle of the V pulley is 25.6 °.

FIG. 35 shows the transmission force on the drive side, FIG. 36 shows the vertical force on the drive side, FIG. 37 shows the transmission force on the driven side, and FIG. 38 shows the vertical force on the driven side. ing.

As is apparent from FIGS. 35 to 38, the calculation results qualitatively agree with the experimental results. Therefore, according to the present invention, the transmission power distribution and the finite element model of the block belt 62 are The vertical force distribution can be accurately predicted, and the life of the block belt 62 can be predicted.

The present invention can also be applied to a multi-axis transmission model having three or more axes. Further, although the present invention is applied to the toothed belt, the flat belt and the block belt (V belt) in each of the above-described embodiments, the present invention is also applicable to transmission belts such as V-ribbed belts. You can

[0104]

As described above, according to the invention of claim 1, the geometric data, the material data, and the external force data are input to the transmission analysis model in which the belt is wound around the pulley to transmit the power, and the finite element is input. By predicting the load sharing characteristic applied to the belt by analysis, the load sharing characteristic of the belt can be properly predicted.

According to the second aspect of the invention, the transmission analysis model is a multi-axis transmission model in which a belt is stretched between a plurality of pulleys for transmission, whereby the load sharing characteristic of the belt in the multi-axis transmission system is predicted. be able to.

According to the invention of claim 3, since the pulley is a toothed pulley and the belt is a toothed belt, the load sharing characteristic of the toothed belt can be predicted.

According to the fourth aspect of the invention, when predicting the load sharing characteristic of the toothed belt, the geometrical data are at least the diameter and center position of the pulley, the number of teeth of the pulley and the belt, the tooth pitch and the tooth profile. Data including dimensions,
The material data is at least the elastic modulus of the belt core, the elastic modulus of the teeth, and the friction coefficient, and the external force data is at least the load torque, angular velocity, and axial load. Data necessary for predicting the characteristics can be properly obtained, and the prediction accuracy can be improved.

According to the fifth aspect of the invention, since the pulley is a flat pulley and the belt is a flat belt, the load sharing characteristic of the flat belt can be predicted.

According to the invention of claim 6, the pulley is a V-pulley and the belt is a V-belt.
It is possible to predict the load sharing characteristic of the belt.

According to the invention of claim 7, the characteristic of the load sharing of the belt predicted by the method of predicting the load sharing of the belt according to claim 1 or 2 is compared with the life characteristic previously obtained according to the load sharing. Then, the life of the belt actually used can be predicted by predicting the life of the belt actually used.

According to the invention of claim 8, in the method of predicting the life of a belt according to claim 7, since the belt is a toothed belt, the life of the toothed belt can be predicted.

According to the ninth aspect of the invention, since the belt is a flat belt, the life of the flat belt can be predicted.

According to the tenth aspect of the invention, since the belt is the V belt, the life of the V belt can be predicted.

According to the invention of claim 11, data input means for inputting geometric data, material data and external force data to a transmission analysis model in which a belt is wound around a pulley for transmission are inputted by this data input means. Based on the data obtained, the load sharing predicting means for predicting the load sharing characteristics applied to the belt by the finite element analysis, and the load sharing characteristics of the belt predicted by the load sharing predicting means are obtained in advance according to the load sharing. The life of the belt can be predicted by providing the life prediction means for predicting the life of the belt actually used as compared with the life characteristics of the belt.

According to the twelfth aspect of the present invention, the life of the belt used in the multi-axis transmission system can be predicted by using the multi-axis transmission model as the transmission analysis model.

According to the invention of claim 13, since the belt is a toothed belt, the life of the toothed belt can be predicted.

According to the fourteenth aspect of the invention, when predicting the life of the toothed belt, as in the fourth aspect of the invention,
As the geometric data, at least the diameter and center position of the pulley, and the data including the number of teeth of the pulley and the belt, the pitch of the teeth, and the tooth profile are input, and the material data is at least the elastic modulus of the belt body, the elastic modulus of the tooth portion, By using the data including the friction coefficient and the external force data including at least the load torque, the angular velocity, and the axial load, the accuracy of predicting the life of the toothed belt can be improved.

[Brief description of drawings]

FIG. 1 is a flow chart diagram showing a processing procedure for predicting the life of a toothed belt using a multi-axis transmission model in Embodiment 1 of the present invention.

FIG. 2 is a block diagram showing a configuration of a belt life prediction device according to the first embodiment.

FIG. 3 is a diagram showing a transmission mechanism of the toothed belt according to the first embodiment.

FIG. 4 is a schematic sectional view of a toothed belt.

FIG. 5 is a diagram showing a shape of a belt tooth portion.

FIG. 6 is a diagram illustrating a main part of a meshing transmission analysis model using a toothed belt.

FIG. 7 is a diagram showing an arrangement according to a model analysis procedure.

FIG. 8 is a plan view of a transmission force distribution measuring device for verifying a tooth portion reaction force distribution of load sharing of a toothed belt.

FIG. 9 is a front view of a transmission force distribution measuring device.

FIG. 10 is a front view of a power transmission measuring pulley.

FIG. 11 shows a pitch difference between the belt and the pulley when there is no tension of +0.002 mm and a tension on the tension side of the belt of 5
FIG. 9 is a characteristic diagram showing an experimental value of a transmission force distribution under a tension condition of 88 N and a slack side tension of 196 N in comparison with a calculated value.

FIG. 12 is a drawing showing data under tension conditions in which the tension on the tension side of the belt is 490 N and the tension on the slack side is 294 N.
FIG.

FIG. 13 is a diagram corresponding to FIG. 11 showing data under tension conditions in which the pitch difference is −0.038 mm, the tension on the belt tension side is 588 N, and the tension on the slack side is 196 N.

FIG. 14 is a characteristic diagram showing a transmission load at startup.

FIG. 15 is a diagram showing a meshing state of the belt and the pulley when the pitch difference is changed.

FIG. 16 is a characteristic diagram showing characteristics of calculated values when the pitch difference is changed.

FIG. 17 is a diagram showing characteristics of maximum tooth reaction force with respect to each pitch difference.

FIG. 18 is a view corresponding to FIG. 16 when the tooth tip compression amount is changed.

FIG. 19 is a diagram showing characteristics of maximum tooth part reaction force with respect to tooth tip compression amount.

FIG. 20 is a schematic diagram of a flat belt transmission mechanism according to a second embodiment.

FIG. 21 is an enlarged sectional view of a flat belt.

22 is a diagram schematically showing a main part of a transmission analysis model using a flat belt in Example 2. FIG.

FIG. 23 is a view corresponding to FIG. 7 showing a biaxial transmission analysis model using a flat belt.

FIG. 24 is a front view showing an experimental apparatus for verifying a load distribution friction force distribution of a flat belt.

FIG. 25 is a front view of a power transmission measuring pulley including a flat pulley.

FIG. 26 is a diagram showing experimental values of frictional force distribution under a tension condition in which the tension on the tension side of the flat belt is 196 N and the tension on the slack side is 98 N, in comparison with calculated values.

FIG. 27 is a view corresponding to FIG. 26 under a tension condition in which the tension on the tension side of the belt is 294 N and the tension on the slack side is 98 N.

FIG. 28 is a diagram showing shear deformation that occurs in the lower cover layer of the flat belt due to rotation of the pulley.

FIG. 29 is a diagram showing calculation results of tension distribution on the driving side under a predetermined tension condition.

FIG. 30 is a characteristic diagram showing calculation results of frictional force distribution when the thickness of the lower cover layer in the flat belt is varied.

FIG. 31 is a characteristic diagram showing calculation results of frictional force distribution when the elastic modulus of the lower cover layer is changed.

FIG. 32 is a diagram schematically showing a block belt transmission mechanism according to a third embodiment of the present invention.

FIG. 33 is a perspective view partially showing the structure of the block belt.

FIG. 34 is a diagram schematically showing a uniaxial transmission analysis model using a block belt.

FIG. 35 is a characteristic diagram showing calculated values of drive-side transmission force distribution characteristics in comparison with experimental values.

FIG. 36 is a diagram corresponding to FIG. 35 showing the vertical force distribution characteristic on the driving side.

FIG. 37 is a view corresponding to FIG. 35, showing the transmission force distribution characteristic on the driven side.

FIG. 38 is a view corresponding to FIG. 35, which shows the vertical force distribution characteristics on the driven side.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Toothed pulley 3 Toothed belt 4 Core body 8 Tooth part 11 Data input part (data input means) 12 Load sharing prediction part (load sharing prediction means) 13 Life prediction part (life prediction means) 41 Flat pulley 42 Flat belt 43 Core body 46 Lower cover layer 61 V pulley 62 Block belt

Claims (14)

[Claims] 1. A transmission analysis model in which a belt is wound around a pulley to transmit power is prepared, and geometric data, material data and external force data are input to the transmission analysis model, and a load applied to the belt by finite element analysis. A load sharing prediction method for a belt, characterized by predicting a sharing property. 2. The belt load sharing prediction method according to claim 1, wherein the transmission analysis model is a multi-axis transmission model in which the belt is laid across a plurality of pulleys for transmission. Prediction method. 3. The belt load sharing prediction method according to claim 1, wherein the pulley is a toothed pulley and the belt is a toothed belt. 4. The belt load sharing prediction method according to claim 3, wherein the geometric data is data including at least the diameter and center position of the pulley, and the number of teeth of the pulley and the belt, the pitch of the teeth, and the tooth profile dimension, The material data is data that includes at least the core body elastic modulus, tooth elastic modulus, and friction coefficient of the belt, and the external force data is data that includes at least load torque, angular velocity, and axial load. Sharing prediction method. 5. The belt load sharing prediction method according to claim 1 or 2, wherein the pulley is a flat pulley and the belt is a flat belt. 6. The belt load sharing prediction method according to claim 1, wherein the pulley is a V pulley and the belt is a V belt. 7. A belt load sharing characteristic predicted by the belt load sharing prediction method according to claim 1 or 2 is compared with a life characteristic previously obtained according to the load sharing,
A belt life predicting method characterized by predicting the life of a belt actually used. 8. The belt life predicting method according to claim 7, wherein the pulley is a toothed pulley and the belt is a toothed belt. 9. The belt life predicting method according to claim 7, wherein the pulley is a flat pulley and the belt is a flat belt. 10. The belt life predicting method according to claim 7, wherein the pulley is a V pulley and the belt is a V belt. 11. A transmission analysis model in which a belt is wound around a pulley to transmit power, and a finite data based on the data input section for inputting the geometric data, material data and external force data, and the data input by the data input section. The load sharing prediction means for predicting the load sharing characteristics applied to the belt by element analysis and the characteristics of the belt load sharing predicted by the load sharing prediction means are compared with the life characteristics previously obtained according to the load sharing. And a belt life predicting device for predicting a belt life actually used. 12. The belt life predicting apparatus according to claim 11, wherein the transmission analysis model is a multi-axis transmission model in which the belt is laid across a plurality of pulleys for transmission. . 13. The belt life predicting apparatus according to claim 11 or 12, wherein the pulley is a toothed pulley and the belt is a toothed belt. 14. The belt life predicting apparatus according to claim 13, wherein the geometric data is data including at least a diameter and a central position of the pulley, and the number of teeth of the pulley and the belt, a pitch of the tooth, and a tooth profile dimension. The data is data including at least the core elastic modulus of the belt, the tooth elastic modulus, and the friction coefficient, and the external force data is data including at least load torque, angular velocity, and axial load. apparatus.