JP2960648B2 - Belt load sharing prediction method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates are those directed to a method of predicting the load distribution characteristics during transmission of the belt.

[0002]

2. Description of the Related Art In general, toothed belts have excellent features such as light weight, large inter-axis distance, no lubrication, and relatively high efficiency. It is widely used from large industrial machines to small office machines. In recent years, toothed belts have also been used for driving a camshaft of an automobile engine, and improvements in performance and reliability have been demanded.

As a theory for elucidating such a transmission mechanism of a toothed belt, there has been conventionally proposed, for example, (1) "Transactions of the Japan Society of Mechanical Engineers, Vol. 42, No. 359" (1976), pp. 2233-2.
241, (2) "Transactions of the Japan Society of Mechanical Engineers, Vol. 44, No. 387"
(1978), pp. 3913-3922, (3)
`` Journal of Mechanical Design paper no, 77-DET-10
0 "(1978), pp. 208-215.

[0004]

However, it cannot be said that the conventional technique described above has achieved satisfactory results. That is, according to the well-known Coulomb friction law, if the friction force is F, the friction coefficient is μ, and the normal force is N,
The friction state includes two states: a fixed state where F <μN and a slip state where F = μN. The state and direction of the friction are defined as the state in which the belt and the pulley are actually driven to rotate. Determined by mechanical behavior.

However, in the conventional transmission technology theory, this is known, and the frictional force, which is one of the transmission powers, is always treated as a slip state. For this reason, despite the meshing transmission, the history dependency of the frictional force having a high ratio to the transmission force is ignored, and it is difficult to predict the load sharing characteristics of the belt well.

[0006] These points are not limited to toothed belts, and the same can be said for general transmission belts such as flat belts and V-belts.

SUMMARY OF THE INVENTION The present invention has been made in view of the foregoing, and an object of the present invention is to improve the method of analyzing a belt transmission mechanism so that the load sharing of a transmission belt such as a toothed belt or a flat belt can be performed. The object of the present invention 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 portion of the belt transmission mechanism, which is in contact with the pulley under the core of the belt, is incorporated into the model of the belt transmission mechanism, and the pulley rotates. Then, the belt transmission mechanism was analyzed using the nonlinear finite element method in a state in which the belt was given a movement close to actual rotation.

That is, the inventions of claims 1 to 4 are methods for predicting the load distribution of the belt. In the invention of claim 1, a transmission analysis model for transmitting the power by winding the belt around a pulley is prepared. On the other hand, input the geometric data, material data and external force data , and
From the start state where the belt is stretched between the pulleys,
While pulling, pulley should be at least
By shifting to a steady state in which the belt rotates by more than the contact angle, the load sharing characteristic applied to the belt is predicted by 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 transmitted between a plurality of pulleys and transmitted.

In the invention according to 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 the center position of the pulley, the number of teeth of the pulley and the belt, the pitch of the teeth, and the tooth profile dimensions. The material data is at least the core elastic modulus of the belt, the tooth elastic modulus,
The data includes a coefficient of friction, and the external force data includes at least a load torque and a shaft load .

[0013]

According to the above construction, in the first aspect of the present invention, geometric data, material data and external force data are input to a transmission analysis model which transmits a belt by wrapping a belt around a pulley, and the transmission analysis model is changed from a start state. With few pulleys
Also reaches a steady state where the belt rotates more than the contact angle with the pulley.
The load sharing characteristic applied to the belt is predicted by finite element analysis. The load sharing characteristics of the belt based on this finite element analysis substantially match the actual characteristics, and thus the load sharing characteristics 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, the load sharing characteristics of the belt used in the multi-axis transmission system are predicted. Can be.

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

According to the fourth aspect of the present invention, when predicting the load sharing characteristics 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 teeth and the tooth profile dimensions are used as geometric data. Is input, and the material data is data including at least the elastic modulus of the core of the belt, the elastic modulus of the teeth, and the friction coefficient, and the external force data is
Since the data includes at least the load torque and the shaft load , data necessary for predicting the load sharing characteristics of the toothed belt can be appropriately obtained, and the prediction accuracy can be improved.

[0017]

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, wherein 1, 1 is a toothed pulley having a plurality of teeth 2, 2,. A toothed belt which is meshed with and wound around the attached pulleys 1, 1;
As shown in detail in FIG. 4, an adhesive rubber layer 5 having the core body 4 embedded therein, a back rubber layer 6 (cover rubber layer) integrally bonded to the back side of the belt of the adhesive rubber layer 5, and an adhesive rubber A tooth rubber layer 7 having a plurality of teeth 8, 8,... Meshing with the teeth 2, 2,. And a tooth cloth 9 (rubber canvas layer) that covers the surface of the tooth portion 8 of FIG.

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

FIG. 2 schematically shows the structure of a prediction device for predicting the life of the toothed belt based on the transmission analysis model of the toothed belt. Reference numeral 11 denotes a belt 3 which is transmitted between a plurality of pulleys 1 and 1. A data input unit for inputting geometric data, material data, and external force data to the 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. The material data includes at least the elastic modulus of the core 4, the elastic modulus of the teeth 8, and the friction coefficient of the belt 3. Further, the external force data includes at least a load torque and a shaft load .

Reference numeral 12 denotes a load sharing predicting 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 respective characteristics of the tooth part reaction force distribution, the frictional force distribution, and the tension distribution are specifically predicted.

Further, reference numeral 13 denotes a life estimating section for estimating the life of the belt 3. The life estimating section 13 includes a characteristic of the tooth portion among the characteristics of the load sharing of the belt 3 predicted by the load sharing estimating section 12. The force distribution characteristics are calculated by using an SN curve (tooth reaction force-
The life of the toothed belt 3 that is actually used is predicted by comparing and comparing with the durability life characteristic curve) and referring to the composite rule or the minor rule.

In this embodiment, a specific processing procedure for estimating the service life of the toothed belt 3 using 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,
Geometric data such as tooth profile dimensions are input to the meshing transmission analysis model. In the next step S2, the elastic modulus of the tension member 4 in the belt 3, enter the elastic modulus of the tooth portion 8, a material data such as friction coefficient, further in step S3, the variation of the load torque, Jikuni
Input external force data such as weight .

FIG. 6 illustrates a main part of an analysis model for meshing transmission by the toothed belt 3. In this model, pitch 8
mm having a tooth portion 8 having an arc tooth shape (S8M type) and a width of 1
A drive system of a 9.1 mm toothed belt 3 and two toothed pulleys 1 and 1 having 24 grooves around which the toothed belt 3 is wound, and a back rubber layer that hardly contributes to transmission in the belt 3 Modeling is omitted for 6 (cover rubber layer). In the modeled belt portion, the portion of the core 4 is a two-node beam element.
(Rubber canvas layer) and the tooth portions 8 are represented by quadrilateral four-node planar elements, respectively.

Since the pulley 1 is extremely hard as compared with the belt 3, it is regarded as a rigid body, and only its outer peripheral shape is represented by a rigid body surface. Also, one node is provided at the center of the pulley 1, and this represents the movement of the pulley 1.

Further, a joining element is provided on a square element surface corresponding to the outer surface 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 contact between the belt 3 and the pulley 1 is established. , Friction and delamination are taken into account. Friction is assumed to be in accordance with 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. FIG.
(A) is an initial arrangement of a two-axis meshing transmission analysis model using the above-described toothed belt, in which two pulleys 1 and 1 represented by a rigid body surface are arranged side by side as close as possible in the horizontal direction. A model of a belt 3 connected in a circle so as to surround these pulleys 1 and 1 is arranged. The belt 3 connected in a circle has an original natural state 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 without contacting the pulley 1.
In the drawing, all the degrees of freedom are restricted for the driving pulley 1 on the left side, and the degrees of freedom other than the horizontal direction are restricted for the driven pulley 1 on the right side.

Then, the process proceeds to step S5, where a mesh for dividing the transmission analysis model into finite elements is generated, and then in step S6, analysis is performed by the finite element method. First, as shown in FIG. 7 (b), a load is applied to the rotating shaft of the driven pulley 1 with respect to the model in the initial arrangement, and the belt 3 stretched between the driving and driven pulleys 1 It is in a state of being stretched by the load W. Next, as shown in FIG. 7 (c), after releasing the restriction on the rotation of the driven pulley 1, a concentrated moment in the clockwise direction in the figure corresponding to the load torque Tr is applied to the driven pulley 1 to start the operation. I do. From this state, as shown in FIG. 7 (d), ejection
At least the moving of the belt 3 to the pulley 1
Forcibly apply a counterclockwise rotation angle displacement larger than the contact angle
To obtain the final target steady state.

Then, in step S7, in the process from the initial arrangement to the steady state, the belt 3
, That is, the distribution of the reaction force of the teeth, the distribution of the frictional force, the distribution of the strain of the heart, the distribution of the tension, and the like.

Next, proceeding to step S8, the tooth reaction force distribution in the output load distribution is compared with an SN curve in which the durability life characteristic is set in advance in accordance with the tooth reaction force distribution. Then, in step S9, it is determined whether or not the number of teeth reaction force cycles during one rotation of the belt is plural. When this determination is NO, the process directly proceeds to step S11. When YES, the process proceeds to step S11 after calculating the degree of fatigue per belt rotation in step S10 according to the compound rule (or minor rule). This step S
At 11, the estimated life of the belt 3 is output.

Therefore, in this embodiment, when estimating the life of the toothed belt 3, first, a multi-axial transmission analysis model in which the toothed belt 3 is stretched between the plurality of pulleys 1 and 1 is used. Geometric data including the diameter and center position of each pulley 1, the number of teeth of the pulley 1 and the belt 3, the tooth pitch and the tooth profile size, the elastic modulus of the core 4 of the belt 3, the elastic modulus of the tooth portion 8, and the coefficient of friction and material data, including, load torque
And external force data including a shaft load . Then, based on these data, the load sharing characteristics applied to the toothed belt 3 are predicted as the respective characteristics of the tooth portion reaction force distribution, the frictional force distribution, and the tension distribution by finite element analysis. Thereafter, among the load sharing characteristics of the toothed belt 3 predicted in this manner, the tooth part reaction force distribution characteristic is an S-N curve in which the durability life characteristic is set in advance in accordance with the tooth part reaction force distribution. In addition to the comparison, the composite 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 characteristics of the toothed belt 3 based on the finite element analysis substantially match the actual characteristics.
The load sharing characteristics can be properly predicted. Therefore, the life of the toothed belt 3 used in the multi-axis transmission system can be predicted.

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 dimensions. The data is data including the elastic modulus of the core 4 of the belt 3, the elastic modulus of the tooth portion 8, and the coefficient of friction.
Since the external force data is data including the load torque and the shaft 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 distribution of the tooth portion reaction force sharing the load 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 reaction force distribution sharing the load of the toothed belt. Reference numeral 21 denotes a base installed on the floor, and 22 denotes a base 21. A fixed shaft 22 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 a front end of the fixed shaft 22, and a load drum 23 having a radius R2 is provided at a rear end. It is attached to the rotating body. Pole 2 on the right floor of base 21
A pulley 25 having an axis in the horizontal front-rear direction is rotatably supported at the upper end of the pole 24.
A wire 26 is connected to the pulley 25 at the upper end of the pole 24.
An end of the wire 26 is connected to the load drum 23, and a load weight W2 is suspended from the other end.
Is given 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 table 29 is movable on the guide rails 28, 28 in the left-right direction. It is placed so as to be able to approach and separate from. A movable shaft 30 extending in the front-rear direction is rotatably supported at the right end of the movable base 29. A torque meter 31 is disposed at the front of an intermediate portion of the movable shaft 30, and a gear box 32 is disposed at the rear. Have been. In addition, the movable shaft 30
A toothed pulley 19 having a radius R1 is rotatably attached to the front end of the shaft.
A test toothed belt 20 between the front toothed pulley 18
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 toothed pulley 19 is rotated by driving the motor 34.

A pulley 35 having a horizontal longitudinal axis is supported at the front end of the left side of the base 21.
Is wound around the middle portion of the wire 36,
5 has a load cell 3 on the left side of the front end of the movable base 30.
7 are connected. On the other hand, a weight W1 for initial tension is suspended from the other end of the wire 35.
By means of 1, a predetermined initial tension T0 is applied to the test belt 18.

At this time, assuming that the tension T1 on the tension side of the belt 18 and the tension T2 on the loose side of the belt 18 are T1 + T2 = 2.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 a power transmission measuring pulley. That is, as shown in FIG. 10, the pulley 18 on the fixed shaft 22 side has a pair of slits L formed by cutting the pulley 18 from the outer peripheral edge toward the center.
1, L1, L2, L2, L3, and L3 are processed into three sets of slits, and the roots of the slits L1 to L3 each have one slit corresponding to the rotation direction of the pulley 18.
A pair of strain gauges 38, 38,... Are attached.
In the strain gauges 38, 38 of the slits L1, L1, the tooth reaction force and the tip friction are applied. In the strain gauges 38, 38 of the slits L2, L2, the tip friction is applied. The strain gauges 38, 38 detect the root friction force, respectively, and the slit portions L1,
The tooth part reaction force can be calculated by subtracting the detection data of the slit parts L2 and L2 from the detection data of L1.

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

[0039]

[Table 1]

FIGS. 11 to 13 show experimental values (shown by solid lines) of the transmission force distribution in the steady state of the belt and pulley in comparison with calculated values (shown by broken lines). In each figure, (a) shows the driving side, and (b) shows the driven side. FIG. 11 shows that the difference in pitch between the belt and the pulley (difference between the tooth pitch of the belt and the tooth pitch of the pulley) when there is no tension is +0.002 mm, the tension on the tension side of the belt is 588 N, and the tension on the loose side is 196 N. Data under tension conditions FIG. 12 shows data under the tension conditions where the above-mentioned pitch difference is the same, the tension on the tension side of the belt is 490 N, and the tension on the loose side is 294 N. FIG. 13 shows that the pitch difference is -0.038.
mm, the tension on the tension side of the belt is 588N, and the tension on the loose side is 196N.

In these figures, the signs of the tooth part reaction force Q, the tooth tip frictional force Ft, and the root frictional force Fb indicate that the direction contributing to the transmission is positive. The horizontal axis indicates the tooth number indicating the position of the meshing region between the belt and the pulley, and the vertical axis indicates the magnitude of the load. And the number of teeth counted in the direction of the meshing exit from which the belt comes off. For this reason, the tension side on the drive side and the loose side on the driven side have tooth numbers of “0”.

FIG. 1 shows the experimental results of the transmission distribution.
1 to 13, there is a great difference between the driving side and the driven side. That is, from the static force balance, the driving force and the driven force have substantially the same transmission force distribution at startup.
FIG. 14 shows the transmission load at the time of startup ((a) in the figure shows the driving side and (b) shows the driven side, respectively). However,
Focusing on one tooth, during the process of rotating the pulley from the start to the steady state, the driving side receives the history of friction due to the change in tension from the tight side to the loose side, and the driven side receives the history of friction in the opposite direction. A change in tension causes a history of friction different from that on the drive side. For this reason, it is considered that the transmission force distribution at the time of startup has changed such that a large difference between the driving side and the driven side occurs in the steady state.

Also, comparing the characteristics of FIGS. 11 and 13, it can be seen that the positive or negative of the pitch difference also produces a large difference in the transmission force distribution. In particular, the location where the maximum value of the tooth reaction force occurs is reversed in both figures. That is, FIG. 15A shows the meshing state on the drive side in the steady rotation state when it is assumed that the pitch difference is 0 and the belt 3 does not expand and contract.
(B) schematically shows the meshing state on the driven side. 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 schematically shows when the pitch difference is negative. Therefore, the meshing state at the time of steady rotation when there is a pitch difference is the meshing state of FIG.
An image is obtained by superimposing the meshing state of (c) or (d). At this time, it is considered that the tooth portion 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. When the pitch difference is negative, on the other hand, when the pitch difference is negative, the opposite is the place where the meshing surfaces match, which coincides with the place where the maximum tooth reaction force in FIGS. 11 and 13 occurs. ing.

Focusing on the root friction on the drive side in FIG. 13, the root friction changes continuously from negative to positive in accordance with the direction of rotation. That is, the direction of the frictional force changes in the middle, and the magnitude of the frictional force becomes zero at the transition. This phenomenon, as mentioned for trapezoidal teeth,
According to the calculation results of the model according to the present invention, which can not be explained by the conventional transmission theory assuming that the state of friction is always a sliding state, considering the two friction states of sticking and sliding and the history incompatibility of the direction. It can be reproduced successfully.

Referring to FIGS. 11 to 13, the frictional force at the tooth tip, which is a feature of the S8M type, is generally small.
The degree of the change is low. Tooth tip compression amount of belt and pulley in the experiment (belt tooth height−pulley groove depth = 0.
10 mm), the surface pressure is small, and the contact surface is located at a position distant from the heart 4 via the teeth 8, so that it is considered that the followability to the movement of the heart 4 is reduced.

When the calculation results of the transmission analysis model according to the present invention are compared with the experimental results, they agree qualitatively on the driving side and the driven side, and in particular, quantitatively agree on the tooth reaction force. It turns out that the transmission analysis according to the present invention is effective.

However, in the transmission analysis, a remarkable peak observed at the meshing outlet is not reproduced. This peak is considered to be due to the addition of the 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 in the analysis model because the division of the elements was coarse. Can be

Further, the degree of matching of the frictional force is slightly worse than the tooth reaction force, because the element division is coarse, the measurement error due to the small slit width at the crest of the measuring pulley, and as described above. A difference in the shear deformation of the rubber / cloth layer, which is directly linked to the root friction, is considered. Since the actual toothed belt has a three-layer structure of a core, rubber and canvas (see FIG. 4), there is a shearing deformation that bends in the middle, but the analysis model has a one-layer structure as shown in FIG. Therefore, simple shear deformation is caused, and the degree of matching of the frictional force is reduced due to this.

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

Next, the present inventor examined the effects of various parameters of the transmission system on the transmission force distribution characteristics using the finite element analysis model according to the present invention. The factors are a pitch difference Δp at which a large influence is observed in the case of a trapezoidal tooth profile, and a tooth tip compression amount Δc which is a feature of the S8M type belt. Further, the number of pulley teeth is set to 28, the tension on the tension side of the belt is set to 588 N,
The slack side tension was set to 196N, 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. FIG. 16A shows the driving side, and FIG. Are respectively shown. The solid line represents the tooth part reaction force Q, and the broken line represents the root friction force Fb.

The numerical values in FIG. 16 are the values of the pitch difference. According to FIG. 16, as in the case of the trapezoidal tooth profile, it can be seen that the transmission force distribution greatly changes due to the pitch difference. 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 the case of a toothed belt mounted on an automobile engine, the load transmission on the drive pulley as the crank pulley is considered to be the strictest.
FIG. 17 shows the characteristic of the maximum tooth part reaction force for each of the pitch differences, focusing on the driving side maximum tooth part reaction force shown in FIG. In FIG. 17, when the pitch difference is -0.014 mm, the maximum tooth part reaction force is minimum.

Under the tension condition that the tension on the tension side of the belt is 588 N and the tension on the loose side is 196 N, 392 (= 5
88-196) N considers that the average tension is acting, the belt is 0.11 (= 392/343000 × 10
0) Since it is stretched by%, for a nominal pitch of 8 mm,
When the pitch difference is -0.009 mm defined under no tension, the actual pitch difference is 0. The pitch difference at which the maximum tooth part reaction force is minimized is more negative than -0.009 mm.
Since the pitch difference is 0.014 mm, the case where the pitch difference is negative is more advantageous for tooth shear fatigue than the case where the pitch difference is positive.

On the other hand, with respect to the tooth tip compression amount shown in FIG. 18, the pitch difference is -0.022 mm, and the chain line in the figure represents the tooth tip frictional 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 in the tooth tip compression amount Δc, so that the frictional force is greatly affected. It can be seen that this also has an effect. In particular, on the driving side, the frictional force acts in a direction to maintain the positional relationship between the tooth portion of the belt and the pulley groove at the time of biting, so that the tooth tip frictional force is in a negative direction. Due to the balance, the tooth reaction force also increases. FIG. 19 shows the tooth tip compression amount Δc.
19, the characteristic of the maximum tooth part reaction force is shown. In FIG. 19, the increase of the tooth tip compression causes the increase of the tooth tip frictional force and the increase of the maximum tooth part reaction force. That is, from the standpoint of only the shear fatigue of the teeth, the tip compression, which is a feature of the S8M type, is disadvantageous, and it is advantageous that there is no tip compression like a trapezoidal tooth profile. However, tooth tip compression has the effect of alleviating the surface pressure at the bottom of the tooth having a small contact area or the polygonal winding of the core, so it cannot be said that it is not always better to have no compression.

(Embodiment 2) FIGS. 20 to 31 show Embodiment 2 (the same parts as those in FIGS. 5 and 7 are denoted by the same reference numerals and their detailed description is omitted). Applied.

FIG. 20 shows a flat belt transmission mechanism, which comprises flat pulleys 41, 41 and a flat belt 42 wound around them. For example, as shown in FIG. 21, the flat belt 42 includes an adhesive rubber layer 44 having a core 43 embedded therein, an upper rubber layer 45 integrally adhered to the 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 of the belt.

FIG. 22 schematically shows a transmission analysis model using a flat belt, and FIG. 22A shows an initial arrangement state.
FIG. 2B shows the final steady state. In this model, the heart 43 involved in transmission in a flat belt is used.
And only the lower cover layer 46,
, A two-node beam element is used, and a four-node plane stress element is used for the lower cover layer 46. Further, the pulley 41 is defined by a circular hard surface having a predetermined outer diameter, and a joining element is arranged on a side of the lower cover layer 46 of the belt 42 that comes into contact with the pulley 41.
Consider contact, friction and delamination between the two. Regarding friction, F is the friction force, μ is the friction coefficient (= constant), and N is the normal force.
In this case, if F <μN, the state is fixed, and F = μN
If so, a general Coulomb rule for a finite slip state is applied.

FIG. 23 shows a two-axis transmission analysis model using a flat belt, and this model simulates the behavior during frictional 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 expressed by a rigid body surface are juxtaposed as close as possible in the horizontal direction, and a model of a flat belt 42 connected in a circular shape is arranged so as to surround these pulleys 41, 41. doing. In the figure, the drive pulley 41 on the left side is restricted to all degrees of freedom and is in a completely fixed state, and the driven pulley 41 on the right side is restricted in degrees of freedom other than the horizontal direction and is in a vertically fixed state.

Next, analysis by the finite element method is executed. As shown in FIG. 23B, a load is applied to the rotating shaft of the driven pulley 41 with respect to the model in the initial arrangement,
The belt 42 stretched between the driving and driven pulleys 41, 41 is tensioned by the axial load W, and a tension T1 and a loose tension T2 are applied to the belt 42. next,
As shown in FIG. 23 (c), while keeping the magnitude and direction of the tension in the same state, the restraint 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 starting moment is given by giving a concentrated moment in the circumferential direction. From this state, as shown in FIG.
A rotational angular displacement in the counterclockwise direction is forcibly applied to the driving pulley 41 to obtain a final target steady state.

In the process from the initial arrangement to the steady state, the load distribution of the belt 42, that is, the frictional force distribution, the tension distribution of the core 43, and the like are obtained. Thereafter, similarly to the first embodiment, the output load sharing characteristic is
The flat belt 4 is compared with a preset durability life characteristic.
The estimated life of 2 is output.

Therefore, in this embodiment, the same operation and effect as in the first embodiment can be obtained.

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

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

On the other hand, the first wire sheave 53 is wound around one end of a wire 58 having an intermediate portion hanging down below the initial tension weight W1.
The other end of 8 is wound around and connected to the second wire sheave 56 on the side opposite to the side where the wire is connected to the first wire sheave 53. A third wire sheave 59 is wound around and suspended at an intermediate portion of the wire 58, and a load weight W2 is suspended around a shaft portion of the third wire sheave 59.
A predetermined load torque is applied to the flat pulleys 52 and 55 by the 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 formed with a pair of slits L, L, and a pulley 5 is formed at the root of the slits L, L.
A pair of strain gauges 3 corresponding to the rotation directions 2
8 and 38 are attached, and the strain gauges 38 and 38
38 detects the frictional force.

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 its lower cover layer is made of CR (chloroprene rubber). The flat pulleys 52 and 55 are made of steel. The main specifications of the flat pulleys 52 and 55 and the flat belt 57 are as shown in Table 2 below.

[0069]

[Table 2]

FIGS. 26 and 27 compare the experimental values (shown by the solid lines) of the frictional force distribution in the steady state of the belt and the pulley with the calculated values (shown by the broken lines and the dashed-dotted lines) from these experiments. (A) of each figure shows the driving side,
(B) shows the driven side. FIG. 26 shows data under tension conditions where the tension of the flat belt is 196 N and the tension of the loose side is 98 N. FIG. Data under conditions. In FIG. 26, the calculated value when the friction coefficient μ is set to μ = 0.5 is indicated by a broken line, and μ
The calculated values when = 0.7 are indicated by dashed lines. In FIG. 27, the friction coefficient μ on the drive side is expressed as μ =
The calculated value when 0.7 is set, and the driven side is μ = 0.5
The calculated values are shown below.

In FIGS. 26 and 27, the abscissa indicates the position of the contact portion, and the position where the belt tension side contacts the pulley was set to 0 °, and the measurement was performed in the direction of the loose side around the center axis of the pulley. Indicates an angle. The vertical axis indicates the magnitude of the load, and the direction of the frictional force is positive in the direction from the tight side to the loose 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 drive side is set to μ = 0.7 and the friction coefficient on the driven side is set to μ = 0.5, they coincide.
Therefore, according to the present embodiment, for the finite element model of the flat belt, by appropriately setting the friction coefficient, the frictional force distribution can be accurately predicted, and the life of the flat belt is predicted. be able to. In particular, if the friction coefficient is made different from each other on the driving side and the driven side, it becomes more advantageous.

Referring to FIGS. 26 and 27,
In both the calculated value and the experimental value, it can be seen that the distribution of the frictional force is greatly different between the driving side and the driven side, and that the direction of the frictional force changes from negative to positive on the driving side. That is,
As shown in FIG. 28, in the flat belt 42 that is in contact with the pulley 41, if the virtual cross section of the lower cover layer 46 is initially at the position of aa ′, the rotation of the pulley 41 in the clockwise direction 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 becomes b
−b ′, and a shear deformation δ occurs. On the drive side, this shearing deformation δ forces the frictional force in the positive direction. Therefore, in order to balance the forces, a reverse direction, that is, a negative frictional force acts in the initial contact region.

This distribution of frictional force on the driving side has a significant effect on the tension distribution of the core 43. That is, from the balance of the lower cover layer 46 shown in FIG. 28, the tension increases in the negative region from the tension side to the loose side, but decreases in the positive region. There is also a high tension range. For example, FIG. 29 shows the calculation result of the tension distribution on the driving side under the tension condition where the tension on the tension side of the flat belt is 196N and the tension on the loose side is 98N.
A maximum tension 40% higher than the tension on the tight side is observed.
The magnitude of the maximum tension is the sum of the tension on the tension side and the sum of the negative frictional forces.

Next, focusing on the frictional state of the contact portion, FIGS. 26 and 27 show the frictional state determined from the calculation results as a fixed state “ST” or a slip state “SL”. On the driving side, the area from the beginning of contact (tension side) to the point where the maximum positive frictional force is generated is the fixed area, and the area after that is the sliding area. That is, FIG.
It is considered that the contact portion has slipped from the time when the shear deformation of the lower cover layer 46 occurs as shown in FIG. 8 and reaches the limit on the right side of FIG. In this sliding region, Euler's theory is established.

On the other hand, on the driven side, most of the area except for both ends of the contact is in a fixed state, and the shear deformation of the lower cover layer 46 due to a change in the tension of the core 43 in the rotation direction and the difference in the curvature cause It is considered that the direction of the shearing deformation is opposite to that of the shearing deformation, and the shearing deformation obtained by combining them has not reached the slip limit.

[0077] When considering belt life, (1) Since the wear of the lower cover layer 46 proceeds in sliding region, reducing the limited slip area available, (2) for the tension member fatigue, the contact portion It is desirable that the maximum tension generated is small, in other words, the sum of the negative frictional forces is small. These are all involved in the drive side, and qualitative evaluation of the belt life can be performed by comparing the frictional force distribution on the drive side.

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

From these figures, it can be seen that the smaller the thickness t and the modulus of elasticity E of the lower cover layer 46, the smaller the sliding area and the smaller the total negative frictional force. It can be seen that the belt life is extended with respect to wear and fatigue of the core 43. In addition, the fatigue of the lower cover layer 46 itself can also be considered.

Embodiment 3 FIGS. 32 to 38 show Embodiment 3 (the same parts as those in FIGS. 5 and 7 are denoted by the same reference numerals and detailed description thereof is omitted). This is applied to a kind of high load transmission block belt.

FIG. 32 shows a block belt transmission mechanism. This transmission mechanism includes a pair of V pulleys 61, 61 and a block belt 62 wound between the 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 and 65 made of rubber or the like, in which a plurality of cores 64, 64,... Notch-shaped fitting grooves 68, 6 for detachably fitting the tension bands 65 in the left and right outer portions in the width direction.
And a large number of blocks 69, 6 whose left and right side surfaces can be brought into contact with the V-shaped belt groove side surface of the V pulley 61.
.., And fitting grooves 68, 68 of each block 69.
Are fitted with tension bands 65, 65, respectively, and a large number of blocks 69, 69,... Are continuously fixed in the longitudinal direction of the belt.

That is, in the belt 62, the upper concave grooves 66, as engaging portions having a constant pitch, extending in the width direction corresponding to each block 69 are formed on the upper surface of each tension band 65.
On the lower surface, lower grooves 67, 67,... Are respectively formed on the lower surface as engaging portions of a constant pitch extending in the width direction of the tension member 65, corresponding to the respective grooves 66. on the other hand,
On the upper wall surface of the fitting groove 68 of each block 69, the tension band 65 is provided.
The ridge 7 as a locking portion that fits into each upper concave groove 66 on the upper surface
On the lower wall surface of the fitting groove 68, 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, and the ridges 70 of each block 69 are formed. , 71
Are respectively engaged with the concave grooves 66 and 67 of the tension band 65 to lock and fix the block 69 in the longitudinal direction of the belt.

FIG. 34 schematically shows a one-axis transmission analysis model using the block belt 62. FIG. 34A shows an initial arrangement state, and FIG. 34B shows a final steady state state. Show. With this model, the belt 62 and the pulley 6
Simulate the behavior at the time of friction transmission between the two. That is, a belt model having at least twice the length of contact with the pulley 61 is prepared, and first, as shown in FIG. 34A, the traveling of the belt 62 is performed as shown in FIG. In the direction, the first half is formed into an arc shape with the pulley 61 wound around, and the second half is arranged linearly in the tangential direction at the end of winding.
Determine the initial placement of the transmission analysis model. Next, analysis by the finite element method is performed. Specifically, the tension in the belt 62 and the tension in the loose side are applied to both ends of the belt 62 in the tangential direction while the rotation of the driving pulley 61 is restrained, and the equilibrium state at the time of startup is converged with respect to the model in the initial arrangement. calculate. Although the drawing assumes a drive-side pulley, the positions of the tension on the tension side and the tension on the loose side may be reversed for the driven pulley.

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

In the process from the initial arrangement to the steady state, the load distribution of the belt 62, that is, the frictional force distribution, the tension distribution of the cores 64, 64,.
Thereafter, in the same manner as in the first embodiment, the estimated life of the belt 62 is output by comparing the output load sharing characteristic with a preset durability life characteristic.

Therefore, in this embodiment, the same operation and effect as those of the first embodiment can be obtained.

FIGS. 35 to 38 show the calculated values of the distribution of the transmission force and the normal 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 indicate the calculated values. The experimental value of the 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 driving side, FIG. 36 shows the vertical force on the driving side, FIG. 37 shows the transmission force on the driven side, and FIG. 38 shows the vertical force on the driven side. ing.

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

The present invention can be applied to a multi-axis transmission model having three or more axes. In each of the above embodiments, the present invention is applied to a toothed belt, a flat belt, and a block belt (V-belt). Can be.

[0091]

As described above, according to the first aspect of the present invention, the geometric analysis data, the material data and the external force data are input to the transmission analysis model transmitted by winding the belt around the pulley, and the transmission analysis model is input. The starting state to the steady state
The load sharing characteristic of the belt can be properly predicted by estimating the load sharing characteristic applied to the belt by the finite element analysis by shifting to .

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 and transmitted, the load sharing characteristics of the belt in the multi-axis transmission system are predicted. be able to.

According to the third aspect of the present invention, since the pulley is a toothed pulley and the belt is a toothed belt, the load sharing characteristics of the toothed belt can be predicted.

According to the fourth aspect of the present invention, when predicting the load sharing characteristics of the toothed belt, 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 shape. Data including dimensions,
The material data is data including at least the core elastic modulus, the tooth modulus, and the friction coefficient of the belt, and the external force data is data including at least the load torque and the axial load . Data necessary for prediction can be appropriately obtained, and the prediction accuracy can be improved.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a processing procedure for estimating 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 illustrating a configuration of a belt life prediction device according to the first embodiment.

FIG. 3 is a diagram illustrating 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 the shape of a belt tooth part.

FIG. 6 is a diagram exemplifying 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 the toothed belt.

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

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

FIG. 11 shows a difference in pitch between the belt and the pulley in the absence of 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 tension conditions where the tension is 88 N and the loose side tension is 196 N, in comparison with calculated values.

FIG. 12 shows data under tension conditions where the tension on the tension side of the belt is 490N and the tension on the loose side is 294N.
FIG.

13 is a diagram corresponding to FIG. 11 showing data under a tension condition where the pitch difference is −0.038 mm, the tension on the tension side of the belt is 588 N, and the tension on the loose side is 196 N.

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

FIG. 15 is a diagram showing an engagement state between a belt and a pulley when a pitch difference is changed.

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

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

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

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

FIG. 20 is a diagram schematically illustrating a flat belt transmission mechanism according to a second embodiment.

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

FIG. 22 is a diagram schematically showing a main part of a transmission analysis model using a flat belt in the second embodiment.

FIG. 23 is a diagram corresponding to FIG. 7 showing a two-axis transmission analysis model using a flat belt.

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

FIG. 25 is a front view of a power transmission measurement pulley composed of a flat pulley.

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

FIG. 27 is a diagram corresponding to FIG. 26 under tension conditions where the tension on the tension side of the belt is 294N and the tension on the loose side is 98N.

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

FIG. 29 is a diagram illustrating a calculation result of a tension distribution on a driving side under a predetermined tension condition.

FIG. 30 is a characteristic diagram showing a calculation result of a 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 a frictional force distribution when the elastic modulus of the lower cover layer is varied.

FIG. 32 is a view 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 a block belt.

FIG. 34 is a diagram schematically showing a one-axis transmission analysis model using a block belt.

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

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

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

FIG. 38 is a diagram corresponding to FIG. 35 showing a vertical force distribution characteristic on the driven side.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Toothed pulley 3 Toothed belt 4 Core body 8 Teeth 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 46 Lower cover layer 61 V pulley 62 Block belt

Continuation of front page (56) References JP-A-3-210671 (JP, A) JP-A-6-282611 (JP, A) JP-A-5-54106 (JP, A) JP-A-4-174080 (JP) , A) Transmission Technology Research Society, edited by "Belt Transmission Technology", Modern Editor, March 1, 1974, p. 19-34 Tomio Koyama, 3 others, "Research on the Strength of Toothed Belts" Transactions of the Japan Society of Mechanical Engineers Vol. 44, No. 387 (1978), pp. 3913-3922 SAE TECHNICAL PAPER SERIES 940690, USA (February 28, 1994), pp. 23-32 (58) Fields investigated (Int. Cl. ⁶ , DB name) F16G 1 / 00-5/20 F16H 7/00-7/24 G06F 17/00-17/50

Claims (4)

(57) [Claims] A transmission analysis model for transmitting power by winding a belt around a pulley is prepared. Geometric data, material data and external force data are input to the transmission analysis model , and the transmission analysis model is transmitted between the pulleys. Activation letter with belt
From the state, at least the pulley is
A steady state where the belt rotates more than the contact angle with the pulley
Until by migration, load distribution method of predicting the belt, characterized in that to predict the load distribution characteristic applied to the belt by the finite element analysis. 2. The belt load sharing method according to claim 1, wherein the transmission analysis model is a multi-axis transmission model in which the belt is transmitted between a plurality of pulleys. Forecasting 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, the number of teeth of the pulley and the belt, the pitch of the teeth and the tooth profile dimensions, The material data is data including at least the core elastic modulus, tooth modulus, and friction coefficient of the belt, and the external force data is data including at least the load torque and the axial load. Method.