JP5237172B2 - Belt transfer performance curve prediction method - Google Patents

Description

  The present invention predicts a transmission performance curve indicating a relationship between a slip ratio and a shaft torque (or slip ratio and effective tension, or slip ratio and shaft power) of a belt wound around a drive pulley and a driven pulley. About.

  When evaluating the transmission performance of a friction transmission belt that transmits power via a pulley, a transmission performance curve showing the relationship between the slip ratio and shaft torque (or effective tension or shaft power) (see FIG. 6 in the embodiment) Is used (see, for example, Patent Document 1). The higher the shaft torque at the allowable slip ratio, the higher the belt transmission performance.

Conventionally, such a transmission performance curve is obtained by a test using a belt transmission system 21 having a configuration in which a belt B is wound around a drive pulley 22 and a driven pulley 24 as shown in FIG. . Specifically, first, the driven shaft 25 is set to a no-load state, and the drive pulley 22 is rotated at a predetermined rotation speed N _B1 . Then, gradually increasing the load of the driven shaft 25, in the process, as well as measuring the rotational speed N _B2 of the driven pulley 24, by measuring the axial torque T _RQ of the driven pulley 24 of each rotational speed N _B2, The relationship between the rotational speed ratio i of the driven shaft 25 and the drive shaft 23 and the shaft torque _TRQ is obtained. Since the slip ratio S is obtained by the following numerical formula 1 using the rotation speed ratio i, the relationship between the slip ratio S and the shaft torque _TRQ is obtained, and a transmission performance curve can be obtained.

ここで、ｉ＝Ｎ_Ｂ２／Ｎ_Ｂ１とする。ｉ_０：無負荷時の回転数比、ｉ：回転数比

Here, i = N _B2 / N _B1 is set. i ₀ : Speed ratio at no load, i: Speed ratio

Japanese Patent Laid-Open No. 2001-59548 (see FIG. 5)

  However, the transmission performance curve obtained by the above-described test shows the belt transmission performance in the same layout as the belt transmission system used in the test. When changing the pulley diameter, belt length, etc. Had to be tested each time, requiring a lot of time and cost.

  Therefore, an object of the present invention is to propose a transmission performance curve prediction method capable of predicting a transmission performance curve of a belt without performing a test under a layout and running conditions that are targets of the transmission performance curve. .

Means for Solving the Problems and Effects of the Invention

The belt transmission performance curve prediction method according to claim 1 is a method for predicting a transmission performance curve indicating a relationship between a slip ratio and a shaft torque of a belt wound around a drive pulley and a driven pulley, wherein the belt A μ-v characteristic acquisition step of acquiring a μ-v characteristic indicating a relationship between a friction coefficient and a sliding speed, a radius and a winding angle of the driving pulley and the driven pulley, a span length, an initial tension, and the μ-v from the characteristics, and v-T _E characteristic deriving step of deriving a v-T _E characteristics showing the relationship between the slip rate and the effective tension of the belt, the sliding speed of the v-T _E characteristics, the peripheral speed of the drive pulley Is used to predict the transmission performance curve of the belt by converting the effective tension of the v-T _E characteristic into the shaft torque using the radius of the driving pulley or the driven pulley. And a transmission performance curve predicting step.

According to this configuration, first, in the μ-v characteristic acquisition step, the μ-v characteristic of the belt is acquired. The μ-v characteristic does not depend on the diameter of the pulley around which the belt is wound, the winding angle, the running speed of the belt, and the like, and is determined by the characteristic of the belt and the material of the pulley. Next, using the μ-v characteristic, the relationship (v-T _E characteristic) between the slipping speed of the belt wound around the driving pulley and the driven pulley and the effective tension is obtained by calculation. The effective tension is a difference between the tension on the tension side and the tension on the loose side of the belt, and the slip speed of the belt is a relative moving speed of the belt with respect to the pulley. Finally, the sliding speed and the effective tension of the resulting v-T _E characteristics, by converting the slip ratio and the shaft torque respectively, predicts the transfer performance curve showing the relationship between the slip ratio and the axial torque.

As described above, since the transfer performance curve under a desired layout and running condition can be predicted by using the μ-v characteristic of the belt, the layout and the running condition that are the targets of the transfer performance curve as in the conventional case. A transmission performance curve can be obtained without performing the above test.
Therefore, even if the radius and initial tension of the driving pulley and driven pulley are changed, there is no need to perform a new test, which saves time and cost compared to the case where the transmission performance curve is obtained by the conventional test. can do.

  According to a second aspect of the present invention, there is provided a method for predicting a transmission performance curve of a belt according to the first aspect, wherein the μ-v characteristic acquisition step is such that the belt is suspended across a test driving pulley, a test driven pulley, and a plurality of idler pulleys. From the state where the test driven pulley is rotated at a predetermined rotational speed with the test driven pulley rotating shaft unloaded using the test apparatus having the above configuration, the load on the test driven pulley rotating shaft is gradually increased. And measuring the sliding speed while increasing the sliding speed of the belt with respect to the test driven pulley, and measuring the slack side tension and the tension side tension of the driven pulley for each sliding speed. And the tension ratio of the slack side tension and the tension side tension for each sliding speed obtained by the measurement step, and the winding angle of the belt with respect to the test driven pulley, Seeking friction coefficient, and having a mu-v characteristic deriving step of deriving the mu-v characteristic.

In this μ-v characteristic acquisition step, a test is performed to change the belt slip speed with respect to the test driven pulley, the tension side tension and the slack side tension at each slip speed are measured, and the friction coefficient is a function of the tension ratio. Thus, the μ-v characteristic indicating the relationship between the sliding speed and the friction coefficient is derived. Since the derived μ-v characteristic is determined by the characteristic of the belt and the pulley material, if the pulley material is the same, the radius and span length of the driving pulley and the driven pulley may be changed. However, the transmission performance curve can be predicted using the same μ-v characteristic.
Further, since the test method performed in this μ-v characteristic acquisition step is the same as the conventional test method for measuring the transmission performance curve, it is possible to predict the transmission performance curve with relatively high accuracy.

  According to a third aspect of the present invention, there is provided the method for predicting the transmission performance curve of the belt according to the first aspect, wherein the μ-v characteristic acquisition step is performed by suspending the belt across a test driving pulley, a test driven pulley, and a plurality of idler pulleys. Using the test apparatus having the above-described configuration, with the test driven pulley incapable of rotating, the rotational speed of the test drive pulley is gradually increased to increase the sliding speed of the belt with respect to the test driven pulley. While measuring the sliding speed and measuring the slack side tension and tension side tension of the test driven pulley for each sliding speed, the slack side tension for each sliding speed obtained by the measuring process Using the tension ratio between the tension side and the tension on the tension side and the winding angle of the belt with respect to the test driven pulley, the friction coefficient is obtained and the μ-v characteristic deriving process is derived. Characterized in that it has and.

  In this μ-v characteristic acquisition step, a test is performed to change the belt slip speed with respect to the test driven pulley, the tension side tension and the slack side tension at each slip speed are measured, and the friction coefficient is a function of the tension ratio. Thus, the μ-v characteristic indicating the relationship between the sliding speed and the friction coefficient is derived. Since the derived μ-v characteristic is determined by the characteristic of the belt and the pulley material, if the pulley material is the same, the radius and span length of the driving pulley and the driven pulley may be changed. However, the transmission performance curve can be predicted using the same μ-v characteristic.

According to a fourth aspect of the present invention, there is provided a method for predicting a belt transmission performance curve, wherein, in the μ-v characteristic deriving step of the third aspect, a friction coefficient μ ₀ obtained from the tension ratio and a winding angle of the test driven pulley is calculated as a friction coefficient. Using the sliding speed v corresponding to μ ₀ and the peripheral speed V _{1 of the} driving pulley, the corrected friction coefficient μ is corrected by the following formula 2, and the μ−v characteristic is corrected using the corrected friction coefficient μ. It is derived. According to this configuration, it is possible to improve the accuracy of the predicted transmission performance curve.

ここで、α及びβは、α＝１〜２、β＝０．１〜０．３の値をとる定数である。

Here, α and β are constants having values of α = 1 to 2 and β = 0.1 to 0.3.

It is a figure which shows the structure of the test apparatus used with the transmission performance curve prediction method of the belt of embodiment of this invention. It is a figure which shows the structure of the belt transmission system with which the transmission performance curve prediction method of the belt of embodiment of this invention is applied. It is a flowchart which shows the transmission performance curve prediction method of the belt of embodiment of this invention. 5 is a graph showing μ-v characteristics. It is a figure for demonstrating the slip of the belt on a pulley. It is a graph which shows a transmission performance curve. It is a figure which shows the structure of another belt transmission system. It is a figure which shows the structure of the belt transmission system of an Example. It is a graph which shows the μ-v characteristic of an Example. It is a graph which shows the transmission performance curve of an Example. It is a figure which shows the structure of the belt transmission system of an Example. It is a graph which shows the transmission performance curve of an Example.

<First Embodiment>
Hereinafter, a first embodiment of the present invention will be described.
The belt transmission performance curve prediction method of the present embodiment derives the μ-v characteristic of the belt B by using the test apparatus 1 as shown in FIG. 1, and uses this μ-v characteristic as shown in FIG. The transmission performance curve of the belt B in the simple belt transmission system 11 is predicted. The belt B applied to the present embodiment may be any of a flat belt, a V belt, a V-ribbed belt, etc., as long as it is a friction transmission belt.

As shown in FIG. 2, the belt transmission system 11 has a configuration in which the belt B is suspended across a drive pulley (Dr) 12, a driven pulley (Dn) 14, and an idler pulley (Id) 16. The drive pulley 12 and the driven pulley 14 are connected to the drive shaft 13 and the driven shaft 15, respectively. The radii of the driving pulley 12 and the driven pulley 14 are R ₁ and R ₂ , respectively, and the wrapping angles of the belt B around the driving pulley 12 and the driven pulley 14 are θ ₁ and θ ₂ , respectively. Moreover, the span length of the slack portion of the belt B (including winding portion of the idler pulley 16) and L _1, the span length of the tight side of the belt B and L _2. The driving pulley 12 is rotationally driven in the direction of the arrow shown in FIG. Further, the initial tension, which is the tension of the belt B before the belt travels, is T _0, and the rotational speed of the drive pulley 12 is N ₁ .

The idler pulley 16 is for controlling the winding angles θ ₁ and θ ₂ and the slack side span length L ₁ . Further, the rotating shaft of the idler pulley 16 is unloaded. Accordingly, the tension T ₁ of the portion between the idler pulley 16 and drive pulley 12, which is the same as the tension T ₁ of the portion between the idler pulley 16 and the driven pulley 14. Therefore, the effective tension T _E of the belt B with respect to the drive pulley 12, the effective tension T _E of the belt B against the driven pulley 14 is the same. Note that the effective tension T _E, the tight side tension T ₂ of the belt B, and that of the difference between the slack side tension T _1.

  The test apparatus 1 shown in FIG. 1 is for acquiring a μ-v characteristic indicating the relationship between the friction coefficient μ of the belt B and the sliding speed v. The μ-v characteristic does not depend on the diameter of the pulley around which the belt is wound, the winding angle, the running speed of the belt, and the like, and is determined by the characteristic of the belt and the material of the pulley.

  The test apparatus 1 has a configuration in which a belt B is suspended over a test drive pulley (Dr) 2, a test driven pulley (Dn) 4, and four idler pulleys (Id) 6 to 9. The test drive pulley 2 and the test driven pulley 4 are connected to the drive shaft 3 and the driven shaft 5, respectively. Note that the layout of the test apparatus 1 (diameter, winding angle, span length, etc. of the test drive pulley 2 and the test driven pulley 4) may not be the same as the layout of the belt transmission system 11, but may be the same. Good. The drive shaft 3 is connected to a motor (not shown), and the test drive pulley 2 is rotationally driven by this motor in the direction of the arrow shown in FIG.

The rotation shafts of the idler pulleys 6 to 9 are movable in a direction orthogonal to the axial direction. The idler pulley 9 is for controlling the winding angle θ _A2 of the belt B with respect to the test driven pulley 4. A dead weight 10 is connected to the rotation shaft of the idler pulley 7. By controlling the weight of the dead weight 10, a desired initial tension is applied to the belt B, and the slack side tension T _A1 of the belt B can be kept substantially constant during belt running.

  Hereinafter, the prediction method of the transmission performance curve of this embodiment is demonstrated.

[Μ-v characteristics acquisition process]
As shown in FIG. 3, first, a test is performed using the test apparatus 1 to obtain a μ-v characteristic indicating the relationship between the friction coefficient μ of the belt B and the slip speed v. This will be specifically described below.

The dead weight 10 is set to a predetermined weight, and a predetermined initial tension is applied to the belt B. Then, the driven shaft 5 is brought into an unloaded state, and the test drive pulley 2 is rotated at a predetermined rotation speed N _A1 . At this time, since the peripheral speed V _A2 of the test driven pulley 4 and the running speed of the belt B are the same, the slip speed v of the belt B with respect to the test driven pulley 4 is zero. The belt sliding speed is the relative moving speed of the belt with respect to the pulley.

Thereafter, the load on the driven shaft 5 is gradually increased, and the sliding speed v of the belt B with respect to the test driven pulley 4 is increased. In this process, the sliding speed v is measured, and the slack side tension T _A1 and the tension side tension T _A2 of the belt B with respect to the test driven pulley 4 for each sliding speed v are measured. Since the traveling speed of the belt B is the same as the peripheral velocity V _A1 of the test drive pulley 2, sliding velocity v, peripheral velocity V _A2 of the test driven pulley 4 and the peripheral velocity V _A1 of the test drive pulley 2 is the difference between, by measuring the rotational speed N _A2 of test driven pulley 4, is determined by the following equation 3.

ここで、Ｒ_Ａ１は試験用駆動プーリ２の半径であり、Ｒ_Ａ２は試験用従動プーリ４の半径である。

Here, R _A1 is the radius of the test drive pulley 2, and R _A2 is the radius of the test driven pulley 4.

Further, according to Euler's theory, the relationship of the following mathematical formula 4 is established between the tension ratio T _A2 / T _A1 and the friction coefficient μ. Therefore, the relationship between the sliding speed v and the friction coefficient μ can be obtained by obtaining the friction coefficient μ using the following formula 4 from the tension ratio T _A2 / T _A1 for each sliding speed v obtained by the test.

ここで、θ_Ａ２は、試験用従動プーリ４に対するベルトＢの巻き付き角である。

Here, θ _A2 is a winding angle of the belt B with respect to the test driven pulley 4.

  FIG. 4A is a graph in which the horizontal axis represents the sliding speed v and the vertical axis represents the friction coefficient μ corresponding to the sliding speed v. The plot data is approximated to a curve by the least square method or the like to derive a μ-v characteristic as shown in FIG. The approximate expression is, for example, an expression like the following Expression 5.

ここで、ａ、ｂ、ｃは、定数係数である。

Here, a, b, and c are constant coefficients.

[V- _TE characteristic deriving step]
Next, as shown in FIG. 3, the acquired μ-v characteristics, pulley radii R ₁ and R ₂ , winding angles θ ₁ and θ ₂ , span lengths L ₁ and L ₂ , and initial tension T ₀ It is used to derive the v-T _E characteristics showing the relationship between the sliding velocity v and the effective tension T _E of the belt B in the belt drive system 11.

Specifically, by selecting several sliding speeds v of the μ-v characteristic and substituting the friction coefficient μ corresponding to each sliding speed v into the following Equation 6 or Equation 7, it corresponds to each sliding velocity v. to calculate the effective tension T _E of the belt B. Thus, the relationship between the sliding velocity v and the effective tension _{T E (v-T E} characteristics) are determined. In order to obtain the v-T _E characteristic, it may be calculated by substituting Equation 5 into Equation 6.

Here it will be described the above equation 6, 7 for calculating the effective tension T _E.

In the belt transmission system 11, when the axial torque of the driven pulley 14 is 0 during belt running, the belt B is fixed to the driven pulley 14 in the entire winding angle θ ₂ and no slip occurs.

When the shaft torque of the pulley 12, 14 is increased (i.e., effective to tension T _E increases), resulting elastic deformation elongation of the belt B by the effective tension T _E, an amount corresponding to this elongation, the belt B is pulley 12, Slide on 14 The angle of this slip at the wound portion is defined as a slip angle φ. The belt B is fixed to the pulleys 12 and 14 in the regions of the angles θ ₁ −φ and θ ₂ −φ of the winding portions of the pulleys 12 and 14. Incidentally, the effective tension _{T E} are the common to the pulleys 12 and 14, also slip angle φ caused by elongation of the belt B through the effective tension _{T E,} a common pulley 12,14. As shown in FIG. 5, for the sake of convenience, the region of the slip angle φ on the pulleys 12 and 14 is defined as a slip region, and the regions of the angles θ ₁ −φ and θ ₂ −φ are defined as fixed regions.

Since Euler's theory is established in the slip region, the tension ratio T ₂ / T ₁ between the slack side tension T ₁ and the tension side tension T ₂ is expressed by the following Equation 8. Incidentally, the friction coefficient mu _phi in Equation 8 shows the friction coefficient in the sliding region.

The above equation 8, since the definition formula of the effective tension _{T E (T E = T 2} -T 1), the tension _T 1, _{T 2} are respectively represented by the following Equation 9 as a function of the effective tension _{T E} The

  Here, in the belt transmission system 11, assuming that the belt tension in the region of the length s is T (s), the Young's modulus is E, and the cross-sectional area is A, the total elongation amount ΔL of the belt B is expressed.

Since the total length of the belt at the time of setting the initial tension T ₀ (at the time of stopping) is the same as that at the time of traveling, in other words, the total elongation of the belt is always the same.

  Although the detailed derivation process is omitted, the following formula 12 is derived from this formula 11. The derivation process from Equation 11 to Equation 12 is as follows: “Kiyoshi Okura, Yoshihiko Ryugo,“ Relationship between initial tension and running tension of friction transmission belt ”, JSME 2006 Annual Conference Proceedings (4 ) [2006-9.18-22, Kumamoto City].

By substituting T ₁ and T ₂ of Equation 9 into Equation 12, the following Equation 13 is obtained.

The slip angle φ increases as the shaft torque of the pulleys 12 and 14 increases. When θ ₁ > θ ₂ , the slip angle φ first reaches the angle θ ₂ . At this time, the belt B slides on the driven pulley 14 in the entire region of the winding portion. This state is called a total slip state. Therefore, substituting phi = theta ₂ in the equation 13, the effective tension T _E is expressed when a total slip at the driven pulley 14. At this time, the mu _phi in Equation 13 shows the friction coefficient at winding angle theta ₂ whole mu. A formula obtained by substituting φ = θ ₂ into Formula 13 is Formula 6 described above.

On the other hand, when θ ₁ <θ ₂ , as the slip angle φ increases, the angle θ ₁ is _first reached. At this time, the belt B is fully slipped on the drive pulley 12. Substituting phi = theta ₁ to the equation 13, the equation 7 described above is obtained, the effective tension T _E is expressed when a total slip at the drive pulley 12.

[Transfer performance curve prediction process]
Next, as shown in FIG. 3, a transfer performance curve is predicted using the obtained _vTE characteristic.

Specifically, first, the slip speed v of the v−T _E characteristic is converted into the slip ratio S.
When θ ₁ > θ ₂ , the driven pulley 14 becomes fully slipped, while the drive pulley 12 does not reach full slip. Therefore, assuming that the running speed of the belt B is V _B , the equation for calculating the slip ratio S is as follows: Equation 14 is obtained.

On the other hand, in the case of θ ₁ <θ ₂ , the drive pulley 12 becomes fully slipped, while the driven pulley 14 does not reach full slip. Therefore, regardless of the magnitude relationship between θ ₁ and θ ₂ , the slip ratio S can be obtained by the following formula 16.

Further, the effective tension _{T E} of _{v-T E} characteristics, the following formula 17 is converted into axial torque _{T RQ2} of the driven pulley 14.

Thus, the _{v-T E} characteristics sliding velocity v and the effective tension _{T E} of, by converting the slip ratio S and the axial torque _{T RQ2} each, the relationship between slip ratio S and the axial torque _{T RQ2} is determined, A transmission performance curve as shown in FIG. 6 is obtained. As described above, it is possible to predict the belt transmission performance curve under the predetermined traveling condition in the belt transmission system 11.

As described above, since the transmission performance curve in a desired layout and running condition can be predicted by using the μ-v characteristic of the belt B, the test using the belt transmission system 11 as in the past is performed. A transmission performance curve can be obtained even if it is not performed.
Therefore, even if the radius and initial tension of the driving pulley 12 and the driven pulley 14 are changed, it is not necessary to perform a new test, and time and cost are compared with the case where the transmission performance curve is obtained by the test as in the conventional case. Can be reduced.

  Further, the μ-v characteristic obtained by the test using the test apparatus 1 does not depend on the diameters, winding angles, belt running speeds, and the like of the pulleys 12 and 14 of the test apparatus 1, and the belt-specific characteristics and pulley material Therefore, if the pulley material is the same, the transmission performance curve can be predicted using the same μ-v characteristic even if the radius, span length, etc. of the pulleys 12 and 14 are changed.

In the present embodiment, the horizontal axis of the transmission performance curves, but the shaft torque T _RQ2 of the driven pulley 14 may be axial torque T _RQ1 of the drive pulley 12.

Also, the horizontal axis of the transmission performance curves may be effective tension T _E, it may be the shaft power W ₂ of shaft power W ₁ or the driven pulley 14 of the drive pulley 12. The shaft powers W ₁ and W ₂ are obtained by the following formula 18, respectively.

Second Embodiment
Next, a second embodiment of the present invention will be described.
The belt transmission performance curve prediction method of this embodiment predicts a transmission performance curve by the same process as that of the first embodiment except that the μ-v characteristic acquisition process is different.

The mu-v characteristic acquisition step of the present embodiment, using the test apparatus 1 of the test apparatus 1 and the same as the configuration used in the first embodiment. Hereinafter, the μ-v characteristic acquisition process of this embodiment will be described in detail.

The dead weight 10 is set to a predetermined weight, a predetermined initial tension is applied to the belt B, the driven shaft 5 is fixed, and the test driven pulley 4 cannot be rotated. In this state, the rotational speed N _A1 test drive pulley 2 is gradually increased from 0, gradually increasing the sliding velocity v of the belt B against the test driven pulley 4. In this process, the sliding speed v is measured, and the slack side tension T _A1 and the tension side tension T _A2 of the belt B with respect to the test driven pulley 4 for each sliding speed v are measured. Since the peripheral speed of the test driven pulley 4 is 0, the slip speed v of the belt B with respect to the test driven pulley 4 is the same as the peripheral speed V _A1 of the test drive pulley 2.

Similar to the first embodiment, using the tension ratio T _A2 / T _A1 for each sliding speed v obtained by measurement and the winding angle θ _A2 of the driven pulley 4 for the test, the friction coefficient is calculated by the above-described formula 4. Ask for. The resulting coefficient of friction and mu _0.

Next, the friction coefficient μ ₀ is converted into a corrected friction coefficient μ using the following equation 19 using the slip speed v corresponding to the friction coefficient μ ₀ and the peripheral speed V ₁ of the drive pulley 12 of the belt transmission system 11. to correct.

ここで、α及びβは、α＝１〜２、β＝０．１〜０．３の値をとる定数である。

Here, α and β are constants having values of α = 1 to 2 and β = 0.1 to 0.3.

  Similar to the first embodiment, the horizontal axis represents the slip velocity v, the vertical axis represents the corrected friction coefficient μ corresponding to the slip velocity v, and then the curve is approximated to derive the μ-v characteristic.

  Using the derived μ-v characteristic, a transmission performance curve is predicted by the same procedure as in the first embodiment. According to the transfer performance curve prediction method of the present embodiment, the same effects as those of the first embodiment can be obtained.

Here, the reason why the friction coefficient μ ₀ is corrected to the corrected friction coefficient μ will be described.
In the first embodiment, the μ-v characteristic is obtained by performing a test for gradually increasing the load of the driven shaft 5. This test method is a conventional test method for measuring a transmission performance curve. Since the test driven pulley 4 is rotating, the slip ratio of the belt on the test driven pulley 4 is 0 or a finite value.
On the other hand, in the present embodiment, a μ-v characteristic is acquired by performing a test in which the driven shaft 5 is fixed and the rotational speed of the drive shaft 3 is gradually increased, and the test driven pulley 4 is in a stopped state. Therefore, the slip ratio on the test driven pulley 4 is always 100%.
Due to these differences, the μ-v characteristics obtained by the two tests are slightly different. However, the first embodiment using the μ-v characteristics obtained by the same test method as in the case of measuring the transmission performance is the same as in the first embodiment. A relatively high accuracy transmission performance curve can be predicted.

Therefore, in the present embodiment, correction is made so that the μ-v characteristic substantially the same as the μ-v characteristic obtained in the first embodiment is obtained. By deriving the μ-v characteristic using the corrected friction coefficient μ, the accuracy is higher than when the μ-v characteristic is derived using the friction coefficient μ ₀ obtained from the tension ratio T _A2 / T _A1 as it is. Thus, it is possible to predict a transmission performance curve with almost the same accuracy as in the first embodiment.

  Note that the above Equation 19 used for the correction is an equation obtained by actually obtaining μ-v characteristics by the test method of the first embodiment and the test method of the present embodiment and comparing the results. .

In the present embodiment, the friction coefficient μ ₀ is corrected to the corrected friction coefficient μ and then an approximate expression of the μ−v characteristic is obtained. However, μ ₀ indicating the relationship between the friction coefficient μ ₀ and the sliding speed v. After obtaining the approximate expression of the −v characteristic, the μ−v characteristic may be derived by correcting the friction coefficient μ ₀ to the corrected friction coefficient μ.

Further, in the present embodiment, by correcting the friction coefficient mu ₀ using the above equation 19, the correction method of the coefficient of friction mu ₀ is not necessarily limited to those according to the above formula 19.

  As described above, as an embodiment of the present invention, the case where the transmission performance curve of the belt transmission system 11 shown in FIG. 2 is predicted has been described as an example, but the configuration of the belt transmission system to which the present invention can be applied is shown in FIG. It is not limited to things. The belt transmission system may be composed of a driving pulley (Dr) and a driving pulley (Dn) as shown in FIGS. 7 and 8, and as shown in FIG. 11, the driving pulley (Dr) ) And the drive pulley (Dn), two or more idler pulleys (Id) may be arranged. As described above, the idler pulley is for controlling the winding angle and the span length, and the idler pulley has no load, so the presence or absence of the idler pulley is the predicted transmission performance curve. Does not affect the accuracy.

  In the first and second embodiments, the μ-v characteristic is acquired using the test apparatus 1 having the configuration shown in FIG. 1, but the configuration of the test apparatus 1 is limited to that shown in FIG. It is not a thing.

  Further, the method for acquiring the μ-v characteristic is not limited to the method described in the first and second embodiments, and may be acquired by performing other tests. Moreover, you may acquire only by calculation.

  In order to verify the belt transmission performance curve prediction method of the present invention, the belt transmission performance curve in the belt transmission system 21 as shown in FIG. Then, a test was performed to compare the actual measurement results obtained by the test. In this test, a V-ribbed belt was used as the belt.

The configuration and running conditions of the belt transmission system 21 are as follows.
[Configuration of belt transmission system 21]
Radius R _{1 of the} driving pulley (Dr) 22 = 0.06 [m]
Radius R _{2 of} driven pulley (Dn) 24 = 0.06 [m]
Belt winding angle θ ₁ = π [rad] with respect to the drive pulley 22
The winding angle θ ₂ of the belt with respect to the driven pulley 24 = π [rad]
Span length L ₁ of the loose side portion of the belt = 0.426 [m]
Span length L ₂ of the belt tension side portion = 0.426 [m]
[Running conditions of belt transmission system 21]
The rotational speed N ₁ of the drive pulley 22 = 2000 [rpm]
Initial belt tension T ₀ = 100 [N] and 150 [N]

In the examples of the present invention, first, a test was performed using the test apparatus 1 shown in FIG. 1 used in the first and second embodiments, and a μ-v characteristic (and a μ ₀ -v characteristic) was derived.
As in the second embodiment, in the test method, the driven shaft 5 of the test apparatus 1 is fixed and the rotational speed of the drive shaft 3 is gradually increased to measure the sliding speed v. The slack side tension T _A1 and the tension side tension T _A2 of the driven pulley 4 for the test were measured. The loose side tension T _A1 is an initial tension T _A0 determined by the weight of the dead weight 10. The tension-side tension T _A2 was obtained by calculating the effective tension T _EA from the measurement result of the shaft torque measuring device installed on the driven shaft 5 and T _A2 = T _EA + T _A1 .

The friction coefficient μ ₀ is calculated from the tension ratio T _A2 / T _A1 using Equation 4 described above, and the friction coefficient μ ₀ corresponding to the slip speed v is plotted on the horizontal axis and the friction coefficient μ ₀ is plotted on the vertical axis. The μ ₀ -v characteristic was obtained by approximating with Equation 5 given above. The result is shown by a thin line in FIG.

Next, this friction coefficient μ ₀ was corrected to a corrected friction coefficient μ using the following formula 20, and a μ-v characteristic indicated by a thick line in FIG. 9 was obtained.

ここで、Ｖ_１は、駆動プーリ２２の周速度である。

Here, V ₁ is the peripheral speed of the drive pulley 22.

Using the obtained μ-v characteristic or μ ₀ -v characteristic, the v- _TE characteristic deriving step and the transfer performance curve predicting step described in the first embodiment are performed, and examples 1 to 4 shown in FIG. The transfer performance curve was predicted. In Examples 1 and 2, μ-v characteristics were used, and in Examples 3 and 4, μ ₀ -v characteristics were used. In Examples 1 and 3, the initial tension T ₀ was set to 100 [N], and in Examples 2 and 4, the initial tension T ₀ was set to 150 [N].

On the other hand, a test was performed using the belt transmission system 21 shown in FIG. 8 to calculate a transmission performance curve. The results are shown in FIG. In the actual measurement result 1, the initial tension T ₀ was 100 [N], and in the actual measurement result 2, the initial tension T ₀ was 150 [N].

In the actual measurement results 1 and 2, the driven shaft 25 is not loaded, the drive shaft 23 is rotated at the rotational speed N ₁ (N _B1 ), and then the load on the driven shaft 25 is gradually increased while the driven pulley 24 The rotational speed N _B2 is measured, the shaft torque T _RQ of the driven shaft 25 for each rotational speed N _B2 is measured, and the slip ratio S is calculated from the rotational speed ratio i of the pulleys 22 and 24 by the above-described equation 1. The transmission performance curve was obtained.

From the result of FIG. 10, it can be seen that the transmission performance curve of the example substantially matches the transmission performance curve of the actual measurement result. In particular, the transmission performance curves of Examples 1 and 2 using the μ-v characteristic are closer to the actual measurement results and have higher accuracy than the transmission performance curves of Examples 3 and 4 using the μ _0- v characteristic. I understand that.

  Further, with respect to the belt transmission performance curve in the belt transmission system 31 as shown in FIG. 11, a test for comparing the prediction result by the belt transmission performance curve prediction method of the present invention with the actual measurement result obtained by the test was performed. In this test, a V-ribbed belt having 6 ribs was used.

As shown in FIG. 11, the belt transmission system 31 includes a drive pulley (Dr) 32, a drive pulley (Dn) 34, and two idler pulleys (Id) 36 and 37. The configuration and running conditions of the belt transmission system 31 are as follows.
[Configuration of belt transmission system 31]
Radius _R 1 = 0.06 of the drive pulley 32 [m]
Radius R ₂ of the driven pulley 34 = 0.05 [m]
The winding angle θ ₁ of the belt with respect to the drive pulley 32 = 2.3719 [rad]
The winding angle θ ₂ of the belt with respect to the driven pulley 34 = 1.0961 [rad]
Span length L ₁ = 0.4153 [m] at the loose side of the belt
Span length L ₂ of the belt tension side portion = 0.514 [m]
[Running conditions of belt transmission system 31]
The rotational speed N ₁ of the driving pulley 32 = 1634 [rpm]
Initial tension T ₀ per rib = 70 [N / rib]

In the example of the present invention, first, a μ-v characteristic was derived by performing a test using a test apparatus having the same configuration as the belt transmission system 31.
Test method, as in the first embodiment, the driven shaft 35 as a no-load state, from the state of the driving pulley 32 is rotated at a predetermined rotational speed N _A1, gradually increasing the load of the driven shaft 35 The sliding speed v was measured, and the slack side tension T _A1 and the tension side tension T _A2 of the driven pulley 34 for each sliding speed were measured. The measurement method was the same as in Examples 1 to 4 described above. Thereafter, the friction coefficient μ was calculated from the tension ratio T _A2 / T _A1 using the above-described formula 4, and the μ-v characteristic was derived.

Using the obtained μ-v characteristic, after the v-T _E characteristic deriving step described in the first embodiment, the slip speed v of the v-T _E characteristic is converted into the slip ratio S, and the slip ratio S If predicted the transfer performance curve showing the relationship between the effective tension T _E per rib. The result is shown as Example 5 in FIG.

  On the other hand, a test was performed using the belt transmission system 31 shown in FIG. 11 to calculate a transmission performance curve. The result is shown as an actual measurement result 3 in FIG.

In the actual measurement result 3, the driven shaft 35 is set to an unloaded state, the drive shaft 33 is rotated at the rotational speed N ₁ (N _B1 ), and then the load on the driven shaft 35 is gradually increased while the rotational speed of the driven pulley 34 is increased. N _B2 was measured, and the shaft torque T _RQ of the driven shaft 35 for each rotation speed N _B2 was measured. The slip ratio S is calculated from the rotational speed ratio i of both the pulleys 22 and 24 by the above-described formula 1, and the effective tension T _E (= T _RQ / R ₂ ) is obtained from the shaft torque T _RQ and the pulley radius R _2. It was determined transfer performance curve showing the relationship between the effective tension T _E per slip ratio S and the first rib.

  From the result of FIG. 12, it can be seen that the transmission performance curve of Example 5 substantially matches the transmission performance curve of the actual measurement result 3.

DESCRIPTION OF SYMBOLS 1 Test apparatus 2 Test drive pulley 3 Drive shaft 4 Test driven pulley 5 Drive shaft 6-9 Idler pulley 10 Dead weight 11, 21, 31 Belt transmission system 12, 22, 32 Drive pulley 13, 23, 33 Drive shaft 14 , 24, 34 Driven pulley 15, 25, 35 Driven shaft 16, 36, 37 Idler pulley B Belt

Claims (4)

A method for predicting a transmission performance curve indicating a relationship between a slip ratio and a shaft torque of a belt wound around a driving pulley and a driven pulley,
A μ-v characteristic acquisition step of acquiring a μ-v characteristic indicating a relationship between a friction coefficient of the belt and a slip speed;
From the radius and winding angle of the drive pulley and the driven pulley, the span length, the initial tension, and the μ-v characteristic, the v-T _E characteristic indicating the relationship between the belt sliding speed and the effective tension is derived v- A _TE characteristic deriving step;
The slip speed of the v-T _E characteristic is converted into a slip ratio using the peripheral speed of the drive pulley, and the effective tension of the v-T _E characteristic is converted using the radius of the drive pulley or the driven pulley. A transmission performance curve prediction step of predicting the transmission performance curve of the belt by converting into shaft torque;
A belt transmission performance curve prediction method comprising: The μ-v characteristic acquisition step includes:
Using a test device having a configuration in which the belt is suspended across a test drive pulley, a test driven pulley, and a plurality of idler pulleys, with the rotating shaft of the test driven pulley being unloaded, the test drive pulley is The sliding speed is measured while gradually increasing the load on the rotating shaft of the test driven pulley from the state rotated at a predetermined rotational speed to increase the sliding speed of the belt relative to the test driven pulley. And a measuring step for measuring the slack side tension and the tension side tension of the driven pulley for each sliding speed;
Using the tension ratio between the slack side tension and the tension side tension obtained by the measurement step and the winding angle of the belt with respect to the test driven pulley, a friction coefficient is obtained, and the μ-v characteristic is obtained. A μ-v characteristic deriving step for deriving
The belt transmission performance curve prediction method according to claim 1, wherein: The μ-v characteristic acquisition step includes:
Using a test apparatus having a configuration in which the belt is suspended across a test drive pulley, a test driven pulley, and a plurality of idler pulleys, the test driven pulley While gradually increasing the number of revolutions to increase the slip speed of the belt relative to the test driven pulley, the slip speed is measured, and the loose tension and tension side of the test driven pulley for each slip speed A measuring process for measuring tension;
Using the tension ratio between the slack side tension and the tension side tension obtained by the measurement step and the winding angle of the belt with respect to the test driven pulley, a friction coefficient is obtained, and the μ-v characteristic is obtained. A μ-v characteristic deriving step for deriving
The belt transmission performance curve prediction method according to claim 1, wherein: In the μ-v characteristic deriving step,
The friction coefficient μ ₀ obtained from the tension ratio and the winding angle of the test driven pulley is expressed by the following formula 1 using the sliding speed v corresponding to the friction coefficient μ ₀ and the peripheral speed V _{1 of the} drive pulley. 4. The belt transmission performance curve prediction method according to claim 3, wherein the correction friction coefficient μ is corrected by the correction friction coefficient μ and the μ-v characteristic is derived using the correction friction coefficient μ.

Here, α and β are constants having values of α = 1 to 2 and β = 0.1 to 0.3.

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