JP4995687B2 - Belt squeal evaluation method and apparatus, and program - Google Patents

Description

  The present invention relates to a belt squeal evaluation method and apparatus, and a program.

  In a friction transmission belt such as a flat belt for power transmission, a V-belt, and a V-ribbed belt, slippage occurs with a pulley under a specific condition such as an excessive load, and so-called belt squealing such as curculol caused by this slippage. Will occur. In particular, the belt noise of the V-ribbed belt for driving an automobile engine auxiliary machine occupies much of the user complaint and is a big problem.

  A great number of reports have been made on the mechanism of belt squeal. For example, it is a report like the following nonpatent literatures 1-4. According to these, the generation mechanism of the belt squeal is as follows. That is, the friction coefficient μ between the belt and the pulley is not constant but depends on the sliding speed v, and the relationship between μ and v (μ-v characteristic) has a negative gradient (that is, dμ / dv <0). This causes a so-called stick slip, which is considered to be the cause of belt squealing.

  Patent Document 5 describes a belt tension measuring method.

J. E. Connell, R. A. Rorrer: Friction induced vibration in V-ribbed belt applications, DE-Vol. 49, Friction, chatter, squeal, and chaos ASME 1992 (1992) K. W. Dalgarno, R. B. Moore, A. J. Day: Tangential slip noise of V-ribbed belts, Proc. Instn. Mech. Engrs, Vol. 213, Part C, (1999) R. Meckstrith, W. Deneszczuk, J. Skrobowski: Accessory drive belt pulley entry friction study and belt chirp noise, Society of Automotive Engineers, inc., 1999-01-1709, (1999) Kiyoshi Okura, Yoshihiko Ryugo; Analysis of squealing phenomenon of engine accessory drive belt, Automotive Engineering Society, Preprint of Scientific Lecture, No. 135-05, (2005) JP 2007-10595 A

  However, there are cases where belt squeal occurs when the μ-v characteristic does not have a negative gradient when the engine is started, stopped, etc., and the conventional theory alone cannot fully explain. Further, the conventional theory only expresses the possibility of occurrence of belt squeezing by the sign of dμ / dv and their relative sizes, and quantitative evaluation of the magnitude of belt squealing at the time of occurrence. Is not done at all.

  The present invention has been made in view of such various points, and its main object is to improve the accuracy of evaluation of belt squealing at the time of starting and stopping as well as during the steady operation of the engine. Another object of the present invention is to quantitatively grasp the magnitude of belt squeal when it occurs.

Means and effects for solving the problems

  The problems to be solved by the present invention are as described above, and the inventors of the present invention have used the squeal noise index SNI (Squeeze Noise Index) given by the following formula (1) as a result of diligent research. We have found that it is possible to express the occurrence of belt squeal by positive and negative, and the size of belt squeal by the magnitude of negative absolute value.

  Where V is the slip speed [m / s] immediately before the occurrence of the belt squeal or the average slip speed [m / s] when the belt squeal occurs, F is the frictional force [N] generated between the belt and the pulley, v Indicates the sliding speed [m / s] between the belt and the pulley.

  Hereinafter, it will be theoretically explained how the inventor of the present invention derived the above formula (1).

  First, please refer to FIG. FIG. 1 is a diagram illustrating a model in which a slip between a belt and a pulley is modeled by a vibration system having one degree of freedom. As shown in the figure, the slip between the belt and the pulley is modeled by a vibration system with one degree of freedom. Here, the belt is represented by a mass m, a spring k, and a damper c, and a pulley in contact with the belt is represented by a base that travels at a speed V. The equation of motion for the mass point m at this time is given by the following equation (2).

  Where m is the mass of the mass (kg), c is the damping coefficient (Ns / m), k is the spring constant (N / m), and F is a frictional force that is a function of the sliding velocity v as shown in FIG. N).

When series expansion frictional force of the F a (v) around v = _{v 0,} the following equation (3). However, the following formula (3) is a quadratic approximation.

Here, when V is taken as v ₀ , the following formula (4) is established, so the above formula (3) becomes the following formula (5).

  Considering only the linear term of the above equation (5) and substituting it into the above equation (2), the following equation (6) is obtained.

  When the value in the parentheses on the left side of the above formula (6) takes a negative value, the motion of the mass point becomes unstable and stick slip, that is, belt squealing occurs. In other words, a necessary condition for the occurrence of the belt squeal is that the velocity gradient of the frictional force becomes negative as shown by the following formula (7).

  Next, regarding the magnitude (energy) when belt squeal occurs, the energy of the belt squeal is proportional to the frictional work rate that the pulley performs on the belt when the belt slips. Here, the frictional power is given by the following formula (8).

  Assuming that the fluctuation of the mass point velocity dx / dt is sinusoidal, and considering the average power for one cycle, the coefficient on the right side of the above equation (8) can be considered to be constant. Disappears and becomes the following formula (9).

  When belt squealing occurs, that is, when stick-slip occurs, the following equation (10) is established at the time of sticking, and the fluctuation of the speed dx / dt can be regarded as a sine wave of amplitude V. (11).

  Since dF / dv at the time of occurrence of the belt squeal is a negative value as described above, the power given by the equations (8) and (9) becomes positive and becomes the energy supplied to the belt. From the above consideration, it can be said that the SNI given by the above equation (1) is an amount proportional to the size of the belt squeal.

  Since the frictional force F is given by the product of the pressing force N and the friction coefficient μ (F = μN), the above equation (1) becomes the following equation (12).

Further, for the belt on the pulley, there is a relationship of N ′ = T / R between the pressing force N ′ per unit length and the tension T via the pulley radius R. From this, when N _t ′ is the tension side pressing force [N / m] and N _s ′ is the loose side pressing force [N / m], the average pressing force N of the belt winding portion is expressed by the following formula (13). Become.

Where L represents the winding length [m], R represents the pulley radius [m], θ represents the winding angle [rad], T _t represents the tension on the tension side [N], and T _s represents the loose side. Tension [N] is indicated. In the above formula (13), it is assumed that the loose side tension is sufficiently smaller than the tension side tension, and the tension side tension is replaced with T. By using the relationship of the above formula (13), the SNI of the above formula (12) is finally expressed by the following formula (14).

  And like the SNI given by the above formula (1), the SNI given by the above formula (14) can be said to be an amount proportional to the size of the belt squeal.

  Based on the above considerations, the inventor of the present invention has the relationship between the tension T and the slip speed v, that is, the Tv characteristic, greatly involved in the belt squeal when starting or stopping the engine. It was considered that the belt squealing at the time of stop or stop may be caused by stick-slip that occurs when the Tv characteristic has a negative slope (dT / dv <0).

  Therefore, in the first aspect of the present invention, a belt squeal evaluation method that occurs when the friction transmission belt slides with respect to the pulley is performed by the following method. That is, a first step for calculating dμ / dv, a second step for calculating dT / dv, and a third step for evaluating belt noise based on dμ / dv and dT / dv. Including. Here, μ represents a coefficient of friction between the friction transmission belt and the pulley, T represents a tension [N] of the friction transmission belt, and v represents a slip speed [between the friction transmission belt and the pulley [ m / s]. According to the above method, the accuracy of the evaluation of the belt squeal not only at the time of steady operation of the engine but also at the start and stop is further improved.

  Furthermore, it is performed by the following method. That is, in the third step, the variable G is obtained based on the following equation (15). According to the above method, since the belt squeal occurs when the variable G becomes negative, the presence or absence of occurrence of the belt squeal can be grasped based on the variable G.

  Furthermore, it is performed by the following method. That is, in the third step, the variable SNI is obtained based on the following equation (16). Is the wrap angle [rad] of the friction transmission belt with respect to the pulley, and V is the slip speed [m / s] immediately before the occurrence of belt squealing or the average slip speed [m / s] when belt squeal occurs. . According to the above method, the presence or absence of occurrence of belt squeezing is grasped by the sign of the variable SNI, and the magnitude of the occurrence of belt squealing is quantitatively grasped by the absolute value of the variable SNI.

  According to a second aspect of the present invention, an evaluation program for a belt squeal generated when a friction transmission belt slides with respect to a pulley includes a first step of acquiring or calculating dμ / dv on a computer, dT / A second step of obtaining or calculating dv and a third step of evaluating belt squeal based on these dμ / dv and dT / dv are executed. According to the above program configuration, the accuracy of evaluation of belt squealing at the time of starting and stopping as well as during steady operation of the engine is further improved.

  The evaluation program further causes the computer to execute the following. That is, in the third step, the variable G is obtained based on the following equation (15). According to the above program configuration, since the belt squeal occurs when the variable G becomes negative, the presence or absence of the belt squeal can be grasped based on the variable G.

  The evaluation program further causes the computer to execute the following. That is, in the third step, the variable SNI is obtained based on the following equation (16). According to the above program configuration, the presence or absence of occurrence of belt squealing is grasped by the sign of variable SNI, and the magnitude when belt squealing occurs is grasped by the absolute value of variable SNI.

  According to the third aspect of the present invention, an apparatus for evaluating a belt squeal generated when a friction transmission belt slides with respect to a pulley is configured as follows. a first means for acquiring or calculating dμ / dv; a second means for acquiring or calculating dT / dv; and a third means for evaluating belt squealing based on these dμ / dv and dT / dv; ,including. According to the above configuration, the accuracy of evaluation of belt squealing at the time of starting and stopping as well as during the steady operation of the engine is further improved.

  The above evaluation apparatus is further configured as follows. That is, the third means obtains the variable G based on the following equation (15). According to the above configuration, since the belt squeal occurs when the variable G becomes negative, the presence or absence of the belt squeal can be grasped based on the variable G.

  The above evaluation apparatus is further configured as follows. That is, in the third step, the variable SNI is obtained based on the following equation (16). According to the above configuration, the presence or absence of occurrence of belt squeezing is grasped by the sign of the variable SNI, and the magnitude of the occurrence of belt squealing is grasped by the absolute value of the variable SNI.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. Please refer to FIG. FIG. 3 is a flowchart showing a processing procedure of an evaluation method for a belt squeal generated when a friction transmission belt slides on a pulley.

  The processing shown in this figure is mainly executed in a computer (belt noise evaluation device, first to third means). That is, the computer includes a CPU, a ROM, a RAM, a storage medium reading device, an output device, and the like. The program (evaluation program) related to the processing shown in FIG. 3 is stored in advance in the ROM, or stored in advance in a removable storage medium such as FD, CDROM, DVDROM, etc. Through the storage device (RAM, etc.) of the computer. Then, the CPU appropriately reads a program stored in the ROM or RAM and executes the processing shown in FIG. The output device is, for example, a display or a printer.

  First, when the program starts (S300), the CPU acquires various data stored in advance in the RAM (S310). The various data are time variations of μ, T, and v (hereinafter, “time variation” will be omitted as appropriate) and μ as shown in FIG. Includes -v characteristics.

  Next, dμ / dv is calculated based on the v and μ-v characteristics acquired in S310 (S320, first step). Further, dT / dv is calculated based on T and v (S330, second step). In order to calculate dT / dv, a relational expression of dT / dv = (dT / dt) / (dv / dt) is used. Moreover, the process of S320 and the process of S330 may differ before and after, and may be performed simultaneously. Further, when dμ / dv and dT / dv are separately calculated and the calculated dμ / dv and dT / dv are already stored in the RAM or the like, these values are stored in the RAM in S320 and S330. It is enough to read and acquire from.

  Then, the variable G is calculated based on the following formula (15) (S340), and the variable SNI is calculated based on the following formula (16) (S350). However, as can be seen by substituting the following equation (15) into the following equation (16), the SNI may be directly calculated.

  Finally, either or both of the variable G and the variable SNI obtained above are output in the form of a graph using the output device (S360), and the program ends (S370).

  See FIG. 5 as an example of the output result. In this graph, when the SNI is negative, it can be judged or evaluated that belt squeal is generated by the above formula (7). In addition, when the SNI is negative, the absolute value thereof quantitatively represents the size of the belt squeal according to the above equation (11). Therefore, the size of the belt squeal is calculated based on the absolute value. It can be grasped quantitatively.

  The preferred embodiments of the present invention have been described above.

  Next, the result of concrete verification about the accuracy of the evaluation by the belt squeal evaluation method will be reported.

<First verification>
The first verification verifies the accuracy of the evaluation during the steady operation of the engine. FIG. 4 is a diagram showing an auxiliary machine layout used for the first verification. FIG. 5 is a diagram showing a comparison between a measurement result of belt squeal at the time of idling (700 rpm), a calculation result of SNI, and a slip speed of the 4-cylinder gasoline engine having the auxiliary machine layout shown in FIG. In FIG. 4, CR is a crank, ALT is an alternator, WP is a water pump, AC is an air conditioning compressor, ID is an idler, and pulley peripheral speed and belt speed on the CR pulley are measured using a laser Doppler velocimeter, respectively. did. The tension on the tension side (ID1 side when viewed from the CR) is measured by a strain gauge attached to the shaft of the ID1 pulley, and similarly, the tension on the loose side (ID2 side when viewed from the CR) is applied to the shaft of the ID2 pulley. It was measured with the attached strain gauge. FIG. 6 shows the measurement results of the Tv characteristic used for the SNI calculation. As the μ-v characteristic, the result shown in FIG. 7 calculated based on the following formula (17) from the measured values of the tension side tension and the loose side tension is used.

  According to FIG. 5, it can be seen that belt squealing occurs at a timing when the SNI shows a large negative value. In other words, it can be said that the SNI can reproduce the presence or absence of occurrence of belt squeal during the steady operation of the engine.

<Second verification>
The second verification is to verify the accuracy of the above evaluation at the time of start-up that is an unsteady operation of the engine. FIG. 8 is a diagram showing an auxiliary machine layout used for the second verification. FIG. 9 is a diagram showing a comparison between a measurement result of belt squeal at the start of the four-cylinder gasoline engine having the accessory layout shown in FIG. 8, a calculation result of SNI, and a slip speed. In FIG. 8, CR, ALT, WP, AC, and ID are as described above. The pulley peripheral speed and belt speed on the CR pulley were measured using a laser Doppler velocimeter, respectively. The tension on the tension side (ID side as viewed from the CR) was measured with a strain gauge attached to the shaft of the ID pulley. In the second verification, the initial tension T ₀ of the belt is changed. FIG. 9 shows the result of T ₀ = 368 (N), and FIG. 10 shows the result of T ₀ = 485 (N). FIG. 11 shows the result of T ₀ = 562 (N). FIG. 12 is a diagram illustrating a measurement result of the Tv characteristic used for the calculation of the SNI. The μ-v characteristic uses the measurement result shown in FIG. 13 measured using a special measuring device. According to FIGS. 9 to 11, it can be seen that the magnitude of the negative SNI value obtained by calculation and the measured occurrence of belt squeal correspond very well.

  Based on the verification results of the first verification and the second verification, the belt squeal evaluation method according to the above embodiment can satisfactorily evaluate the belt squeeze not only at the time of steady operation of the engine but also at the start and stop. I understand.

  The above-described belt squeal evaluation method described above should be effectively used in the following situations, for example.

<Example 1>
At the time of development of a new engine, we are currently studying the design of an auxiliary drive belt. Here, a simulation is performed using the given auxiliary machine layout, auxiliary machine specifications, etc., and the feasibility of the auxiliary machine system is examined based on the calculation results as shown in (a) to (c) below, the optimum belt Selection etc. are performed.
(A) Tension fluctuation of each belt span (b) Slip rate (slip speed) on each auxiliary pulley
(C) String vibration of each belt span

  However, the most important pronunciation (occurrence of belt squeal) in the feasibility of the auxiliary system could not be studied, so only the empirical judgment was made with reference to the slip rate as a result of simulation. Was responding to the actual situation while looking at the results of the engine test run.

  In response to the above situation, the squeal index SNI based on the present invention is calculated based on the calculation block diagram shown in FIG. 14 and the flowchart of FIG. The degree of influence (quantitative size of the belt squeal) can be ascertained, and the development man-hours and costs can be greatly reduced.

  In FIG. 14, “auxiliary machine layout” means the shaft arrangement and pulley diameter of auxiliary machines such as WP and ALT with respect to CR. Similarly, the “auxiliary machine load condition” means, for example, the shaft torque of an auxiliary machine such as WP or ALT or shaft work at various engine speeds. The “belt specification” means, for example, a belt cross-sectional shape, belt rigidity, density, or friction coefficient. The “engine specification” means the number of revolutions, the number of cylinders, or the rotational fluctuation rate at each revolution number. The “slip rate” is a value obtained by dividing the slip speed v by the pulley peripheral speed or the belt running speed.

<Utilization example 2>
When a problem arises that a belt squeals during a trial run of a newly developed engine, it has been dealt with by trial and error, depending on the experience and intuition of the person in charge based on the measurement results. On the other hand, if the squeal index SNI is calculated based on various measurement data, it will be clear whether tension fluctuation or friction is the main cause, which greatly increases the man-hours and costs for solving the problem. It can be shortened.

Diagram showing the slip between the belt and pulley modeled by a vibration system with one degree of freedom Diagram illustrating the relationship between friction force and sliding speed The flowchart which shows the procedure of the process of the evaluation method of the belt squeal generated when a friction transmission belt slides with respect to a pulley. The figure which shows the auxiliary machine layout used for 1st verification The figure which shows the measurement result of the belt squeal at the time of idling (700 rpm) of the 4-cylinder gasoline engine which has an auxiliary machine layout shown in FIG. 4, the calculation result of SNI, and the comparison of a sliding speed. The figure which shows the measurement result of TV characteristic Diagram showing an example of μ-v characteristics The figure which shows the auxiliary machine layout used for 2nd verification The figure which shows the measurement result of the belt squeal at the time of starting of the 4-cylinder gasoline engine which has an auxiliary machine layout shown in FIG. 8, the calculation result of SNI, and the comparison of slip speed Figure similar to Figure 9 Figure similar to Figure 9 The figure which shows the measurement result of TV characteristic Diagram showing an example of μ-v characteristics Calculation block diagram

Claims (9)

In the evaluation method of the belt squeal generated when the friction transmission belt slides against the pulley,
a first step of calculating dμ / dv;
a second step of calculating dT / dv;
A third step of evaluating belt squealing based on these dμ / dv and dT / dv;
The evaluation method of the belt squeal characterized by including.
Here, μ represents a coefficient of friction between the friction transmission belt and the pulley, T represents a tension [N] of the friction transmission belt, and v represents a slip speed [between the friction transmission belt and the pulley [ m / s]. In the evaluation method of the belt squeal according to claim 1,
In the third step, a variable G is obtained based on the following equation (15).
Evaluation method of belt squeal characterized by

In the evaluation method of the belt squeal according to claim 2,
In the third step, a variable SNI is obtained based on the following equation (16).
Evaluation method of belt squeal characterized by

Is the wrap angle [rad] of the friction transmission belt with respect to the pulley, and V is the slip speed [m / s] immediately before the occurrence of belt squealing or the average slip speed [m / s] when belt squeal occurs. . In the evaluation program for belt squealing that occurs when the friction transmission belt slides against the pulley,
On the computer,
a first step of obtaining or calculating dμ / dv;
a second step of obtaining or calculating dT / dv;
A third step of evaluating belt squealing based on these dμ / dv and dT / dv;
A belt squeal evaluation program characterized in that In the belt squeal evaluation program according to claim 4,
In the third step, a variable G is obtained based on the following equation (15).
Belt squeal evaluation program characterized by

In the belt squeal evaluation program according to claim 5,
In the third step, a variable SNI is obtained based on the following equation (16).
Belt squeal evaluation program characterized by

In an evaluation device for belt squealing generated when the friction transmission belt slides against the pulley,
a first means for obtaining or calculating dμ / dv;
a second means for obtaining or calculating dT / dv;
A third means for evaluating belt squealing based on these dμ / dv and dT / dv;
A belt squeal evaluation device characterized by comprising: In the evaluation apparatus of the belt squeal according to claim 7,
The third means obtains a variable G based on the following equation (15).
Belt squeal evaluation device characterized by that

In the belt squeal evaluation device according to claim 8,
In the third step, a variable SNI is obtained based on the following equation (16).
Belt squeal evaluation device characterized by that

Images