JP4133768B2 - Transmission belt vibration analysis method and apparatus, and program - Google Patents

Description

  The present invention relates to a vibration analysis method and apparatus for a transmission belt, and a program. In particular, the present invention relates to a vibration analysis method and apparatus for a transmission belt that performs longitudinal vibration analysis using a vibration analysis model, and a program.

Conventionally, for a drive system that transmits power using a transmission belt (hereinafter abbreviated as “transmission belt drive system”), the generation of slip noise caused by the slip of the belt, the generation of heat generated by the slip, etc. In order to prevent the shortening of the service life, the design is performed in consideration of load, belt tension, pulley rotation speed, belt speed, pulley diameter, pulley layout, and the like. The design of the transmission belt drive system is performed based on a vibration analysis technique that analyzes vibration using a vibration analysis model.
In general, this vibration analysis technology uses a vibration analysis model to calculate the belt tension, pulley angular acceleration, pulley angular velocity, belt speed, belt displacement, slip ratio, etc. as accurately as possible. ing. The actual transmission belt drive system can be designed based on the numerical values calculated by the vibration analysis technique.

  For example, in the technique of Patent Document 1, a transmission belt drive system as a whole is modeled as a vibration, a modal parameter is calculated by eigenvalue analysis, a variable tension is calculated, and a combined tension is calculated along with a static tension calculation result. Discloses a vibration analysis technique for detecting a slip ratio.

  In the technique of Patent Document 2, the belt span portion is modeled as a spring, and vibration is calculated based on a vibration calculation model that changes the spring constant depending on whether the strain applied to the belt span portion is tensile strain or compression strain. An analysis technique is disclosed.

  Moreover, in the technique of Patent Document 3, a belt on the pulley is divided into nodes in a minute section in the longitudinal direction, and a vibration analysis model in which the nodes are connected by an elastic element or a rigid element is used. Has disclosed a vibration analysis technique for performing vibration analysis with contact and separation. Further, in this vibration analysis model, the belt element is divided into nodes of a minute section.

JP-A-1-288656 JP-A-7-2559539 JP 2001-31456 A

  However, in the vibration analysis model in the conventional vibration analysis technology, the slip ratio of the belt is obtained by a conditional expression that secures the required transmission power represented by Euler's expression (Eiterwein's expression) by friction transmission, It does not accurately represent the slip rate that changes from moment to moment. Therefore, in the vibration analysis of the transmission belt drive system performed with the vibration analysis model in the conventional vibration analysis technology, there is a difference between the value obtained by the calculation and the actual measurement value, so that the vibration analysis of the transmission belt drive system can be accurately performed. There is a problem that you can not. Along with this problem, in the conventional vibration analysis technology, it is difficult to perform vibration analysis of the transmission belt drive system using a vibration analysis model, not only by actual measurement, in order to grasp the slip ratio in time series, There is also a problem that it takes a lot of labor to perform the vibration analysis because it is necessary to carry out the test by testing the experimental apparatus each time.

  The present invention has been made in view of the above problems, and provides a vibration analysis method and apparatus for a transmission belt, and a program capable of accurately performing vibration analysis of a transmission belt drive system using a vibration analysis model. Is.

Means and effects for solving the problems

  The vibration analysis method for a transmission belt according to the present invention, when analyzing the longitudinal vibration of a transmission belt drive system comprising at least a pulley composed of driving and driven pulleys and a transmission belt wound around these pulleys, Using a vibration analysis model in which a belt portion between each pulley and a pulley adjacent to each pulley is modeled by a forked model, the angular velocity of the driving pulley, the angular velocity of each pulley other than the driving pulley, and the A vibration analysis method for a transmission belt, wherein the belt speed and belt displacement of each pulley, the belt tension of each belt portion, and the slip ratio between each pulley and the belt are repeatedly calculated with a step width H until a convergence condition is satisfied. The angular velocity of the driving pulley is a calculation formula including a harmonic function that simulates the rotation of a crankshaft included in the driving pulley. The belt tension of each belt portion is calculated by applying the belt speed of each pulley including the driving pulley and the belt displacement of each pulley to the Forked model, and the angular velocity of each pulley other than the driving pulley is calculated. Is calculated by applying the Runge-Kutta method with a step width H to the angular acceleration of each pulley calculated from the belt tension of each belt portion, the load torque of each pulley, and the rotational moment of inertia of each pulley, The slip rate on the pulley is calculated from a predetermined slip rate function with the belt tension of each belt part as a variable, and the belt displacement of each pulley is calculated from the slip rate on each pulley and the angular velocity of each pulley. The calculation is performed by applying a Runge-Kutta method having a step width H to the belt speed of each pulley.

  The vibration analysis device for a transmission belt according to the present invention analyzes the longitudinal vibration of a transmission belt drive system including at least a pulley including a drive and a driven pulley and a transmission belt wound around the pulley. Using a vibration analysis model in which a belt portion between each pulley and a pulley adjacent to each pulley is modeled by a forked model, the angular velocity of the driving pulley, the angular velocity of each pulley other than the driving pulley, and the Transmission belt vibration analyzer for repeatedly calculating belt speed and belt displacement of each pulley, belt tension of each belt portion, and slip ratio between each pulley and belt with a step width H until a convergence condition is satisfied. The angular velocity of the driving pulley is a calculation formula including a harmonic function that simulates the rotation of a crankshaft included in the driving pulley. The belt tension of each belt portion is calculated by applying the belt speed of each pulley including the driving pulley and the belt displacement of each pulley to the Forked model, and the angular velocity of each pulley other than the driving pulley is calculated. Is calculated by applying the Runge-Kutta method with a step width H to the angular acceleration of each pulley calculated from the belt tension of each belt portion, the load torque of each pulley, and the rotational moment of inertia of each pulley, The slip rate on the pulley is calculated from a predetermined slip rate function with the belt tension of each belt part as a variable, and the belt displacement of each pulley is calculated from the slip rate on each pulley and the angular velocity of each pulley. The calculation is performed by applying a Runge-Kutta method having a step width H to the belt speed of each pulley.

  When analyzing a longitudinal vibration of a transmission belt drive system including at least a pulley including a drive and a driven pulley and a transmission belt wound around the pulley, the program according to the present invention causes the computer to analyze each pulley. And a vibration analysis model in which a belt portion between the pulley adjacent to each pulley is modeled by a forked model, the angular velocity of the driving pulley, the angular velocity of each of the pulleys other than the driving pulley, and each of the pulleys A belt speed and a belt displacement, a belt tension of each belt portion, and a slip ratio between each pulley and the belt are repeatedly calculated with a step width H until a convergence condition is satisfied, The angular velocity of the drive pulley is calculated from a calculation formula including a harmonic function that simulates the rotation of the crankshaft included in the drive pulley. The belt tension of each belt portion is calculated by applying the belt speed of each pulley including the drive pulley and the belt displacement of each pulley to the Forked model, and the angular velocity of each pulley other than the drive pulley is Applying the Runge-Kutta method with a step width H to the angular acceleration of each pulley calculated from the belt tension of each belt portion, the load torque of each pulley and the rotational moment of inertia of each pulley, The upper slip ratio was calculated from a predetermined slip ratio function using the belt tension of each belt portion as a variable, and the belt displacement of each pulley was calculated from the slip ratio on each pulley and the angular velocity of each pulley. The calculation is performed by applying a Runge-Kutta method having a step width H to the belt speed of each pulley.

  According to this, in the vibration analysis model of the transmission belt drive system, obtain the time series data of the angular speed of each pulley and the time series data of the belt speed calculated from the slip ratio on each pulley obtained from the slip ratio function. Can do. Since the slip work rate can be calculated using the effective tension, the slip rate, and the belt speed, it is possible to predict the sound generation phenomenon and the heat generation friction phenomenon. In addition, since vibration analysis can be performed for all pulleys, changes in the winding angle, pulley diameter, number of belt ribs, and the like of each pulley can be examined in advance. In addition, the calculated slip ratio on each pulley can grasp the angular velocity of each pulley and the state of the belt speed on that pulley based on an accurate slip state. It is possible to analyze the behavior and to accurately respond to the acceleration / deceleration driving of the drive pulley.

  The slip ratio function is defined by the following equation when the slip ratio S, the constant K, the pulley radius R, the friction coefficient μ, the belt winding angle α, the tension side tension Tt, and the slack side tension Ts. Is preferred.

  According to this, since the slip ratio function is empirically determined, the time series data of the slip ratio can be accurately expressed.

  The convergence condition is that the time series data group of the belt tension generated every time the repetition time of the step width H corresponds to the fluctuation period of the harmonic function elapses, and the nth time series data group and n It is preferable that the difference obtained by comparing the −1st time-series data group at the same time step point is equal to or less than a predetermined determination value.

  According to this, vibration analysis of the transmission belt drive system can be standardized.

  Further, the convergence condition is preferably defined by the following equation when a predetermined determination value is α, a tension side tension Tt, and a slack side tension Ts.

| Tt (n) / Ts (n) −Tt (n−1) / Ts (n−1) | <α

  According to this, the determination value is determined based on the belt portion of the driving pulley where the ratio of the tension side tension and the slack side tension becomes the largest, and the vibration analysis of the transmission belt drive system can be further standardized.

  The best mode for carrying out the present invention will be described below with reference to the drawings.

First, the configuration of the transmission belt drive system according to the present embodiment will be described with reference to FIG. FIG. 4 shows a transmission belt drive system T according to the embodiment of the present invention.
In this transmission belt drive system T, a three-cylinder engine having six pulleys is taken as an example.

  As shown in FIG. 4, the pulley 1 is a crank pulley composed of a V-ribbed pulley as a drive pulley. The pulley 1 is integrally mounted on a crankshaft of an engine (not shown), and rotates with a predetermined rotational fluctuation by the crankshaft.

  The pulleys 3 to 6 are V-ribbed pulleys as driven pulleys. More specifically, the pulley 3 is a W / P (water pump) pulley. The pulley 4 is an ACG pulley. The pulley 5 is an I / D (idler) pulley. The pulley 6 is an A / C (air conditioner compressor) pulley.

  Between the pulley (drive pulley) 1 and the pulleys (driven pulleys) 3 to 6, the belt 7 is hung on the inner surface as a transmission belt composed of a V-rib belt having a plurality of parallel ribs (not shown) on the inner periphery. It is wrapped around.

The pulley 2 is a tension pulley composed of a flat pulley arranged at a position higher than that on the side of the pulley 1. The pulley 2 always presses the span 7b and the span 7c, which are slack sides, in the belt portion between the pulley 1 and the pulley 3, that is, the belt 7 rotating in the clockwise direction, toward the inner surface side of the belt 7. A dry auto tensioner that automatically adjusts the belt tension is constructed.
The span between pulley 1 and pulley 2 is span 7b, the span between pulley 2 and pulley 3 is span 7c, the span between pulley 3 and pulley 4 is span 7d, and the span between pulley 4 and pulley 5 is span 7c. Is a span 7e, a span between the pulley 5 and the pulley 6 is a span 7f, and a span between the pulley 6 and the pulley 1 is a span 7a. The belt tension means a belt tension between spans (belt portions).

A processing procedure of the vibration analysis method for the transmission belt drive system according to this embodiment for analyzing the vibration of the belt in the longitudinal direction of the transmission belt drive system T having the above configuration will be described with reference to FIG. FIG. 1 is a flowchart showing a processing procedure of a vibration analysis method for a transmission belt drive system according to the present embodiment.
Note that the processing of the vibration analysis method for the transmission belt drive system according to the present embodiment described below can be read and executed by the CPU as a program in the computer as well. Further, this program can be installed in various computer storage devices by recording it in a removable storage medium such as a CD-ROM, FD, or MO.

First, in step S1, vibration analysis model conditions are input. Here, the conditions of the vibration analysis model include the number of pulleys (N = 6 in the present embodiment), the presence / absence of an auto tensioner (present in this embodiment), and the characteristics of the alternator pulley (the presence / absence of a one-way clutch structure). ) (None in this embodiment), coordinates of each pulley (pulleys 1 to 5 in this embodiment), diameter, moment of inertia, steady torque, dimensions of auto tensioner (pulley 2 in this embodiment)・ Various characteristics.
In addition, related calculations are performed based on the input conditions. Specifically, a reference layout (pulley layout at initial tension) is calculated. In the calculation of the reference layout, calculate the X and Y coordinates of the auto tensioner, calculate the contact angle, belt length, each span length (reference span length), calculate the tension at the reference time, and calculate the slip factor of each pulley. Do. However, the reference span length around the auto tensioner is the span length (tangential length) before and after the A / T pulley (pulley 2 in this embodiment) in the reference layout, and the winding length on the A / T pulley. The total length of one-half of the total winding length of two pulleys adjacent to each other in the front-rear direction is defined as a reference span length around A / T at the initial tension.

  Next, in step S2, initial values of the belt displacement on each pulley and the angular velocity of the pulley are input.

  In the loop R1, the processes in steps S3 to S11 described below are repeated until the convergence condition is satisfied.

  In the loop R1, first, in step S3, n + 1 is updated as n. Note that the initial value of n is 0.

  Next, in the loop R2, the processes in steps S4 to S10 described below are repeated until t ≧ n × cycle. Here, the period means a fluctuation period of a harmonic function that simulates rotation of a crankshaft included in a drive pulley (pulley 1 in the present embodiment) described later.

  In the loop R2, first, in step S4, t + H is updated as t. The initial value of t is 0, and H is the calculation time interval.

  In step S5, the angular velocity of the drive pulley (pulley 1 in the present embodiment) is obtained from a calculation formula including a harmonic function that simulates the rotation of the crankshaft included in the drive pulley (pulley 1 in the present embodiment). Preferably, since the rotational characteristics of the crankshaft are determined by the engine, the speed waveform obtained by actual machine measurement is Fourier transformed, and the crankshaft angular speed is set as a time function expressed by the following equation.

In step S6, the belt tension of each belt portion (in the present embodiment, spans 7a to 7f) is calculated.
Hereinafter, the calculation of the belt tension of each belt portion in step S6 will be described in more detail with reference to FIG. FIG. 2 is a flowchart showing a processing procedure for calculating the belt tension of each belt portion.

First, in step S601, it is determined whether the span is before or after the auto tensioner (A / T).
If the span is not before or after the auto tensioner (step S601: NO), a general belt tension is calculated in step S602. On the other hand, in the case of the span before and after the auto tensioner 7 (step S601: YES), the belt tension of the auto tensioner is calculated in step S603.
In the present embodiment, the spans before and after the auto tensioner refer to the spans 7b and 7c that are adjacent to the pulley 2 forming the auto tensioner. And the span of a general span means the spans 7a, 7d, 7e, and 7f other than the spans before and after the pulley 2 forming the auto tensioner.

Here, in the traveling simulation of the transmission belt, some belt tensions sometimes become minus (−) in calculation. However, since it does not actually become minus (−), a method for calculating the belt tension will be described below based on FIG. 5 while considering the phenomenon in this case. FIGS. 5A to 5D are diagrams showing the bulging phenomenon of the slack side span belt in the biaxial transmission belt drive system.
Consider a simple two-axis case as shown in FIG. When a load is applied, the belt tension of the span A increases as shown in FIG. 5B, and the belt tension of the span B decreases. When the load is further increased, the belt tension of the span B decreases to near zero. In such a low tension region, the bending rigidity of the belt is effective, and the belt swells as shown in FIG. 5D instead of the straight line as shown in FIG.
However, even in such a bulging state, the belt is clearly in a state different from the natural standing state (a state in which the belt is restored to a ring shape in which the internal stress of the belt is relaxed). That is, this bulge has a shape that follows a substantially elliptic curve, and in order to maintain this substantially elliptic shape, an external force that overcomes the internal stress of the belt is required. An external force that deforms a ring-shaped belt into a substantially elliptical state is generally referred to as an external force that opposes the bending stress of the belt. Although this external force is given by belt tension, in the vibration analysis method according to the present embodiment, each driven pulley shaft varies in angular velocity with respect to the angular velocity input (harmonic function input) input to the drive pulley.
Therefore, the angular velocity fluctuation of a pair of adjacent pulleys becomes a forced displacement input, and the belt tension of this span is determined. Each belt span is calculated by assuming a forked model as shown in FIG.

The general belt tension in step S602 is calculated from the belt displacement and belt speed on each pulley obtained by solving the Runge-Kuttagill differential equation described later. However, the tension of the most tension side span (in this embodiment, the span 7a between the pulley 1 and the pulley 6) is calculated by obtaining a fixed point on the drive pulley from the angular velocity of the drive pulley obtained in step S5. To do.
Specifically, the belt tension is calculated by the following equation.

The belt tension of the auto tensioner (A / T) in step S603 is calculated as follows. First, the coordinates of the pulley are calculated from the arm angle of the auto tensioner (in this embodiment, the pulley 2). Then, the contact angle between the belt and the pulley is obtained, and the span length increment before and after the auto tensioner is calculated from the contact angle. Thus, the belt tension of the auto tensioner is obtained from the belt speed of the auto tensioner, the belt displacement, and the length increment.
Specifically, the belt tension is calculated by the following equation.

In Step S602 or Step S603, since the tension is usually calculated using an elastic curve expressed by a linear relationship, the belt tension may be negative (compressed state) depending on the calculation result. Therefore, in step S604, the belt tension at the time of low tension is corrected.
That is, when the belt tension Ti calculated in step S602 or step S603 is smaller than a predetermined value Tsp, the belt tension is corrected by the following equation.

The above equation for correcting the belt tension is obtained as follows.
First, a four-ribbed V-rib belt with different lengths is used, and two running test machines each having a pulley diameter of Φ60 and Φ120 are used for two running test machines having two axes of a driving pulley and a driven pulley. The experiment was performed with the rib belt of Formula 4 attached.
The load is set to no load, and the experimental method is to change the distance between the shafts while rotating at 2000 rpm and take the relationship with the force between the shafts. The distance between the shafts is the amount of movement of the moving side bearing box. The results measured with the load cell are shown in FIGS.
7A to 7D, the vertical axis is obtained by dividing the measured axial force by 2 and further dividing by the number of ribs 4 to obtain the belt tension per rib. The horizontal axis is the amount of change in the inter-axis distance, but the straight line portion of the experimental data is extrapolated and the point where the belt tension crosses zero (X axis) is set to zero. The point (●) in the figure is experimental data, and the solid line is a correction curve described later.
In the four experiments, it can be seen that the belt tension deviates from the straight line when the belt tension is 36 N / rib or less. The belt tension that begins to deviate is Tsp, and below that, correction is required. Although various correction formulas can be considered, a method of approximation by a simple exponential function formula will be described below.

That is, as shown in FIG. 8, the formula for calculating the tension using the elongation (X) is changed from a proportional formula based on an elastic coefficient (AE / L) to an exponential function formula.
When A is a cross-sectional area, E is an elastic coefficient, and L is a reference length, the following relationship is established from the relational expression of stress (tension) -strain (elongation) in FIG. X0, Tsp, and AE / L are constants determined by given conditions (experimental data).
Tsp = (AE / L) × X0 (Formula 1)
Tsp-Ta = (AE / L) × Xa (Formula 2)
Organizing Equation 1 and Equation 2
X0−Xa = Ta × (L / AE) (Formula 3)
X0 = Tsp × (L / AE) (Formula 4)
It becomes.
Finally, T = Tsp × exp ((X0−Xa) / X0−1) and Equations 3 and 4 are used to calculate the tension T when elongation X = (X0−Xa).
T = Tsp × exp (Ta / Tsp-1)
Thus, the above equation for correcting the belt tension is derived.

Next, in step S7, the angular acceleration and angular velocity of each pulley are calculated.
Hereinafter, the calculation of the angular acceleration and angular velocity of each pulley in step S7 will be described in more detail based on FIG. FIG. 3 is a flowchart showing the processing procedure for calculating the angular acceleration and angular velocity of each pulley and A / T arm.

As shown in FIG. 3, first, in step S701, the angular speed of the auxiliary pulley is obtained. Here, the auxiliary machine pulley means a pulley excluding the drive pulley. In the present embodiment, the auxiliary pulleys correspond to the pulleys 3, 4, 5, and 6.
Specifically, the angular acceleration is calculated using the moment of inertia of each auxiliary pulley, the steady torque applied to the auxiliary pulley, the solution of the Runge-Kuttagill differential equation, and the following equation. The angular velocity of each auxiliary pulley is calculated by applying the Runge-Kutta method with a step width of H time to the angular acceleration obtained by the following equation.

Next, in step S702, the torque applied to the arm of the auto tensioner (A / T) is calculated.
Specifically, in the present embodiment, the arm of the auto tensioner due to the belt tension is determined from the geometrical relationship such as the magnitude and direction of the load applied to the pulley 2 by the belt 7 and the length and arm angle of the arm of the auto tensioner. Torque is required.

In step S703, the difference (PP) between the torque applied to the auto tensioner (A / T) and the friction torque is calculated.
Specifically, PP is calculated by the following equation.

  Next, in step S704, it is determined whether PP <0 (the friction torque is larger) and whether the auto tensioner angular velocity is reversed, that is, whether there is a moment when the auto tensioner (A / T) is stopped.

If it is determined that there is a moment when the auto tensioner is stopped (step S704: YES), the angular velocity and angular acceleration of the auto tensioner (A / T) are set to 0 in step S705.
On the other hand, when it is determined that there is no moment when the auto tensioner (A / T) stops (step S705: NO), the angular acceleration and angular velocity of the auto tensioner (A / T) are calculated in step S706.
Specifically, the angular acceleration of the auto tensioner is calculated by the following equation. The angular velocity of the arm of the auto tensioner is calculated by applying the Runge-Kutta method with a step width of H time to the angular acceleration obtained by the following equation.

In step S8, the slip ratio is calculated.
Specifically, the slip ratio is calculated using the following slip ratio function.

  Here, the constant K in the slip ratio function is determined based on experimental data. Specifically, the slip rate and torque experimental results with the winding angle α shown in FIG. 9 as variables and the slip ratio and torque experimental results with initial tension shown in FIG. 10 as variables are determined. The torque is obtained by calculating (Tt−Ts) × R where Tt is the tension on the tension side, Ts is the tension on the slack side, and R is the pulley diameter.

The experiment shown in FIG. 9 was performed under the conditions of a pulley shaft diameter of 80 mm and an initial tension of 25 kgf assuming a transmission belt drive system having a five-axis layout including five pulleys. The experiment shown in FIG. 10 was carried out under the conditions of a pulley diameter φ80 mm and a winding angle 180 °, assuming a transmission belt drive system having a biaxial layout composed of two pulleys.
In FIG. 9, Δ marks are experimental values of α = 61 °, and ● marks are experimental values of α = 86 °. In FIG. 10, Δ marks are experimental values with an initial tension of 24 kgf, ● marks are experimental values with an initial tension of 48 kfg, and ◇ marks are experimental values with an initial tension of 72 kgf.

Based on these experimental values, a constant K of the slip ratio function is obtained. In addition, the simulation result of the slip ratio function to which the obtained constant K is applied is also shown in FIGS.
In FIG. 9, the dotted line is the simulation result of α = 61 °, and the solid line is the simulation result of α = 86 °. In FIG. 10, the solid line is the simulation result of 24 kgf, the thick line is the simulation result of the initial tension of 48 kfg, and the dotted line is the simulation result of the initial tension of 72 kgf.

Next, in step S9, the belt speed and belt displacement on each pulley are calculated based on the slip ratio obtained in step S8.
Specifically, the belt speed is calculated by the following equation. The belt displacement is calculated by applying the Runge-Kutta method with a step width of H time to the belt speed obtained by the following equation.

  Then, the termination condition of the loop R2 is determined, and when the time t ≧ n × cycle, the loop R2 is terminated.

  When the loop R2 is completed, in step S10, the data such as the belt tension, the angular velocity of each pulley, the slip rate, and the belt velocity obtained as described above are recorded as time series data for one cycle of the above-described harmonic function fluctuation cycle. The data is output to an output device such as a display or a printer.

  Next, in step S11, it is determined whether n is larger than M. Here, M is an arbitrary maximum calculation number set in advance by the user, and when the fluctuation period of the harmonic function M cycles elapses (step S11: YES), the vibration analysis process is terminated as not converging. It means that. Accordingly, the process is continued until the period of M cycles of the harmonic function has elapsed (step S11: NO).

  Then, when the termination condition of the loop R1 is determined and the convergence condition is satisfied, the loop R1 is terminated and the process is terminated.

  Here, the convergence condition is determined by the difference in the belt tension ratio on the drive pulley for one period before and after the fluctuation period of the harmonic function. That is, the ratio of the time-series data of the tension side belt tension on the driving pulley of the nth cycle recorded in step S10 and the time series data of the slack side belt tension, and the tension side belt tension on the driving pulley of the (n-1) th cycle. The time-series data of the slack side belt tension and the time-series data of the slack side belt tension are compared at the step points at the same time, and if the difference between each step point is smaller than a predetermined reference value, the convergence condition is satisfied. . Specifically, it is expressed by the following formula. The predetermined reference value is set in advance by the user.

  In the present embodiment, the tension side belt tension corresponds to the belt tension of the span 7a, and the slack side belt tension corresponds to the belt tension of the span 7b.

  Here, each step of the vibration analysis method for the transmission belt shown in FIGS. 1 to 3 is configured by, for example, a general-purpose personal computer as each part (means) of the vibration analysis device for the transmission belt. Such a personal computer stores hardware such as a CPU, ROM, RAM, hard disk, FD and CD drive device, and the hard disk includes a program (this program is a removable medium such as a CD-ROM, FD, or MO). In this case, it is possible to install the software on various recording media so that it can be installed on various computers. The above steps are constructed by combining these hardware and software.

  The data obtained in each step of the transmission belt vibration analysis method is displayed on a display (not shown) or printed by a printer, thereby notifying the operator of the transmission belt vibration analysis device.

  Thus, according to the vibration analysis method and apparatus of the transmission belt and the program according to the present embodiment, in the vibration analysis model of the transmission belt drive system T, the time-series data of the angular velocity of each pulley, and the slip ratio function It is possible to acquire time-series data of the belt speed calculated from the slip ratio obtained from (Steps S5 to S9 in FIG. 1). Since the slip work rate can be calculated using the effective tension, the slip rate, and the belt speed, it is possible to predict the sound generation phenomenon and the heat generation friction phenomenon. In addition, since vibration analysis can be performed for all pulleys, changes in the winding angle, pulley diameter, number of belt ribs, and the like of each pulley can be examined in advance. Furthermore, since the calculated slip ratio (step S8 in FIG. 1) makes it possible to grasp the angular velocity of each pulley and the belt speed on the pulley based on the accurate slip state, the transmission belt can be obtained in a minimum time. The behavior of the drive system T can be analyzed, and the drive pulley 1 can be accurately responded to the acceleration / deceleration drive.

  Further, since the slip ratio function is empirically determined in the vibration analysis model of the transmission belt drive system T (see step S8 in FIG. 1, FIG. 9 and FIG. 10), the time series data of the slip ratio is accurately expressed. be able to.

  In the vibration analysis model of the transmission belt drive system T, the convergence condition is determined based on the belt portion of the drive pulley 1 in which the ratio of the tension side tension to the slack side tension is the largest (loop R1 in FIG. 1). The vibration analysis of the transmission belt drive system T can be further standardized.

  The preferred embodiments of the present invention have been described above. However, the present invention is not limited to the above-described embodiments, and various vibration analyzes are possible as long as they are described in the claims. .

  For example, the present invention can be applied to a transmission belt drive system other than the transmission belt drive system T as in the above embodiment. For example, although the transmission belt drive system T provided with the auto tensioner has been described in the above embodiment, the present invention can also be applied to a transmission belt drive system not provided with the auto tensioner.

  Further, the correction of the belt tension in step S604 in FIG. 2 is not limited to the exponential function formula in the above embodiment, and various other formulas may be considered as long as the formula is a curve relation that attenuates as the tension decreases but does not become zero. It is done.

Next, an embodiment in which the present invention is specifically implemented will be described with reference to FIGS.
The transmission belt drive system used in this embodiment is the transmission belt drive system T shown in FIG. 4 described above. Actually, in the transmission belt drive system T, the pulley diameters of the pulleys 1 to 6 are φ130 mm, φ80 mm, φ110 mm, φ55 mm, φ80 mm, and φ115 mm, respectively, the rotational speed of the drive pulley 1 is 900 rpm, and the ACG pulley 4 is An experiment of vibration analysis was conducted with no load.

FIG. 11 is a diagram illustrating simulation results and experimental results regarding the belt tension of spans (spans 7e and 7f) before and after the I / D pulley (pulley 5). In FIG. 11, the dotted line is the experimental data actually measured, the thick line is the simulation result to which the present invention is applied, and the solid line is the simulation result to which the conventional technique is applied.
As shown in FIG. 11, compared with the experimental data, the simulation result using the conventional technique has a higher maximum belt tension and a time delay. On the other hand, the simulation results to which the present invention is applied almost coincide. Therefore, it can be seen that the present invention can accurately perform vibration analysis of the transmission belt drive system T using the vibration analysis model.

FIG. 12 is a diagram showing simulation results and experimental results for the center position of the auto tensioner pulley (pulley 2). In FIG. 12, the dotted line is the experimental data actually measured, the thick line is the simulation result to which the present invention is applied, and the solid line is the simulation result to which the conventional technique is applied.
As shown in FIG. 12, when compared with the experimental data, the simulation result applying the conventional technique is greatly deviated, and the simulation result applying the present invention is almost the same. Therefore, it can be seen that the present invention can accurately perform vibration analysis of the transmission belt drive system T using the vibration analysis model.

FIG. 13 is a diagram showing simulation results for the pulley angular speed (circumferential speed) of the crank pulley (pulley 1) and the ACG pulley (pulley 4). In FIG. 13, the solid line represents the pulley angular speed of the crank pulley 1 applied to the present invention, and the thick line represents the simulation result of the pulley angular speed of the ACG pulley 4 to which the present invention is applied.
As shown in FIG. 13, it can be seen from the simulation result of the pulley angular speed of the ACG pulley 4 compared with the crank pulley 1 that the present invention can accurately perform the vibration analysis of the transmission belt drive system T using the vibration analysis model.

FIG. 14 is a diagram illustrating a simulation result of the slip ratio between the belt of the ACG pulley (pulley 4) and the A / C pulley (pulley 6) and the pulley. FIG. 14 shows the slip ratio in percentage. In FIG. 14, the solid line is the slip ratio of the ACG pulley to which the present invention is applied, and the thick line is the slip ratio of the A / C pulley to which the present invention is applied.
Here, as shown in FIG. 11, there is a time during which the belt tension of the belt portions (span 7e, 7f) on both sides of the I / D pulley 5 is reduced to near zero. Further, as shown in FIG. 13, there is a portion where the pulley angular velocity of the ACG pulley 4 is reduced (decelerated). As shown in FIG. 14, a positive load is applied to the A / C pulley 6, and the pulley angular speed of the A / C pulley becomes smaller than the belt speed. Although the slip ratio is positive, the simulation results in FIG. 14 are similar. On the other hand, since a negative load torque acts on the ACG pulley 5 as the belt decelerates, the slip ratio between the ACG pulley 5 and the belt 7 becomes negative, but the simulation result of FIG. ing. Therefore, it can be seen that the present invention can accurately perform vibration analysis of the transmission belt drive system T using the vibration analysis model.

It is a flowchart figure which shows the procedure of the process of the vibration analysis method of the transmission belt drive system which concerns on this embodiment. It is a flowchart figure which shows the procedure of the process of calculation of the belt tension of each belt part. It is a flowchart figure which shows the procedure of a process of calculation of the angular acceleration and angular velocity of each pulley and A / T arm. 1 shows a transmission belt drive system T according to an embodiment of the present invention. (A)-(d) is a figure which shows the swelling phenomenon of the belt of a slack side span in a biaxial transmission belt drive system. It is a figure which shows a forked model. (A)-(d) is the result of having experimented the tension | tensile_strength at the time of a low tension | tensile_strength in the driving test machine which consists of 2 axes | shafts. It is a figure which shows the type | formula which correct | amends belt tension. It is a figure which shows the experimental result of the slip ratio and torque which made winding angle (alpha) variable. It is a figure which shows the experimental result of the slip ratio and torque which made initial tension variable. It is a figure which shows the simulation result and experimental result about the belt tension of the span before and behind an I / D pulley. It is a figure which shows the simulation result about the center position of an auto tensioner pulley, and an experimental result. It is a figure which shows the simulation result about the pulley angular velocity of a crank pulley and an ACG pulley. It is a figure which shows the simulation result about the slip ratio between the belt of an ACG pulley and an A / C pulley, and a pulley.

Explanation of symbols

1 Drive pulley (crank pulley)
2 Driven pulley (A / T pulley)
3 Driven pulley (W / P pulley)
4 Driven pulley (ACG pulley)
5 Driven pulley (I / D pulley)
6 Driven pulley (A / C pulley)
7 Transmission belt 7a Span (belt part)
7b Span (belt part)
7c Span (belt part)
7d Span (belt part)
7e Span (belt part)
7f Span (belt part)
T Transmission belt drive system

Claims (6)

When analyzing longitudinal vibrations of a transmission belt drive system including at least a drive and driven pulleys and a transmission belt wound around the pulleys, the pulleys and pulleys adjacent to the pulleys Using a vibration analysis model in which the belt portion between the two is modeled by a forked model, the angular velocity of the driving pulley, the angular velocity of each pulley other than the driving pulley, the belt velocity and belt displacement of each pulley, A vibration analysis method for a transmission belt that repeatedly calculates a belt tension of a belt portion and a slip ratio between each pulley and the belt with a step width H until a convergence condition is satisfied,
The angular velocity of the drive pulley is calculated from a calculation formula including a harmonic function that simulates the rotation of a crankshaft included in the drive pulley,
The belt tension of each belt portion is calculated by applying the belt speed of each pulley including the drive pulley and the belt displacement of each pulley to the forked model,
The angular velocity of each pulley other than the drive pulley is the Runge-Kutta with step width H to the angular acceleration of each pulley calculated from the belt tension of each belt portion, the load torque of each pulley, and the rotational moment of inertia of each pulley. Apply the law,
The slip ratio on each pulley is calculated from a predetermined slip ratio function with the belt tension of each belt portion as a variable,
The belt displacement of each pulley is calculated by applying a Runge-Kutta method with a step width H to the belt speed of each pulley calculated from the slip ratio on each pulley and the angular velocity of each pulley. Vibration analysis method. When the slip ratio function is a slip ratio S, a constant K, a pulley radius R, a friction coefficient μ, a belt winding angle α, a tension side tension Tt, and a slack side tension Ts,

The vibration analysis method for a transmission belt according to claim 1, wherein: The convergence condition is
With respect to the time series data group of the belt tension generated every time the repetition time of the step width H corresponds to the fluctuation period of the harmonic function, the nth time series data group and the n−1th time series data The vibration analysis method for a transmission belt according to claim 1 or 2, wherein a difference between the group and the step point at the same time is equal to or less than a predetermined determination value. The convergence condition is that when the predetermined determination value is α, the tension side tension Tt, and the slack side tension Ts,
| Tt (n) / Ts (n) −Tt (n−1) / Ts (n−1) | <α
The vibration analysis method for a transmission belt according to claim 3, wherein: When analyzing longitudinal vibrations of a transmission belt drive system including at least a drive and driven pulleys and a transmission belt wound around the pulleys, the pulleys and pulleys adjacent to the pulleys Using a vibration analysis model in which the belt portion between the two is modeled by a forked model, the angular velocity of the driving pulley, the angular velocity of each pulley other than the driving pulley, the belt velocity and belt displacement of each pulley, A vibration analysis device for a transmission belt that repeatedly calculates a belt tension of a belt portion and a slip ratio between each pulley and the belt with a step width H until a convergence condition is satisfied,
The angular velocity of the drive pulley is calculated from a calculation formula including a harmonic function that simulates the rotation of a crankshaft included in the drive pulley,
The belt tension of each belt portion is calculated by applying the belt speed of each pulley including the drive pulley and the belt displacement of each pulley to the forked model,
The angular velocity of each pulley other than the drive pulley is the Runge-Kutta with step width H to the angular acceleration of each pulley calculated from the belt tension of each belt portion, the load torque of each pulley, and the rotational moment of inertia of each pulley. Apply the law,
The slip ratio on each pulley is calculated from a predetermined slip ratio function with the belt tension of each belt portion as a variable,
The belt displacement of each pulley is calculated by applying a Runge-Kutta method with a step width H to the belt speed of each pulley calculated from the slip ratio on each pulley and the angular velocity of each pulley. Vibration analysis equipment. When analyzing longitudinal vibration of a transmission belt drive system including at least a pulley including a drive and driven pulley and a transmission belt wound around the pulley, the computer is adjacent to the pulley and the pulley. Using a vibration analysis model in which the belt portion between the pulleys is modeled by a forked model, the angular velocity of the driving pulley, the angular velocity of each pulley other than the driving pulley, the belt velocity and belt displacement of each pulley, and A program for repeatedly calculating the belt tension of each belt portion and the slip ratio between each pulley and the belt with a step width H until a convergence condition is satisfied,
The angular velocity of the drive pulley is calculated from a calculation formula including a harmonic function that simulates the rotation of a crankshaft included in the drive pulley,
The belt tension of each belt portion is calculated by applying the belt speed of each pulley including the drive pulley and the belt displacement of each pulley to the forked model,
The angular velocity of each pulley other than the drive pulley is the Runge-Kutta with step width H to the angular acceleration of each pulley calculated from the belt tension of each belt portion, the load torque of each pulley, and the rotational moment of inertia of each pulley. Apply the law,
The slip ratio on each pulley is calculated from a predetermined slip ratio function with the belt tension of each belt portion as a variable,
The belt displacement of each pulley is calculated by applying a Runge-Kutta method with a step width H to the belt speed of each pulley calculated from the slip rate on each pulley and the angular velocity of each pulley.

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