JP4978420B2 - Method for predicting running heat of belt body and running resistance prediction method - Google Patents

Description

  The present invention relates to a running heat prediction method and a running resistance prediction method for a belt body.

A method for predicting the heat generation energy of a rotating body including a viscoelastic material such as an automobile tire and predicting the rolling resistance of the rotating body from the generated heat energy is known (Vol. 56, pp. 543 to 543 of the Japan Rubber Association). 551, 1983).
In the above method, the tire heat is predicted by obtaining the strain energy by the mechanical analysis or the numerical analysis represented by the finite element method based on the relational expressions shown in the following formulas (1) and (2). The rolling resistance is predicted by dividing this by the travel distance.
Tire heat generation = Strain energy x Material loss factor (1)
Tire rolling resistance = tire heat generation ÷ distance traveled (2)

When mechanical analysis is used in the conventional method, there is a disadvantage in that detailed results of stress, strain, or strain energy that are different for each part of the tire cannot be obtained.
The finite element method has static analysis and dynamic analysis, but the static analysis requires a short calculation time, but there is a disadvantage that the effect of viscoelasticity of the material cannot be taken into account. Although the viscoelasticity of the material can be taken into account, there is a disadvantage that it lacks practicality because of the long calculation time required for the analysis.
In addition, when a periodically changing stress is applied to a viscoelastic body such as rubber, a phase difference occurs between the generated strain and the area of the hysteresis loop defined by the change in strain with the stress is the heat generated by the deformation, That is, it corresponds to lost energy lost by deformation.
However, since the viscoelastic effect cannot be taken into account in the static analysis, there is a problem that heat generation cannot be obtained from the area of the hysteresis loop.
Therefore, a method for deriving heat generation energy data of a rotating body has been proposed in spite of using the static analysis (see Patent Document 1).
This method calculates the finite order of Fourier series expansion of stress and strain for one round of the rotating body, calculates the amplitude and phase of the change characteristic curve for each Fourier order, and distorts the phase lag according to the loss factor of the material. Based on the calculation of the area of the hysteresis loop for each Fourier order given to the value, the sum of the product of the Fourier order and the hysteresis loop area is derived, and a series of calculation processes are repeatedly executed for all components of stress and strain, and the sum for each component is calculated. Is calculated.
Japanese Patent No. 3969821

However, since the above-described conventional method is based on the premise that the stress and strain for one rotation of the rotating body are handled as a primary waveform, the heat generation energy of a belt body such as a conveyor belt of a belt conveyor apparatus having a different shape from the rotating body. It was impossible to predict.
The present invention has been made in view of such circumstances, and an object of the present invention is to predict a belt body running heat generation and a running which are advantageous for easily and accurately predicting heat generation energy or running resistance of the belt body. It is to provide a resistance prediction method.

In order to achieve the above object, the present invention provides a belt body running heat generation that predicts, using a computer, heat generated from the belt body when the belt body including a viscoelastic material travels on a plurality of rotating rollers. In the prediction method, the computer includes input means for inputting data, processing means for processing data input by the input means, and output means for outputting data processed by the processing means. And a predetermined length along the traveling direction within a range that does not contact the rotating rollers disposed on both sides of the one rotating roller around a contact position where one rotating roller contacts the belt body in the traveling direction. A portion of the belt body located in a range is a unit belt body, and the processing means is in a state where the unit belt body is stationary, The stress received from the two rotating rollers and the strain generated in the unit belt body according to the stress are obtained by finite element method analysis based on the analysis data input through the input means. A stress-strain generation step for generating respective change characteristic curves, and Fourier series expansion of the stress and strain change characteristic curves from a first order to an N-th order (N is a natural number of 2 or more) Fourier order. A waveform generation step for obtaining a waveform representing the stress and strain for each of the phases, and a phase of the strain waveform for each Fourier order is specified by a loss tangent tan δ of the viscoelastic material. a delay distortion waveform generation step for generating a delay distortion waveform by delaying by δ, For each order, the area of the hysteresis loop formed from the stress waveform and the delayed strain waveform is obtained, and the product of the area and the Fourier order is summed from the first order to the Nth order to obtain the inside of the cross section of the unit belt body. Generating a heat generation energy density generated at one point and calculating a product of the heat generation energy density and the volume of the region including the one point to generate heat generation energy in the region, and the waveform generation step And a heat generation energy generation step for calculating a heat generation energy generated in the entire unit belt body by repeatedly executing the delay distortion waveform generation step and the heat generation energy density generation step for the entire unit belt body. And an output for outputting the traveling heat generation energy via the output means It includes a step, wherein the predetermined length, the stress and the dimension sufficient to fully represent the characteristics indicated by the first-order component of distortion, and rotating roller adjacent to the one rotating roller acting on the unit belt body It is characterized by being shorter than the distance .
Further, the present invention provides a traveling resistance force that is a force that acts on the rotating roller from the belt body in a direction opposite to the traveling direction when the belt body including the viscoelastic material travels on a plurality of rotating rollers. Is a method of predicting the running resistance of the belt body using a computer,
The computer includes input means for inputting data, processing means for processing the data input by the input means, and output means for outputting the data processed by the processing means. The belt positioned within a predetermined length range along the traveling direction in a range not contacting the rotating rollers arranged on both sides of the one rotating roller with a center at a contact position where one rotating roller contacts the belt body The body part is a unit belt body, and the processing means generates stress on the unit belt body according to the stress that the unit belt body receives from the one rotating roller in a state where the unit belt body is stationary. The strain and strain are obtained by obtaining the strain by finite element analysis based on the analysis data input through the input means. A stress-strain generation step for generating respective change characteristic curves, and Fourier series expansion of the stress and strain change characteristic curves from the first order to the Nth order (N is a natural number of 2 or more) Fourier series. A waveform generation step for obtaining a waveform representing the stress and strain for each order, and a phase of the strain waveform with respect to a phase of the stress waveform for each Fourier order is specified by a loss tangent tan δ of the viscoelastic material. A delay distortion waveform generation step for generating a delay distortion waveform by delaying by a predetermined δ, and determining an area of a hysteresis loop formed from the stress waveform and the delay distortion waveform for each Fourier order, Generated at one point in the cross section of the unit belt body by summing the product with the order from the first order to the Nth order A heating energy generation step of generating a heating energy density in the region by calculating a product of the heating energy density and the volume of the region including the one point, the waveform generation step, and the delay A traveling heat generation energy generating step of calculating a traveling heat generation energy generated in the entire unit belt body by repeatedly executing a distortion waveform generation step and the heat generation energy density generation step for the entire unit belt body, and the traveling A running resistance generation step for generating the running resistance force by the product of the heat generation energy and the predetermined length; and an output step for outputting the running resistance force through the output means ; Features of the primary component of the stress and strain acting on the unit belt body The dimension sufficient to represent the minute, and wherein the shorter than the distance between the rotation roller adjacent to the one rotating rollers.

  According to the present invention, the position where one rotating roller is in contact with the belt body as a center is not in contact with the rotating rollers arranged on both sides of the one rotating roller, and is in a predetermined length range along the traveling direction. The belt body part to be used is a unit belt body, and the running heat energy and running resistance force of this unit belt body are predicted, so the running heat energy and running resistance force of the entire belt body can be predicted easily and accurately. Can do.

Next, a running heat prediction method and a running resistance prediction method for a belt body according to an embodiment of the present invention will be described with reference to the drawings.
First, the heat generation energy generated when the viscoelastic body is a rotating body and is deformed by rotating the rotating body on the surface will be described.
FIG. 1A shows the stress and strain characteristics of the viscoelastic body with the position as the horizontal coordinate, and FIG. 1B shows the hysteresis loop characteristics of the stress and strain with the strain as the horizontal coordinate and the stress as the vertical coordinate. .
As shown in FIG. 1A, in the viscoelastic body, the phase of the strain ε is delayed by δ with respect to the stress σ (0 <δ <π / 2).
As shown in FIG. 1 (B), the hysteresis loop of the viscoelastic body becomes an ellipse, and the area A of the ellipse is energy lost during deformation of one cycle (one cycle of the waveform).
A = π · f · g · sin δ (3)
(Where f: amplitude of stress σ, g: amplitude of strain ε)
The energy A corresponds to the heat generation energy generated in the viscoelastic body.
Thus, if the amplitude f of the stress σ, the amplitude g of the strain ε, and the phase difference δ are known, the heat generation energy can be calculated.
Therefore, the stress σ and the strain ε are obtained by analysis using a static finite element method.
The characteristics of the heat generation energy of a rotating body including a viscoelastic material are described in, for example, Shigeo Iwayanagi “Rheology” Asakura Shoten.
Therefore, the heat energy is calculated for the belt body by the same method as described above. However, unlike the rotating body, the belt body cannot apply the concept of one-turn deformation.
Accordingly, in the present invention, focusing on the fact that the belt body travels in contact with a plurality of rotating rollers arranged at intervals in the traveling direction, the unit belt body is divided into a predetermined length range. By handling it, the heat energy is predicted using the same method as the rotating body.

First, the belt body which is the object of the method of the present invention will be described.
FIG. 2 is an explanatory diagram of the belt body 10.
In the present embodiment, the belt body 10 is a conveyor belt used in the belt conveyor device 2.
The belt conveyor device 2 includes, for example, a driving roller (not shown), a driven roller, and a plurality of rotating rollers 4 provided at a predetermined interval between the rollers, and the belt body 10 includes the driving roller and the driving roller. A plurality of rotating rollers 4 and driven rollers are provided around the rotating rollers 4.
The belt body 10 travels on the plurality of rotating rollers 4 when the driving roller is rotationally driven by a driving source such as a motor.
The belt body 10 is configured by laminating a plurality of layers including one or more layers including a viscoelastic material in the thickness direction.
Specifically, the belt body 10 includes, for example, a cloth core body layer, steel cord layers provided on both surfaces of the core body layer, and a cover rubber layer that covers the outer sides of both steel cord layers. Alternatively, it includes a cushion rubber layer, steel cord layers provided on both sides of the cushion rubber layer, and a cover rubber layer that covers the outside of both steel cord layers. Of course, the configuration of the belt body 10 is not limited to these.
The cover rubber layer and the cushion rubber layer are made of a polymer made of natural rubber or synthetic rubber and a filler made of carbon black, silica, etc. Therefore, the cover rubber layer and the cushion rubber layer are made of a viscoelastic material. ing. Moreover, the viscoelastic material which comprises a cover rubber layer and a cushion rubber layer is also called a compound.

FIG. 3A is an explanatory diagram showing a distribution of stress σ applied to the belt body 10 in a stationary state, and FIG. 3B is an explanatory diagram showing a distribution of strain ε generated in the belt body 10 in a stationary state.
3A and 3B, the horizontal axis indicates the position p in the longitudinal direction (traveling direction) of the belt body 10, and P0 indicates the position where the belt body 10 contacts the outer peripheral surface of one rotating roller 4. Yes.
Since the belt body 10 is in contact with the rotating roller 4 at the position P0, as shown in FIG. 3A, the stress σ applied to the belt body 10 has a maximum value at the position P0, and the belt body 10 has a maximum value from the position P0. The stress σ gradually decreases as the distance increases in the longitudinal direction, and the stress σ becomes almost zero when the distance exceeds a predetermined distance.
As shown in FIG. 3 (B), the strain ε applied to the belt body 10 becomes a maximum value at the position P0, gradually decreases from the position P0 in the longitudinal direction of the belt body 10, and when the distance ε exceeds a predetermined distance. The stress σ is almost zero.
That is, when the belt body 10 is stationary, the phase of the strain ε with respect to the phase of the stress σ is not delayed.
Here, when the belt body 10 travels, the phase of the strain ε is delayed with respect to the stress σ as in the case of the rotating body described above, and therefore the heat generation energy is calculated from the area of the hysteresis loop of the stress σ and the strain ε. can do.
Here, as shown in FIG. 2, rotation rollers 4 ′, 4 ″ disposed on both sides of one rotation roller 4 around the contact position P 0 where one rotation roller 4 contacts the belt body 10 in the traveling direction. A portion of the belt body 10 that is located in a range of a predetermined length L along the traveling direction in a range that does not contact is treated as a unit belt body 12. Then, the rotation of the unit belt body 12 traveling a predetermined length L is performed. The heat generation energy is predicted in the same way as one rotation (one cycle) of the body.
Note that the predetermined length L may be a dimension that can sufficiently represent the characteristics represented by the primary components of the stress σ and the strain ε when the stress σ and the strain ε are considered for the unit belt body 12.
Therefore, the predetermined length L may be the same as the one span that is the dimension between the rotating rollers, that is, the same distance as the distance between the rotating roller 4 at the reference position P0 and the adjacent rotating roller 4 ′ (4 ″). In addition, if the predetermined length L is one span, the heat generation energy for one span can be predicted.

In calculating the heat generation energy of the unit belt body 12, the stress and strain are expanded in Fourier series. That is, as shown in FIG. 4, the first-order component σ1 (single-wave sine wave), the second-order component σ2 (half-wave sine wave), and the third-order component σ3 ( (Sin wave of 1/3 wavelength),..., And distortion is similarly decomposed into a sum of primary component, secondary component, tertiary component,.
Then, the area of the hysteresis loop is obtained for each order, and the heat generation energy is obtained based on the sum of the areas.

Next, the basic principle of the method for predicting the heat generation energy of the unit belt body 12 will be described.
FIGS. 5A1 and 5B1 are diagrams showing examples of stress distribution (stress change characteristic curve) and strain distribution (strain change characteristic curve) obtained from the calculation results.
FIGS. 5A2 and 5A3 are diagrams showing the waveforms of the primary, secondary,... Components obtained by Fourier series expansion of the stress curve of (A1), and show up to the secondary.
FIGS. 5B2 and 5B3 are diagrams showing the waveforms of the first-order, second-order,... Components obtained by Fourier series expansion of the strain curve of (B1), showing up to the second order.
6A is a stress waveform of the primary component, FIG. 6B is a strain waveform of the primary component, and FIG. 6C is a diagram showing a hysteresis loop of the primary component based on the stress waveform and strain waveform of the primary component. is there.
FIG. 7A is a stress waveform of the secondary component, FIG. 7B is a strain waveform of the secondary component, and FIG. 7C is a diagram showing a hysteresis loop of the secondary component based on the stress waveform and strain waveform of the secondary component. is there.
First, the stress and strain characteristics of the unit belt body 12 are analyzed by the finite element method, and the stress and strain with reference to local coordinates are obtained for each element of the unit belt body 12.
At this time, the length direction of the unit belt body 12, the direction of the element width orthogonal to the length, and the direction of the element thickness orthogonal to both the length direction and the width direction are considered for each element.
Next, the stress and strain of one component at the center of one element in the cross section of the unit belt body 12 are obtained, and the stress and strain of points adjacent to each other in the length direction are sequentially obtained, and the stress f (p) of the unit belt body 12 is obtained. And strain g (p). However, p shows the position of the unit belt body 12 in the length direction.
Here, the relationship between the position p in the unit belt body 12 and the phase angle θ in the rotating body will be described. The section L of interest is the predetermined length L of the unit belt body 12 described above, and this section L is defined as one cycle. If it considers, position p and phase angle theta will be related by the following relational expressions.
θ = 360 · (p / L) [°]
The one component indicates one component of all components of stress and strain (a total of six components including three components in the compressive tension direction and three components in the shear direction).
Then, as shown in FIG. 5, the stress f (p) and the strain g (p) are developed into finite-order Fourier series, and the amplitude _An and the phase _Bn are obtained for each order.
In this case, it is necessary to set the order for performing the Fourier series expansion to a high order that does not lose the characteristics of the waveform. For example, when the length of the contact portion on the outer periphery of the rotating roller 4 with respect to the model length (unit length) L is Lr, the length Lr can be divided into 10 to 100, that is, 10 L / Lr to 100 L. The order of / Lr is selected.
That is, the stress and strain are expanded to the Fourier order of the Nth order (N is a natural number of 2 or more), respectively, so that the waveform representing the stress change characteristic and the curve of the strain change characteristic are represented for each Fourier order. A waveform is required.

Strain g (p) is 6, as shown in FIG. 7, after giving a phase lag δ of meeting the loss factor of the viscoelastic material, the area S _n of the hysteresis loop was calculated for each order, based on its the sum _{S c} of the product of order n and the area _{S n} equation (4), determined in accordance with equation (5). Here, the phase delay δ corresponds to δ specified by the loss tangent tan δ of the viscoelastic material.
S _n = π · A _n ^f · A _n ^g · sin (B _n ^f −B _n ^g + δ) (4)
S _c = Σn · S _n (5)

Stress, repeated over the course for all components of the strain, it obtains the sum of the sum S _c of each component with the heating energy density, the product Edi of the volume V of the entire element obtained the heating energy density,

として求め、このＥｄｉをその位置における発熱エネルギーとする。
次いで、単位ベルト体１２全体について以上の過程を反復実行し、単位ベルト体１２全体の発熱エネルギーＥｄ、すなわち単位ベルト体１２が所定長Ｌ走行したときの発熱エネルギーＥｄを求める。
また、この発熱エネルギーＥｄから走行抵抗力を算出することができる。走行抵抗力は、ベルト体が複数の回転ローラー４上を走行する際に、回転ローラー４に対してベルト体１２から前記走行方向と逆向きに作用する力である。
発熱エネルギーＥｄは、実際には単位ベルト体１２が所定長Lを通過した際に回転ローラー４等によって受ける変形によって起こると考えられ、一方、単位ベルト体１２が回転ローラー４上を通過する際に回転ローラー４が受ける走行方向と逆向きの力（反力）が走行抵抗力となる。
この走行抵抗力には、単位ベルト体１２と回転ローラー４間の粘着や摩擦、あるいは粘弾性、ローラー上を乗り越える積荷の位置エネルギー変化などの影響が含まれる。
このうち、粘弾性に起因する走行抵抗力をＦｖとすると、この抵抗力が所定長Ｌに渡って作用した場合の仕事量は、Ｆｖ・Ｌとなる。
この仕事量は、注目する区間である所定長Ｌにおいて単位ベルト体１２が変形を受けたときの粘弾性によるエネルギー損失（熱として散逸する）と等価と考えられるので、
Ｆｖ・Ｌ＝Ｅｄ……（７）
となり、
即ち粘弾性に起因する走行抵抗力Ｆｖは所定長Ｌにおいて発生する損失エネルギーＥｄ（発熱エネルギー）を所定長Ｌで割ることにより、
Ｆｖ＝Ｅｄ／Ｌ……（８）
として求められる。
なお、実際に回転ローラー４上で検出される抵抗力には、粘弾性以外の要素が考えられるため、上記の式によって求められた走行抵抗力は実際に生じる走行抵抗力よりも低い。

This Edi is defined as the heat generation energy at that position.
Next, the above process is repeated for the entire unit belt body 12, and the heat energy Ed of the entire unit belt body 12, that is, the heat energy Ed when the unit belt body 12 travels a predetermined length L is obtained.
In addition, the running resistance can be calculated from the heat generation energy Ed. The traveling resistance force is a force that acts on the rotating roller 4 from the belt body 12 in the direction opposite to the traveling direction when the belt body travels on the plurality of rotating rollers 4.
It is considered that the heat generation energy Ed is actually caused by the deformation received by the rotating roller 4 or the like when the unit belt body 12 passes the predetermined length L, while the unit belt body 12 passes over the rotating roller 4. A force (reaction force) opposite to the traveling direction received by the rotating roller 4 becomes the traveling resistance force.
This running resistance includes influences such as adhesion and friction between the unit belt body 12 and the rotating roller 4, viscoelasticity, and a change in the potential energy of the load over the roller.
Of these, when the running resistance force resulting from viscoelasticity is Fv, the work amount when this resistance force acts over a predetermined length L is Fv · L.
Since this work amount is considered to be equivalent to energy loss (dissipated as heat) due to viscoelasticity when the unit belt body 12 is deformed in a predetermined length L that is a target section,
Fv · L = Ed (7)
And
That is, the running resistance force Fv caused by viscoelasticity is obtained by dividing the loss energy Ed (heat generation energy) generated at the predetermined length L by the predetermined length L,
Fv = Ed / L (8)
As required.
In addition, since elements other than viscoelasticity can be considered in the resistance force actually detected on the rotating roller 4, the travel resistance force obtained by the above formula is lower than the actually generated travel resistance force.

FIG. 8 is a block diagram showing the configuration of the computer 20 used for executing the method of the present invention.
The computer 20 includes a CPU 22, a ROM 24, a RAM 26, a hard disk device 28, a disk device 30, a keyboard 32, a mouse 34, a display 36, a printer 38, an input / output interface 40, and the like connected via an interface circuit and a bus line (not shown). have.
The ROM 24 stores a control program and the like, and the RAM 26 provides a working area.
The hard disk device 28 stores a program for realizing the method of the present invention.
The disk device 30 records and / or reproduces data on a recording medium such as a CD or a DVD.
The keyboard 32 and the mouse 34 receive operation inputs from the operator.
The display 36 displays and outputs data, and the printer 38 prints and outputs data. The display 36 and the printer 38 output data.
The input / output interface 40 exchanges data with an external device.
In this embodiment, the CPU 22, keyboard 32, mouse 34, disk device 30, and input / output interface 34 constitute the input means 20A (FIG. 9), and the CPU 22 constitutes the processing means 20B (FIG. 9). 36, the printer 38, the disk device 30, the input / output interface 40, and the like constitute the output means 20C (FIG. 9).

FIG. 9 is a functional block diagram of the computer 20.
As shown in FIG. 9, the computer 20 is functionally configured to include an input unit 20A, a processing unit 20B, and an output unit 20C.
The input means 20A inputs data necessary for obtaining the stress and strain of the unit belt body 12 by the finite element method, which will be described later.
The processing unit 20B obtains stress and strain by the finite element method based on the data input by the input unit 20A, and calculates heat generation energy and running resistance based on the above-described principle. The stored program is loaded into the RAM 26, and the CPU 22 operates based on the program.
The output means 20C outputs data composed of the calculation results by the processing means 10B.

Next, the travel heat generation prediction method and the travel resistance prediction method for the belt body according to the present embodiment will be described with reference to the flowchart shown in FIG.
First, in a state where the unit belt body 12 is stationary, the stress that the unit belt body 12 receives from one rotating roller 4 and the strain generated in the unit belt body 12 according to the stress are input via the input unit 20A. Curves of change characteristics of stress and strain are respectively generated by obtaining by finite element method analysis based on the analysis data (step S10).
Specifically, as shown in FIG. 9, as the analysis data, the shape data D1, material data D2, boundary data D3, load data D4, and the like of the unit belt body 12 are input via the input means 20A. Based on the data for analysis, the processing means 20B performs an operation so as to convert it into stress and strain referring to the local coordinates, so that stress and strain at one point (center of the one element) in the cross section of the unit belt body 12 are obtained. Ask for.
As a result, stresses and strains at points adjacent to each other along the longitudinal direction of the unit belt body 12 are sequentially obtained, thereby obtaining stress curves and strain curves which are curves of stress and strain change characteristics for the unit length L, respectively.

Next, the stress and strain change characteristic curves are respectively expanded from the first order to the Nth order (N is a natural number of 2 or more) Fourier order to obtain waveforms representing stress and strain for each Fourier order ( Step S12: Waveform generation step).
Next, a delayed strain waveform is generated by delaying the phase of the strain waveform by δ specified by the loss tangent tan δ of the viscoelastic material with respect to the phase of the stress waveform for each Fourier order (step S14: Delay distortion waveform generation step).
Then, the area by summing measuring the area S _c of the hysteresis loop which is formed from a stress wave and delay distortion waveform for each Fourier orders, the product of the area S _c and Fourier orders from the primary to N-th order obtaining the sum of S _c (step S16).
Next, it is determined whether or not the above-described steps S12, S14, and S16 have been executed for all stress and strain components (step S18). If the determination result is negative, the process proceeds to step S12 and the same process is repeated.
If the determination result of step S18 is affirmative, the energy density of the one point the sum of the sum S _c for each component, determine the product Edi of the volume V of the region including the one point as this energy density, the this product Edi It calculates | requires for every said area | region as the heat_generation | fever energy in the area | region containing one point in a cross section (step S20). That is, steps S16, S18, and S20 correspond to the heat generation energy generation step in the claims.
Next, it is determined whether or not the above-described operations of steps S12 to S20 have been performed on the entire unit belt body 12 (step S22). If the determination result is negative, the process proceeds to step S12 and the above-described processing is repeated. Execute.
If the determination result in step S22 is affirmative, the sum of the heat generation energy obtained in step S20 is calculated as the heat generation energy of the entire unit belt body 12, that is, the heat generation energy Ed when the unit belt body 12 travels the unit length L. (Step S24). That is, steps S22 and S24 correspond to the travel heat energy generation step in the claims.
Next, the traveling resistance force Fv received when the unit belt body 12 travels from the heat generation energy Ed is calculated based on the above-described equation (8) (step S26: traveling resistance generation step).
Then, the heat generation energy Ed and the running resistance force Fv are output from the output means 20C (step S28).

As described above, according to the present embodiment, in the traveling direction, the single rotation roller 4 does not come into contact with the rotation rollers 4 arranged on both sides of the single rotation roller 4 around the contact position where the rotation body 4 contacts the belt body 10. By making the portion of the belt body 10 located within the range and the range of the predetermined length L along the traveling direction as the unit belt body 12, the traveling heat generation energy and the traveling resistance force of the unit belt body 12 can be predicted. As a result, it is possible to easily and accurately predict the running heat energy and running resistance of the entire belt body 10, so that it is possible to easily and accurately evaluate the heating energy and running resistance of the belt body 10, which has been difficult in the past. This is advantageous in improving design efficiency.
Further, as described above, the structure of the belt body 10, that is, the unit belt body 12, includes a core body layer, a steel cord layer, a cover rubber layer and a cushion rubber layer made of a viscoelastic material. Using the data for analysis of the body 10 (shape data D1, material data D2, boundary data D3, and load data D4), the stress and strain at each position of the unit belt body 12 are obtained by finite element method analysis, and these stress and strain Since the heat generation energy and the travel resistance force are calculated based on the above, the travel heat generation energy and the travel resistance force reflecting the structure of the belt body 10 can be easily and accurately predicted.

  In the present embodiment, the case where the belt body 10 is used for the belt conveyor device 10 has been described. However, the present invention is widely applicable to a belt body including a viscoelastic material.

(A) shows the stress and strain characteristics of the viscoelastic body with the position as the abscissa coordinate, and (B) shows the hysteresis loop characteristics of stress and strain with the strain as the abscissa coordinate and the stress as the ordinate coordinate. is there. 3 is an explanatory diagram of a belt body 10. FIG. (A) is explanatory drawing which shows distribution of the stress (sigma) added to the belt body 10 in a stationary state, (B) is explanatory drawing which shows distribution of distortion | strain (epsilon) which arises in the belt body 10 in a stationary state. It is a figure explaining decomposing | disassembling the stress curve of the unit belt body 12 into the component of primary, secondary, tertiary .... (A1), (B1) are diagrams showing examples of stress distribution (stress change characteristic curve) and strain distribution (strain change characteristic curve) obtained from the calculation results; (A3) is a diagram showing the waveforms of the first, second,... Components obtained by Fourier series expansion of the stress curve of (A1). (B2) and (B3) are Fourier transforms of the strain curve of (B1). It is a figure which shows the waveform of the component of 1st order, 2nd order, ... obtained by series expansion. (A) is a stress waveform of a primary component, (B) is a strain waveform of a primary component, and (C) is a diagram showing a hysteresis loop of a primary component based on the stress waveform and strain waveform of the primary component. (A) is a stress waveform of a secondary component, (B) is a strain waveform of a secondary component, and (C) is a diagram showing a hysteresis loop of a secondary component based on the stress waveform and strain waveform of those secondary components. It is a block diagram which shows the structure of the computer 20 used in order to perform the method of this invention. 2 is a functional block diagram of a computer 20. FIG. It is a flowchart chart which shows the driving | running | working heat generation prediction method and driving | running | working resistance prediction method of the belt body of this Embodiment.

Explanation of symbols

  10: Belt body, 12: Unit belt body, 20: Computer, L: Predetermined length.

Claims (4)

When a belt body including a viscoelastic material travels on a plurality of rotating rollers, a heat generation prediction method for the belt body that predicts heat generated from the belt body using a computer,
The computer includes input means for inputting data, processing means for processing data input by the input means, and output means for outputting data processed by the processing means,
In a range where one rotating roller is in contact with the belt body in the traveling direction and is not in contact with the rotating rollers disposed on both sides of the one rotating roller, and in a predetermined length range along the traveling direction. A portion of the belt body positioned as a unit belt body,
The processing means is
Analysis in which the unit belt body is input via the input means with stress received by the unit belt body from the one rotating roller and strain generated in the unit belt body in response to the stress while the unit belt body is stationary. A stress-strain generation step for generating curves of stress and strain change characteristics by obtaining by finite element method analysis based on data for
Waveform generation for obtaining a waveform representing the stress and strain for each Fourier order by expanding the series of the stress and strain change characteristics from the first order to the Nth order (N is a natural number of 2 or more) Fourier series. Steps,
Delay strain waveform generation for generating a delayed strain waveform by delaying the phase of the strain waveform by δ specified by the loss tangent tan δ of the viscoelastic material with respect to the phase of the stress waveform for each Fourier order. Steps,
A cross section of the unit belt body is obtained by obtaining an area of a hysteresis loop formed from the stress waveform and the delayed strain waveform for each Fourier order, and summing the product of the area and the Fourier order from the first order to the Nth order. A heat generation energy generation step of generating heat generation energy density generated at one point, and generating heat generation energy in the region by calculating a product of the heat generation energy density and the volume of the region including the one point;
Travel that calculates travel heat energy generated in the entire unit belt body by repeatedly executing the waveform generation step, the delayed distortion waveform generation step, and the heat generation energy density generation step for the entire unit belt body. An exothermic energy generation step;
An output step of outputting the travel heat energy through the output means;
Including
The predetermined length is a dimension that is sufficient to sufficiently represent the characteristics represented by the primary components of the stress and strain acting on the unit belt body, and is shorter than the distance between the one rotating roller and the adjacent rotating roller. A method for predicting heat generation from running of a belt body. In order to derive the stress and strain change characteristic curve in the stress strain generation step, the stress and strain at one point in the cross section of the unit belt are obtained, and the stress and strain at points adjacent to the running direction of the unit belt body are sequentially determined. Done by calculating,
The method of predicting heat generated by running a belt body according to claim 1. When a belt body including a viscoelastic material travels on a plurality of rotating rollers, a running resistance force, which is a force acting on the rotating roller from the belt body in a direction opposite to the traveling direction, is calculated using a computer. A prediction method for predicting the running resistance of a belt body,
The computer includes input means for inputting data, processing means for processing data input by the input means, and output means for outputting data processed by the processing means,
In a range where one rotating roller is in contact with the belt body in the traveling direction and is not in contact with the rotating rollers disposed on both sides of the one rotating roller, and in a predetermined length range along the traveling direction. A portion of the belt body positioned as a unit belt body,
The processing means is
Analysis in which the unit belt body is input via the input means with stress received by the unit belt body from the one rotating roller and strain generated in the unit belt body in response to the stress while the unit belt body is stationary. A stress-strain generation step for generating curves of stress and strain change characteristics by obtaining by finite element method analysis based on data for
Waveform generation for obtaining a waveform representing the stress and strain for each Fourier order by expanding the series of the stress and strain change characteristics from the first order to the Nth order (N is a natural number of 2 or more) Fourier series. Steps,
Delay strain waveform generation for generating a delayed strain waveform by delaying the phase of the strain waveform by δ specified by the loss tangent tan δ of the viscoelastic material with respect to the phase of the stress waveform for each Fourier order. Steps,
A cross section of the unit belt body is obtained by obtaining an area of a hysteresis loop formed from the stress waveform and the delayed strain waveform for each Fourier order, and summing the product of the area and the Fourier order from the first order to the Nth order. A heat generation energy generation step of generating heat generation energy density generated at one point, and generating heat generation energy in the region by calculating a product of the heat generation energy density and the volume of the region including the one point;
Travel that calculates travel heat energy generated in the entire unit belt body by repeatedly executing the waveform generation step, the delayed distortion waveform generation step, and the heat generation energy density generation step for the entire unit belt body. An exothermic energy generation step;
A running resistance generating step for generating the running resistance by a product of the running heat energy and the predetermined length;
An output step of outputting the running resistance force through the output means;
Including
The predetermined length is a dimension that is sufficient to sufficiently represent the characteristics represented by the primary components of the stress and strain acting on the unit belt body, and is shorter than the distance between the one rotating roller and the adjacent rotating roller. A method for predicting the running resistance of a belt body. In order to derive the stress and strain change characteristic curve in the stress strain generation step, the stress and strain at one point in the cross section of the unit belt are obtained, and the stress and strain at points adjacent to the running direction of the unit belt body are sequentially determined. Done by calculating,
The method for predicting the running resistance of the belt body according to claim 3 .

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