JPH1164122A - Stress calculating method in hollow roll and manufacture of hollow roll by use of this - Google Patents

Abstract

PROBLEM TO BE SOLVED: To prevent the breaking trouble of a shaft part and the damage by operation stop by calculating the stress added to the shaft part in the corner part between the shaft part and a panel board part, taking the stress concentration in the corner part into consideration. SOLUTION: When the stress of the corner part between a shaft part and a panel board part in a two-shaft type hollow roll, stress concentration is taken into consideration. Namely, it can be calculated from stress δ = coefficient of stress concentration α× load stress δ0 . When a concentrated stress W is added to the position of a length (a) from both end surfaces. 1A in a double end supported hollow roll with a diameter (d) and a length 2L, the load stress δ0 in the part (a) can be determined by the expression I. M represents the bending moment in the point (a). When the hollow roll is a stepped round shaft 2 (R: the radius of a major diameter part 2A, t: the width of the major diameter part 2A, d: the diameter of a minor diameter part 2B, r: the curvature radius of the corner part between the major and minor diameter parts 2A, 2B), the coefficient of stress concentration α when the bending moment M is added can be determined by the expression II. In the expression, Const is constant, (f), (g), and (h) represent functions of parameters r/d, R/d, t/D.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a hollow roll such as a bridle roll or a looper roll used in a thin plate process line, which is provided with at least one end plate and a shaft integrally formed at each end. A method for calculating a stress applied to a shaft portion at a corner portion between a shaft portion and a head plate portion in a hollow roll having both shafts separated from each other, and a hollow roll using the same. And a method for producing the same.

[0002]

2. Description of the Related Art Conventionally, there are three types of hollow rolls of this type, as shown in FIGS. The hollow roll 100 shown in FIG. 18 is provided with one end plate 101, 101 forming both end surfaces, and a through shaft 102 integrally provided so as to penetrate therethrough (hereinafter, type A). A hollow roll). In the illustrated example, outer shafts 102A, 102A protruding outward from the end surfaces are welded to the end plates 101, 101 at both ends in a penetrating state, and an inner shaft 102B is bridged and fixed between the outer shafts 102A, 102A. , A through shaft 102 is formed.

In recent years, in order to reduce costs,
A hollow roll having at least one end plate portion and a shaft portion integral with the end plate portion at each of both ends and having both shafts separated from each other (hereinafter, also referred to as a double-shaft type hollow roll) is used. It has become. As an example of this, a hollow roll 110 shown in FIG. 19 has two end plates 111, 111 and two end plates 1 1
A shaft 112 welded to each of the shafts 11 and 111 is provided, and both shafts 112 and 112 are provided separately (hereinafter, referred to as “shafts”).
Type B hollow roll). Further, the hollow roll 120 shown in FIG. 20 has one end plate 121 on each end surface on which a shaft portion 121A protruding outward in the rotation axis direction is formed. (Hereinafter also referred to as a type C hollow roll).

When these hollow rolls are actually used, the maximum stress is applied to the joint between the end plate and the shaft. Therefore, the roll maker obtains the stress applied to the joint, and this stress is less than the allowable stress. Rolls are designed and manufactured as follows. Conventionally, a roll maker has designed a type A hollow roll by examining the roll strength using the “Luhr (Lure) equation”. When this Luhr's equation is applied to the type A hollow roll calculation model 130 shown in FIG. 21, the stress at each joint between the end plates 131, 131 and the end plate bosses 131A, 131A is expressed as follows. .

That is, considering a case where a concentrated load W is applied to the center of the roll shell 130A in the width direction, a reaction force W / 2 against the bearing acts on both ends of the outer shafts 132A and 132A, and the bearing reaction force W / 2, the outer shafts 132A, 13A at the respective portions of the end plate bosses 131A, 131A.
The bending moment M ₀ received by 2A is expressed by equation (1). M ₀ = (L−a) W / 2 (1) where L is the distance from the center of the roll shell 130A in the width direction to the point of application of the bearing reaction force, and a is the distance between the end plates 131. is there.

[0006] In addition, the end plate by bending moment M ₀ 13
The bending moment M _F acting on 1 (2-1) - (2-
3) It is expressed by the equation. _{M F = M 0 / (1} + G) ··· (2-1) G = K1 · J / (a · t 3) ··· (2-2) J = π · d 4/64 ··· (2 -3) Here, K1 is a value determined from the relationship shown in FIG.
In addition, t is the thickness of the mirror plates 131, 131, and d is the radius of the internal shaft 132b.

Further, the bending stress σ ₁ acting on each of the end plate bosses 131A, 131A by the bending moment M _F is expressed by the following equation (3). σ ₁ = L 1 · M _F / (ra · t ² ) (3) where L 1 is a value determined from the relationship shown in FIG.
Also, ra is the radius of the mirror plate.

On the other hand, the direct stress σ ₂ generated by the concentrated load W in each of the head boss portions 131A, 131A is expressed by the following equation (4). σ ₂ = (W / 2) / (2πri · t) (4) where ri is the radius of the head boss.

[0009] From the above, (1) to (3) each end plate boss 131A from equation determines the bending stress sigma ₁ acting on 131A, whereas (4) each end plate boss 131A from the equation, 131A
The total stress σ at each joint between the end plates 131, 131 and the end plate bosses 131A, 131A is calculated by calculating the direct stress σ ₂ generated in Can be. σ = σ ₁ + σ ₂ (5)

[0010]

However, for twin-roll type hollow rolls such as type B and type C, there has been no stress calculation formula such as the Luhr's formula described above. Therefore, conventionally, for the twin-shaft type hollow roll, the stress was calculated using the Luhr's formula and the roll was designed. However, the calculation result was not accurate.
In some cases, the designed and manufactured hollow roll does not have sufficient strength to withstand actual use. As a result, cracks were generated at the corners between the shaft and the end plate, and the cracks frequently occurred due to the cracks. When such troubles occur, operation stoppage is unavoidable, and a large amount of damage is incurred due to the inability to achieve the planned production volume.

[0011] As shown in Table 1, the present applicant has disclosed a type B
In the case of the roll No. 110X in FIG. 19 and the type C roll 120X in FIG. 20, cracks have occurred and the shaft has been broken many times in the past. When a stress was calculated by the Luhr's formula and FEM (finite element method) analysis for the hollow roll experiencing the shaft breakage trouble, the stress calculation result by the Luhr's formula was 30 times greater than that of the FEM analysis. ~
It had as much as 50% error. The stress calculation result by the FEM analysis has an error of only about 10% as compared with the stress measurement result using the load cell, and is extremely accurate.

[0012]

[Table 1]

Accordingly, a main object of the present invention is to provide a stress calculation method and a stress calculation method capable of accurately calculating a stress applied to a shaft portion at a corner between a shaft portion and a head plate portion in a two-shaft type hollow roll. An object of the present invention is to propose a method for manufacturing a hollow roll used, thereby preventing breakage trouble of a shaft portion and avoiding damage caused by stoppage of operation.

[0014]

According to the present invention, which solves the above-mentioned problems, at least one end plate has at least one end plate and a shaft integral with the end plate, and both shafts are separate. In the hollow roll, a stress applied to the shaft portion at a corner between the shaft portion and the end plate portion is calculated in consideration of stress concentration at the corner portion.

More specifically, the load stress applied to the shaft portion at the corner portion and at least the thickness of the head plate portion, the radius of the head plate portion, the radius of curvature of the corner portion, and the shaft diameter of the shaft are determined. It is proposed to calculate the stress applied to the shaft at the corner based on the stress concentration factor expressed as a function.

On the other hand, as an invention in which the above calculation method is applied to the manufacture of a hollow roll, each end has at least one end plate portion and a shaft portion integral with the end plate portion, and both shafts are separate bodies. A method of manufacturing a hollow roll, wherein a stress concentration at a corner portion between the shaft portion and the end plate portion is taken into consideration, and a relationship between a stress applied to the shaft portion at the corner portion and a dimension of the hollow roll is determined. Based on the dimensions, the dimensions of the hollow roll are determined so that the stress applied to the shaft portion at the corner portion is equal to or less than an allowable stress, and a method of manufacturing a hollow roll is proposed, wherein the hollow roll is manufactured according to the dimensions. You.

[0017]

DESCRIPTION OF THE PREFERRED EMBODIMENTS As described above, the present invention takes into account the stress concentration in calculating the stress at the corner between the shaft and the end plate in the double-shaft hollow roll as described above. That is, the calculation method according to the present invention is basically expressed by the following equation (6). Stress σ = Stress concentration coefficient α × Load stress σ ₀ (6) Therefore, in order to obtain the stress in this stress calculation formula, it is necessary to first obtain the stress concentration coefficient α and the load stress σ ₀ . Further, in order to use the same expression in the design of the hollow roll, each of the stress concentration coefficient α and the applied stress σ ₀ is represented by the size of each portion of the roll, whereby the right side of Expression (6) is represented by the size of each portion of the roll. It is necessary to obtain the calculated stress calculation formula. Hereinafter, a procedure for deriving the stress calculation formula according to the request will be described in detail.

[Calculation Formula of Load Stress] FIG. 1 shows a basic model for deriving a formula for calculating a load stress (bending stress) σ ₀ at a corner portion between a shaft and a head plate in a two-shaft type hollow roll. Is shown. Now the diameter d, at both ends support the hollow cylinder 1 of length 2L, given the state plus the concentrated load W at each length a both end faces 1A, from 1A, the applied stress sigma ₀ at a portion of a next It can be expressed by the following equation (7). M is the bending moment at point a. still,
“a” assumes the distance from the end face of the hollow roll to the outer end plate, as understood in comparison with FIG. 2 or FIG. 3 described later.

[0019]

(Equation 1)

[Calculation formula of stress concentration coefficient] Regarding the stress concentration coefficient, the hollow roll is formed by a stepped round shaft 2 (R:
Radius of large diameter portion 2A, t: width of large diameter portion 2A, d: small diameter portion 2
The diameter of B, r: the radius of curvature of the corner between the large-diameter portion 2A and the small-diameter portion 2B) can be considered, and the calculation formula can be derived. That is, when the bending moment M is applied to the stepped round shaft 2, the stress concentration coefficient α can be expressed by the following equation (8). This equation defines parameters with reference to FIG. 5-20 on page 260 and FIG. 5-22 on page 270 of the Machine Design Handbook (Maruzen).

[0021]

(Equation 2)

Here, _Const is a constant. Also,
f, g, and h are parameters r / d, R / d, and t, respectively.
/ D.

For each of these functions, other functions can be fixed. For example, f (r / d) defines other functions g (R / d) and h (t / D) as constant.
As a specific method, there is a method of obtaining the relationship between r / d and α by FEM analysis or actual measurement using a load cell, and selecting a function corresponding to the relationship from, for example, a collection of mathematical formulas. As for the constant _Const , f (r / d) obtained by substituting each function determined as described above into equation (8).
G (R / d) · h (t / D) and α. [Specific Example 1 of Stress Calculation Formula; In the Case of Type B Hollow Roll] FIG. 3 shows the above-mentioned type B hollow roll (refer to FIG. 19), that is, the axial roll is separated from both ends of the tubular roll shell 10A. Outer end plate 11A and inner end plate 11B, and these outer and inner end plates 11A,
11B, and a shaft 12 welded to the shaft 12B.
Numeral 12 denotes a calculation model 10 of a hollow roll separated from another. In the figure, each symbol corresponds to the dimensions of each part of the model as shown below. w: uniform load in the width direction applied to the outer peripheral surface of the roll shell 10A a: axial length from the fulcrum of the shaft 12 to the outer end plate 11A b ₁ : length from the outer end plate 11A to the inner end plate 11B b ₂ : Length from the inner end plate 11B to the center in the width direction of the roll shell 10A c: Length of the region in which the uniform load w is applied in the roll shell 10A width direction d: Corner between the shaft 12 and the outer end plate 11A The diameter of the nearby shaft 12 r: the radius of curvature of the corner between the shaft 12 and the outer head plate 11A R: the radius of the outer head plate t ₁ : the thickness of the outer head plate 11A t ₂ : the thickness of the inner head plate 11B L: The length from the end of the shaft 12 to the center in the width direction of the roll shell 10A. Therefore, the load stress σ ₀ in this model can be expressed as follows from the above-described equation (7). M is the bending moment at point a.

[0024]

(Equation 3)

In order to derive an equation for calculating the stress concentration coefficient α, first, the dimensions (a, b ₁ ,
b ₂ , c, d, r, R, t ₁ , t ₂ ) when one is changed and the other is fixed, the maximum stress σ applied to the shaft 12 at the corner between the shaft 12 and the outer end plate 11. _max to F
Determined by EM analysis. Examples of the analysis are shown in FIGS. From these analysis results, it can be seen that parameters affecting σ _max are a, d, r, R and t ₁ . next,
The relationship among the stress concentration coefficient α and r / d, R / D, and t ₁ / d is determined as follows. That is, the load stress σ ₀ under the respective dimensional conditions used in the FEM analysis is obtained from the above-mentioned equation (9). Load stress σ at each dimensional condition obtained as a result
₀ corresponds to the maximum stress obtained by the FEM analysis, respectively. Therefore, the stress concentration coefficient α at each dimensional condition is obtained from the above-described equation (6) from the relationship between the two stresses under each dimensional condition. From this result, α and r / d, R /
D, the relationship with t ₁ / d is determined. FIGS. 13 to 15 show graphs of the relationship between α and r / d, R / D, and t ₁ / d obtained from the above-described analysis examples.

When such relations are obtained, a function corresponding to each relation is determined by referring to a collection of mathematical formulas.
Each function of the above equation (8) is determined. From the graphs of FIGS. 13 to 15, functions f (r / d), g (R / d), h (t / D)
Is as follows.

[0027]

(Equation 4)

Thereafter, f (r / d) · g (R / d) · h (t) obtained by substituting the determined functions into equation (8).
/ D) and determining the constant _{C Onst} based on the relationship between alpha.
FIG. 16 shows a graph of the relationship of the expression (10). Since the constant C _{on st} is determined to be 1.6 from the slope of this graph, by substituting this value and the function of equation (10) into equation (8), the equation for calculating the stress concentration coefficient α is derived as follows. You.

[0029]

(Equation 5)

The calculation formula of the applied stress σ ₀ (formula (9)) and the calculation formula of the stress concentration coefficient α (formula (11)) derived as described above are calculated according to the formula (6). By substituting into the equation, a stress calculation equation in which the maximum stress σ _max is expressed by the dimensions (a, d, r, R and t ₁ ) of each part of the hollow roll is obtained.

[Specific Example 2 of Stress Calculation Formula; Case of Type C Hollow Roll] On the other hand, as for the type C hollow roll shown in FIG. 20, as shown in FIG. Rolled end plate 21 to roll shell 20A
Considering the calculation model provided on each of the two end faces, a stress calculation formula can be derived in the same manner as in the specific example 1 described above.
The following equation (12) shows the result of deriving the equation for calculating the load stress σ _{0, and} the following equation (13) shows the result of deriving the equation for calculating the stress concentration coefficient α.
This is shown in Expression (14) and Expression (14). The derivation procedure of this example is the same as that of the specific example described above, and can be easily understood by those skilled in the art.

[0032]

(Equation 6)

[0033]

(Equation 7)

[0034]

(Equation 8)

Here, w: uniform load applied to the outer peripheral surface of the roll shell 20A in the width direction a: axial length from the fulcrum of the shaft 22 to the mirror plate 21 b: center of the roll shell 20A from the mirror plate 21 in the width direction C: Length in the width direction of the roll shell 20A in a region where a uniform load w is applied d: Diameter of the shaft 22 near the corner between the shaft 22 and the end plate 21 r: Corner portion between the shaft 22 and the end plate 21 R: radius of the end plate 21 t: plate thickness of the outer end plate 21 L: length from the end of the shaft 22 to the center in the width direction of the roll shell 20A [Application to design and manufacture of a hollow roll] In the stress calculation formula according to the present invention, the stress is represented by the dimensions of each part of the roll, and therefore can be used as it is in the design and manufacture of the roll. In other words, for the type B roll, the above-described load stress calculation formula (9)
And calculation formula of stress concentration factor (11) obtained by substituting the equation (6), on the basis of the maximum stress sigma _max stress calculation formula expressed in dimensions of the hollow roll each part, the maximum stress sigma _max
The dimensions of each part of the roll are determined so that the value is smaller than the allowable stress, and the hollow roll can be manufactured according to these dimensions.

On the other hand, the same applies to the type C roll, and the stress calculation is obtained by substituting the equation (12) for the applied stress and the equation (13) or (14) for the stress concentration coefficient into the equation (6). Based on the formula, the dimensions of each part of the roll are determined so that the maximum stress σ _max is smaller than the allowable stress, and the hollow roll can be manufactured according to these dimensions.

More specifically, the radius of curvature r of the corner portion and the thickness t (t ₁ ) of the head plate are determined by comparing the maximum stress with the allowable stress, and other dimensions (from the fulcrum of the shaft to the head plate). The length a in the axial direction, the diameter d of the shaft at the corner portion, the radius R of the end plate, and the like can be determined from the conditions of each facility (dimensions of the treated steel plate, tension applied to the steel plate, etc.).

As will be apparent from the following embodiment, since the maximum stress can be accurately obtained according to the stress calculation formula according to the present invention, the strength can be improved by designing using the stress calculation formula according to the present invention. A problem-free hollow roll can be obtained.

[Embodiment] The present invention is applicable to hollow rolls (that is, those designed by Luhr's formula) which are applicable to type B and type C rolls and used in actual factory equipment. Using the stress calculation formulas shown in Examples 1 and 2, the stress applied to the shaft at the corner between the shaft and the head plate (the outer head plate in type B) was calculated. As a comparative example, FEM analysis under the same conditions and stress calculation by Luhr's equation were also performed.

Table 2 shows the names of the hollow rolls used for the experiment.
Shows the type, dimensions, and whether there is any breakage trouble in the past.
The “presence or absence of breakage trouble in the past” indicates that the applicant has experienced breakage troubles (presence) and has not experienced (breakage) in the past regarding hollow rolls designed by the Luhr equation. Things.

Table 3 shows the results of the stress calculation. still,
In the table, the symbols of the roll dimensions correspond to the symbols of the respective dimensions of the model shown in FIG. 3 for the type B roll, and correspond to the symbols of the respective dimensions of the model shown in FIG. 17 for the type C roll. .

[0042]

[Table 2]

[0043]

[Table 3]

Considering the calculation results from Table 3, firstly, the maximum stress obtained by the Luhr's equation has a very large error of 30 to 50% as compared with that of the FEM analysis, and a variation is recognized. Moreover, as shown in Calculation Examples 2 to 5, Lu
It can be seen that the maximum stress obtained from the hr equation tends to be smaller than that of the FEM analysis. This tendency means that when a twin-shaft type hollow roll is designed using the Luhr's formula, there is a high possibility that the stress applied to the shaft at the corner between the shaft and the end plate will be underestimated. It is easy for a person skilled in the art to easily imagine that the hollow roll designed as described above causes shaft breakage due to insufficient strength of the corner portion. The presence or absence of breakage trouble shown in Table 2 also supports this.

On the other hand, in the example of the present invention, the error with respect to the maximum stress obtained by the FEM analysis is about 10% or less,
There is no discrepancy. Therefore, according to the stress calculation formula according to the present invention, it can be seen that an accurate stress value equivalent to that obtained by the FEM analysis can be obtained for a two-shaft type hollow roll.

[0046]

As described above, according to the present invention, it is possible to accurately calculate the stress applied to the shaft at the corner between the shaft and the end plate in the double shaft type hollow roll. Thus, it is possible to prevent breakage of a part from occurring and to prevent damage due to operation stoppage.

[Brief description of the drawings]

FIG. 1 is a diagram showing a basic model of a stress calculation formula.

FIG. 2 is a diagram showing a model for deriving a calculation formula for a stress concentration coefficient.

FIG. 3 is a longitudinal sectional view showing a model for deriving a stress calculation formula of a type B hollow roll.

FIG. 4 is an FEM analysis result.

FIG. 5 is an FEM analysis result.

FIG. 6 shows the results of FEM analysis.

FIG. 7 is an FEM analysis result.

FIG. 8 is an FEM analysis result.

FIG. 9 shows an FEM analysis result.

FIG. 10 shows the results of FEM analysis.

FIG. 11 shows an FEM analysis result.

FIG. 12 shows the result of FEM analysis.

FIG. 13 is a graph showing the relationship between r / d and α-1.

FIG. 14 is a graph showing the relationship between R / d and α-1.

FIG. 15 is a graph showing the relationship between t ₁ / d and α-1.

FIG. 16 f (r / d) · g (R / d) · h (t / D)
4 is a graph showing the relationship between α and α.

FIG. 17 is a longitudinal sectional view showing a model for deriving a stress calculation formula of a type C hollow roll.

FIG. 18 is a longitudinal sectional view schematically showing a type A hollow roll.

FIG. 19 is a longitudinal sectional view schematically showing a type B hollow roll.

FIG. 20 is a longitudinal sectional view schematically showing a type C hollow roll.

FIG. 21 is a longitudinal sectional view showing a model for deriving a stress calculation formula of a type A hollow roll.

FIG. 22 is a graph showing the relationship between ri / ra and each of k1 and L1.

[Explanation of symbols]

1 ... Basic model for deriving load stress calculation formula, 1A ... End plate,
2 ... Model for deriving a stress concentration coefficient calculation formula, 2A ... Large diameter portion, 2B small diameter portion, 10 ... Model for deriving a stress calculation formula of a type B hollow roll, 11A ... Outer end plate, 11B ... Inner end plate, 12 ... Shaft, 20 ... Model for deriving the stress calculation formula of type C hollow roll, 21 ... Mirror body, 22 ... Shaft, 100
... type A hollow roll, 101 ... head plate, 102 ... shaft,
110: Type B hollow roll, 111: End plate, 112
... Shaft, 120 ... Type C hollow roll, 121 ... End plate,
122 ... end plate part.

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁶ Identification symbol FI // G06F 17/00 G06F 15/20 D

Claims (3)

[Claims] 1. A hollow roll having at least one end plate at each end and a shaft integral with the end, and having two shafts separated from each other. A stress calculation method for a hollow roll, wherein a stress applied to a shaft portion at a corner portion is calculated in consideration of a stress concentration at the corner portion. 2. A stress applied to a shaft portion at the corner portion and at least a function of a thickness of the head portion, a radius of the head portion, a radius of curvature of the corner portion, and a shaft diameter of the shaft. The stress calculation method for a hollow roll according to claim 1, wherein the stress applied to the shaft portion at the corner portion is calculated based on the stress concentration coefficient. 3. A method of manufacturing a hollow roll having at least one end plate and a shaft integral with the end plate at each of both ends, wherein both shafts are separated from each other. The stress applied to the shaft portion at the corner portion is allowed based on the relationship between the stress applied to the shaft portion at the corner portion and the dimension of the hollow roll, taking into account the stress concentration at the corner portion with the end plate portion. A method of manufacturing a hollow roll, comprising determining a size of the hollow roll so as to be equal to or less than a stress, and manufacturing the hollow roll according to the size.