Zhang et al 2019d - Revision history

Rimni at 11:53, 12 February 2021

2021-02-12T11:53:01Z

Show changes

Scipediacontent at 10:31, 26 March 2020

2020-03-26T10:31:52Z

Rimni at 08:30, 25 March 2020

2020-03-25T08:30:58Z

Rimni at 08:29, 25 March 2020

2020-03-25T08:29:47Z

Rimni at 08:29, 25 March 2020

2020-03-25T08:29:05Z

Rimni at 08:23, 25 March 2020

2020-03-25T08:23:32Z

Rimni at 08:22, 25 March 2020

2020-03-25T08:22:45Z

Rimni at 08:22, 25 March 2020

2020-03-25T08:22:17Z

Rimni at 15:57, 24 March 2020

2020-03-24T15:57:45Z

Rimni at 15:55, 24 March 2020

2020-03-24T15:55:33Z

@@ Line 222: / Line 222: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"| [[Image:Draft_Test_882172868-image14-c.png|460px]]
+|style="padding:10px;"| [[Image:Zhang_et_al_2019d_2676_Figura7.png|460px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 7'''. Functional fitting curve of maximum structural stress and fillet radius
@@ Line 276: / Line 276: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"| [[Image:Draft_Test_882172868-image18-c.png|460px]]
+|style="padding:10px;"| [[Image:Zhang_et_al_2019d_7237_Figura9.png|460px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding-bottom:10px;"| '''Figure 9'''. Functional fitting curve of minimum fatigue life and fillet radius

← Older revision		Revision as of 08:30, 25 March 2020
Line 197:		Line 197:


−	Based on the above finite element model, the stress nephogram of the fork was calculated by static solution, as illustrated in Figure 5. Figure 5 ~~clearly~~ indicates that under concentrated load, the fork has stress concentration problem in the fillet area of the fork root. The finite element calculation results are in accordance with the theoretical force analysis, which verifies the accuracy of the model to a certain extent. However, the maximum stress of the structure is 144.5 MPa, which is greater than the allowable stress 119.8 MPa. When the fork is subjected to continuous load, it may cause the surface to be damaged or even broken due to insufficient strength. Therefore, it is necessary to carry out structural improvement design on the original fork, and the main part of optimization is the stress concentration area, that is, the fillet area of the fork root.	+	Based on the above finite element model, the stress nephogram of the fork was calculated by static solution, as illustrated in Figure 5. Clearly Figure 5 indicates that under concentrated load, the fork has stress concentration problem in the fillet area of the fork root. The finite element calculation results are in accordance with the theoretical force analysis, which verifies the accuracy of the model to a certain extent. However, the maximum stress of the structure is 144.5 MPa, which is greater than the allowable stress 119.8 MPa. When the fork is subjected to continuous load, it may cause the surface to be damaged or even broken due to insufficient strength. Therefore, it is necessary to carry out structural improvement design on the original fork, and the main part of optimization is the stress concentration area, that is, the fillet area of the fork root.

	{\| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"		{\| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"

@@ Line 156: / Line 156: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math display="inline">n\leq \frac{{\sigma }_s}{{\sigma }_{max}}=\frac{539}{119.06}\approx 4.5</math>
+| <math display="inline">n\leq \displaystyle\frac{{\sigma }_s}{{\sigma }_{max}}=\displaystyle\frac{539}{119.06}\approx 4.5</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (5)

@@ Line 115: / Line 115: @@
 |}
-Under the concentrated load <math>P</math>, the horizontal section is subjected to bending moment and shearing force, while the vertical section is subjected to bending moment and tension force. The vertical section below <math>A-A</math> section is dangerous, and the maximum normal stress of the dangerous section is the sum of bending stress and axial stress. The bending stress and axial stress are obtained by the following formulas, respectively.
+Under the concentrated load <math>P</math>, the horizontal section is subjected to bending moment and shearing force, while the vertical section is subjected to bending moment and tension force. The vertical section below <math>A-A</math> section is dangerous, and the maximum normal stress of the dangerous section is the sum of bending stress and axial stress. The bending stress and axial stress are obtained by the following formulas, respectively
 {| class="formulaSCP" style="width: 100%; text-align: center;"
@@ Line 149: / Line 149: @@
 |}
-where <math>M_\max</math> and <math>W</math> are the maximum bending moment and bending section modulus, respectively; <math>F</math> is the cross-section area of vertical section;  <math display="inline">{\sigma }_s</math> is the material yield strength, and for the 40Cr,  <math display="inline">{\sigma }_s</math> is not less than 539 MPa; <math>N</math> is the structural safety factor, which can be calculated by Eq.(4).
+where <math>M_\max</math> and <math>W</math> are the maximum bending moment and bending section modulus, respectively; <math>F</math> is the cross-section area of vertical section;  <math display="inline">{\sigma }_s</math> is the material yield strength, and for the 40Cr,  <math display="inline">{\sigma }_s</math> is not less than 539 MPa; <math>N</math> is the structural safety factor, which can be calculated by Eq.(4)
 {| class="formulaSCP" style="width: 100%; text-align: center;"

@@ Line 24: / Line 24: @@
 Fork’s related structural design and detail have a significant impact on the overall performance of a forklift. In this paper, the structural stress analysis and strength calculation of the fork were carried out firstly, and the rated load calculations considering dynamic and unbalanced conditions were performed. Also, the restraint conditions were analyzed. Then, a finite element model was established using ANSYS software. In particular, the fork’s structure was optimized by increasing the fillet radius of the fork root and the variation rules between the fillet radius and the maximum structural stress and minimum fatigue life were numerically studied, which was in accordance with the mathematical models of ExpAssoc and Logistic regression, and the corresponding fitting coefficients of ''R''<sup>2</sup> was respectively equal to 0.99 and 0.96. Overall, the stress concentration issue of the fork root was improved and the structural strength perquisite was satisfied when using a fillet radius of 75 ''mm''. Both the numerical calculations and theorized mechanical analysis show consistency, where the stress concentration was observed in the fork root’s fillet area, testifying the accuracy of the established finite element model. The numerous methods employed in this work lay an important theoretical basis for the structural optimization of the target fork.
-'''Keywords:'''Fork, finite element modeling, stress analysis, fatigue life, structural optimization
+'''Keywords:''' Fork, finite element modeling, stress analysis, fatigue life, structural optimization
 ==1. Introduction==

← Older revision		Revision as of 08:22, 25 March 2020
Line 229:		Line 229:

	Figure 6 makes it clear that the stress concentration always exists in the fillet area of the fork root, and the maximum stress decreases with the increase of the fillet radius, which is mainly because the fillet structural of fork root is strengthened. This conclusion is consistent with the research results in Ref. [19]. And the maximum stress with the fillet radius of 75mm is 117.98 MPa, less than the 1.82 MPa of the allowable stress.		Figure 6 makes it clear that the stress concentration always exists in the fillet area of the fork root, and the maximum stress decreases with the increase of the fillet radius, which is mainly because the fillet structural of fork root is strengthened. This conclusion is consistent with the research results in Ref. [19]. And the maximum stress with the fillet radius of 75mm is 117.98 MPa, less than the 1.82 MPa of the allowable stress.
−

	Figure 7 visually reflects that the maximum stress of the fork root varies non-linearly with the increase of the fillet radius. That is, when the radius of fillet is less than 45 mm, the maximum stress decreases rapidly, and the fillet radius has a great influence on the structure stress; when the radius of fillet is greater than 45 mm, the maximum stress decreases to be stable, which means that the fillet radius has little influence on the structure stress; the fitting results demonstrate that the correlation between the fillet radius and the maximum stress is in accordance with ExpAssoc model, and the mathematical model is expressed as		Figure 7 visually reflects that the maximum stress of the fork root varies non-linearly with the increase of the fillet radius. That is, when the radius of fillet is less than 45 mm, the maximum stress decreases rapidly, and the fillet radius has a great influence on the structure stress; when the radius of fillet is greater than 45 mm, the maximum stress decreases to be stable, which means that the fillet radius has little influence on the structure stress; the fitting results demonstrate that the correlation between the fillet radius and the maximum stress is in accordance with ExpAssoc model, and the mathematical model is expressed as

@@ Line 242: / Line 242: @@
 | style="width: 5px;text-align: right;white-space: nowrap;" | (6)
 |}
 In the formula, the specific values of the fitting parameters are listed in Figure 7. The fitting coefficients of <math>R^2</math> reaches 0.99, indicating that ExpAssoc model describes the variation between the fillet radius and the maximum stress well.
@@ Line 263: / Line 262: @@
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7)
 |}
 In the formula, the specific values of the fitting parameters are listed in Figure 9. It can be found that when the fillet radius is less than 45mm, the slope of the curve is larger, indicating that the minimum structure fatigue life increases greatly, and the fatigue life of the structure is significantly affected; Conversely, the influence of the larger fillet radius on the fatigue life becomes smaller, which also corresponds to the relationship between the fillet radius and the maximum stress.

@@ Line 51: / Line 51: @@
 The model equipment consists of three parts: a fork frame, four forks and four fastening screws. Actually, cargoes with a certain load are placed directly on the fork. Under the action of the hydraulic cylinder system, the door frame drives the fork to realize the lifting, descending and loading and unloading of cargoes. Four forks are evenly and symmetrically distributed on the fork device. In order to facilitate force analysis and later numerical calculation, only a single fork was taken to analyze, and its structural parameters were specified by relevant standards [15,19].
-As is shown in Figure 2, the main structural parameters of the fork are horizontal length ''l'', vertical section height ''h'' and vertical section size ''a''×''b'', in which ''a'' is the thickness and ''b'' is the width, ''R ''is the fillet radius of the fork root.
+As is shown in Figure 2, the main structural parameters of the fork are horizontal length <math>l</math>, vertical section height <math>h</math> and vertical section size <math>a\times b</math>, in which <math>a</math> is the thickness and <math>b</math> is the width, <math>R</math> is the fillet radius of the fork root.
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
@@ Line 61: / Line 61: @@
-The lifting weight ''Q'' and the load center distance ''c'' basically determine the overall appearance size of the fork. According to ISO/DIS 1214-79 standard, when the rated load of this forklift is 3 tons (<math>Q=3</math>T), the load center distance is ''c''=500mm. The basic size parameters of the fork were obtained from the relevant standards and measurements, as listed in Table 1.
+The lifting weight <math>Q</math> and the load center distance <math>c</math> basically determine the overall appearance size of the fork. According to ISO/DIS 1214-79 standard, when the rated load of this forklift is 3 tons (<math>Q=3</math>T), the load center distance is <math>c=500</math>mm. The basic size parameters of the fork were obtained from the relevant standards and measurements, as listed in Table 1.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 <span style="text-align: center; font-size: 75%;">'''Table 1. '''Structural parameters of the fork model (Unit: mm)</span></div>
-{| style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:45%;"
+{| style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:55%;"
 |-
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''Parameters'''
@@ Line 76: / Line 76: @@
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>l=1070</math>
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Two hinge pivot center distance
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'<math>d=512</math>
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>d=512</math>
 |-
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Vertical Height
@@ Line 88: / Line 88: @@
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>R=25</math>
 |}
 ===2.2 Force analysis and strength calculation===

@@ Line 61: / Line 61: @@
-The lifting weight ''Q'' and the load center distance ''c'' basically determine the overall appearance size of the fork. According to ISO/DIS 1214-79 standard, when the rated load of this forklift is 3 tons (''Q''=3''T''), the load center distance is ''c''=500mm. The basic size parameters of the fork were obtained from the relevant standards and measurements, as listed in Table 1.
+The lifting weight ''Q'' and the load center distance ''c'' basically determine the overall appearance size of the fork. According to ISO/DIS 1214-79 standard, when the rated load of this forklift is 3 tons (<math>Q=3</math>T), the load center distance is ''c''=500mm. The basic size parameters of the fork were obtained from the relevant standards and measurements, as listed in Table 1.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-<span style="text-align: center; font-size: 75%;">'''Table 1. '''Structural parameters of the fork model (Unit: ''mm'')</span></div>
+<span style="text-align: center; font-size: 75%;">'''Table 1. '''Structural parameters of the fork model (Unit: mm)</span></div>
 {| style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:45%;"
@@ Line 74: / Line 74: @@
 |-
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Horizontal length
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|''l''=1070
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>l=1070</math>
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Two hinge pivot center distance
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|''d''=512
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'<math>d=512</math>
 |-
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Vertical Height
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|''h''=655
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>h=655</math>
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Extension distance
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|''e''=73
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>e=73</math>
 |-
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Section size
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|''a''=45; ''b''=125
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>a=45</math>; <math>b=125</math>
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Fillet radius of the fork root
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|''R''=25
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<math>R=25</math>
 |}