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MODELING OF ELASTIC STRAIGHTENING IN THE PROCESS OF PRODUCTION OF COIL (HELICAL) CYLINDRICAL SPRINGS Mirza Krajnović1, Adnan Mustafić2, Mensur Demirović3 Summary: Production of coil cylindrical springs is the most common process of metals shaping by the process of cold deformation. Accuracy is the most important factor in spring production industry. One of the main occurences during manufacturing of these parts is elastic straightening i.e. elastic deformation in the material after removal of tool. After formation, elastic straightening causes deviation from designed (desirable) shape and as a result products have quality problem and difficulties during installation. Hence, control of elastic streightening in the process of production of coil (helical) components is one of the key problems during production. This paper presents results of physical experiment aiming to obtain an adequate regression models which serve for anticipation of elastic streightening and force in the spring at certain length of deformation, which is in function of material and its constructive and geometrical characteristics. Key words: Coil (helical) springs, elastic straightening, mathematical model, planning of experiments 1. INTRODUCTION Spring bending process on machine WIM 4 CNC is done by winding of wire on tool (mandrel). Subsequent to winding is release process i.e. unwinding of spring in oposite direction. Result of this process is increase of spring diameter in comparison with mandrel for the value of elastic straightening.In literature, there are no expressions for calculation (analysis) of elastic straightening in the process of spring bending, therefore, selection of mandrel is done based on experience and by means of „try – make mistake“ method which implies more time for machine adjustments, rejections with view to selection of material and in the end results in an increase of spring closing price. Inner diameter, number of twists and spring height is changed during the process of spring bending due to elastic testing.Intensity of elastic straightening dependson series of factors: wire material, mandrel geometry, winding torque, winding speed etc.Unlike other types of processings, variables which are influencingelastic 1

MSc. MirzaKrajnović, Gradačac, Opruge Krajnović d.o.o, ([email protected]) MSc.Adnan Mustafić, Tuzla, Faculty of Mechanical Engineering ([email protected]) 3 MSc. Mensur Demirović, Tuzla, Tehnopetrol d.o.o, ([email protected]) 2

Mirza Krajnović, Adnan Mustafić, Mensur Demirović

streightening are not clearly defined in available literature related to process of spring bending. In order to get corresponding diameter, defined in technical documentation, it is necessary to select suitable mandrel diameter. An adequate mathematical model which links value of elastic straightening of known spring parameters would allow direct selection of mandrel diameter, enable decrease of initial rejections and reduce time required for machine adjustment. 2. PLANNING OF EXPERIMENTAL RESEARCHING Figure 1 presents model of spring bending process. 1. Subsequent to spring bending process is process of elastic straightening when spring diameter is increased in comparison to mandrel diameter. 2. Intensity of elastic straightening depends on: material tensile strength (σ m), material diameter (dz), mandrel diameter (Dt), number of twists (z), bending torque (Ms), distance between the twists (h), bending speed (vs) etc. Input parameters are: material (different tensile strength σv,c and n); tool geometry (different mandrel diameters); geometry of wire (different wire diameters). Output parameters are: inner spring diameter (D); force applied by spring at length l (F(l)).

Fig 1. Schematic layout of input/ output parameters during modeling of coil cylindrical springs bending process In order to make experiment for selection of the most influential factors of material properties, uniaxial tensile test was carried out on spring materials of different tensile strength which is most commonly used in the process of production of coil cylindrical springs. Correlation analysis was performed in order to identify and select material properties which influence elastic straightening. Parameters ε r, Fu of spring steel were defined previously by uniaxial tensile test of wire EN 10270-1. Table 1.Results of Correlation analysis of material properties Km φ σn C Y

2

Km

φ

σn

C

Y

1 0,358918 0,391567 0,873875 -0,12344 X4

1 -0,4689 0,747855 -0,93801 X1

1 -0,00619 0,634902 X2

1 -0,54209 X3

1

Modeling of elastic straightening in the process of production of coil (helical) cilindrical springs

Due to constraints of different variable values φ, it was not possible to combine them in the experiment, thus second-ranked value of material parameter δn was taken into account. Beside that, division of material into classes based on value δn was performed in accordance with standard for spring material EN 10270 – 1. This represents an extra reason for defining of δnas variable. For the purpose of selection of the most influential parameters (apart from wire diameter) related to spring geometry, an experiment was carried out. Correlation analysis was performed based on this experiment. Fluctuation levels of variable K (distance between the twists) were defined in the experiment which included pressure, tension and torsion springs, which were distinguished (during bending on machine WIM 4 CNC) based on the distance between the twists. Correlation analysis was carried out based on obtained results with aim of identification of spring parameters whose change causes significant alteration of elastic straightening output variable. Results indicate the following: Increase of distance between the twists increases elastic straightening because it enlarges curvature radius during bending, however, there is no high level of correlation. Increase of speed significantly affects intensity of elastic straightening what is expected considering it is a word about cold deformation of material at low bending speed. When selecting varying value of mandrel diameter Dt it is necessary to pay attention to wire diameter up to which is possible to bend the spring. If mandrel diameter is bigger than allowed, it comes to deformation during bending process and as a result product cannot be bent to desired shape.

Fig 2. Demonstration of spring bent at bigger mandrel diameter than allowed Figure 3 presents max mandrel diameters which will not cause deformation during bending process. Deformed spring is demonstrated in Fig 2.

Fig 3.Demonstration of acceptable mandrel diameters and wire diameters 3

Mirza Krajnović, Adnan Mustafić, Mensur Demirović

Based on constraints related to spring deformation (Fig 2 and 3), and in order to include mentioned fluctuation levels, the following independent and flexible experiments will be divided in two groups: Experiment 1 – includes wire diameter from 1,00 to 3,00 mm and mandrel diameter from 14,00 to 16,00 mm. Experiment 2 - includes wire diameter from 2,00 to 3,00 mm and mandrel diameter from 20,00 to 30,00 mm. 3. EXECUTION OF EXPERIMENT AND ANALYSIS OF RESULTS For Experiment 1 were used complete a multifactorial orthogonal plan an experiment with three replicates at each point of the experiment (a total of 81 experiments), while in Experiment 2 wire diameter varied on two levels (a total of 54 experiments). Based on plan matrixes given in the Table 1 and as a result of regression analysis, the following regression models were obtained: Model for intensity of elastic straightening ΔEI i.e. difference between spring diameters after elastic straightening and mandrel diameter: 2 2 ΔEIH = -3,163 + 1,906dz + 0,04586dt -0,407dzDt + 0,0017n + 0,647dz 0,000338ndz CI Model for force in spring at defined length FH,: 2 FH = -173,48 + 27,01dz - 2,356dzdt - 0,00123ndt - 56,46dz + 0,01589ndz + 30,18dt 0,922dt CI Here, subscript „H“ is related to output variables after cold deformation of springs. Aforesaid regression models are adequate (F-test) and have high levels of 2 2 determination: R ΔEI=0,99, a R FH=0,95 which indicates high matching level of fitted models and experimental data. 2

4, 5

6,0

4,0 5, 0 3, 5 4, 0

2, 5

EI

EI

3,0

3, 0

2,0 1, 5

2,0

1,0

2200, 0

15,6

1, 0 0, 5 0,0 1, 0 1,2

1933,3 1666, 7 1,4

1,7 dz

1,9

2, 1

2,3

2,6

1400, 0 2, 8

3,0

14,7 Sn

0, 0 1,0

13,8 1, 2

dt

12,9 1, 4

1, 7 dz

1, 9

2,1

2, 3

2, 6

12, 0 2, 8

3,0

Fig 4. Dependency of elastic straightening on tensile strength, wire diameter and mandrel diameter (*Sn=n) Above figure clearly shows that with decrease of wire diameter elastic straightening increases and this increase is even more emphasized in cases of bigger mandrel diameters (this is highlighted by significance of coefficient with interaction of these two values). In the same way, increase of tensile strength and mandrel diameter (in diapason of their fluctuation) causes increase of elastic straightening, as expected.

4

Modeling of elastic straightening in the process of production of coil (helical) cilindrical springs

„Experiment 2“ includes wire diameters from 2,00 to 3,00 mm and mandrel diameters in range from 20,00 to 30,00 mm. Models for intensity of elastic straightening and spring force (before heat treatment) were gained after regression analysis had been conducted:

ΔEIH = -5,015 + 2,293dz - 0,00311ndz + 3,14618E-06n + 0,350dt CI 2 FH = - 34,03 + 35,99dz - 1,069dzdt + 0,134dt + 0,04209n - 0,000637ndt - 3,781dt 2

5,86285E-06n CI 2 Both regression models are adequate and have high levels of determination R 2 =0,91& R FH=0,958. 2

6,0

ΔEIH

8,0 7, 0

5, 0 6,0 4,0

EI

EI

5, 0 3,0

4,0 3, 0

2, 0 2,0 2111,1

1, 0

1755,6

0,0 2, 0 2,1

Sn

2,3

2, 4

2, 6

2, 7

2,8

dz

2, 0 2,1

1400, 0 2,9

24,4

0,0

1577,8 2,2

28,9 26, 7

1, 0

1933,3

3, 0

dt

22, 2 2,2

2,3 dz

2,4

2,6

2, 7

2,8

20,0 2,9

3,0

Fig 5. Dependency of elastic straightening on tensile strength, wire diameter and mandrel diameter (*Sn=n) Fig 5 clearly shows that increase of tensile strength leads to increase of elastic straightening but this dependency is not linear. In the same way, decrease of wire diameter leads to increase of elastic straightening what is even more emphasized in cases of bigger mandrel diameters. Regression model which predicts force in the spring, at defined route, is also 2 adequate and has high level of determination R =0,973. 20, 0

30, 0

18,0 25, 0

16, 0 14,0

20,0

10,0

Ft

Ft

12,0 15,0

8,0 10, 0

6, 0 4,0

2111,1 1933,3

2, 0

1755,6

0,0 2, 0 2, 1 2, 2 2, 3 dz

1577,8 2,4

2, 6

2,7

2,8

1400, 0 2,9

3, 0

Sn

3, 0

5,0 2,7 0,0 2, 3 30,0 28, 9 27, 8 26, 7 25, 6 24,4 2, 0 23, 3 22, 2 21, 1 20,0 dt

dz

Fig 6. Dependency of force on tensile strength, wire diameter and mandrel diameter (*Sn=n) Tensile strength has equal impact except that the intensity of that impact is considerably lower (Fig on the left). On the other hand, decrease of mandrel diameter 5

Mirza Krajnović, Adnan Mustafić, Mensur Demirović

intensifies force in the spring what is more emphasized in case of max values of wire diameters (Fig on the right). 4. CONCLUSION On the basis of conducted experimental testing and analysis of result, the following basic conclusions can be made: Experimental-mathematical modeling of intensity of elastic straightening and force in the spring (as dependant and flexible values) in the function of material, spring and mandrel geometry (after bending in cold condition by constant torque and after heat treatment) leads to creation of adequate regression models which are suitable for anticipation and which enable the following: To select suitable tool (knowing the value of elastic straightening) using directly regression model and in that way avoid „try – make mistake“ method; To predict, at early stage, (knowing the force in spring for defined deformation level) characteristics of spring which is in early phase of design; Using the model for anticipation instead of traditional approach „try-make mistake“ we are able to reduce time required for preparation and adjusting of machine and to reduce rejections owing to selection of suitable tool. Regression models for the same dependant and flexible values are also adequate and have high determination coefficient and thus can be used for anticipation too. 5. LITERATURE [1] Krajnović, M. MODELING OF ELASTIC STREIGHTENING IN THE PROCESS OF PRODUCTION OF COIL CYLINDRICAL SPRINGS (Master thesis), Faculty of Mechanical Engineering in Tuzla; Tuzla 2012. [2] Ekinović, S. METHODS OF STATISTICAL ANALYSIS in Microsoft Excel, Faculty of Mechanical Engineering in Zenica; Zenica 1997. [3] Jurković, M. MATHEMATICAL MODELING OF ENGINEERING PROCESSES AND SYSTEMS, Faculty of Mechanical Engineering in Bihać; Bihać 1999.

6

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MODELING OF ELASTIC STRAIGHTENING IN THE PROCESS OF PRODUCTION OF COIL (HELICAL) CYLINDRICAL SPRINGS Mirza Krajnović1, Adnan Mustafić2, Mensur Demirović3 Summary: Production of coil cylindrical springs is the most common process of metals shaping by the process of cold deformation. Accuracy is the most important factor in spring production industry. One of the main occurences during manufacturing of these parts is elastic straightening i.e. elastic deformation in the material after removal of tool. After formation, elastic straightening causes deviation from designed (desirable) shape and as a result products have quality problem and difficulties during installation. Hence, control of elastic streightening in the process of production of coil (helical) components is one of the key problems during production. This paper presents results of physical experiment aiming to obtain an adequate regression models which serve for anticipation of elastic streightening and force in the spring at certain length of deformation, which is in function of material and its constructive and geometrical characteristics. Key words: Coil (helical) springs, elastic straightening, mathematical model, planning of experiments 1. INTRODUCTION Spring bending process on machine WIM 4 CNC is done by winding of wire on tool (mandrel). Subsequent to winding is release process i.e. unwinding of spring in oposite direction. Result of this process is increase of spring diameter in comparison with mandrel for the value of elastic straightening.In literature, there are no expressions for calculation (analysis) of elastic straightening in the process of spring bending, therefore, selection of mandrel is done based on experience and by means of „try – make mistake“ method which implies more time for machine adjustments, rejections with view to selection of material and in the end results in an increase of spring closing price. Inner diameter, number of twists and spring height is changed during the process of spring bending due to elastic testing.Intensity of elastic straightening dependson series of factors: wire material, mandrel geometry, winding torque, winding speed etc.Unlike other types of processings, variables which are influencingelastic 1

MSc. MirzaKrajnović, Gradačac, Opruge Krajnović d.o.o, ([email protected]) MSc.Adnan Mustafić, Tuzla, Faculty of Mechanical Engineering ([email protected]) 3 MSc. Mensur Demirović, Tuzla, Tehnopetrol d.o.o, ([email protected]) 2

Mirza Krajnović, Adnan Mustafić, Mensur Demirović

streightening are not clearly defined in available literature related to process of spring bending. In order to get corresponding diameter, defined in technical documentation, it is necessary to select suitable mandrel diameter. An adequate mathematical model which links value of elastic straightening of known spring parameters would allow direct selection of mandrel diameter, enable decrease of initial rejections and reduce time required for machine adjustment. 2. PLANNING OF EXPERIMENTAL RESEARCHING Figure 1 presents model of spring bending process. 1. Subsequent to spring bending process is process of elastic straightening when spring diameter is increased in comparison to mandrel diameter. 2. Intensity of elastic straightening depends on: material tensile strength (σ m), material diameter (dz), mandrel diameter (Dt), number of twists (z), bending torque (Ms), distance between the twists (h), bending speed (vs) etc. Input parameters are: material (different tensile strength σv,c and n); tool geometry (different mandrel diameters); geometry of wire (different wire diameters). Output parameters are: inner spring diameter (D); force applied by spring at length l (F(l)).

Fig 1. Schematic layout of input/ output parameters during modeling of coil cylindrical springs bending process In order to make experiment for selection of the most influential factors of material properties, uniaxial tensile test was carried out on spring materials of different tensile strength which is most commonly used in the process of production of coil cylindrical springs. Correlation analysis was performed in order to identify and select material properties which influence elastic straightening. Parameters ε r, Fu of spring steel were defined previously by uniaxial tensile test of wire EN 10270-1. Table 1.Results of Correlation analysis of material properties Km φ σn C Y

2

Km

φ

σn

C

Y

1 0,358918 0,391567 0,873875 -0,12344 X4

1 -0,4689 0,747855 -0,93801 X1

1 -0,00619 0,634902 X2

1 -0,54209 X3

1

Modeling of elastic straightening in the process of production of coil (helical) cilindrical springs

Due to constraints of different variable values φ, it was not possible to combine them in the experiment, thus second-ranked value of material parameter δn was taken into account. Beside that, division of material into classes based on value δn was performed in accordance with standard for spring material EN 10270 – 1. This represents an extra reason for defining of δnas variable. For the purpose of selection of the most influential parameters (apart from wire diameter) related to spring geometry, an experiment was carried out. Correlation analysis was performed based on this experiment. Fluctuation levels of variable K (distance between the twists) were defined in the experiment which included pressure, tension and torsion springs, which were distinguished (during bending on machine WIM 4 CNC) based on the distance between the twists. Correlation analysis was carried out based on obtained results with aim of identification of spring parameters whose change causes significant alteration of elastic straightening output variable. Results indicate the following: Increase of distance between the twists increases elastic straightening because it enlarges curvature radius during bending, however, there is no high level of correlation. Increase of speed significantly affects intensity of elastic straightening what is expected considering it is a word about cold deformation of material at low bending speed. When selecting varying value of mandrel diameter Dt it is necessary to pay attention to wire diameter up to which is possible to bend the spring. If mandrel diameter is bigger than allowed, it comes to deformation during bending process and as a result product cannot be bent to desired shape.

Fig 2. Demonstration of spring bent at bigger mandrel diameter than allowed Figure 3 presents max mandrel diameters which will not cause deformation during bending process. Deformed spring is demonstrated in Fig 2.

Fig 3.Demonstration of acceptable mandrel diameters and wire diameters 3

Mirza Krajnović, Adnan Mustafić, Mensur Demirović

Based on constraints related to spring deformation (Fig 2 and 3), and in order to include mentioned fluctuation levels, the following independent and flexible experiments will be divided in two groups: Experiment 1 – includes wire diameter from 1,00 to 3,00 mm and mandrel diameter from 14,00 to 16,00 mm. Experiment 2 - includes wire diameter from 2,00 to 3,00 mm and mandrel diameter from 20,00 to 30,00 mm. 3. EXECUTION OF EXPERIMENT AND ANALYSIS OF RESULTS For Experiment 1 were used complete a multifactorial orthogonal plan an experiment with three replicates at each point of the experiment (a total of 81 experiments), while in Experiment 2 wire diameter varied on two levels (a total of 54 experiments). Based on plan matrixes given in the Table 1 and as a result of regression analysis, the following regression models were obtained: Model for intensity of elastic straightening ΔEI i.e. difference between spring diameters after elastic straightening and mandrel diameter: 2 2 ΔEIH = -3,163 + 1,906dz + 0,04586dt -0,407dzDt + 0,0017n + 0,647dz 0,000338ndz CI Model for force in spring at defined length FH,: 2 FH = -173,48 + 27,01dz - 2,356dzdt - 0,00123ndt - 56,46dz + 0,01589ndz + 30,18dt 0,922dt CI Here, subscript „H“ is related to output variables after cold deformation of springs. Aforesaid regression models are adequate (F-test) and have high levels of 2 2 determination: R ΔEI=0,99, a R FH=0,95 which indicates high matching level of fitted models and experimental data. 2

4, 5

6,0

4,0 5, 0 3, 5 4, 0

2, 5

EI

EI

3,0

3, 0

2,0 1, 5

2,0

1,0

2200, 0

15,6

1, 0 0, 5 0,0 1, 0 1,2

1933,3 1666, 7 1,4

1,7 dz

1,9

2, 1

2,3

2,6

1400, 0 2, 8

3,0

14,7 Sn

0, 0 1,0

13,8 1, 2

dt

12,9 1, 4

1, 7 dz

1, 9

2,1

2, 3

2, 6

12, 0 2, 8

3,0

Fig 4. Dependency of elastic straightening on tensile strength, wire diameter and mandrel diameter (*Sn=n) Above figure clearly shows that with decrease of wire diameter elastic straightening increases and this increase is even more emphasized in cases of bigger mandrel diameters (this is highlighted by significance of coefficient with interaction of these two values). In the same way, increase of tensile strength and mandrel diameter (in diapason of their fluctuation) causes increase of elastic straightening, as expected.

4

Modeling of elastic straightening in the process of production of coil (helical) cilindrical springs

„Experiment 2“ includes wire diameters from 2,00 to 3,00 mm and mandrel diameters in range from 20,00 to 30,00 mm. Models for intensity of elastic straightening and spring force (before heat treatment) were gained after regression analysis had been conducted:

ΔEIH = -5,015 + 2,293dz - 0,00311ndz + 3,14618E-06n + 0,350dt CI 2 FH = - 34,03 + 35,99dz - 1,069dzdt + 0,134dt + 0,04209n - 0,000637ndt - 3,781dt 2

5,86285E-06n CI 2 Both regression models are adequate and have high levels of determination R 2 =0,91& R FH=0,958. 2

6,0

ΔEIH

8,0 7, 0

5, 0 6,0 4,0

EI

EI

5, 0 3,0

4,0 3, 0

2, 0 2,0 2111,1

1, 0

1755,6

0,0 2, 0 2,1

Sn

2,3

2, 4

2, 6

2, 7

2,8

dz

2, 0 2,1

1400, 0 2,9

24,4

0,0

1577,8 2,2

28,9 26, 7

1, 0

1933,3

3, 0

dt

22, 2 2,2

2,3 dz

2,4

2,6

2, 7

2,8

20,0 2,9

3,0

Fig 5. Dependency of elastic straightening on tensile strength, wire diameter and mandrel diameter (*Sn=n) Fig 5 clearly shows that increase of tensile strength leads to increase of elastic straightening but this dependency is not linear. In the same way, decrease of wire diameter leads to increase of elastic straightening what is even more emphasized in cases of bigger mandrel diameters. Regression model which predicts force in the spring, at defined route, is also 2 adequate and has high level of determination R =0,973. 20, 0

30, 0

18,0 25, 0

16, 0 14,0

20,0

10,0

Ft

Ft

12,0 15,0

8,0 10, 0

6, 0 4,0

2111,1 1933,3

2, 0

1755,6

0,0 2, 0 2, 1 2, 2 2, 3 dz

1577,8 2,4

2, 6

2,7

2,8

1400, 0 2,9

3, 0

Sn

3, 0

5,0 2,7 0,0 2, 3 30,0 28, 9 27, 8 26, 7 25, 6 24,4 2, 0 23, 3 22, 2 21, 1 20,0 dt

dz

Fig 6. Dependency of force on tensile strength, wire diameter and mandrel diameter (*Sn=n) Tensile strength has equal impact except that the intensity of that impact is considerably lower (Fig on the left). On the other hand, decrease of mandrel diameter 5

Mirza Krajnović, Adnan Mustafić, Mensur Demirović

intensifies force in the spring what is more emphasized in case of max values of wire diameters (Fig on the right). 4. CONCLUSION On the basis of conducted experimental testing and analysis of result, the following basic conclusions can be made: Experimental-mathematical modeling of intensity of elastic straightening and force in the spring (as dependant and flexible values) in the function of material, spring and mandrel geometry (after bending in cold condition by constant torque and after heat treatment) leads to creation of adequate regression models which are suitable for anticipation and which enable the following: To select suitable tool (knowing the value of elastic straightening) using directly regression model and in that way avoid „try – make mistake“ method; To predict, at early stage, (knowing the force in spring for defined deformation level) characteristics of spring which is in early phase of design; Using the model for anticipation instead of traditional approach „try-make mistake“ we are able to reduce time required for preparation and adjusting of machine and to reduce rejections owing to selection of suitable tool. Regression models for the same dependant and flexible values are also adequate and have high determination coefficient and thus can be used for anticipation too. 5. LITERATURE [1] Krajnović, M. MODELING OF ELASTIC STREIGHTENING IN THE PROCESS OF PRODUCTION OF COIL CYLINDRICAL SPRINGS (Master thesis), Faculty of Mechanical Engineering in Tuzla; Tuzla 2012. [2] Ekinović, S. METHODS OF STATISTICAL ANALYSIS in Microsoft Excel, Faculty of Mechanical Engineering in Zenica; Zenica 1997. [3] Jurković, M. MATHEMATICAL MODELING OF ENGINEERING PROCESSES AND SYSTEMS, Faculty of Mechanical Engineering in Bihać; Bihać 1999.

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