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Effect of variational friction and elastic deformation of die on oscillating cold forging for spline shaft
Accepted Manuscript Title: Effect of variational friction and elastic deformation of die on oscillating cold forging for spline shaft Authors: Qi Zhang, Ningyu Ben, Kai Yang PII: DOI: Reference:
S0924-0136(17)30001-8 http://dx.doi.org/doi:10.1016/j.jmatprotec.2017.01.001 PROTEC 15076
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
20-5-2016 27-12-2016 4-1-2017
Please cite this article as: Zhang, Qi, Ben, Ningyu, Yang, Kai, Effect of variational friction and elastic deformation of die on oscillating cold forging for spline shaft.Journal of Materials Processing Technology http://dx.doi.org/10.1016/j.jmatprotec.2017.01.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of variational friction and elastic deformation of die on oscillating cold forging for spline shaft Qi Zhang*, Ningyu Ben, Kai Yang
School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
* Corresponding author. Institute: School of Mechanical Engineering, Xi’an Jiaotong University Address: No.28, Xianning West Road, Xi’an, Shaanxi 710049, PR China Tel. : +86 29 82668607, +86 18629087688 Fax : +86 29 82668607 E-mail address: [email protected]
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Abstract Oscillating cold forging (OCF) is an extrusion method with pulse ram motion. Compared with conventional cold forging (CCF), the OCF can greatly reduce the forming force, which can be contributed to the factors including friction, elastic deformation of die and the metal flow according to the simulations and experiments. To investigate the differences between the OCF and CCF, forming experiment, hardness test and micro observation were performed. In consideration of the different friction condition and variational velocity, a friction modal considering sliding and velocity was used in simulation. The force-stroke curve got from the horizontal oscillating extrusion machine shows that OCF can reduce the load about 25% than CCF and that oscillating frequency affects the friction as well as the forming force. Moreover, the results of experiment and simulation indicate the surface quality of OCF is better than CCF because lower friction leads to less metal pileup.
Keywords Oscillating cold forging; Spline shaft; Friction; Metal flow;
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1. Introduction The forging process is influenced by many factors such as the friction conditions, die shape, material properties and forging load. To reduce the forming force, many methods have been proposed. Osakada et al. (2005) performed a spline forging method with flashless die. Sagisaka et al. (2013) adopted the environmentally friendly lubricants for cold forging. Because of efficiency and load reduction, the oscillating technique is widely used in the forming process. While forming long shaft by oscillating method, the forming force is reduced obviously compared to the conventional forming. Hence, the product geometry and quality are ensured due to the load reduction. To find the explanations for the mechanism of load reduction, some relevant works have been done. It is widely believed that the main reason causing load reduction is the rebuilding of the lubricating film during the back stroke of the die. Matsumoto et al. (2011) proposed a method for maintaining lubrication in the backward extrusion of deep holes. The lubrication of the forming method with pulse punch motion is better than that of conventional forming method. Siegert and Möck (1996) found the forming force could be reduced by applying ultrasonic oscillating die for wire drawing. Maeno et al. (2011) found that the compression load was partially released during the forming plate. The reason was that the re-lubricating of the plate surface. What’s more, they examined the effects of the relationship of load and number of stress relaxation on the reduction in compressive load. Ali et al. (2007) investigated the effect of ultra-low-frequency pulse on the tearing during deep drawing. Two parameters, amplitude and frequency of the pulsed force, were experimented. Khan et al. (2007) developed a phenomenological model based on the slice method combined with a Norton–Hoff viscoplastic law. This constitutive model can be used in the 3
oscillating process simulation. Furthermore, the material flow is also affected by the change of friction conditions. Higher friction leads to a restraint in the axial material flow. Mori et al. (2007) studied the forming process of the tubes by oscillating cold forging. The tubes were obtained a uniform expansion in the bulging region by an oscillating internal pressure. Siegert et al. (1997) found that using closed-loop control can change the friction force in deep drawing process. Groche et al. (2014) studied the closed-loop control of the final product’s geometry in oscillating cold forging process. Owing to the rebuilding of the lubricating film during the back stroke, the forming force and material flow could be controlled by the press. The excellent work above proved that the cause of load reduction in oscillating cold forging is the rebuilding of lubricating film. However, the elastic of die and material property change during the forming process are also important factors. How the friction, elastic deformation of die and the metal flow contribute to the force decrease are still not clear. In this paper, the forming process and products of conventional cold forging (CCF) and oscillating cold forging (OCF) are compared by the spline forging with experiments and simulation. Hence, the effects of deformable die, the change of friction and material flow are investigated on the process. Moreover, the friction model is related to the velocity of die, which can analyze the oscillating process accurately.
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2. Experimental background 2.1 Process of oscillating cold forging Oscillating cold forging is a kind of bulk metal forming process. The forming motion of the die is superimposed by a reciprocating motion. Compared to conventional cold forging, the forming force is decreased and the product quality is improved. Owing to the rebuilding of lubricating film during the reciprocating motion, the friction condition is improved. Take the oscillating forming process of spline for example, the process includes five steps as shown in Fig.1. The first step is the workpiece clamping; the second step is that the axial holder moves down to position the workpiece; then the die feeds in an oscillating way; afterwards, the axial holder and the die return to their initial positions; and then, the workpiece is picked up. When the forming process is finished, the vibration will stop. From the viewpoint of efficiency, the vibration in withdrawal is not necessary. Although a little springback occurs after forming, the direct withdrawal won’t affect the quality obviously as long as the returning velocity are steady. As both the CCF and OCF have the same process, the withdrawal is not compared in this research.
2.2 Experimental set up The experimental equipment (see Fig.2) was composed of the hydraulic power supply, feeding device, clamping device, control unit, displacement sensors, load sensors and forging die set. The illustration of the die was shown in Fig.3. To reduce the friction and optimize the material flow, the length of calibration bench is 7mm and the entry angle is 31.93°. The module of gear is 1.75 and the number of teeth is 10. The bottom of die (the tooth tip of workpiece) was designed larger than the specified diameter to reduce the connection region and then reduce the friction. The pressure of the hydraulic power supply was 0-15MPa, which can provide a maximum force of 5
300kN. The process of oscillating forging was performed by a hydraulic pressure servo cylinder. The measuring system was composed of force sensor, grating-rule sensor and computer. The force sensor was installed between the die and the servo cylinder to collect the axial force. The precision of the grating-rule sensor is ±10μm and the grid distance is 0.02mm. The mover of the sensor was fixed with the hydraulic cylinder piston. The length of the workpiece is 280mm and the diameter is 17.9 mm. The required diameter of tooth tip is18.225mm and the reference circle is 17.34mm. The bottom tooth of die was designed to leave the room for material flowing. The material is AISI 1045A which is widely used for transmission. At the beginning of the test, the workpiece was clamped by the clamping device. The die was made to move ahead and back by servo cylinder. To verify the influence of the frequency of back stroke on the load, the frequency value was set 20Hz, 15Hz and 10Hz. The velocity of the die was 18mm/s. So the frequency 20Hz, 15Hz and 10Hz were corresponding to the amplitude 0.6-0.3mm, 0.8-0.4mm and 1.2-0.6mm. The type of lubricant is liquid lubricant，of which the parameter µ is 0.485 Pa·S. The pressure of spray nozzle is 0.1MPa. Whether the time is enough to allowing lubricant to fill the blank or not is verified as bellow (Fig.4). When the die moved back, the lubricant flow was shown as below: Due to the different distance between the upper and lower boundary, the calculation should be divided as two parts. As is shown in Fig.4, these two parts are: circle flow Q1 in the period t1 and circular cone flow Q2 in the period t2. Both of them are nearly determined through Reynolds equation (the detailed long derivations, which are started from Navier-Stokes (N-S) equations, are added into the appendix.):
Q1
b 3 b p U 12l1 2
6
(1)
Q2 Among them, as
bh1h2 h1h2 ( p U ) h1 h2 6l2
(2)
Q is the flow of lubricant; b is the equivalent width which is approximated
d in circle condition;
is the height of circle flow;
the length from the circle flow entrance to the end;
is the viscosity of lubricant; l is
p is the differential pressure from the circle
flow entrance to the end; U is the velocity of the die; h1 is the height of the circle flow entrance;
h2 is the height of the end. From fluid mechanics:
b l1 t1
(3)
dl2 (h1 h2 ) 2t2
(4)
Q1
Q2 From geometrical relationship：
h1 sin 60
(5)
h2 h1 l2 tan 30
(6)
Then, the relationship of parameter t, l and
t1
p can be expressed as the equation below:
l1 p p U 12l1 2 2
(7)
l2 (h1 h2 ) 2 2 (8) t2 h1h2 p h1h2 ( U ) 6l2 0.6 As for OCF which the frequency is 10Hz, h1 is mm, p is 0.1Mpa, U is 18mm/s 3 and
is 0.485 Pa·S.
The equation is ploted as 3D surface in the Fig.4 and Fig.5 below. As the Fig.5 shows, the time to make the length of lubrican flow more than 0.5mm is about 0.02s, which is enough for the process. 7
The lower
is better for flow. The chosen lubricant,
is 0.485 Pa·S, is satisfied for working
process.
2.3 Material properties The specimen was a dog-bone-shaped specimen with a gage length of 25mm and a diameter of 8mm (Fig.6). The mild steel AISI 1045A was chosen as the testing material. The chemical compositions are shown in Table.1, The experiment was performed on INSTRON 5982 material testing machine with three strain rate 0.1s-1, 0.01s-1 and 0.001s-1. The results of tension test are shown in Fig.7.
2.4 FE model Transvalor FORGE NxT, one of the commercial software for metal forming process, was used to simulate the oscillating cold forging process. Due to the symmetry of die and billet, one tenth of them was built as the 3D FE model, as is shown in Fig.8. Besides the die and billet, the manipulator was used to fix the billet during the process. An oscillating hydraulic press was set on the die fixing ring. The oscillating method in simulation was the same with that in experiment as shown in Fig.9. The material model was a viscoplastic flow law according to the "HanselSpittel" constitutive model as shown in Eq.9. The parameters were determined by fitting the stress-strain curve in tension test as shown in Fig.7 and Table 2. m3
A m m e 1
2
(9)
Among them, m1 and m3 define the material's sensitivity to strain. m2 depends on the material's sensitivity to the strain rate. The workpiece and the die are defined as elastic-plastic deformation. Because the lubricant is cycled around, heat will be taken away. So, the influence of temperature has not been taken into 8
account. The temperature has not found increasing in experiment. Remeshing was used in the simulation. The remesh on period was set as every 1mm. Meanwhile, the re-mesh deformation was set as every 20% deformation. All the part in simulation were meshed. The element type is tetrahedral mesh. The mesh size is 0.2mm on the range of deformation and 0.8mm on the other part. Due to the analysis of the friction conditions and lubricant rebuilding in section 2.2, the friction condition is related to the real contact area and the sliding velocity. To be accurate, the IFUM friction model was used in the Forge secondary development to analyze nonlinear loads. This model is proposed by Behrens (2011), which is capable of describing the frictional shear stress for contact pairs with components undergoing plastic deformation, taking into account the realistic influence of the sliding velocity. The friction model is able to distinguish between fully elastic and plastic deformation. The real contact area between workpiece and die surface according to Mikic (1974) and the instantaneous local stress state are examined. It adheres to the true contact surface and determines a local friction shear stress. The lower the real contact area, the smaller is the transferred friction shear stress. The mathematical formulation of the friction model is given by the following equation:
R 0.3 1
Among them,
Eq Eq N 1 exp N m k y y y
f vrel
(10)
R is the friction force, m is the friction factor, which needs to ensure by
fitting the experimental force-stroke data. N is the normal stress, Eq is the equivalent stress,
y
is the yield stress, vrel is the relative sliding velocity.
f (vrel ) exp
1 vrel 2 ( ) 2 C
(11)
The sliding velocity means the average relative velocity between the workpiece and the die. The effect of sliding velocity in the friction model was first proposed by Chen and Kobayashi (1978). 9
Parameter C serves to adjust the influence of the sliding velocity on frictional shear stress between the workpiece and the die. Fig.10 shows the curve of the functional relationship for various values of C. The impact of the sliding velocity on the frictional shear stress state between the workpiece and the die was considered. The parameters of m and C in simulation are confirmed by fitting the results from experiment owing to the different lubrication in this paper. The friction law was written into the software by Fortran Language. Due to the secondary development of the software, some parameters and variables are predefined in the software in order to be able to use them as the parameter or variable of a user law, such as N (normal stress) and
y
(yield stress). As for the special oscillating friction conditions, the general friction test is hard
to reflect the real condition in experiment. But the force-stroke curve was measured directly in experiment. Fitting the force-stroke curve is an another method of ensuring friction factors, which is also widely used in tribology research. Therefore, the parameters of m and C have been changed until the maximum force-stroke results deviation between simulation and experiment are lower than 5% (Fig.19). Such the simulations have been done on the premise of other factors are constant. Also, the parameters were not fitted without basis. The parameter m referred to the friction analysis by Behrens et al. (2011) and Groche and Heß (2014), which was set from 0.05 to 0.35. The parameter C was set from 0 to 10, referred to Behrens et al. (2011).
3. Results and discussion 3.1 Simulation results and discussion Fig.11 shows the Von-Mises stress and velocity distribution of the workpiece under different conditions. Section A-A is applied to show the Von-Mises stress of the cross-section of spline. By comparing the three feeding conditions (f=10Hz, f=15Hz, f=20Hz), the stress in the forming field 10
decreases with the increase of frequency. During the forming process, the metal flow can be divided into three parts. One part is flowing along the axis; another is flowing to the top of the tooth; and the rest is flowing against the forming motion of the die. As is shown in Fig.11, the great friction leads to more metal pileup and higher stress. The big differences of OCF and CCF are reflected in the back stroke. The Von-mises stress distribution and velocity of the workpiece are shown in Fig.11 at 0.01second after back stroke. The springback of workpiece is happened with the die backing. When the die is moving with vibration, more material flow into the tooth tip which is benefit for spline forming. Fig.12 shows the diameters of formed splines in different working conditions. The diameters of the spline formed in the high friction condition is larger than that formed in the low friction, along the moving trace of die. The nodes were selected by every 2mm from the bottom of spline, which were got to compared with the spline formed in experiments at the same position. The measurement was done to describe the differences on metal flow between different parameters. The diameter of the workpiece formed by OCF is uniform. However, the rear diameter of the workpiece formed by CCF is larger than the front one. The material pileup is obvious in CCF process and it brings lager metal flow resistance about. The elastic deformation is oscillated with the forming die in OCF as shown in Fig.13. In the feeding stroke, the elastic displacement of the die in OCF (maximum is about 0.07mm) is bigger than that in CCF (maximum is about 0.06mm). But the elastic springback is happened in back stroke. Due to the change of workpiece shape, the elastic deformation is also different in every oscillating step. Total power of the process includes plastic power, elastic power and friction power. The curves 11
of different power-time were filtered to avoid the noise, which are shown in Fig.14. Among these, the difference of friction power in CCF and OCF is the biggest (shown in Fig.14 (c)), which means friction change makes more contribution to the force reduction. Due to the visco-plastic force changing with the strain rate, the plastic power of OCF decreases with the frequency increasing (shown in Fig.14 (b)). The plastic power in CCF is also larger than OCF especially in the later half. Another reason is that more and more material pileup with the die feeding. The elastic power of the die in OCF and CCF are different too (shown in Fig.14). The negative section of the curve means the elastic springback. The different elastic springback of the die contributes to lubricant rebuilding as well as friction induction. In summary, the combination of friction and other factors such as the elastic deformation of die, the visco-plastic forging forces and material flow make the OCF process forming efficient.
3.2 Experimental results and discussion Fig.15 shows the force-stroke curve of CCF and OCF. Compared to the force of CCF, the force of OCF is decreased by 25% at the end of forging. As the force is decreased in oscillating forging, the size and surface quality are improved. The spline forged by CCF is shown in Fig.16. It can be clearly seen that there are a lot of scratches and indentations on the tooth surface of spline. However, the spline formed by oscillating cold forging has a smooth tooth surface as shown in Fig.17. The shape of die, the lubricant and all the other experimental condition were same in two process. In contrast, the scratches were found in CCF which means the lubricant film in CCF was broken. Because of high friction force and inhomogeneous flow of metal, the diameter of spline shaft is changed significantly in CCF process. Fig.18 shows the diameters of the spline shaft along axial direction. As is shown in Fig.18, there are less differences in the diameter of the spline shaft formed 12
by OCF, which indicates that the deformation of spline is uniform and the metal pileup is not obvious. Meanwhile, it can be seen that the diameters of the spline shaft by using CCF are changed greatly. This phenomenon is owing to the high friction force and large metal flow resistance, which cause the forming force increasing and the metal pileup. By changing the frequency of OCF, three different stroke-force curves of the OCF were obtained in Fig.15. It can be seen that the forging force decreases with the forging frequency increasing. Relating with Fig.11, it can be concluded that the lower stress and less material pileup make force induction in OCF. At the high frequencies, the metal tends to flow to tooth tip. This metal flow benefits the rebuilding of lubricant film, leading to a lower forging force. The influence of the different friction conditions on the forming load was investigated. The force-stroke data of the simulation with different parameters of m and C are compared to the experiments with the curve shown in Fig.19. The parameters of m and C are confirmed in Table 3, as the maximum force-stroke results deviation between simulation and experiment are lower than 5% (shown in Fig.19). The simulation results and friction factor were approved to represent the experiments by comparing force-stroke in Fig.19. So the condition with the same friction factor but different process can be achieved in simulation. For the CCF, the force-stroke data of the simulation with three different friction factor m and relevant C are shown in Fig.20 (a). It can be seen that the force is increased with the friction factor m and relevant C increasing. As we can see in Fig.20 (b), the curve shows that lubricant film affects the forming force stronger than other factors. The forming force of CCF is reduced by 17% by decreasing friction as same with OCF. With the same friction but different process, the forming force is reduced 8% by taking out the effect of friction. 13
3.3 Hardness test Vickers microhardness test was carried out to evaluate the experimental workpiece. Some points on the top and bottom of the tooth were measured as shown in Fig.21. And also, the equivalent strain of the simulation results is plotted in Fig.21. Every tooth was measured and the average results are shown in Fig.22. For the point 5, the highest value of hardness 305.6HV5 occurs in CCF, which is larger than 275.1HV5 in OCF (f=20Hz). The hardness at the bottom of the tooth was decreased by 10%. The difference of hardness is attributed to the difference of deformation. The deformation at the bottom of the tooth is greater than that at the top. And the deformation of the workpiece by CCF is greater than that by OCF. Moreover, the hardness of point 5-8, formed by the OCF, has little difference compared with that formed by the CCF. In forming process, the deformation resistance is increased with the plastic deformation. The bigger deformation means more material was affected. What’s more, the equivalent strain is related to the material workhardening. The higher strain, the larger hardness. The relationship of strain and hardness is shown in the Fig.23 below. This indicates that the metal flow in OCF is more uniform than that in CCF.
3.4 Microstructure The microstructure of the parts A and B are shown in Fig 24, 25. In the three figures, part (a) is the spline formed by CCF and part (b) is that formed by OCF (f=20Hz). As we can see, the deformation of the grain in part (b) is more significant than that in part (a). Known from Fig.24, the variation of the strain in the surface layer is considerably changed. Corresponding to the microstructure, the grain in the surface layer is compressed in CCF. As is shown in part (a) of the Fig.24, the metal in the surface layer is compressed so seriously that the width of grain refinement is about 50 m . However, the deformation of the grain in part (b) is uniform. This phenomenon is 14
related to stress relaxation during the back stroke in the OCF, which indicates the deformation is homogeneous and the metal flows easily. Fig.25 shows the microstructure of the tooth tip. In part (a), the grain in the surface layer is compressed considerably. But the metal flow in part (a) is not as significant as that in part (b). This phenomenon indicates that more metal flows to other region rather than to tooth tip in CCF. The metal flow in OCF is more beneficial to the forming of the spline than that in CCF.
4. Summary and outlook In this paper, the oscillating cold forging (OCF) and the conventional cold forging (CCF) have been investigated by both experiment and simulation. The differences of forming force, friction condition and material flow between the OCF and the CCF were discussed. And also, the effects of elastic deformation of die and the change of hardness are studied by experiment and simulation. The main conclusions are summarized as follows: (1) The forming force of the OCF decreases 25% compared to the CCF, during the forming process of the spline shaft. The factors can be concluded as friction condition, the elastic deformation of die, hardness and metal flow (17% of the reduction is caused by friction and 8% by others). (2) Scratches and indentations can be observed on the tooth surface of spline by using CCF. However, the spline formed by OCF has smooth tooth surface. The higher oscillating frequency in OCF leads to lower friction and less metal pileup in the spline shaft. For further investigation, the constitutive relationship should be built according to the stress station rather than the simplified model was used in this paper. Strain rate has to be took into account. 15
Furthermore, the change of grain which observed from TEM and the phenomenon on other metal type are being studied.
Acknowledgements The authors are grateful to the Key Technologies R & D Program of Shaanxi province of China (grant no. 2014K08-34) for funding this study.
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Derivations of the equations in Section 2.2
The velocity of the flow between two flat is u , v w 0 . Because of the viscosity, the velocity gradient u / z is existed. According to the equation of continuity, u / x 0 . Besides, the direction y is so large that u / y can be ignored. As for the incompressible fluid, the NavierStokes (N-S) equations can be simplified as below: 1 1 1
p 2u 2 0 x z p 0 x p 0 z
(1)
From the latter two equations, pressure p is only changed in x direction and u is only the function of z. Because of the distance of two flat is constant in x direction, the gradient of p is uniform. So, p p2 p dp p 1 x dx l l
(2)
2u 2u z 2 x 2
(3)
d 2u 1 dp p l dz 2 dx
(4)
Then, the first equation is:
After integral, u
p 2 z C1 z C2 2 l
(5)
The boundary conditions are: z 0, u U z , u 0
After substituting the condition (6) into (5):
17
(6)
C1
p 2 U z , C2 U 2 l
(7)
u
p z ( z ) z U 1 2 l
(8)
So,
If the lower slab is stable, the equation (8) is: u
p z ( z ) z +U 2 l
(9)
And the flow is:
Q ubdz
(10)
b 3 p b U 12 l 2
(11)
0
Then, Q
The liquid in the gap is seemed as parallel velocity, u u z , v w 0 p p dp p y 0, z 0, y dx
(12)
As for the flow between two slant slab, the rate of change of the pressure dp/dx is not constant. So, the N-S equation can be simplified as below: d 2u 1 dp dz 2 dx
(13)
1 dp 2 z C1 z C2 2 dx
(14)
After double integral for z: u
The boundary conditions are: z 0, u U z , u 0
Taken into the equation (14):
18
(15)
1 dp U h , C2 U 2 dx h
(16)
1 2 dp z z hz U 1 2 dx h
(17)
C1
So, the equation (14) is u
The flow Q, crossed any section, is: h h 1 dp z Q ubdz z 2 hz U 1 bdz 0 0 2 dx h
(18)
After integral: Q
bh3 dp bh U 12 dx 2
(19)
The gradient of pressure along the x is: dp 6U 12 2 3Q dx h bh
(20)
h h1 x tan
(21)
dx dh / tan
(22)
6U 12Q dp 3 2 dh bh tan h tan
(23)
From Fig.2:
So,
Taken into equation (20):
After integral: p
6 Q 6U C 2 bh tan h tan
(24)
As for the boundary conditions are h=h1, p=p1, the constant parameter C is: 6 Q 6U bh12 tan h1 tan
(25)
6 Q 1 1 6U 1 1 2 2 b tan h1 h tan h1 h
(26)
C p1
Taken into (24): p p1
19
When the boundary conditions are h=h2, p=p2: p2 p1
6 Q 1 1 6U 1 1 2 2 b tan h1 h2 tan h1 h2
(27)
The difference of the pressure is: p p1 p2
6Q h12 h22 b tan h12 h22
6U h2 h1 tan h1h2
(28)
Due to the equation tan (h1 h2 ) / l , the flow Q can be expressed as below: Q
bh1h2 h1h2 p U h1 h2 6l
(29)
When the confine is gradient and mobile, the flow of lubricant can be divided to two parts: Circle flow Q1 and Circular cone flow Q2 , which are nearly determined through Reynolds equation:
b 3 b p U 12l 2
(30)
bh1h2 h1h2 ( p U ) h1 h2 6l
(31)
Q1 Q2 Among them,
Q is the flow of lubricant; b is the equivalent width which is approximated
as d in circle condition;
is the height of circle flow;
the length from the circle flow entrance to the end;
is the viscosity of lubricant; l is
p is the differential pressure from the circle
flow entrance to the end; U is the velocity of the die; h1 is the height of the circle flow entrance;
h2 is the height of the end. 20
From fluid mechanics:
b l1 t1
(32)
dl2 (h1 h2 ) 2t2
(33)
Q1
Q2 From geometrical relationship：
h1 sin 60
(34)
h2 h1 l2 tan 30
(35)
Then, the relationship of parameter t, l and
t1
p can be expressed as the equation below:
l1 p p U 12l1 2 2
l2 (h1 h2 ) 2 2 t2 h h p h1h2 ( 1 2 U ) 6l2 As for OCF which the frequency is 10Hz, h1 is
and
(36)
(37)
0.6 mm, p is 0.1Mpa, U is 18mm/s 3
is 0.485 Pa•S. The equation is ploted as 3D surface in the Fig.4 and Fig.5 below. As the figures show, the time
to make the length of lubrican flow more than 0.5mm is about 0.02s, which is enough for the process. The lower
is better for flow. The chosen lubricant, is 0.485 Pa•S, is satisfied for working
process.
21
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T. Maeno, K. Osakada, K. Mori, 2011. Reduction of friction in compression of plates by load pulsation. International
Journal of Machine Tools & Manufacture 51, 612-617.
Tewari S P, Shanker A, 1994. Effects of longitudinal vibration on tensile properties of weldments. Welding Journal
73, 65-67.
Yoshihiro Sagisaka, Tamotsu Nakamura, Kunio Hayakawa, Itaru Ishibashi, 2013. Evaluation of environmentally
friendly lubricant for aluminum cold forging using friction test based on spline extrusion. Journal of Manufacturing
Processes 15, 96–101.
Fig.1 Forming process
Fig.2 The oscillating extrusion machine
Fig.3 The size of the die (Unit: mm)
Fig.4 Lubricant flow condition
Fig.5 Flated surface (b) of the relationship of parameter t,
l
and p
Fig.6 Shape of specimen
Fig.7 True stress-strain curve for simulation
Fig.8 3D FE model
Fig.9 Stroke-time curve of the OCF (f=20Hz)
Fig.10 Variation of C for the velocity function f(vrel)
Fig.11 Von-Mises stress and velocity distribution of the workpiece in different condition
Fig.12 Diameters of the top of the tooth with different friction condition
Fig.13 Distribution of elastic displacement of the die in CCF and OCF (f=20Hz)
(a) Total power in CCF and OCF (f=10Hz) (b) Comparison of plastic power in CCF and OCF (c) Comparison of friction power in CCF and OCF (d) Comparison of elastic power of the die in CCF and OCF (f=20Hz) Fig.14 Power in different processes
Fig.15 Force-stroke curve the OCF compared with the CCF
Fig.16 Spline formed by normal forging
Fig.17 Spline formed by oscillating forging
Δs is the distance to the top of the spline; D is the diameter of shaft. Fig.18 Diameters of the spline along the axial direction
Fig.19 Force-stroke curve of CCF and OCF experiment with different friction condition
(a) CCF with different friction factor
(b) CCF and OCF with the same friction factor m=0.02
Fig.20 Force-stroke curve of CCF and OCF with different friction condition
Fig.21 Equivalent strain distribution along the section surface
Fig.22 Vickers microharness of the OCF and the CCF
Fig.23 The relationship of strain and hardness
Fig.24 Microstructure of the part A by the CCF (a) and the OCF (b)
Fig.25 Microstructure of the part B by the CCF (a) and the OCF (b)
Fig.1 Flow between two flat
Fig.2 Flow between two slant flat
Table 1 chemical compositions of AISI 1045A
C 0.34-0.52
(wt.%)
Mn
Si
S
0.51-0.81
0.28-0.48
0.01-0.069
P 0.017-0.044
Table 2 Parameters in Eq.9
A 874.31
m1
m2
0.1908
0.025
m3
0.0031
Table 3 Friction factors got from fitting in Fig.20 Frequency (Hz)
m
C
0
0.15
10
10
0.125
5
15
0.1
2.5
20
0.08
1
S0924-0136(17)30001-8 http://dx.doi.org/doi:10.1016/j.jmatprotec.2017.01.001 PROTEC 15076
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
20-5-2016 27-12-2016 4-1-2017
Please cite this article as: Zhang, Qi, Ben, Ningyu, Yang, Kai, Effect of variational friction and elastic deformation of die on oscillating cold forging for spline shaft.Journal of Materials Processing Technology http://dx.doi.org/10.1016/j.jmatprotec.2017.01.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of variational friction and elastic deformation of die on oscillating cold forging for spline shaft Qi Zhang*, Ningyu Ben, Kai Yang
School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
* Corresponding author. Institute: School of Mechanical Engineering, Xi’an Jiaotong University Address: No.28, Xianning West Road, Xi’an, Shaanxi 710049, PR China Tel. : +86 29 82668607, +86 18629087688 Fax : +86 29 82668607 E-mail address: [email protected]
1
Abstract Oscillating cold forging (OCF) is an extrusion method with pulse ram motion. Compared with conventional cold forging (CCF), the OCF can greatly reduce the forming force, which can be contributed to the factors including friction, elastic deformation of die and the metal flow according to the simulations and experiments. To investigate the differences between the OCF and CCF, forming experiment, hardness test and micro observation were performed. In consideration of the different friction condition and variational velocity, a friction modal considering sliding and velocity was used in simulation. The force-stroke curve got from the horizontal oscillating extrusion machine shows that OCF can reduce the load about 25% than CCF and that oscillating frequency affects the friction as well as the forming force. Moreover, the results of experiment and simulation indicate the surface quality of OCF is better than CCF because lower friction leads to less metal pileup.
Keywords Oscillating cold forging; Spline shaft; Friction; Metal flow;
2
1. Introduction The forging process is influenced by many factors such as the friction conditions, die shape, material properties and forging load. To reduce the forming force, many methods have been proposed. Osakada et al. (2005) performed a spline forging method with flashless die. Sagisaka et al. (2013) adopted the environmentally friendly lubricants for cold forging. Because of efficiency and load reduction, the oscillating technique is widely used in the forming process. While forming long shaft by oscillating method, the forming force is reduced obviously compared to the conventional forming. Hence, the product geometry and quality are ensured due to the load reduction. To find the explanations for the mechanism of load reduction, some relevant works have been done. It is widely believed that the main reason causing load reduction is the rebuilding of the lubricating film during the back stroke of the die. Matsumoto et al. (2011) proposed a method for maintaining lubrication in the backward extrusion of deep holes. The lubrication of the forming method with pulse punch motion is better than that of conventional forming method. Siegert and Möck (1996) found the forming force could be reduced by applying ultrasonic oscillating die for wire drawing. Maeno et al. (2011) found that the compression load was partially released during the forming plate. The reason was that the re-lubricating of the plate surface. What’s more, they examined the effects of the relationship of load and number of stress relaxation on the reduction in compressive load. Ali et al. (2007) investigated the effect of ultra-low-frequency pulse on the tearing during deep drawing. Two parameters, amplitude and frequency of the pulsed force, were experimented. Khan et al. (2007) developed a phenomenological model based on the slice method combined with a Norton–Hoff viscoplastic law. This constitutive model can be used in the 3
oscillating process simulation. Furthermore, the material flow is also affected by the change of friction conditions. Higher friction leads to a restraint in the axial material flow. Mori et al. (2007) studied the forming process of the tubes by oscillating cold forging. The tubes were obtained a uniform expansion in the bulging region by an oscillating internal pressure. Siegert et al. (1997) found that using closed-loop control can change the friction force in deep drawing process. Groche et al. (2014) studied the closed-loop control of the final product’s geometry in oscillating cold forging process. Owing to the rebuilding of the lubricating film during the back stroke, the forming force and material flow could be controlled by the press. The excellent work above proved that the cause of load reduction in oscillating cold forging is the rebuilding of lubricating film. However, the elastic of die and material property change during the forming process are also important factors. How the friction, elastic deformation of die and the metal flow contribute to the force decrease are still not clear. In this paper, the forming process and products of conventional cold forging (CCF) and oscillating cold forging (OCF) are compared by the spline forging with experiments and simulation. Hence, the effects of deformable die, the change of friction and material flow are investigated on the process. Moreover, the friction model is related to the velocity of die, which can analyze the oscillating process accurately.
4
2. Experimental background 2.1 Process of oscillating cold forging Oscillating cold forging is a kind of bulk metal forming process. The forming motion of the die is superimposed by a reciprocating motion. Compared to conventional cold forging, the forming force is decreased and the product quality is improved. Owing to the rebuilding of lubricating film during the reciprocating motion, the friction condition is improved. Take the oscillating forming process of spline for example, the process includes five steps as shown in Fig.1. The first step is the workpiece clamping; the second step is that the axial holder moves down to position the workpiece; then the die feeds in an oscillating way; afterwards, the axial holder and the die return to their initial positions; and then, the workpiece is picked up. When the forming process is finished, the vibration will stop. From the viewpoint of efficiency, the vibration in withdrawal is not necessary. Although a little springback occurs after forming, the direct withdrawal won’t affect the quality obviously as long as the returning velocity are steady. As both the CCF and OCF have the same process, the withdrawal is not compared in this research.
2.2 Experimental set up The experimental equipment (see Fig.2) was composed of the hydraulic power supply, feeding device, clamping device, control unit, displacement sensors, load sensors and forging die set. The illustration of the die was shown in Fig.3. To reduce the friction and optimize the material flow, the length of calibration bench is 7mm and the entry angle is 31.93°. The module of gear is 1.75 and the number of teeth is 10. The bottom of die (the tooth tip of workpiece) was designed larger than the specified diameter to reduce the connection region and then reduce the friction. The pressure of the hydraulic power supply was 0-15MPa, which can provide a maximum force of 5
300kN. The process of oscillating forging was performed by a hydraulic pressure servo cylinder. The measuring system was composed of force sensor, grating-rule sensor and computer. The force sensor was installed between the die and the servo cylinder to collect the axial force. The precision of the grating-rule sensor is ±10μm and the grid distance is 0.02mm. The mover of the sensor was fixed with the hydraulic cylinder piston. The length of the workpiece is 280mm and the diameter is 17.9 mm. The required diameter of tooth tip is18.225mm and the reference circle is 17.34mm. The bottom tooth of die was designed to leave the room for material flowing. The material is AISI 1045A which is widely used for transmission. At the beginning of the test, the workpiece was clamped by the clamping device. The die was made to move ahead and back by servo cylinder. To verify the influence of the frequency of back stroke on the load, the frequency value was set 20Hz, 15Hz and 10Hz. The velocity of the die was 18mm/s. So the frequency 20Hz, 15Hz and 10Hz were corresponding to the amplitude 0.6-0.3mm, 0.8-0.4mm and 1.2-0.6mm. The type of lubricant is liquid lubricant，of which the parameter µ is 0.485 Pa·S. The pressure of spray nozzle is 0.1MPa. Whether the time is enough to allowing lubricant to fill the blank or not is verified as bellow (Fig.4). When the die moved back, the lubricant flow was shown as below: Due to the different distance between the upper and lower boundary, the calculation should be divided as two parts. As is shown in Fig.4, these two parts are: circle flow Q1 in the period t1 and circular cone flow Q2 in the period t2. Both of them are nearly determined through Reynolds equation (the detailed long derivations, which are started from Navier-Stokes (N-S) equations, are added into the appendix.):
Q1
b 3 b p U 12l1 2
6
(1)
Q2 Among them, as
bh1h2 h1h2 ( p U ) h1 h2 6l2
(2)
Q is the flow of lubricant; b is the equivalent width which is approximated
d in circle condition;
is the height of circle flow;
the length from the circle flow entrance to the end;
is the viscosity of lubricant; l is
p is the differential pressure from the circle
flow entrance to the end; U is the velocity of the die; h1 is the height of the circle flow entrance;
h2 is the height of the end. From fluid mechanics:
b l1 t1
(3)
dl2 (h1 h2 ) 2t2
(4)
Q1
Q2 From geometrical relationship：
h1 sin 60
(5)
h2 h1 l2 tan 30
(6)
Then, the relationship of parameter t, l and
t1
p can be expressed as the equation below:
l1 p p U 12l1 2 2
(7)
l2 (h1 h2 ) 2 2 (8) t2 h1h2 p h1h2 ( U ) 6l2 0.6 As for OCF which the frequency is 10Hz, h1 is mm, p is 0.1Mpa, U is 18mm/s 3 and
is 0.485 Pa·S.
The equation is ploted as 3D surface in the Fig.4 and Fig.5 below. As the Fig.5 shows, the time to make the length of lubrican flow more than 0.5mm is about 0.02s, which is enough for the process. 7
The lower
is better for flow. The chosen lubricant,
is 0.485 Pa·S, is satisfied for working
process.
2.3 Material properties The specimen was a dog-bone-shaped specimen with a gage length of 25mm and a diameter of 8mm (Fig.6). The mild steel AISI 1045A was chosen as the testing material. The chemical compositions are shown in Table.1, The experiment was performed on INSTRON 5982 material testing machine with three strain rate 0.1s-1, 0.01s-1 and 0.001s-1. The results of tension test are shown in Fig.7.
2.4 FE model Transvalor FORGE NxT, one of the commercial software for metal forming process, was used to simulate the oscillating cold forging process. Due to the symmetry of die and billet, one tenth of them was built as the 3D FE model, as is shown in Fig.8. Besides the die and billet, the manipulator was used to fix the billet during the process. An oscillating hydraulic press was set on the die fixing ring. The oscillating method in simulation was the same with that in experiment as shown in Fig.9. The material model was a viscoplastic flow law according to the "HanselSpittel" constitutive model as shown in Eq.9. The parameters were determined by fitting the stress-strain curve in tension test as shown in Fig.7 and Table 2. m3
A m m e 1
2
(9)
Among them, m1 and m3 define the material's sensitivity to strain. m2 depends on the material's sensitivity to the strain rate. The workpiece and the die are defined as elastic-plastic deformation. Because the lubricant is cycled around, heat will be taken away. So, the influence of temperature has not been taken into 8
account. The temperature has not found increasing in experiment. Remeshing was used in the simulation. The remesh on period was set as every 1mm. Meanwhile, the re-mesh deformation was set as every 20% deformation. All the part in simulation were meshed. The element type is tetrahedral mesh. The mesh size is 0.2mm on the range of deformation and 0.8mm on the other part. Due to the analysis of the friction conditions and lubricant rebuilding in section 2.2, the friction condition is related to the real contact area and the sliding velocity. To be accurate, the IFUM friction model was used in the Forge secondary development to analyze nonlinear loads. This model is proposed by Behrens (2011), which is capable of describing the frictional shear stress for contact pairs with components undergoing plastic deformation, taking into account the realistic influence of the sliding velocity. The friction model is able to distinguish between fully elastic and plastic deformation. The real contact area between workpiece and die surface according to Mikic (1974) and the instantaneous local stress state are examined. It adheres to the true contact surface and determines a local friction shear stress. The lower the real contact area, the smaller is the transferred friction shear stress. The mathematical formulation of the friction model is given by the following equation:
R 0.3 1
Among them,
Eq Eq N 1 exp N m k y y y
f vrel
(10)
R is the friction force, m is the friction factor, which needs to ensure by
fitting the experimental force-stroke data. N is the normal stress, Eq is the equivalent stress,
y
is the yield stress, vrel is the relative sliding velocity.
f (vrel ) exp
1 vrel 2 ( ) 2 C
(11)
The sliding velocity means the average relative velocity between the workpiece and the die. The effect of sliding velocity in the friction model was first proposed by Chen and Kobayashi (1978). 9
Parameter C serves to adjust the influence of the sliding velocity on frictional shear stress between the workpiece and the die. Fig.10 shows the curve of the functional relationship for various values of C. The impact of the sliding velocity on the frictional shear stress state between the workpiece and the die was considered. The parameters of m and C in simulation are confirmed by fitting the results from experiment owing to the different lubrication in this paper. The friction law was written into the software by Fortran Language. Due to the secondary development of the software, some parameters and variables are predefined in the software in order to be able to use them as the parameter or variable of a user law, such as N (normal stress) and
y
(yield stress). As for the special oscillating friction conditions, the general friction test is hard
to reflect the real condition in experiment. But the force-stroke curve was measured directly in experiment. Fitting the force-stroke curve is an another method of ensuring friction factors, which is also widely used in tribology research. Therefore, the parameters of m and C have been changed until the maximum force-stroke results deviation between simulation and experiment are lower than 5% (Fig.19). Such the simulations have been done on the premise of other factors are constant. Also, the parameters were not fitted without basis. The parameter m referred to the friction analysis by Behrens et al. (2011) and Groche and Heß (2014), which was set from 0.05 to 0.35. The parameter C was set from 0 to 10, referred to Behrens et al. (2011).
3. Results and discussion 3.1 Simulation results and discussion Fig.11 shows the Von-Mises stress and velocity distribution of the workpiece under different conditions. Section A-A is applied to show the Von-Mises stress of the cross-section of spline. By comparing the three feeding conditions (f=10Hz, f=15Hz, f=20Hz), the stress in the forming field 10
decreases with the increase of frequency. During the forming process, the metal flow can be divided into three parts. One part is flowing along the axis; another is flowing to the top of the tooth; and the rest is flowing against the forming motion of the die. As is shown in Fig.11, the great friction leads to more metal pileup and higher stress. The big differences of OCF and CCF are reflected in the back stroke. The Von-mises stress distribution and velocity of the workpiece are shown in Fig.11 at 0.01second after back stroke. The springback of workpiece is happened with the die backing. When the die is moving with vibration, more material flow into the tooth tip which is benefit for spline forming. Fig.12 shows the diameters of formed splines in different working conditions. The diameters of the spline formed in the high friction condition is larger than that formed in the low friction, along the moving trace of die. The nodes were selected by every 2mm from the bottom of spline, which were got to compared with the spline formed in experiments at the same position. The measurement was done to describe the differences on metal flow between different parameters. The diameter of the workpiece formed by OCF is uniform. However, the rear diameter of the workpiece formed by CCF is larger than the front one. The material pileup is obvious in CCF process and it brings lager metal flow resistance about. The elastic deformation is oscillated with the forming die in OCF as shown in Fig.13. In the feeding stroke, the elastic displacement of the die in OCF (maximum is about 0.07mm) is bigger than that in CCF (maximum is about 0.06mm). But the elastic springback is happened in back stroke. Due to the change of workpiece shape, the elastic deformation is also different in every oscillating step. Total power of the process includes plastic power, elastic power and friction power. The curves 11
of different power-time were filtered to avoid the noise, which are shown in Fig.14. Among these, the difference of friction power in CCF and OCF is the biggest (shown in Fig.14 (c)), which means friction change makes more contribution to the force reduction. Due to the visco-plastic force changing with the strain rate, the plastic power of OCF decreases with the frequency increasing (shown in Fig.14 (b)). The plastic power in CCF is also larger than OCF especially in the later half. Another reason is that more and more material pileup with the die feeding. The elastic power of the die in OCF and CCF are different too (shown in Fig.14). The negative section of the curve means the elastic springback. The different elastic springback of the die contributes to lubricant rebuilding as well as friction induction. In summary, the combination of friction and other factors such as the elastic deformation of die, the visco-plastic forging forces and material flow make the OCF process forming efficient.
3.2 Experimental results and discussion Fig.15 shows the force-stroke curve of CCF and OCF. Compared to the force of CCF, the force of OCF is decreased by 25% at the end of forging. As the force is decreased in oscillating forging, the size and surface quality are improved. The spline forged by CCF is shown in Fig.16. It can be clearly seen that there are a lot of scratches and indentations on the tooth surface of spline. However, the spline formed by oscillating cold forging has a smooth tooth surface as shown in Fig.17. The shape of die, the lubricant and all the other experimental condition were same in two process. In contrast, the scratches were found in CCF which means the lubricant film in CCF was broken. Because of high friction force and inhomogeneous flow of metal, the diameter of spline shaft is changed significantly in CCF process. Fig.18 shows the diameters of the spline shaft along axial direction. As is shown in Fig.18, there are less differences in the diameter of the spline shaft formed 12
by OCF, which indicates that the deformation of spline is uniform and the metal pileup is not obvious. Meanwhile, it can be seen that the diameters of the spline shaft by using CCF are changed greatly. This phenomenon is owing to the high friction force and large metal flow resistance, which cause the forming force increasing and the metal pileup. By changing the frequency of OCF, three different stroke-force curves of the OCF were obtained in Fig.15. It can be seen that the forging force decreases with the forging frequency increasing. Relating with Fig.11, it can be concluded that the lower stress and less material pileup make force induction in OCF. At the high frequencies, the metal tends to flow to tooth tip. This metal flow benefits the rebuilding of lubricant film, leading to a lower forging force. The influence of the different friction conditions on the forming load was investigated. The force-stroke data of the simulation with different parameters of m and C are compared to the experiments with the curve shown in Fig.19. The parameters of m and C are confirmed in Table 3, as the maximum force-stroke results deviation between simulation and experiment are lower than 5% (shown in Fig.19). The simulation results and friction factor were approved to represent the experiments by comparing force-stroke in Fig.19. So the condition with the same friction factor but different process can be achieved in simulation. For the CCF, the force-stroke data of the simulation with three different friction factor m and relevant C are shown in Fig.20 (a). It can be seen that the force is increased with the friction factor m and relevant C increasing. As we can see in Fig.20 (b), the curve shows that lubricant film affects the forming force stronger than other factors. The forming force of CCF is reduced by 17% by decreasing friction as same with OCF. With the same friction but different process, the forming force is reduced 8% by taking out the effect of friction. 13
3.3 Hardness test Vickers microhardness test was carried out to evaluate the experimental workpiece. Some points on the top and bottom of the tooth were measured as shown in Fig.21. And also, the equivalent strain of the simulation results is plotted in Fig.21. Every tooth was measured and the average results are shown in Fig.22. For the point 5, the highest value of hardness 305.6HV5 occurs in CCF, which is larger than 275.1HV5 in OCF (f=20Hz). The hardness at the bottom of the tooth was decreased by 10%. The difference of hardness is attributed to the difference of deformation. The deformation at the bottom of the tooth is greater than that at the top. And the deformation of the workpiece by CCF is greater than that by OCF. Moreover, the hardness of point 5-8, formed by the OCF, has little difference compared with that formed by the CCF. In forming process, the deformation resistance is increased with the plastic deformation. The bigger deformation means more material was affected. What’s more, the equivalent strain is related to the material workhardening. The higher strain, the larger hardness. The relationship of strain and hardness is shown in the Fig.23 below. This indicates that the metal flow in OCF is more uniform than that in CCF.
3.4 Microstructure The microstructure of the parts A and B are shown in Fig 24, 25. In the three figures, part (a) is the spline formed by CCF and part (b) is that formed by OCF (f=20Hz). As we can see, the deformation of the grain in part (b) is more significant than that in part (a). Known from Fig.24, the variation of the strain in the surface layer is considerably changed. Corresponding to the microstructure, the grain in the surface layer is compressed in CCF. As is shown in part (a) of the Fig.24, the metal in the surface layer is compressed so seriously that the width of grain refinement is about 50 m . However, the deformation of the grain in part (b) is uniform. This phenomenon is 14
related to stress relaxation during the back stroke in the OCF, which indicates the deformation is homogeneous and the metal flows easily. Fig.25 shows the microstructure of the tooth tip. In part (a), the grain in the surface layer is compressed considerably. But the metal flow in part (a) is not as significant as that in part (b). This phenomenon indicates that more metal flows to other region rather than to tooth tip in CCF. The metal flow in OCF is more beneficial to the forming of the spline than that in CCF.
4. Summary and outlook In this paper, the oscillating cold forging (OCF) and the conventional cold forging (CCF) have been investigated by both experiment and simulation. The differences of forming force, friction condition and material flow between the OCF and the CCF were discussed. And also, the effects of elastic deformation of die and the change of hardness are studied by experiment and simulation. The main conclusions are summarized as follows: (1) The forming force of the OCF decreases 25% compared to the CCF, during the forming process of the spline shaft. The factors can be concluded as friction condition, the elastic deformation of die, hardness and metal flow (17% of the reduction is caused by friction and 8% by others). (2) Scratches and indentations can be observed on the tooth surface of spline by using CCF. However, the spline formed by OCF has smooth tooth surface. The higher oscillating frequency in OCF leads to lower friction and less metal pileup in the spline shaft. For further investigation, the constitutive relationship should be built according to the stress station rather than the simplified model was used in this paper. Strain rate has to be took into account. 15
Furthermore, the change of grain which observed from TEM and the phenomenon on other metal type are being studied.
Acknowledgements The authors are grateful to the Key Technologies R & D Program of Shaanxi province of China (grant no. 2014K08-34) for funding this study.
16
Derivations of the equations in Section 2.2
The velocity of the flow between two flat is u , v w 0 . Because of the viscosity, the velocity gradient u / z is existed. According to the equation of continuity, u / x 0 . Besides, the direction y is so large that u / y can be ignored. As for the incompressible fluid, the NavierStokes (N-S) equations can be simplified as below: 1 1 1
p 2u 2 0 x z p 0 x p 0 z
(1)
From the latter two equations, pressure p is only changed in x direction and u is only the function of z. Because of the distance of two flat is constant in x direction, the gradient of p is uniform. So, p p2 p dp p 1 x dx l l
(2)
2u 2u z 2 x 2
(3)
d 2u 1 dp p l dz 2 dx
(4)
Then, the first equation is:
After integral, u
p 2 z C1 z C2 2 l
(5)
The boundary conditions are: z 0, u U z , u 0
After substituting the condition (6) into (5):
17
(6)
C1
p 2 U z , C2 U 2 l
(7)
u
p z ( z ) z U 1 2 l
(8)
So,
If the lower slab is stable, the equation (8) is: u
p z ( z ) z +U 2 l
(9)
And the flow is:
Q ubdz
(10)
b 3 p b U 12 l 2
(11)
0
Then, Q
The liquid in the gap is seemed as parallel velocity, u u z , v w 0 p p dp p y 0, z 0, y dx
(12)
As for the flow between two slant slab, the rate of change of the pressure dp/dx is not constant. So, the N-S equation can be simplified as below: d 2u 1 dp dz 2 dx
(13)
1 dp 2 z C1 z C2 2 dx
(14)
After double integral for z: u
The boundary conditions are: z 0, u U z , u 0
Taken into the equation (14):
18
(15)
1 dp U h , C2 U 2 dx h
(16)
1 2 dp z z hz U 1 2 dx h
(17)
C1
So, the equation (14) is u
The flow Q, crossed any section, is: h h 1 dp z Q ubdz z 2 hz U 1 bdz 0 0 2 dx h
(18)
After integral: Q
bh3 dp bh U 12 dx 2
(19)
The gradient of pressure along the x is: dp 6U 12 2 3Q dx h bh
(20)
h h1 x tan
(21)
dx dh / tan
(22)
6U 12Q dp 3 2 dh bh tan h tan
(23)
From Fig.2:
So,
Taken into equation (20):
After integral: p
6 Q 6U C 2 bh tan h tan
(24)
As for the boundary conditions are h=h1, p=p1, the constant parameter C is: 6 Q 6U bh12 tan h1 tan
(25)
6 Q 1 1 6U 1 1 2 2 b tan h1 h tan h1 h
(26)
C p1
Taken into (24): p p1
19
When the boundary conditions are h=h2, p=p2: p2 p1
6 Q 1 1 6U 1 1 2 2 b tan h1 h2 tan h1 h2
(27)
The difference of the pressure is: p p1 p2
6Q h12 h22 b tan h12 h22
6U h2 h1 tan h1h2
(28)
Due to the equation tan (h1 h2 ) / l , the flow Q can be expressed as below: Q
bh1h2 h1h2 p U h1 h2 6l
(29)
When the confine is gradient and mobile, the flow of lubricant can be divided to two parts: Circle flow Q1 and Circular cone flow Q2 , which are nearly determined through Reynolds equation:
b 3 b p U 12l 2
(30)
bh1h2 h1h2 ( p U ) h1 h2 6l
(31)
Q1 Q2 Among them,
Q is the flow of lubricant; b is the equivalent width which is approximated
as d in circle condition;
is the height of circle flow;
the length from the circle flow entrance to the end;
is the viscosity of lubricant; l is
p is the differential pressure from the circle
flow entrance to the end; U is the velocity of the die; h1 is the height of the circle flow entrance;
h2 is the height of the end. 20
From fluid mechanics:
b l1 t1
(32)
dl2 (h1 h2 ) 2t2
(33)
Q1
Q2 From geometrical relationship：
h1 sin 60
(34)
h2 h1 l2 tan 30
(35)
Then, the relationship of parameter t, l and
t1
p can be expressed as the equation below:
l1 p p U 12l1 2 2
l2 (h1 h2 ) 2 2 t2 h h p h1h2 ( 1 2 U ) 6l2 As for OCF which the frequency is 10Hz, h1 is
and
(36)
(37)
0.6 mm, p is 0.1Mpa, U is 18mm/s 3
is 0.485 Pa•S. The equation is ploted as 3D surface in the Fig.4 and Fig.5 below. As the figures show, the time
to make the length of lubrican flow more than 0.5mm is about 0.02s, which is enough for the process. The lower
is better for flow. The chosen lubricant, is 0.485 Pa•S, is satisfied for working
process.
21
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Fig.1 Forming process
Fig.2 The oscillating extrusion machine
Fig.3 The size of the die (Unit: mm)
Fig.4 Lubricant flow condition
Fig.5 Flated surface (b) of the relationship of parameter t,
l
and p
Fig.6 Shape of specimen
Fig.7 True stress-strain curve for simulation
Fig.8 3D FE model
Fig.9 Stroke-time curve of the OCF (f=20Hz)
Fig.10 Variation of C for the velocity function f(vrel)
Fig.11 Von-Mises stress and velocity distribution of the workpiece in different condition
Fig.12 Diameters of the top of the tooth with different friction condition
Fig.13 Distribution of elastic displacement of the die in CCF and OCF (f=20Hz)
(a) Total power in CCF and OCF (f=10Hz) (b) Comparison of plastic power in CCF and OCF (c) Comparison of friction power in CCF and OCF (d) Comparison of elastic power of the die in CCF and OCF (f=20Hz) Fig.14 Power in different processes
Fig.15 Force-stroke curve the OCF compared with the CCF
Fig.16 Spline formed by normal forging
Fig.17 Spline formed by oscillating forging
Δs is the distance to the top of the spline; D is the diameter of shaft. Fig.18 Diameters of the spline along the axial direction
Fig.19 Force-stroke curve of CCF and OCF experiment with different friction condition
(a) CCF with different friction factor
(b) CCF and OCF with the same friction factor m=0.02
Fig.20 Force-stroke curve of CCF and OCF with different friction condition
Fig.21 Equivalent strain distribution along the section surface
Fig.22 Vickers microharness of the OCF and the CCF
Fig.23 The relationship of strain and hardness
Fig.24 Microstructure of the part A by the CCF (a) and the OCF (b)
Fig.25 Microstructure of the part B by the CCF (a) and the OCF (b)
Fig.1 Flow between two flat
Fig.2 Flow between two slant flat
Table 1 chemical compositions of AISI 1045A
C 0.34-0.52
(wt.%)
Mn
Si
S
0.51-0.81
0.28-0.48
0.01-0.069
P 0.017-0.044
Table 2 Parameters in Eq.9
A 874.31
m1
m2
0.1908
0.025
m3
0.0031
Table 3 Friction factors got from fitting in Fig.20 Frequency (Hz)
m
C
0
0.15
10
10
0.125
5
15
0.1
2.5
20
0.08
1