Precision cold die forging of a ring gear by divided flow method

Int. J. Mach. Tools Manufact. Vol. 35. No. 8. pp. 11115-1113. 1995 Copyright ~) 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 08~1-6955/9559.511 + .00

Pergamon

PRECISION

COLD DIE FORGING OF A RING DIVIDED FLOW METHOD

GEAR

BY

K. KONDO¢ and K. OHGA:~ (Received 20 January 1994; in final form 26 July 1994) Abstract--The process utilizing divided material flow is applied to working a ring gear. When the specimen is of a larger height and the ratio of the height to the radial thickness is large, the central material flow in the radial direction produces a time lag in both the upper and a lower material flow which causes a product defect. The theoretical calculation suggests that the above phenomenon can be eliminated when the side shape of a specimen is swollen at the central portion. Various experiments are carried out based on the above estimate. The experiment makes clear that it is useful to swell the side shape. When the side shape is that of a beer-barrel with a small radius of curvature, the working pressure is reduced. A ring gear of high accuracy can be forged under the mean pressure of about 2.6 times the final uni-axial compressive yield stress of the worked material.

1.

INTRODUCTION

As an effective way of improving the accuracy of cold forged products, a process utilizing divided material flow has been proposed by the authors [1-3]. In this process, a relief-hole is set artificially into the material. The filling of a die cavity with material is preceeded by the reduction of the relief-hole. In this way, a precisely shaped product is forged under a low working pressure. Ring gears are widely used as an actual machine part. Most of the products have been manufactured mainly by machining. In machining, the long working time and low material usage is a big problem. Needless to say, it would be more economical if the products could be produced by forging. This research aims to make clear the applicability of this process to a ring gear. 2.

2.1.

THEORETICAL ANALYSIS

Preliminary consideration

When the process utilizing divided material flow is combined with the conventional closed die forging as shown in Fig. 1, the process becomes more useful [4-8]. i~ ~Da d

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Fig. 1. Two steps forging process proposed by the authors.

tDepartment of Mechanical Engineering, Faculty of Engineering, Nagoya University, Furo-cho, Chikusaku, Nagoya-shi, 464-01 Japan. ,Department of Mechanical Engineering, Numazu National College of Technology, 3600. Ooka. Numazushi, 410, Japan. !105

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K. Kondo and K. Ohga

resistance a.Y ( FrJctJona] on the depressing p]atens )

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UnfJ]]ed portion { Product defect }

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( FrJctiona7 resistance) on the slde-wa]]s Fig. 2. An example of product defect in a spur gear.

In this two step forging process, when the value of Ho/ra or Ho/W shown in Fig. 1 is increased, an unfilled portion remains on the worked material as shown in Fig. 2 and causes a product defect. A ring gear has a comparatively small radial thickness. In order to reduce the working load, when a ring specimen is adopted, the value ho/W increases. It is important, therefore, to adopt some means to eliminate the above defect. If the defect arises during the first step, the defect can not be eliminated during the second forming step either because a new inward material flow is added in the second step. This means that the ratio of the height to the radial thickness becomes larger, that is, the defect is increasingly accelerated. First, the initiation of this defect is considered theoretically. 2.2. Simple working model for analysis When a ring gear is worked by the two step forging process shown in Fig. 1, it is complicated to analyze precisely the profile of the product. Here, a simple working model is adopted to examine the profile. In forming a ring gear, the material flow into a toothed die cavity is restricted by the toothed side-walls of the die, so the material deformation in the cavity can be considered similar to that of a plane strain state. As shown in Fig. 3, therefore, the simple working model of a plane strain deformation to a rectangular block is adopted and the profile of the worked material is analyzed. The upper bound elemental technique or U B E T is adopted in the analysis. The Zaxis direction is the depth of the specimen and the deformation is restricted by the Y. / //~-"

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two rigid side-walls. In the analysis, a non-uniform deformation is assumed to occur only in the Y-axis direction. The assumed kinematically admissible velocity fields are also shown in Fig. 3. The specimen is sliced into equal pieces in the Y-axis direction. The number of slices can be varied freely. The coefficients, ak, bk and ck in the formulae can be selected arbitrarily. They must, however, satisfy the continuous condition of the velocity on the boundary surface of the worked material. Based on the assumed velocity fields, the dissipation rate H? of the total energy can be calculated. The rate W is minimized by use of the quasi-Newton method in mathematics. 2.3.

Calculation of results and their consideration

In a ring gear, the thickness of a tooth is quite small compared to its whole size. This corresponds to the smaller depth W. Accordingly, in Fig. 3, the initial size of the rectangular block is taken as 10 mm in 2H, 10 mm in 2B and 2.5 mm in W. Figure 4 shows the calculated results of deformation for a quarter portion of the material. In Fig. 4, the value fa is the edge surface friction factor on the depressing platens and the value fb is the surface friction factor on the side-walls. These values are varied from zero to 0.577. Each surface frictional resistance is related to the following equations of F, = f , Y and Fb = fb Y, where Y is the uni-axial compressive yield stress of the worked material. Figure 4(a) shows the profile of the worked material when the friction factors, fa and fb are both equal to 0.05, corresponding to a low frictional condition. In this case, the material deforms almost entirely with a straight profile throughout the test. Figure 4(b) shows the result when the factors, fa and fb are both equal to 0.30, corresponding to a middle frictional condition. In this case, a new concave profile arises in the central portion. From the above, it is said that the surface friction on both the depressing platens and the side-walls influences intensely the profile of the worked material. Figure 4(c) shows the result when f, and fb are both equal to 0.50, corresponding to a high frictional condition. The frictional resistances act more intensely and the large concaved profile is built up. If this concave profile exists in the first working step, it can be easily seen that the product defect shown in Fig. 2 will occur. Therefore, it is important not to make any concave profile arise during the process. In this analysis method, the calculation procedure can be easily reversed by changing the calculation program a little. As mentioned above, the product defect is apt to arise in the second working step, therefore, it is desirable to make a sufficiently convex profile at the first working step.

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Fig. 5. Sizes and the side shapes of adopted specimens. Table 1. Dimensions of an adopted super ring gear N u m b e r of tooth Module ( m m ) Pressure angle A d d e n d u m modification coefficient Tooth profile: Standard full depth tooth

68 1.0 20 ° 0

As an example of the desirable convex profile, @ shown in Fig. 4(d) is adopted. This means large swelling at the central portion of the material worked at 60% of the depression shown in Fig. 4(b). The reverse calculation is carried out by using this convex profile as the initial material shape. Figure 4(d) shows the result. When the side specimen shape (~) shown in Fig. 4(d) is selected, no concave profile arises during the working. That is, the result of the calculation suggests the following. When the side shape of a specimen is swollen at the central portion, the surface frictional resistance itself has no capacity to absorb the swollen shape and change it to a concave profile throughout the working. The material deformation makes good progress continuously with the swollen shape. This means that the product defect mentioned above can be eliminated clearly. 3.

EXPERIMENTAL CONDITIONS

Firstly, as shown in Fig. 5(a), the outer side of the usual ring specimen is chamfered at 28° for simplicity of specimen preparation. This new specimen is called a two faced specimen, hereafter. The usual ring specimen shown in Fig. 5(b) is also adopted in the experiment. The outer diameter of these specimens is equal to the root circular diameter of an adopted ring spur gear. In the ring specimen, the ratio of the height to the radial thickness is about 1.5. Therefore, the product defect mentioned above may easily occur. Next, the experiment is carried out based on the calculation result. Table 1 shows the dimensions of an adopted involute external spur ring gear. The specimen used is a commercially pure aluminium or A1050BE shown in Table 2. The lubricant used is a beef-tallow and the working temperature is room temperature. Figure 6 shows the working procedure. The two faced specimen is put into the toothed die and the mandrel which has an equal diameter to the inner one of the specimen is inserted into the inner hole. As the first working step, the conventional closed die forging is started and stopped at a moderate working load. Next, the mandrel is rearranged to make a relief portion of the material. The second working step, or the process utilizing divided flow, is started. In this step, it is important to adjust the external and the internal material flow. The mandrel is therefore inserted into the relief portion moderately. The value of this insertion is called a flow restriction value k, hereafter. The upper and lower values of k are equal to each other. Table 2. Material property of the specimen Material JIS Heat treatment n-powers law

Commercially pure aluminium A1050BE 400°C x 1 hr (Annealing) cr = 130 e"2s (MPa)

Precision Cold Die Forging

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Fig. 6. Working procedure and tool construction.

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Fig. 7. Definition of filled-up rate B*.

After the second working step is completed, a tooth top of the product is observed in detail. The items to be observed are the unfilled length l*, the maximum unfilled depth d,,~ and the filled-up length L* as shown in Fig. 7. The percentage of the filledup length to the product height is defined as the filled-up rate B*. 4.

EXPERIMENTAL RESULTS AND THEIR CONSIDERATION

Figure 8 shows an example of the appearance of the tooth top and the schematic profile when the usual ring specimen is adopted. The product defect mentioned in section 2 is observed clearly at the central portion of the tooth top. Various experiments using the ring specimen shown in Fig. 5(b) are performed by changing the flow restriction value k and the working pressure p. From the experiments, it is confirmed to be much more difficult to make the value d,,~ zero. Therefore, the usual ring specimen is not suitable for working a ring gear. Figure 9(a) shows the result when the two faced specimen is adopted. The abscissa denotes the final working pressure p~ of the first step and the ordinate denotes the final working pressure p~ of the second step. The flow restriction value k is set to 0.5 ram. The white circular marks shown in Fig. 9(a) mean that the material fill-up percentage 8" is under 90% and the half blackened marks mean over 90% in B*. The

Fig. 8. An example of appearance of the tooth top and the schematic side profile.

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200 300 400 Working pressure p~ MPa (a) The case of k=O.5mm

Fig. 9. Filled-up state of the two faces specimen.

blackened mark means complete fill-up. In Fig. 9(a), it is confirmed that the product defect observed in the usual ring specimen is eliminated by using the two faced specimen. That is, it is useful to swell the side shape of the specimen. Figure 9(b) shows the result when the flow restriction value k is set to 1.0 mm. As in Fig. 9(a), the product without any defect can be obtained. The working pressure, however, becomes larger. This means that there exists an optimum flow restriction value k in this working. When the value k is set to 0.5 mm, the fractional working pressure p*~/Y* of the blackened mark is about 3.7, where Y* is the uni-axial compressive yield stress of the material at the final stage of the second working step. The value Y* can be obtained by the n-powers law shown in Table 2. The material property is changed to A1050BD as shown in Fig. 10. Figure 10 also shows the results. The abscissa denotes the fractional working pressure P*2/Y*. The result in A1050BE is added in Fig. 10 for comparison. When A1050BE is used as the material property, the value p~/Y* which gives 100% in 8* is about 3.7. On the other hand, when A1050BD is used, the value P*2/Y* becomes lower and the product without any defect can be obtained within 3.3 in p~. Y*. It is confirmed that this is influenced by the sizes of the surface roughness of the work material. In the above experiments, the two faced specimens are used throughout. The specimen shape, however, is not always the best. Moreover, a beef-tallow is used as the lubricant and this is not always ideal, either. Better working conditions are therefore examined. At first, the four faced specimen shown in Fig. 11 is adopted. This four faced specimen is made by machining the outer sharply pointed portion of the two faced specimen shown in Fig. 5(a). Additionally, lubrication using a chemical treatment, or Al-bond and soap, is newly adopted. This lubrication is used widely in actual production. Figure 11 shows the result, where A1050BD is used and the value k is set to 1.0 mm. In Fig. 11, when the lubricant is a beef-tallow, even if the value P*2/Y* is given over 3.4, a completely filled-up product cannot be obtained. On the other hand, when the Materia] property of the specimen Material Commercially pure alum~n~um dIS AIO5OBD Heat treatment 320'Cxlhr(Annea]~n~) n-powers law

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lubrication is Al-bond and soap, the completely filled-up product can certainly be obtained at a value of 2.7 in P*2/Y*. This value is low in comparison with a series of experimental data observed above and is therefore worth noticing. In an actual production, the swollen specimen must be prepared as quickly as possible. If this swollen specimen can be formed by upsetting, it is very desirable. In this case, the side shape of the specimen comes a beer-barreled one. Firstly, as shown in Fig. 12(b), the barreled specimen is approximated by a four faced specimen which can be made easily. As shown in Fig. 12(a), the barreled specimen can be thought of as the specimen which varies the angle 0 continuously. Figure 13 shows the experimental result of the approximated four faced specimen,

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Fig. 14. Filled-up state of the barreled specimen

where A1050BD is used as the material property. When the approximated four faced specimen with radius of curvature R of 10.4 mm is adopted in the experiment, an unfilled section arises at the central portion of the tooth top. This case, therefore, is not suitable for working a ring gear. When the approximated four faced specimen with 4.0 mm in R is adopted, the completely filled-up product, or the product with zero in A and B, is obtained at 335 MPa in p~. On the other hand, when the approximated four faced specimen with 5.2 mm in R is adopted, even if the same pressure is given to the specimen, the precisely shaped product is never obtained. This means that the approximated four faced specimen with a smaller radius in curvature is preferable for the working. Next, the actual barreled specimen whose radius R is 4.0 mm is prepared by upsetting. This specimen is examined. Figure 14 shows the result. The data of the approximated four faced specimen with 4.0 mm in R is also added in Fig. 14 for comparison. When the actual barreled specimen is used, the completely filled-up product is obtained at 308 MPa in p$. The pressure p~ becomes considerably lower than these above and the fractional working pressure p~/Y* is about 2.6. Therefore, it can be considered that the two step forging process adopted in this research is also applicable to the actual specimen of steel etc. A low carbon steel of S10C is now used in the experiment with the working conditions shown in Fig. 15. As shown in Fig. 15(b), the precisely shaped product in the tooth

Working condition of (b) Material Low carbon steel, Annealed JIS S~OC Side shape Barreled Bonder~te Lubrication Bonda]ube (a) MO5OBD

(b) SIOC

Temperature Room temp.

Fig. 15. Aluminium and steel products worked by the two steps forging process.

Precision Cold Die Forging

1113

top could also be obtained. The fractional working pressure is about 2.6 and this value is the same as the one in the above pure aluminium. From the above, it is confirmed that if the side shape of a specimen is suitably selected, a ring gear without any defect can be forged precisely under a low working pressure. 5.

CONCLUSION

The precision cold die forging utilizing divided material flow is applied to the working of a ring gear. The obtained results are as follows. (1) The theoretical calculation suggests the following items. When a ratio of the height to the radial thickness of a specimen is set large, a defect arises near the central portion of the product. This defect depends on the dimensions of the surface frictions on both the depressing platens and the side-walls of the toothed die. In order to eliminate this defect, it is useful to swell the side shape of the specimen. (2) The experimental results have made the following items clear. When a thin thickness ring specimen is worked under the floating die system, an unfilled portion arises at the central portion of the tooth top. In order to eliminate this defect, it is effective to swell the side shape of the specimen as suggested from the calculation. A barrel-shaped specimen with a small radius of curvature is useful for reducing the working pressure. A precisely shaped ring gear without any defect can be obtained at the low mean working pressure of about 2.6 times the final uni-axial compressive yield stress of the worked material. From the above, the process utilizing divided material flow is useful for working a ring gear. REFERENCES [1] K. Ohga and K. Kondo, Research on precision die forging utilizing divided flow (First report, Theoretical analysis of processes utilizing flow relief-axis and relief-hole, Bull. JSME 25(209), 1828-1835 (1982). [2] K. Ohga, K. Kondo and T. Jitsunari, Research on precision die forging utilizing divided flow (Second report, Experimental study of processes utilizing flow relief-axis and relief-hole), Bull. JSME 25(209), 1836-1842 (1982). [3] K. Ohga, K. Kondo and T. Jitsunari, Research on precision die forging utilizing divided flow (Third report, Study on an optimum combination by 'two step method' proposed anew), Bull. JSME 25(209), 1843-1850 (1982). [4] K. Ohga, K. Kondo and T. Jitsunari, Research on precision die forging utilizing divided flow (4th Report, Influence of restricting a centripetal flow), Bull. JSME 26(218), 1434-1441 (1983). [5] K. Ohga, K. Kondo and T. Jitsunari, Research on precision die forging utilizing divided flow (5th Report, Application to actual machine parts), Bull. JSME 28(244), 2451-2459 (1985). [6] K. Kondo, T. Jitsunari and K. Ohga, Investigation on cold die forging of a gear utilizing divided flow (1st Report, Examination of applicable condition for a spur gear), Bull. JSME 28(244), 2442-2450 (1985). [7] K. Kondo, Developments of new precision cold die forging processes, Proc. 1st Int. Con. on Tech. o f Plasticity, pp. 878-887, Tokyo (1984). [8] K. Kondo, K. Ohga and K. Hori, Investigation into forming processes of various spur gears, Proc. 2rid Int. Con. on Tech. o f Plasticity, pp. 1089-1096, Stuttgart (1987).