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Continuous generating grinding—Tooth root machining and use of CBN-tools
CIRP Annals - Manufacturing Technology 61 (2012) 291–294
Contents lists available at SciVerse ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Continuous generating grinding—Tooth root machining and use of CBN-tools Jens Ko¨hler *, Andreas Schindler, Stephan Woiwode Institute of Production Engineering and Machine Tools, Leibniz Universita¨t Hannover, Germany Submitted by A. Ber (1), Haifa, Israel.
A R T I C L E I N F O
A B S T R A C T
Keywords: Gear grinding Dressing Cubic boron nitride (CBN)
Profile accuracy, no burning and residual compressive stresses at the tooth root fillet are required for the durability of highly stressed gears. This paper reveals the challenges for continuous generating grinding with corundum and CBN. For this purpose, material removal simulations and experimental investigations were carried out to gain knowledge of the tool–workpiece contact conditions. The potential of CBN tools was analysed due to the fact that the mechanical loads at the grinding worm tip result in high profile wear of the corundum tools. In this context, especially the interrelationship between the dressing strategy and the workpiece quality was investigated in detail. ß 2012 CIRP.
1. Introduction The gear lifetime mainly depends on the residual stresses at the tooth flanks, root fillet and surface roughness. Pitting and micro pitting on tooth flanks is caused by Hertzian stress and primarily influenced by surface roughness and lubrication conditions [1]. Compressive residual stresses up to 600 MPa and a low surface roughness enhance the bearing capability of the tooth flanks [1,2]. Fatigue cracks, which result from high bending stresses, mostly occur at the root fillet especially when a small root fillet radius is generated. In contrast to surface damages, fatigue cracks cause tooth breakage resulting in a gear transmission failure [3]. Consequently, high compressive residual stresses are required in the root fillet area to avoid the formation and growth of fatigue cracks [4–6]. In comparison, the influence of the root-fillet surface roughness on the formation of fatigue cracks is not significant [7]. In order to improve the wear resistance of generated tooth flanks, most gears in modern transmissions are heat-treated. The resulting geometry deviation requires a further finishing process, which is grinding in most cases [8,9]. The common process in the industry is continuous generating grinding. Although profile grinding of the tooth root fillet can increase the gear lifetime up to 30% [7], continuous generating grinding has been applied for it infrequent. The main reason for this could be the missing knowledge of the tool–workpiece contact conditions and the resulting thermo-mechanical loads on the workpiece in continuous generating grinding. This may lead to tensile residual stress and a high wear rate of the grinding wheel. One approach to handle this problem is the use of CBN grinding wheels [10]. 1.1. Continuous generating gear grinding The kinematics of continuous generating grinding is similar to the rolling motion of two gears. In this process, several gear teeth
* Corresponding author. 0007-8506/$ – see front matter ß 2012 CIRP. http://dx.doi.org/10.1016/j.cirp.2012.03.033
are in contact with the grinding worm. At the same time, several theoretical points of contact occur for each of the teeth in contact. The involute of a tooth flank and the tooth root are determined by the process kinematics [11,12]. During the contact of tool and workpiece a sliding motion between the tooth flanks appears, defining the cutting speed vc for the material removal. In order to machine the entire tooth width of the gear, an axial movement is required which is specified by the feed rate vf (Fig. 1a). The common tool concepts for continuous generating grinding are vitrified-bonded tools with corundum and electroplated CBN (cubic boron nitride) as a cutting material. Vitrified-bonded corundum tools can be dressed easily and they are considerably more favourable than galvanic CBN tools. However, galvanic CBN tools enable high material removal rates and consequently a higher productivity. Vitrified-bonded CBN tools in general combine the advantages of both tool concepts: a long tool lifetime and a good dressability. So far, vitrified-bonded CBN grinding tools have not been used for continuous generating grinding. On the one hand, a reason might be the fact that there are no detailed investigations with these tools. On the other hand, CBN grains lead to a high wear rate of the dressing tool during dressing. Thus, conventional dressing strategies cannot be applied. For an efficient use of CBN tools it is required to reduce the dressing tool wear rate and to generate an advantageous worm topography [10,11]. 1.2. Grinding worm dressing The tool geometry and its topography are adjusted by the dressing process to achieve the required gear surface and subsurface properties. Typical dressing tools are form and profile rollers as well as master gears [10,11]. Due to the simultaneous dressing of all grinding wheel threads, the master gears provide a remarkable reduction of the dressing time [10,13]. Dressing with form rollers can be compared with thread turning (Fig. 1b). The specific geometry of the grinding worm results in high demands on the process kinematics. Due to the kinematic coupling of the involved NC axes of the grinding machine, the worm speed vcd and
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292
Fig. 1. Kinematics of continuous generating grinding (a) and tool dressing (b).
the axial dressing feed velocity vfad are synchronized to each other. In conventional grinding processes, a dressing speed ratio between qd = 0.8–1.2 is used for the dressing of CBN tools. At these dressing speed ratios, the wear rate of the dressing tool is very low. Due to the kinematic coupling of the NC axes in continuous generating grinding machine tools and inefficient dressing spindles for low rotational speeds, it was previously not possible to reach this range for continuous generating grinding. Speed ratios of about qd = 20, which generally result in high wear of the dressing tool, are therefore applied. In addition, this leads to a closed topography of the grinding layer which may result in grinding burn and a decrease of the productivity [10].
Fig. 2. Calculation of the characteristic values for continuous generating grinding.
Fig. 3. Variation of the gear tip geometry and dressing strategy.
2. Experimental set-up and methods 2.1. Grinding experiments and process characterization In order to characterize the continuous generating grinding process, corundum tools were used in the experiments. Since the flank machining process has already been analysed in [10,14–16], the focus is on the root machining. The process parameters were kept constant. The variation of the tool tip geometry was defined with respect to the DIN standard 3972 [17]. Grinding and dressing experiments were carried out on a KAPP KX1 gear grinding machine using case hardened and shot-peened spur gears made of steel 20MnCr5 (see Table 1). The grinding allowance was removed in one step without an axial shift of the tool. Grinding forces were measured with a Kistler 9167A dynamometer. In order to characterize the macro geometrical wear of the grinding tool, the profile of the ground gear tooth space was measured by the precision coordinate measuring machine Leitz PMM 866. In addition, the tooth flank roughness was measured by a Mahr Perthometer PGK. The gear subsurface integrity was characterized by residual stresses measured via an Xray diffractometer XRD 3000P applying the sin2 c method. 2.2. Material removal simulation The material removal during grinding was simulated according to the experimental investigations to gain knowledge of the tool– workpiece contact conditions. For this purpose, a two-dimensional material removal routine was developed according to Meijboom [18] using the numerical computing environment MATLAB. The tool profile is modelled according to the DIN standard 3972 [17]. The workpiece profile is built according to an exemplary tooth space measurement of a real unmachined gear. Cutting areas in cross section normal to the gear are calculated by Boolean operations, while the tool and workpiece profiles are repositioned incrementally analogue to the process kinematics. Fig. 2 presents the calculation of characteristic values. The chip cross-sectional area Aw is spanned between workpiece and tool
profile geometries of two proximate time steps depending on the time increment Dt. By multiplying the sum of all removed areas Aw by the feed per gear revolution f it is possible to calculate the material removal volume Vw. The material removal rate Qw subjected to a single machined tooth space can be determined by dividing the material removal volume Vw by the tooth space machining time. With the simultaneous, multiple tooth space machining the accumulated material removal rate is higher than Qw subjected to a single machined tooth space. 3. Characterization of the machining process In order to generate the worm profile (worm 1), a doubletapered dressing roller (dresser 1) with a defined external radius was used. While dressing the worm tooth flanks, the dressing roller was used as a profile roller, whereas the conditioning of the worm tooth tip was realized by a path controlled profiling using the profile radius of the dressing tool. The advantage of this method is the time saving profiling of the flank profile. At the same time, a high flexibility for the generation of the addendum profiles is assured (Fig. 3). The variation of the worm gear tip geometry leads to different material removal rates Qw and consequently affects machining forces Fx and Fy (Fig. 4a). Particularly the increasing tool addendum leads to a higher radial depth of cut arr in the tooth root area as well as a higher material removal rate Qw subjected to a single machined tooth space. Consequently, the process forces increase. The variation of worm tip radii leads to a noticeable change of the material removal rate Qw, although it only influences the maximum machining forces significantly when the tool addendum is small. Higher machining forces cause amongst others a higher load on the tool. Due to the helix angle, the tool wear cannot be determined by common methods like graphite grinding. Therefore, the abrasive macro geometrical tip wear is quantified by the profile deviations of the ground workpiece. Measured deviations in the
Table 1 Applied tool and workpiece specifications. Dressing tool
Grinding tools
Ground gears
Dressing roller Dresser 1: grain size Dresser 2: grain size External diameter dd Pressure angle ad Profile radius rpd
Worm 1: 71A120I14V85-10 Worm 2: A80J10V Worm 3: B126M7/6V Normal module mn0 Numb, of threads Z0 Pressure angle an0
Normal module mn Number of teeth z Pressure angle an Helix angle b Hob profile DIN3972
D301 D501 150 mm 208 0.51 mm
4.5 1 208
4.5 24 208 08 BPIII
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to reduce the dressing speed ratio in order to decrease the dressing tool wear rate and to gain an advantageous tool topography.
4. Grinding with vitrified-bonded CBN worms
tooth root fillet area are always higher than on the tooth flanks even for an identical normal depth of cut. The maximum profile deviation normal to the ground gear space surface is presented in Fig. 4b. The increase of the worm addendum and decrease of the tip fillet radii leads to greater profile deviations. Since these two variables affect the removed material volume Vw root in the tooth root directly, the whole material removal of all tooth spaces in this area can be used to estimate the maximum profile deviation and therefore the grinding worm tip macro wear. In order to quantify the structural changes of the workpiece subsurface due to the machining process, in the first step the residual stress profile of an unmachined workpiece was measured (black line in Fig. 5). A typical residual stress depth profile after the heat treatment and shot-peening has been observed. After grinding the residual stresses at the workpiece surface have been determined. These results are presented by the shaded areas. It was not possible to exactly determine the removed material allowance at the measuring point for unmachined gears due to concentricity errors of up to 35 mm. These dimensional errors affect the cutting depth. With respect to this, the shaded areas have a variation width of 70 mm (35 mm). Depending on the grinding tool tip geometry, different material volumes have been cut, though the measured values correspond to different distances to the unground surface of the gear. The residual stresses of ground surfaces correlate with the residual stresses in the corresponding depth of the unmachined gear. Due to the grinding process the residual stresses in the tooth root subsurface are shifted towards compressive residual values. This indicates that the original residual stress state of the workpiece is positively influenced by the tooth root area grinding. The grinding of tooth roots leads to advantageous subsurface properties. The high wear of corundum tools, which leads to high profile deviations, is faced with the use of CBN tools offering an improved wear behaviour. However, the dressing of the CBN worm for continuous generating grinding is demanding. The approach is
CBN tools lead to a higher productivity and to a good wear resistance resulting in an improved workpiece quality compared to corundum tools. In order to compare the wear behaviour, gears are ground with vitrified-bonded CBN and corundum tools without intermediate dressing. The same process parameters where used for the machining of both series. The tool wear was quantified by determining the tooth width W4 across four teeth for each ground gear. Out of this data the tooth width alteration is determined as the change of the tooth width compared to the first ground gear. An increasing tool wear leads though to an increased tooth width. When the fifth gear was ground with CBN, the tooth width increase was one third of the gears ground with a corundum tool. In addition, the increase of the tooth width started to decrease after machining the fifth gear for the CBN tool (Fig. 6a). Thus, the full grinding allowance of the tooth flanks can be removed by a single operation without significant wear of the grinding tool. Furthermore, the influence of the dressing speed ratio on the process performance was analysed. To this day, the dressing speed ratio was limited due to a missing technology for a dressing unit in the machine tools. For this reason, a new dressing unit was developed to provide low dressing speeds and a sufficient torque to cope with the high dressing forces at low dressing speed ratios. High dressing speed ratios lead to a smooth tool topography and offer less space for chips while grinding with high removal rates. They can also cause friction, thermal damage and higher process forces. In Fig. 6b, the average roughness height Ra of the ground gear is plotted against a batch of ten gears. Here, the roughness of the workpiece approximates to Ra = 1 mm. This condition is reached after machining the fifth gear for the used CBN grinding worm. In order to avoid a quasi-constant grinding layer topography, dressing after each ground gear is necessary. A quasi stationary topography should be obtained directly after dressing to keep the ground surface roughness constant (Ra = 1.0 mm). Therefore, a dressing ratio of qd 4 is recommended (Fig. 6b). To analyse the impact of the dressing conditions on the surface quality, the dressing speed ratio was varied between qd = 1.2 and 6. In Fig. 7, the roughness values are plotted against the dressing speed ratio. Here, the roughness values increase with a decreasing dressing speed ratio and converge against Ra = 1 mm. The dressing effect is in direct relation with the grinding wheel topography. In order to obtain a sharp and open topography of the grinding layer, the dressing speed ratio qd was reduced by lowering the dressing tool speed vd while keeping the grinding tool speed vcd constant. Thus, the dressing process is carried out in the same time. With a reduction of the dressing speed ratio qd for the used CBN tool the process forces could be slightly lowered.
Fig. 5. Subsurface residual stresses after grinding.
Fig. 6. Tool wear of CBN and corundum tools.
Fig. 4. Effect of material removal values on grinding forces and gear profile deviation.
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developed to reduce the dressing speed ratio to values applied for conventional grinding processes. The impact of adapted dressing strategies on the grinding wheel layer and the workpiece quality was analysed. Here, small dressing speed ratios of qd = 1.2 lead to a more open grinding layer topography and to reduced grinding forces. With the results presented further investigations for the tooth root machining with vitrified CBN grinding tools are currently in progress. The wear behaviour of different dressing tool specifications for CBN grinding worms is also subject of current research activities. Acknowledgements Fig. 7. Influence of the dressing speed ratio on the gear surface roughness.
The authors would like to thank Prof. A. Ber and Prof. B. Denkena, the German Research Foundation (DFG) and the Federal Ministry of Education and Research for their organizational and financial support within the projects ‘‘Contact conditions by continuous generating grinding of the gear tooth root (DE447/741)’’ and ‘‘Higher productivity for continuous generating grinding through optimized dressing of vitrified CBN worms (KF2328103LK0)’’, which is carried out in cooperation with Dr. Kaiser Diamantwerkzeuge GmbH & Co. KG, Celle, Germany.
References
Fig. 8. Influence of the dressing speed ratio on the mean process forces.
Furthermore the thermal influences of the grinding process on the workpiece have been determined applying a temper etch inspection according to the ISO standard 14104 [19]. The results show, that less grinding burn is detected by applying CBN tools compared to corundum tools. Apart of the workpiece topography also the process forces are influenced by the change of the gear topography due to the dressing speed ratio. The process forces were determined by the first five machined gears. The mean values of Fx = 49.1 N and Fy = 72.7 N (Fig. 8) are measured for qd = 6. The reduction to qd = 1.2 causes a sharp and open grinding layer topography (Fig. 7), which leads to reduced process forces Fx = 46.2 N and Fy = 64.2 N. It appears that a significant difference of the measured mean forces for the material removal cannot be set up before the first gear is ground. This could be assigned to the grinding-in process of the previously dressed grinding tool. 5. Conclusion This paper analysed the continuous generating grinding of the gear tooth root with a focus on residual stresses in the subsurface layer and the macroscopic wear at the tool tip. The experiments show that the residual stresses in the tooth roots can be improved. However, corundum tools show a poor wear behaviour due to the resulting tool–workpiece contact conditions in the tooth root. In order to eliminate the high wear of corundum tools, the performance of vitrified-bonded CBN worms was analysed experimentally. For CBN grinding worms a technology was
[1] Ho¨hn, B.-R., Joachim, F., Tobie, T., Hergesell, M., Ho¨sle, H., Steinberger, G., 2007, Grauflecken - Gru¨bchen - Einfluß der Graufleckigkeit auf die Gru¨bchentragfa¨higkeit einsatzgeha¨rteter Zahnra¨der, FVA (Ed.), 196. [2] Betzold J, Pucelik J, Eisenberg S (2007) Eigenspannungen als Messgro¨ße zur Qualita¨tssicherung. Materialwissenschaft und Werkstofftechnik 38:263–273. [3] NN, 1979, Zahnscha¨den an Zahnradgetrieben, DIN 3979, Deutsches Institut fu¨r Normung. [4] Bahre K (1978) Zum Mechanismus der Wechselfestigkeitssteigerung durch Werkstoffverfestigung und Druckeigenspannungen nach einer Oberfla¨chenbehandlung. Materialwissenschaft und Werkstofftechnik 9:45–56. [5] Benedetti M, Fontanari V, Ho¨hn B-R, Oster P, Tobie T (2002) Influence of Shot Peening on Bending Tooth Fatigue Limit of Case Hardened Gears. International Journal of Fatigue 24:1127–1136. [6] Shaw BA (2003) The Role of Residual Stress on the Fatigue Strength of High Performance Gearing. International Journal of Fatigue 25:1279–1283. [7] Klocke, F., Kempa, B., Schlattmeier, H., 2000, Zahnfußtragfa¨higkeitssteigerung durch optimiertes Schleifen der Zahnfußausrundung, FVA (Ed.), 97. [8] Bausch, T., 2011, Innovative Zahnradfertigung – Verfahren, Maschinen und Werkzeuge zur kostengu¨nstigen Herstellung von Stirnra¨dern mit hoher Qualita¨t, 4. [9] Kohlhoff T, So¨lter J, Brinksmeier E (2011) Influence of the Turning Process on the Distortion of Discs for Gear Manufacture. Production Engineering Research Development 5:613–620. [10] Reichstein M, Catoni F (2006) Grinding of the Gears with Vitreous Bonded CBN-Worm. CIRP Annals – Manufacturing Technology 55:355–358. [11] Karpuschewski B, Knoche H-J, Hipke M (2008) Gear Finishing by Abrasive Processes. CIRP Annals – Manufacturing Technology 57:621–640. [12] Klocke F, Brinksmeier E, Weinert K (2005) Capability Profile of Hard Cutting and Grinding Processes. CIRP Annals – Manufacturing Technology 54:22–45. [13] Wegener K, Hoffmeister H-W, Karpuschewski B, Kuster F, Hahmann WC, Rabiey M (2011) Conditioning and Monitoring of Grinding Wheels. CIRP Annals – Manufacturing Technology 60:757–777. [14] Stimpel, F., 2009, Technologische Kenngro¨ßen fu¨r das kontinuierliche Wa¨lzschleifen von Evolventenverzahnungen, Phd-thesis, Leibniz Universita¨t Hannover. [15] Tu¨rich, A., 2001, Werkzeug-Profilerzeugung fu¨r das Verzahnungsschleifen, Phd-thesis, Universita¨t Hannover. [16] Denkena B, de Leon L, Stimpel F (2009) Characteristic Values for ContinuousGenerating Grinding of Gears. Transactions of the North American Manufacturing Research Institution of SME 37:121–128. [17] NN, 1952, Bezugsprofile von Verzahnwerkzeugen, DIN 3972, Deutsches Institut fu¨r Normung. [18] Meijboom, L.H.M., 1979, Erho¨hung der Wirtschaftlichkeit beim Wa¨lzschleifen durch Verbesserung des Zerspanvorganges, Phd-thesis, RWTH Aachen. [19] NN, 1997, Gears – Surface Temper Etch Inspection after Grinding, ISO14104.
Contents lists available at SciVerse ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Continuous generating grinding—Tooth root machining and use of CBN-tools Jens Ko¨hler *, Andreas Schindler, Stephan Woiwode Institute of Production Engineering and Machine Tools, Leibniz Universita¨t Hannover, Germany Submitted by A. Ber (1), Haifa, Israel.
A R T I C L E I N F O
A B S T R A C T
Keywords: Gear grinding Dressing Cubic boron nitride (CBN)
Profile accuracy, no burning and residual compressive stresses at the tooth root fillet are required for the durability of highly stressed gears. This paper reveals the challenges for continuous generating grinding with corundum and CBN. For this purpose, material removal simulations and experimental investigations were carried out to gain knowledge of the tool–workpiece contact conditions. The potential of CBN tools was analysed due to the fact that the mechanical loads at the grinding worm tip result in high profile wear of the corundum tools. In this context, especially the interrelationship between the dressing strategy and the workpiece quality was investigated in detail. ß 2012 CIRP.
1. Introduction The gear lifetime mainly depends on the residual stresses at the tooth flanks, root fillet and surface roughness. Pitting and micro pitting on tooth flanks is caused by Hertzian stress and primarily influenced by surface roughness and lubrication conditions [1]. Compressive residual stresses up to 600 MPa and a low surface roughness enhance the bearing capability of the tooth flanks [1,2]. Fatigue cracks, which result from high bending stresses, mostly occur at the root fillet especially when a small root fillet radius is generated. In contrast to surface damages, fatigue cracks cause tooth breakage resulting in a gear transmission failure [3]. Consequently, high compressive residual stresses are required in the root fillet area to avoid the formation and growth of fatigue cracks [4–6]. In comparison, the influence of the root-fillet surface roughness on the formation of fatigue cracks is not significant [7]. In order to improve the wear resistance of generated tooth flanks, most gears in modern transmissions are heat-treated. The resulting geometry deviation requires a further finishing process, which is grinding in most cases [8,9]. The common process in the industry is continuous generating grinding. Although profile grinding of the tooth root fillet can increase the gear lifetime up to 30% [7], continuous generating grinding has been applied for it infrequent. The main reason for this could be the missing knowledge of the tool–workpiece contact conditions and the resulting thermo-mechanical loads on the workpiece in continuous generating grinding. This may lead to tensile residual stress and a high wear rate of the grinding wheel. One approach to handle this problem is the use of CBN grinding wheels [10]. 1.1. Continuous generating gear grinding The kinematics of continuous generating grinding is similar to the rolling motion of two gears. In this process, several gear teeth
* Corresponding author. 0007-8506/$ – see front matter ß 2012 CIRP. http://dx.doi.org/10.1016/j.cirp.2012.03.033
are in contact with the grinding worm. At the same time, several theoretical points of contact occur for each of the teeth in contact. The involute of a tooth flank and the tooth root are determined by the process kinematics [11,12]. During the contact of tool and workpiece a sliding motion between the tooth flanks appears, defining the cutting speed vc for the material removal. In order to machine the entire tooth width of the gear, an axial movement is required which is specified by the feed rate vf (Fig. 1a). The common tool concepts for continuous generating grinding are vitrified-bonded tools with corundum and electroplated CBN (cubic boron nitride) as a cutting material. Vitrified-bonded corundum tools can be dressed easily and they are considerably more favourable than galvanic CBN tools. However, galvanic CBN tools enable high material removal rates and consequently a higher productivity. Vitrified-bonded CBN tools in general combine the advantages of both tool concepts: a long tool lifetime and a good dressability. So far, vitrified-bonded CBN grinding tools have not been used for continuous generating grinding. On the one hand, a reason might be the fact that there are no detailed investigations with these tools. On the other hand, CBN grains lead to a high wear rate of the dressing tool during dressing. Thus, conventional dressing strategies cannot be applied. For an efficient use of CBN tools it is required to reduce the dressing tool wear rate and to generate an advantageous worm topography [10,11]. 1.2. Grinding worm dressing The tool geometry and its topography are adjusted by the dressing process to achieve the required gear surface and subsurface properties. Typical dressing tools are form and profile rollers as well as master gears [10,11]. Due to the simultaneous dressing of all grinding wheel threads, the master gears provide a remarkable reduction of the dressing time [10,13]. Dressing with form rollers can be compared with thread turning (Fig. 1b). The specific geometry of the grinding worm results in high demands on the process kinematics. Due to the kinematic coupling of the involved NC axes of the grinding machine, the worm speed vcd and
J. Ko¨hler et al. / CIRP Annals - Manufacturing Technology 61 (2012) 291–294
292
Fig. 1. Kinematics of continuous generating grinding (a) and tool dressing (b).
the axial dressing feed velocity vfad are synchronized to each other. In conventional grinding processes, a dressing speed ratio between qd = 0.8–1.2 is used for the dressing of CBN tools. At these dressing speed ratios, the wear rate of the dressing tool is very low. Due to the kinematic coupling of the NC axes in continuous generating grinding machine tools and inefficient dressing spindles for low rotational speeds, it was previously not possible to reach this range for continuous generating grinding. Speed ratios of about qd = 20, which generally result in high wear of the dressing tool, are therefore applied. In addition, this leads to a closed topography of the grinding layer which may result in grinding burn and a decrease of the productivity [10].
Fig. 2. Calculation of the characteristic values for continuous generating grinding.
Fig. 3. Variation of the gear tip geometry and dressing strategy.
2. Experimental set-up and methods 2.1. Grinding experiments and process characterization In order to characterize the continuous generating grinding process, corundum tools were used in the experiments. Since the flank machining process has already been analysed in [10,14–16], the focus is on the root machining. The process parameters were kept constant. The variation of the tool tip geometry was defined with respect to the DIN standard 3972 [17]. Grinding and dressing experiments were carried out on a KAPP KX1 gear grinding machine using case hardened and shot-peened spur gears made of steel 20MnCr5 (see Table 1). The grinding allowance was removed in one step without an axial shift of the tool. Grinding forces were measured with a Kistler 9167A dynamometer. In order to characterize the macro geometrical wear of the grinding tool, the profile of the ground gear tooth space was measured by the precision coordinate measuring machine Leitz PMM 866. In addition, the tooth flank roughness was measured by a Mahr Perthometer PGK. The gear subsurface integrity was characterized by residual stresses measured via an Xray diffractometer XRD 3000P applying the sin2 c method. 2.2. Material removal simulation The material removal during grinding was simulated according to the experimental investigations to gain knowledge of the tool– workpiece contact conditions. For this purpose, a two-dimensional material removal routine was developed according to Meijboom [18] using the numerical computing environment MATLAB. The tool profile is modelled according to the DIN standard 3972 [17]. The workpiece profile is built according to an exemplary tooth space measurement of a real unmachined gear. Cutting areas in cross section normal to the gear are calculated by Boolean operations, while the tool and workpiece profiles are repositioned incrementally analogue to the process kinematics. Fig. 2 presents the calculation of characteristic values. The chip cross-sectional area Aw is spanned between workpiece and tool
profile geometries of two proximate time steps depending on the time increment Dt. By multiplying the sum of all removed areas Aw by the feed per gear revolution f it is possible to calculate the material removal volume Vw. The material removal rate Qw subjected to a single machined tooth space can be determined by dividing the material removal volume Vw by the tooth space machining time. With the simultaneous, multiple tooth space machining the accumulated material removal rate is higher than Qw subjected to a single machined tooth space. 3. Characterization of the machining process In order to generate the worm profile (worm 1), a doubletapered dressing roller (dresser 1) with a defined external radius was used. While dressing the worm tooth flanks, the dressing roller was used as a profile roller, whereas the conditioning of the worm tooth tip was realized by a path controlled profiling using the profile radius of the dressing tool. The advantage of this method is the time saving profiling of the flank profile. At the same time, a high flexibility for the generation of the addendum profiles is assured (Fig. 3). The variation of the worm gear tip geometry leads to different material removal rates Qw and consequently affects machining forces Fx and Fy (Fig. 4a). Particularly the increasing tool addendum leads to a higher radial depth of cut arr in the tooth root area as well as a higher material removal rate Qw subjected to a single machined tooth space. Consequently, the process forces increase. The variation of worm tip radii leads to a noticeable change of the material removal rate Qw, although it only influences the maximum machining forces significantly when the tool addendum is small. Higher machining forces cause amongst others a higher load on the tool. Due to the helix angle, the tool wear cannot be determined by common methods like graphite grinding. Therefore, the abrasive macro geometrical tip wear is quantified by the profile deviations of the ground workpiece. Measured deviations in the
Table 1 Applied tool and workpiece specifications. Dressing tool
Grinding tools
Ground gears
Dressing roller Dresser 1: grain size Dresser 2: grain size External diameter dd Pressure angle ad Profile radius rpd
Worm 1: 71A120I14V85-10 Worm 2: A80J10V Worm 3: B126M7/6V Normal module mn0 Numb, of threads Z0 Pressure angle an0
Normal module mn Number of teeth z Pressure angle an Helix angle b Hob profile DIN3972
D301 D501 150 mm 208 0.51 mm
4.5 1 208
4.5 24 208 08 BPIII
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to reduce the dressing speed ratio in order to decrease the dressing tool wear rate and to gain an advantageous tool topography.
4. Grinding with vitrified-bonded CBN worms
tooth root fillet area are always higher than on the tooth flanks even for an identical normal depth of cut. The maximum profile deviation normal to the ground gear space surface is presented in Fig. 4b. The increase of the worm addendum and decrease of the tip fillet radii leads to greater profile deviations. Since these two variables affect the removed material volume Vw root in the tooth root directly, the whole material removal of all tooth spaces in this area can be used to estimate the maximum profile deviation and therefore the grinding worm tip macro wear. In order to quantify the structural changes of the workpiece subsurface due to the machining process, in the first step the residual stress profile of an unmachined workpiece was measured (black line in Fig. 5). A typical residual stress depth profile after the heat treatment and shot-peening has been observed. After grinding the residual stresses at the workpiece surface have been determined. These results are presented by the shaded areas. It was not possible to exactly determine the removed material allowance at the measuring point for unmachined gears due to concentricity errors of up to 35 mm. These dimensional errors affect the cutting depth. With respect to this, the shaded areas have a variation width of 70 mm (35 mm). Depending on the grinding tool tip geometry, different material volumes have been cut, though the measured values correspond to different distances to the unground surface of the gear. The residual stresses of ground surfaces correlate with the residual stresses in the corresponding depth of the unmachined gear. Due to the grinding process the residual stresses in the tooth root subsurface are shifted towards compressive residual values. This indicates that the original residual stress state of the workpiece is positively influenced by the tooth root area grinding. The grinding of tooth roots leads to advantageous subsurface properties. The high wear of corundum tools, which leads to high profile deviations, is faced with the use of CBN tools offering an improved wear behaviour. However, the dressing of the CBN worm for continuous generating grinding is demanding. The approach is
CBN tools lead to a higher productivity and to a good wear resistance resulting in an improved workpiece quality compared to corundum tools. In order to compare the wear behaviour, gears are ground with vitrified-bonded CBN and corundum tools without intermediate dressing. The same process parameters where used for the machining of both series. The tool wear was quantified by determining the tooth width W4 across four teeth for each ground gear. Out of this data the tooth width alteration is determined as the change of the tooth width compared to the first ground gear. An increasing tool wear leads though to an increased tooth width. When the fifth gear was ground with CBN, the tooth width increase was one third of the gears ground with a corundum tool. In addition, the increase of the tooth width started to decrease after machining the fifth gear for the CBN tool (Fig. 6a). Thus, the full grinding allowance of the tooth flanks can be removed by a single operation without significant wear of the grinding tool. Furthermore, the influence of the dressing speed ratio on the process performance was analysed. To this day, the dressing speed ratio was limited due to a missing technology for a dressing unit in the machine tools. For this reason, a new dressing unit was developed to provide low dressing speeds and a sufficient torque to cope with the high dressing forces at low dressing speed ratios. High dressing speed ratios lead to a smooth tool topography and offer less space for chips while grinding with high removal rates. They can also cause friction, thermal damage and higher process forces. In Fig. 6b, the average roughness height Ra of the ground gear is plotted against a batch of ten gears. Here, the roughness of the workpiece approximates to Ra = 1 mm. This condition is reached after machining the fifth gear for the used CBN grinding worm. In order to avoid a quasi-constant grinding layer topography, dressing after each ground gear is necessary. A quasi stationary topography should be obtained directly after dressing to keep the ground surface roughness constant (Ra = 1.0 mm). Therefore, a dressing ratio of qd 4 is recommended (Fig. 6b). To analyse the impact of the dressing conditions on the surface quality, the dressing speed ratio was varied between qd = 1.2 and 6. In Fig. 7, the roughness values are plotted against the dressing speed ratio. Here, the roughness values increase with a decreasing dressing speed ratio and converge against Ra = 1 mm. The dressing effect is in direct relation with the grinding wheel topography. In order to obtain a sharp and open topography of the grinding layer, the dressing speed ratio qd was reduced by lowering the dressing tool speed vd while keeping the grinding tool speed vcd constant. Thus, the dressing process is carried out in the same time. With a reduction of the dressing speed ratio qd for the used CBN tool the process forces could be slightly lowered.
Fig. 5. Subsurface residual stresses after grinding.
Fig. 6. Tool wear of CBN and corundum tools.
Fig. 4. Effect of material removal values on grinding forces and gear profile deviation.
J. Ko¨hler et al. / CIRP Annals - Manufacturing Technology 61 (2012) 291–294
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developed to reduce the dressing speed ratio to values applied for conventional grinding processes. The impact of adapted dressing strategies on the grinding wheel layer and the workpiece quality was analysed. Here, small dressing speed ratios of qd = 1.2 lead to a more open grinding layer topography and to reduced grinding forces. With the results presented further investigations for the tooth root machining with vitrified CBN grinding tools are currently in progress. The wear behaviour of different dressing tool specifications for CBN grinding worms is also subject of current research activities. Acknowledgements Fig. 7. Influence of the dressing speed ratio on the gear surface roughness.
The authors would like to thank Prof. A. Ber and Prof. B. Denkena, the German Research Foundation (DFG) and the Federal Ministry of Education and Research for their organizational and financial support within the projects ‘‘Contact conditions by continuous generating grinding of the gear tooth root (DE447/741)’’ and ‘‘Higher productivity for continuous generating grinding through optimized dressing of vitrified CBN worms (KF2328103LK0)’’, which is carried out in cooperation with Dr. Kaiser Diamantwerkzeuge GmbH & Co. KG, Celle, Germany.
References
Fig. 8. Influence of the dressing speed ratio on the mean process forces.
Furthermore the thermal influences of the grinding process on the workpiece have been determined applying a temper etch inspection according to the ISO standard 14104 [19]. The results show, that less grinding burn is detected by applying CBN tools compared to corundum tools. Apart of the workpiece topography also the process forces are influenced by the change of the gear topography due to the dressing speed ratio. The process forces were determined by the first five machined gears. The mean values of Fx = 49.1 N and Fy = 72.7 N (Fig. 8) are measured for qd = 6. The reduction to qd = 1.2 causes a sharp and open grinding layer topography (Fig. 7), which leads to reduced process forces Fx = 46.2 N and Fy = 64.2 N. It appears that a significant difference of the measured mean forces for the material removal cannot be set up before the first gear is ground. This could be assigned to the grinding-in process of the previously dressed grinding tool. 5. Conclusion This paper analysed the continuous generating grinding of the gear tooth root with a focus on residual stresses in the subsurface layer and the macroscopic wear at the tool tip. The experiments show that the residual stresses in the tooth roots can be improved. However, corundum tools show a poor wear behaviour due to the resulting tool–workpiece contact conditions in the tooth root. In order to eliminate the high wear of corundum tools, the performance of vitrified-bonded CBN worms was analysed experimentally. For CBN grinding worms a technology was
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