Force Prediction in Thread Milling

Transcription

1 A. C. Araujo and J. L. Silveira Department o Mehanial Engineering EE & COPPE - UFRJ P.O. Box Rio de Janeiro, RJ. Brazil anna@urj.br jluis@urj.br Fore Predition in Thread Milling A mehanisti approah or modeling the thread milling proess is presented. The mehanis o utting or thread milling is analyzed as an end milling proess with modiied utting edge. The geometry o threads is added to the geometry o the end milling tool to alulate the hip load area. The linear path is simulated and values o the speii energy rom end milling are used to ompute the utting ores involved. A omparison between the simulation o the utting ores or a speii tool in two dierent situations is made to present the ore behavior aquired rom the model. Keywords: Thread milling, mehanisti models, ore predition S. Kapoor Department o Mehanial and Industrial Engineering UIUC - Urbana IL USA s-kapoor@uiu.edu Introdution Threading a workpiee is a undamental metalworking proess. Threads an be produed in a variety o ways, involving two basi methods: plasti deormation working or metal utting. The dominant method used in industry is plasti deormation working. Conventional bolts and srews, or example, are mostly made by this method. Threads produed by plasti deormation are stronger beause o the grain struture than those produed by utting, although orming annot ahieve the high auray and preision required in many appliations. Threads made o brittle materials also annot be produed by plasti deormation working. In suh ases, thread utting is neessary (Smith, The ommon utting proesses or produing internal threads are tapping and thread milling (Stephenson and Agapiou, Tapping is used to make internal threads with the same diameter o the tool. It is done by eeding the utting tool into the hole until the desired thread depth is ahieved, then reversing the tap to bak it out o the hole and remove it rom the workpiee. Thread milling tools an produe internal threads with any diameter bigger than the tool diameter as well as external threads. In thread milling, the mahine tool exeutes the thread in one single pass. The tool goes down to the hole and begins the utting rom the deepest part to the top in a helial path, or it begins at the top and goes until the end o the hole. Some geometries o thread milling tools an be observed in Fig. 1. Figure 1a shows a single utting edge whih produes one pith per eed rotation, Fig. 1b presents a single straight tool with only one utting edge and Fig. 1 shows a helial thread tool with some utting lutes. In thread milling high tool pressure are generated whih an result into an exessive tool deletion and tool breakage when milling at ull thread. 1 Presented at COBEF 003 II Brazilian Manuaturing Congress, 18-1 May 003, Uberlândia, MG. Brazil. Paper aepted Otober, 003. Tehnial Editor: Alisson Roha Mahado. ( Figure 1. Thread milling tools Single utting edge, Single straight thread lute, ( Helial thread lute (Emuge, 00. Many authors developed models or predition o ores in mahining. These inlude analytial, experimental, mehanisti and numerial methods (Ehmann et al., In thread utting by tapping, a mehanisti method or the predition o ores was presented by Dogra et al. (00. A number o papers desribing the thread milling operation have been published (Smith, 1989, Koelsh, 1995, Stephenson and Agapiou, 1996 but there is no model to predit the ores involved in the proess. The objetive o this artile is to present a mehanisti model or thread milling. The tool geometry analyzed involves triangular and metri threads. The thread milling tool in this artile has helial lutes and its geometry is analyzed as a modiied end milling tool. Tool run out is added to the model and some examples o thread milling proesses are presented. Nomenlature d e external tool diameter, mm d i internal tool diameter, mm d E external workpiee diameter, mm d I internal workpiee diameter, mm d h hole diameter, mm d(z loal diameter, mm e width o ut, mm t eed per tooth, mm H thread height, mm K n normal speii utting pressure, N/mm K radial speii utting pressure, N/mm K z axial speii utting pressure, N/mm N number o lutes p thread pith, mm t hip thikness, mm V utting speed, m/min 8 / Vol. XXVI, No. 1, January-Marh 004 ABCM

2 Fore Predition in Thread Milling Greek Symbols α rake angle, deg. δ angle or the total engagement o a utting edge, deg. ζ angle between the lutes, deg. λ helix angle, deg. ξ thread angle, deg. ϕ 1 initial angle o ontat ϕ inal angle o ontat φ angular position o a point in a lute ψ angular position o the leading point o the utting edge Subsripts e relative to external tool diameter E relative to external workpiee diameter i relative to internal tool diameter I relative to internal workpiee diameter,n,z relative to the tool reerential x,y,z relative to the workpiee reerential Thread Milling Geometry Tool Geometry The threads studied in this artile are metri and triangular. The thread variables presented in Fig. a are: thread pith, p, thread angle, ξ, external workpiee diameter, d E, internal workpiee diameter, d I, and thread height H. The relation between the diameters an be written as: p d I d E (1 tan ( ξ / where nt(z is: p z nt(z d i +, tan( ξ / d(z p z nt(z de, tan( ξ / i nt(z is odd; i nt(z is even; (3 z nt (z Integer Part (4 p The tool motion is irular in the plane normal to the tool-axis and linear in the diretion o the tool-axis with a stationary workpiee to generate the thread. The workpiee is predrilled and the diameter o the hole is alled d h. The width o ut (or radial depth o ut is e(z: d(z dh e(z (5 Cutting Geometry The utting geometry o the thread milling proess is dierent than the ommon end milling beause the utting edge is not a straight line and the tool ollows a irular trajetory. Following the approah used by Tlusty and MaNeil (1975 the ontat interae in thread milling proess an be desribed as shown in Fig. 3, where the depth o ut, b, an be observed. Figure 3. Contat phases. Figure. Tool and thread geometries Thread geometry, Tool geometry. The thread milling tool is very similar to an end milling tool. The tool geometry o a helial thread lute is presented in Fig. b. The helix angle λ, the rake angle α (not shown in the igure, the internal and external diameters d i and d e and the number o lutes N deine the tool geometry. The angle between the lutes is: π ζ ( N and the number o eah lute is n, 1 n N. The loal diameter d(z is written as a untion o the height z, d i d(z d e, alulated as ollows: The ontat surae is divided in three phases: A, where the length o ative utting edge inreases in time, B, where it is onstant, and C where it dereases. There are two dierent types o ontat surae geometry aording to the relation between the angle δ, deined in Eq. (6, and the ontat angle: Type I and Type II. It is a Type I geometry i δ ϕ, and Type II ours i δ ϕ ϕ 1. b tan λ δ (6 The ontat angle is deined as the dierene between the initial angle ϕ 1 and the inal angle ϕ. Two auxiliary angles were deined by Tlusty and MaNeil (1975 to analyze the lute movement through the three phases A, B and C. The irst one is angle ψ, whih indiates the angular position o the leading point o the utting edge. The other one is angle φ, whih indiates the position o the other points o the same lute. For a known ψ, the range o values d e J. o the Braz. So. o Meh. Si. & Eng. Copyright 004 by ABCM January-Marh 004, Vol. XXVI, No. 1 / 83

3 or φ is between φ i and φ, and it hanges or eah phase and eah position θ o the tool as shown in Table 1. The range o values or ψ in eah phase is shown on Table and the limits o eah phase are alled ψ 1, ψ, ψ 3 and ψ 4. Table 1. Limits o φ i (θ and φ (θ in A, B and C (Araujo and Silveira, 001. Type I Type II Phase φ i (θ φ (θ φ i (θ φ (θ For ψ 1 < θ ψ - Phase A ϕ 1 θ ϕ 1 θ For ψ < θ ψ 3 - Phase B θ - δ θ ϕ 1 ϕ For ψ 3 < θ ψ 4 - Phase C θ - δ ϕ θ - δ ϕ Table. Values o ψ 1, ψ, ψ 3 and ψ 4 or Type I and Type II. Type I Type II ψ 1 ϕ 1 ϕ 1 ψ ϕ 1 + δ ϕ ψ 3 ϕ ϕ 1 + δ ψ 4 ϕ + δ ϕ + δ For a helial tool, the height z an be expressed as a untion o the position o the tool θ and the point angle φ: di ( θ φ z( θ, φ (7 In the ase I, shown in Fig. 4a, the tool eed veloity does not hange diretion, as ours in end milling. In ase II the tool uts in a the irular path, Fig. 4b. a Case I b Case II Figure 4. Tool path ases. Case I For up milling the initial angle is zero. In ase I the inal angle is written as: where b tan λ ϕ (8 r. e Case II In ase II (Fig. 5, the inal angle is written as: ϕ de de ro. dh di 4ro arsin (9 4dhro Figure 5. Chip thikness or ase II. The unut hip thikness or any point o the utting edge, loated in the height z and by the angle φ (Fig. 5, an be written as (Sabberwall, 1960: Fore Predition t( φ, z t (z sinφ (10 Elemental normal and ritional ores are required to the determination o utting ores or a given geometry. The mehanisti modelling approah is a ombination o analytial and empirial methods in whih the ores are proportional to the hip load (Kline and DeVor, The speii utting energies, K n, K and K z, have been shown as a untion o hip thikness t and utting speed V (Dogra et al., 00. ln ln F F n KnA K A ( Kn a 0 + a1 ln( t + a ln( V + a3 ln( t ln( V ( K b + b ln( t + b ln( V + b ln( t ln( V (11 (1 The oeiients a 0, a 1, a, a 3, b 0, b 1, b and b 3 are alled speii utting energy oeiients. They are dependent on the tool and workpiee materials and also on the utting speed and the hip thikness. They are determined rom alibration tests or a given tool workpiee ombination and or a given range o utting onditions. Chip Cross Area The untion o hip ross area or the irst lute A 1 (θ is: where db is (Sabberwal, 1960: φ A1( θ t( φ, z db (13 φ i d(z db dφ (14 Using the Eq. (3, Eq. (7 and Eq. (10, the area A 1 (θ an be alulated as: φ d(z( θ, φ A1 t( φ, z( θ, φ dφ (15 φ i The limits φ i (θ and φ (θ are untions o the θ and the utting phase o θ, as shown in Table 1. In order to add the ontributions o 84 / Vol. XXVI, No. 1, January-Marh 004 ABCM

4 Fore Predition in Thread Milling all lutes, the hip ross-setional area untion or eah lute (n is written as: A n φ ( θ+ζ(n 1 ( θ+ζ(n 1 t( φ, z( θ, φ φ i d(z( θ, φ dφ In Eq. (15 φ i and φ are also written as a untion o n. The total area A(θ is alulated as: Tool Run Out N (16 A An (17 n 1 Cutter run out exists in all kinds o milling operations and results in variations in the undeormed hip thikness, loal ores and mahined surae harateristis. The run out an be due to utter axis oset, eentriity (ρ or utting points positioning oset (ε, shown in Fig. 6, and it depends prinipally on the harateristis o the spindle and tool holder. The hip thikness in presene o run out is rewritten as (Kline and DeVor, 1983: t( θ, φ, n tsinφ + ρ(os( θ ε φ os( θ ε φ nζ (18 os( θ + ζ(n 1 sin( θ + ζ(n 1 0 R n sin( θ + ζ(n 1 os( θ + ζ(n 1 0 ( The area or all lutes is written as: Examples N A R R n An ( n 1 In order to analyze the ores proile in thread milling, our examples are presented in this artile. Speii pressure in these examples will be the same and are given by K 900 N/mm, K n 500 N/mm and K z 100 N/mm. The tool used in the simulation has the ollowing parameters: p1.5 mm, λ 30 o, N 4 and ξ 60 o. The geometry o ut and the veloities are: d E 10 mm, ω 1400 rpm, t 0.06 mm. The values or eentriity and o set or the run out ase are: ρ 0.04 mm and ε 10 o. Example I In this example the depth o ut is b 1.5 mm, just one pith. To illustrate the example I, Fig. 7 presents the hip ross area and the utting ore with and without tool run out. Example II The depth o ut in this example is b 5 mm. Figure 8 presents the hip ross area and the utting ore with and without tool run out or this ase. Figure 6. Tool run out (Kline and DeVor, Fore Computation To alulate the omponents o the utting ores using the speii utting ores K, K n and K z, a untion A R (θ has to be introdued (Araujo and Silveira, 001. Fx' Fx Kx K F Fy' Fy A K y AR Kn (19 Fz' Fz Kz Kz In at, the untion A R (θ is the rotation matrix R(θ multiplied by the area. os( θ sin 0 R sin os 0 ( For eah lute the rotation matrix R n (θ is: Example III In this example the depth o ut is b 10 mm and Fig. 9 presents the hip ross area and the utting ore with and without tool run out or this example. Example IV In example IV the depth o ut is b 0 mm. The hip ross area and the utting ore with and without tool run out or this example are presented in Fig. 10. Conlusions A mehanisti model have been developed or thread milling. The model takes into aount the thread utting edge and the linear movement o the tool. The ores were predited or our depths o uts. The results show the eets o the inreasing the depth o ut on the utting ores. The thready lute ontribute or another requeny osillation in hip ross area and onsequently in utting ores as ompared to the straight utting edge. In order to improve the model, the ontat stresses between the threads and the tool need to be added. J. o the Braz. So. o Meh. Si. & Eng. Copyright 004 by ABCM January-Marh 004, Vol. XXVI, No. 1 / 85

5 ( ( (d Figure 7. Example I. Chip ross area, Chip ross area with run out, ( Cutting ores, (d Cutting ores with run out. (d Figure 8. Example II. Chip ross area, Chip ross area with run out, ( Cutting ores, (d Cutting ores with run out. 86 / Vol. XXVI, No. 1, January-Marh 004 ABCM

6 Fore Predition in Thread Milling ( ( (d Figure 9. Example III. Chip ross area, Chip ross area with run out, ( Cutting ores, (d Cutting ores with run out. (d Figure 10. Example IV. Chip ross area, Chip ross area with run out, ( Cutting ores, (d Cutting ores with run out. J. o the Braz. So. o Meh. Si. & Eng. Copyright 004 by ABCM January-Marh 004, Vol. XXVI, No. 1 / 87

7 Aknowledgements This projet is ulilled with the ellowship grant reeived rom CNPq, a Brazilian ounil or sientii and tehnologial development. The authors are grateul or the ounil and the University o Illinois at Urbana Champaign or the support. Reerenes Araujo, A.C. and Silveira, J.L., 001, The Inluene o the Speii Cutting Fore on End Milling Models, Proeedings o the 16th Brazilian Congress o Mehanial Engineering, CD-Rom, Uberlândia, MG, Brazil. Dogra, A.P.S., Kapoor, S.G. and DeVor, R.E., 00, Mehanisti Model or Tapping Proess with Emphasis on Proess Faults and Hole Geometry, Journal o Manuaturing Siene and Engineering, Vol. 14, pp Ehmann, K.F., Kapoor, S.G., DeVor, R.E. and Lasoglu, I., 1997, Mahining Proess Modeling: A Review, Journal o Manuaturing Siene and Engineering, Vol. 119, pp Emuge Catalogs, 00. Smith, G., 1989, Advaned Mahining: The Handbook o Cutting Tehnology, IFS Publiations, UK. Kline, W.A., DeVor, R.E., 1983, The Eets o Run-Out on Cutting Geometry and Fores in End Milling International Journal o Mahine Tool Design and Researh, Vol. 3, pp Koelsh, J.R., Ot. 1995, Thread Milling Takes on Tapping, Manuaturing Engineering. Sabberwall, 1960, Chip Setion and Cutting Fore During the Milling Operation, Annals o the CIRP, pp Stephenson, D.A. and Agapiou, J.S., 1996, Metal Cutting Theory and Pratie, Marel Dekker, In. New York, NY. Tlusty, J. and MaNeil, 1975, Dynamis o Cutting in End Milling, Annals o the CIRP, Vol. 4/1, pp / Vol. XXVI, No. 1, January-Marh 004 ABCM