================ Gears machining by milling tools =================== 1 That's me!
My name is Fabio Sada. I was born in 1954 in Milano, where i studied up to University and where i have been working since 1978 as production technologist at a primary firm active in heavy industrial plants supply (coil mills, continous casting etc). During my job I worked about machining methods, CNC part-programs, setup equipements, tools also regards to gear machining ( hobbing, rack-cutter machining and grinding) so that I ideated a new way of machining gears by milling instead of by hobbing, and I created some EDP tools for simulating new process and make ordinary calculations about gears, but without testing this new way in my job. It would be for me very satisfying if any gear manufacturer be interested in this idea and try to put it into real practice.
-Fabio Sada -Via San Pancrazio 20 -20060 Gessate (MI) - Italy - e-mail : sada.gessate@tiscalinet.it
4 Introducing The machining of gears involute is actually carried out by by using hobs or rack-cutter, on their own proper machine, usually followed by grinding. Altough for small modeles hobbing technology for machining involute surface before grinding is probably the best one, for large modules hobbing takes a lot of problems, since both the machine tool and tools become very expensive and very little flexible. Then it is necessary to handle a very heavy and delicate tooly, while machine table is required to turn at high speed without any precision loss. Gear machining by milling may be a good answer to such problems, with machining time very interesting and a lot of further advantages. For low-quality gears milling might be used as the final involute machining. In the following chapters we'll show that gear milling is geometrically correct, technically executable and economically convenient, and that for large modules the hobbing technology is obsolete, although the only apparent technical evolution of hobs and hobbing machines. 5 New! create involute by milling !! This new way uses a generating method and consists of creation of micro-planes or micro-lines that belong to involute surface. This may happen because involute surface has some characters:. -If you imagine to cut the gear with a plane tangent to base cylinder, you will obtain some straight lines costanly sloped as base helix angle; There will be more than one parlel lines for each side, and their distance (in trasverse and normal directions) is equal to respectively base trasverse pitch and base normal pitch. While tangent plane rolls over base cylinder, the lines move (but remain equally spaced ad oriented each other) according to the very simple rolling law over base cylinder: [1] delta X = Rb * delta ROT [radiants] If the cut contains the whole central teeth, as for gears with a few teeth, you will find that the distance between first left-side line and first right-side line of central teet is equal to trasverse (normal) base thickness. This happens also if you imagine anyway to continue involute profile forward base circle for any number of teeth. Then (and this are probably the most importan carachteristic) the teeth surface immediately close to section is always normal to our imaginary plane, and this surface is anyway always convex, so that may be substituted by micro-planes tangent to real surface, with a small positive error. A daily show of this simple rules comes from span measurement: just imagine to substitue plates with a milling tool and place it at the first contact. I defined two different machining modes, each with its own advantages:. CONTINOUS MODE:. -The gear is placed on a rotary table (B-axe). -The milling tool is placed on a square-head indexed as base helix angle. -Its edge lays constantly in Z axe on plane tangent to base cylinder. -The gear rotates (B) and mill moves (X) according to rolling law; In each moment a circular arc substitutes the real generating line. -Final form error depends upon milling path width, tool diameter and mimimum curvature radius (innest X position). In case you wish to have a constant feed along involute profile, it is necessary to fit X-Feed according to [fig26A][fig27A][fig28A] : [2] FeedX = Feed on profile * rb / Rcurv It is also necessary to verify that this value doesn't become too large, as curvature radius becomes very small. [fig24A][fig04U][fig05U][fig19U][fig20U]. MULTI-PLANE MODE:. -The gear is placed on a rotary table. -The milling tool is placed on a square-head indexed as base helix angle. -Both gear and tool are moved in any position that respects rolling law. -In this X-B fixed positions the milling tool moves along Z and creates a small plane tangent to real involute surface. -Final form error depends upon the number of planned cuts and minimum curvature radius (innest X position). -A special case is made by first rough machining by a thin milling tool [fig33A][fig34U]. Both methods may be considered as a special condition of modified rolling, in case tool pressure angle becomes ZERO. 5.1 Machine setup for both milling modes. Toolaxe index = base helix angle. Zero-offset X : Centerline of rotary table. Zero-offset Y : where you want, but better on an intermediate section where it is possible to center a pre-existing spacewith. Zero-offset Z : Centerline of rotary table. Zero offset B : Centerline of tooth or spacewidth, with their own delta-X contribution; If center of tooth is used, for B=0 then X cut position must already be equal to half trasverse base thickness. Tool position T along Z: [3] T = rb + rtool Rolling law during movement:_ [4] delta B [rad] = delta X / rb [5] B = B0 + X / rb Helix law for different Y-levels: [6] delta B-offset [rad] = 2 * 3.14159 * Y / lead Feed fitting law , only in continous mode: [7] Feed X = Feed on profile * (rb / X) Distance of eventual 2nd rear tool, that operates over a close teeth [8] L = normal base pitch 6 Mode 1 : Continous rolling milling mode This method may be carried out ONLY after spacewidth rough machining! [fig02A][fig03U], better if followed by a proper root undercut made with rounded mill. [fig12A][fig13U] show innest position layout. [fig15A][fig16A] show start and arrive conditions. In this machining mode milling tool center moves along X over a plane tangent to base cylinder, while gear on the table turns, according to rolling law shown before, with a simple NC command from (X1,B1) to (X2,B2) with Z=base radius. In case the gear is not exactly centered on the table, the movement must involve also Z-axe and must be shared into n partial positions, each of them with properly re-calcoulated X-B intermediate values according to value and current direction of center desplacenment vector; in this case some form error occours since a continue formula is linearized into n steps. Extreme positions may be easily calculated according to tip diameter and (for example) active profile starting diameter. Both these values may be modified according to milling path width and tool angle: [9] Extra radius = path width / 2 * TAN(beta0) In enclosed example this extra is considered only for multi-cut planning. Form error: both values of path width and tool diameter lead to a first value F1 representing the arrow operated by milling tool movement in local tangent plane [fig19U]. [10] F1 = Rtool - ( SQR ( Rtool ^ 2 - (path width / 2) ^ 2 ) ) This value and minimum curvature radius lead to the true form error F2 [fig20U][fig27A]: [11] F2 = rcurv -( SQR ( rcurv ^ 2 - F1 ^ 2 ) ) (tabled in [fig20U] with entrance in column 1) For example, for Dtool=250 mm and pathwidth=60 mm you have F1=4,50 mm. In case of minimum curvature radius = 75 mm you may have a form error = 0,122 mm , that lowers to 0,017 mm for radius=500 mm . Although these are good values, they may be easily reduced: if you operate an extra-position of tool along Z, UNDER the level of tangent plane and equal to 1/2 of F1 value (2,24 mm in example), then real error F2 lowers very much, since the true value F1 to be considered is the half ([fig20U] with entrance in column 2): [12] F2 = rcurv -( SQR ( rcurv ^ 2 -( F1 / 2 ) ^ 2 )) leads to better values:: rcurv = 75 form error 0,030 mm instead of 0,112 mm : = 517 form error 0,004 mm instead of 0,017 mm A further improvement may come from insert cutting edge, in case it offers a flat front edge. In any case form error [fig04U][fig05U] lowers when tool diameter increases or path width reduces [fig18A]. 7 Mode 2 : Multi-plane machining with stopped table In this machining mode the milling tool moves along its own plane while other machine axes are stopped, so thet it may be carried out also over whole-teeth, not rough machined gears, and over machines with a good static precision but not a good dynamic one. [fig12A][fig13U] show milling in innest conditions. In this case I suggest to operate first both cuts on left and right flank, and then increase both X-position and cut depth. Also in this case extreme positions may be easily calculated according to tip diameter and (for example) active profile starting diameter. Both these values may be modified according to milling path width and tool angle: [9] Extra radius = path width / 2 * TAN(beta0) In enclosed example this extra is considered only for multi-cut planning. [fig06A][fig07A][fig08A][fig09A][fig10A][fig11A]. A proper EDP software may be used for planning cutting positions, so to have equal and minimum form error for each integer quantity of cuts. Single unit cut will be repeated for all teeth and for all axial sections planned. Since form error depends upon curvature radius, best results will be for gears with a lot of teeth , but in case of further grinding this is not a problem anyway. In case of spur gears it is better to machine the whole facewidth at one time for each planned position. 8 Cut with two spaced milling tools In case you use two equal milling tools spaced as the normal base pitch [fig12A][fig13U], you will machine at one time two different surfaces on adiacent tooth, relative to 2 different curvature radius according to:. [13] R rear = R front + normal base pitch * COS(beta0) For better understand what happens with two milling tools, it is necessary to define Krc ratio that represents cut-lenght operated by rear milling tool and whole cut lenght: [14] Krc = (Lctot - normal base pitch * COS(beta0)) / Lctot That shows covering action of rear milling tool. 8.1 Continous mode In case of two milling tools in continous mode, active path of front tool may begin at an intermediate position, since rear tool has already machined initial path during cut before. Best condition occours when Krc value is exactly 0,50 , that means that both tools begin active cut at the same time other than along the same path lenght. Obviously the first cut for each axial set of cut must be done along a whole path. In this way machining time may be reduced up to 50%, expecially when Feed value along X must be kept constant, and the reduction is anyway good also when it is possible to fit feed value according to current curvature radius of REAR tool. In fact, the position difference over profile path corresponding to a fixed difference of curvature radius becomes smaller as curvature radius lowers, so that with feed auto-fitting the front tool has a real feed over profile lower than optimal one. Cut starting position of front tool along the path may be reached with a high feed with correct X position, or with a small tool desplacement along X . - For values of krc up to 0,50 [fig27A] the first contact is done by front tool, and feed fitting may be referred to front tool position; As rear tool begins to cut, feed must reduced since must be referred to rear tool position; Milling path along X is constant for any value of krc. - For values of krc over 0,50 [fig28A] the first contact is done by rear tool, and whole feed fitting is referred to its position. For example, in case of gears in example we have following machining time for each cut path, for a reference feed on profile = 100 mm/min in both fitted and not-fitted feed (values T100P and T100C in [fig25A][fig26A]):.
: WITH NO fit WITH fit : PINION: : with 1 tool : 0,901 0,609 : with 2 tool : 0,522 0,424 : : WHEEL: : with 1 tool : 0,649 0,581 : with 2 tool : 0,380 0,357 It is clear that feed fitting is more convenient in case of pinion, when curvature radius changes very much in relativ value, and then use of 2 tools is more convenient for machining wheels, since both front and rear cut move along the profile with small real feed differences. Best machining results occour when krc value is close to 50% and it is possible to fit feed value continously. Warning: feed fitting is not a matter of CNC performances ( since it is always possible to share cut path into 10-20 steps and assign a proper feed value to each one ) but depends upon the position error of B-X axes when feed changes: it shouldn't be a problem for a modern machine, but it could be the same. Instead of in order to reduce machining time, second tool might be placed a little more spaced and be used for reducing material stock to be removed by front tool along the external path ( usually corresponding to greatest amount of over-stock). In this case whole path must be run by front tool, even with a certain penalty since rear tool commands feed value anyway. 8.2 Multi-plane mode In this case the second tool allows to reduce the number of cuts, and each cut operates at two different curvature radius on two following teeth. Since tool distance is strictly defined, the cuts planning must be optimized in reference to front tool or rear tool extreme positions, so that the number of cuts for a certain form error doesn't succeed in reaching the half value [fig06A] [fig09A] [fig07A] [fig11A]. Also in this case the value krc leads to refer planning mode to front or rear tool extreme positions. A simple simulation shows that the distance between two cuts ( for an assigned form error ) become larger as curvature radius reduces: this means that a cut planning referred to rear tool will be certainly satisfying if properly translated to front tool. It is only necessary to check relative position between innest rear tool position and outest front tool position. For values of krc over 0,5 it is better to plan cuts in reference to tip circle curvature radius ([fig10A] with plan edge=Re). For values of krc up to 0,5, it is better to plan cuts in reference to a virtual external circle corresponding to innest cuvature radius + 2 x [base normal pitc] * COS(beta). in order to assure complete covering to front tool position ([fig11A] with plan edge=ri+2*P). For example, we show cut plannigs and their form error for gears in example:
: n=8 n=7 n=6 n=5 n=4 n=3 n=2 : PINION: : 1 tool : 0,071 0,095 0,131 0,196 0,327 0,634 1,769 : 2 tools: 0,023 0,031 0,044 0,065 0,108 0,210 0,584 : : WHEEL: : 1 tool : 0,016 0,021 0,030 0,045 0,074 0,146 0,403 : 2 tools: 0,005 0,006 0,008 0,012 0,020 0,039 0,108 That shows how second tool is convenient also in multi-plane mode. 9 Something more : first rough cut with disc milling tool First rough cut may be done by a thin milling tool disc-shaped, instead by an ordinary double-cone milling tool, with lower chips removal and lower machine stress [fig33A][fig34U]. 10 Something more : Milling by an hobbing machine Milling machining of gears might be carried out also by hobbing machines in both cutting modes, in case the machine offers the chance of positioning milling tool in tangential direction. In case stroke lenght along this axe be too short ( then not so good for machining large wheels with large curvature radius ) a good help might come by allowing to inclinate tool axe in transverse plane, for example as normal pressure angle, so that milling path always happens close to machine center-line [fig16A][fig17A][fig21A]. In this case tool moves along X-Z axes instead of along Z axe or X axe alone. 11 Limits in machining gears by milling Since both machining modes shown above operate a substitution of real expected surface with something different ( an arc in case of continous mode, and a plane in multi-cut mode) some form errors occour. This means that gears milling may be used without problems ONLY in case of further grinding (expecially for multi-plane machining mode) or in case of low-quality gears, for which continous mode milling might be satisfying enough. But don't forget that also hobbing has quite the same problems, since a good hob in AA class may be built only in brazed-blade mode, needs a proper sharpening, and its quality depends upon re-sharpening process too, while indexable insert hobs hardly reach quality A and often stop at B. Gears milling is then a comparable alternative to hobbing, just because both process might lead to a comparable quality. 12 Advantages in gears milling 12.1 * Gear design * Every geometric parameter of gear may be dimensioned in absolute freedom, without any necessity of follow standard values, up to operate even a difference in normal pressure angle of working and not-workimg flank, in order to improve stress strenght without overloading bushings. This kind of freedom is already given by grinfding process too, so that couple milling + grinding offers a complete manufacturing process. * Module value may be set very large, since milling tool dimensions are not very affected by module value (as happens in hobbing). * Central gap in double-helical gears may be dimensioned only in reference to grinding and milling necessity, that are usually lower tha hobbing ones. * Both milling and grinding operate in single-share mode, so that it is possible to machine partial toothing, also for pieces that have some volumes OVER root diameter. Large gears may be machined by sectors, with proper milling paths. * All design chances correspond to macxhining opportunities for gear manufacturers that work only for other firms, that may face any machining request without care about hobs availability. 12.2 * Machine tool (CNC Machining center with rotary table). * The machine, also if mainly used for toothing, still owns its performances, and may be used as an ordinary machining center over other kind of products or other surface on a gear. * In case of fast table it is possible to operate turning machining. * Machine may be used for a previous check of geametric conditions of gear, due to heat treatment for example. * The same machine may operate , other than involute cut, also first rough machining and/or root fillet machining. * With proper CNC software, it is possible to machine also large spur bevel gears, for any generating lenght. (Available photos on request) * Machining of long pinions may be improved by using a rotary table with horizontal axe, with edge and intermediate counter-supports. * Respect to hobbing machines, speed table in continous milling modes is very lower than in hobbing mode, with speed ratio about 60:1 - 80:1 and table is stopped in ulti-plane mode. This means that CNC equipement is very cheaper (Don't forget that any supply offer of hobbing machine shows different prices according to required maximum table speed!). * No tool rotation control is required. * In case of machining of pinions with just a few teeth, there is non limit to cutting speed. * In case of power failure , no damage occours in multi-plane mode and low damages occour in continous mode (Anyway less tha in hobbing mode, when both hob and gear have high speed at the momento of power failure). * Machining center suppliers are quite numerous and behave in correct anti-trust mode. 12.3 * Tooling * One only milling tool is good for machining a large range of modules on both right and left flanks, so that it is not necessary to buy a wide set of tools, and in double R/L execution too. Although standard milling tools may be used successfully, it is possible to design some special cutters for gear milling; they would cost a little more than a standard tool, but would cost quite a little anyway. I am personally sure that any milling tool supplier would be very happy to may develop such a new product !!. * Delivery time of standard milling tool is very short. * Milling tool is very cheap. The whole tools set in milling mode has a cost enormously lower than corresponding hobs set, also if properly normalized and carefully handled and sharpened. Don't forget that brazed skyving hobs must be re-sharpened and have a limited lifetime. * Tools suplliers are a lot and operate in trade conditions, while hob suppliers are just a few. * Milling tool is light, may be handled easily and also automatic tool change may be used. * Milling tool diameter may be quite small since cutting speed is easily controlled by rotation speed. * All cutting inserts move at the same speed, and in hobs cutting speed depends upon insert position over the hob. * Milling tool usually takes one only type of insert. * A lot of HM qualities and geometries are available. * HM inserts for milling are standard, cheaper and offer a greater number of cutting edges available. * It is possible and fast to change inserts on-board. * Milling tool is not required to be as precise as an hob. * Not necessary have R/L tools. * No re-sharpening is necessary. * Also hardened materials may be machined. 12.5 * Machining conditions * Cutting action is immediately productive, without initial and final partial phases as it happens in hobbing. No extra-streoke is required also for large helix angle. * Centering of pre-existing surfaces is easy. * Cutting speed is undependent and may be set according to HM performances. * In case of use of 2 milling tools, machining time may reduce up to 50%. * Stock removal is greater than in hob-skyving operation. * It is possible to choose different scan policies, in both continuos and multi-plane mode. * Feed and rotation may be stopped instantly without further problems. * Crash consequences are less grave than while hobbing. * Machining action is easily in sight. * Low table speed permits an easy chips removal. * It is not necessary to assure perfect position of gear on the rotary table; it is enough to know desplacement vector and consider it in additional offset position during machining. In continous mode it is necessary to share the path and calculate a proper modified goal according to center desplacement. In multi cut mode the table is stopped in a well known position during single cut and local offset modification is very easy. 13 Machining time 13.1 Continous mode In case of gear machininig by continous mode, the milling tool runs along teeth profile, from tip circle down to diameter that it is necessary to warrant. For usual teeth dimensions the lenght of this path is about 2 - 2,2 x normal module. In case it is possible to fit Feed value along X in order to have constant feed value along the profile, ([fig15A][fig16A]) according to: [15] FEED (X) = FEED profile * Rb / X current thus: [16] FEED (X) = FEED profile * KFeed with KFEED = Rb / X active maching time for a path-lenght s= 2,2 * module may be calculated by: [17] Tunit = s / Frel = 2,20 * mn / Frel and for the whole gear, consisting in Z teeth cut in L/p levels: [18] Ttotal = Tunit * z * L / p = 2,2 * mn * Z * L / (p * Frel) In case feed on profile Frel = 150 mm/nin and p = 50 mm will be: [19] Ttotal = Tunit * z * (L / 50) = mn * z * L / 3409 For example, with (Frel=150 p=50) mn=30 z=28 L=500 will lead to 123' = 2,05 h for each flank , thus 4,10 h for whole facewidth, that might reduce to about 2,50 in case of double tool. By using an HM insert hob diam 360 mm , with cutting parameters: Vt=110 n=97 a=1,25 L=500+250=750 we have about 173'=2,90 h for whole facewidth. This may seem a good result, but if you consider all remaining service activities (handling, insert change, offset, controls etc) and the cost of tool and inserts, I think to may say that milling is anyway a convenient way of machining. Don't forget that 1 only milling cut may remove much more material stock than a HM skyving unit action. 13.2 Multi-plane mode. Machining time in multi-plane mode will be a little higher than in continous mode, because there are more many not-cutting movements and some paths are partially covered each other. Only a real test may show the difference, and I extimate machining time in multi-plane mode might be about 1,2 * continous mode time. 14 Machining diagram 14.1 Continous milling mode
: ( 3 levels loop ) : SETTING UP: : PLOT of tool and gear assembly : verify dimensions : INPUT DATA of design gear parameters mn,alfa,beta,X,b,da : INPUT limit curvature radius start-arrive and axial step : INPUT gear center desplacement error (eventual) : COMPUTE indexing,rolling and helix parameters : : MACHINING: : FOR FLANK = R,L : INDEX tool axe = base helix angle : COMPUTE offset values due to tool and tool holder : FOR AXIAL LEVEL = BOTTOM TO TOP : COMPUTE offset values due to helix (eventual) : FOR TEETH = 1 TO Z : COMPUTE offset values due to gear index : COMPUTE total offset values : EXECUTE unit cut from r-start to r-end : (in case of center desplacement: divide unit cut into : fractions with linear approx) : NEXT TEETH : NEXT AXIAL LEVEL : NEXT FLANK : END 14.2 Multi-plane mode
: (4 levels loop) : START : SETTING UP: : PLOT of tool and gear assembly : verify dimensions : INPUT DATA of design gear parameters mn,alfa,beta,X,b,da : COMPUTE all optimized planning chances from 2 to 8 cuts : CHOOSE best cutting plan according to max out-tool : INPUT gear center desplacement error (eventual) : COMPUTE indexing,rolling and helix parameters : : MACHINING: : FOR FLANK = R,L : INDEX tool axe = base helix angle : COMPUTE offset values due to tool and tool holder : FOR PLANNED CURVATURE RADIUS = LONGEST TO SHORTEST : COMPUTE gear rotation according to current curvature radius : ASSIGN micro-cut parameters : FOR TEETH = 1 TO Z : COMPUTE offset values due to gear index : FOR AXIAL LEVEL = BOTTOM TO TOP : COMPUTE offset values due to helix (eventual) : (in case of center desplacement: COMPUTE additional : offset values) : COMPUTE total offset values : EXECUTE unit cut cycle : NEXT AXIAL LEVEL : NEXT TEETH : NEXT PLANNED CURVATURE RADIUS : NEXT FLANK : END 15 Comparision between hobbing and milling
: Some notes are referred to one only machining mode: : ** : referred to milling by continous rolling mode : * : referred to milling by multi-plane cuts mode | Technology | |----------------------------------------------------------------------------| | H O B B I N G | M I L L I N G | | | | |============================================================================| | gear design | |----------------------------------------------------------------------------| | Module value up to 30-35 | No limit to module value | | | | | Maximum diameter related to | No limit to diameter in case of | | machine dimensions | machining of partial sectors | | | | | Pressure angle must be standard | Any pressure angle may be machined | | Immediate machining only if hob | Immediate machining of any kind of | | is available | gear | | | | | Teeth must be simmetric | Teeth may have different pressure | | | angle on working and backlash flanks | | | | | Central groove must be wider | Central groove may be thinner | | | | | Toothing must be possible on | Toothing may be interrumpted by filling| | complete 360 degrees tour | volumes OUT OF root diameter | | | | |============================================================================| | Machine tool | |----------------------