Substitute of hob choose with computation

The Reason Of Errors Caused By The Replacement Gear Hob Is Analyzed, and The Calculating Formulas Of Error Values Are Given.

Keywords:r　 of 　 of Original Gear of 　 of Supposed Gear of 　 of Base Pitch of 　 of Skew Variable of 　 of Eplacement Gear Hob 1.

Substitute of hob choose should order goods batch is small, delivery time is short, make special hobbing cutter wasteful or when manufacturing cycle does not allow, can use substitute hob will machine gear. Use substitute hob can reduce tool cost, reduce product cost, assure date of delivery. Alleged substitute hob is modulus, pressure angle and be differred by the modulus of treatment gear, pressure angle, but base pitch (basic circle pitch) equal or the hob of close. Substitute hob can be used at rough machining only commonly (namely semi-manufactured goods is machined) . With substitute the gear that hob treatment gives can appear inclined variable, because this must be calculated,go out substitute of the inclined variable of hob and gear cut deep, be accorded with in order to make to use a requirement by treatment gear. Choose substitute the principle of hob is: Choose as far as possible base pitch and by treatment gear base pitch equal or the hob of close, the gear inclined variable that such treatment give is equal to 0 or very small, it is zero hour when inclined variable, substitute hob also can be used at precision to ask the finish machining of not high gear. 2.

The relation of fictitious gear and original gear sets gear parameter to be: Di of round diameter of а of D of the external diameter De, diameter that divide a circle, root, law to circle of N of pressure angle α , cent to modulus Mn, law to San of the transverse tooth thickness that divide a circle, law а of helix angle β , tine counts Z. Set substitute hob parameter is: Law to modulus Mn ′ , law to ′ of N of pressure angle α . Narrate to facilitate, but will use substitute the gear that hob treatment gives is called " fictitious gear " , the parameter of fictitious gear and substitute hob is identical, namely modulus, pressure angle is Mn ′ , α N ′ respectively. When the other parameter of affirmatory hypothesis gear, must make clear the relation of the original gear of fictitious gear and requirement. The author establishs the relationship of fictitious gear and original gear by undermentioned principle: The standard that sets fictitious gear to go up in cent circle is S а N to arc transverse tooth thickness, the helix angle on cent circle is β а , use namely substitute the law that hob machines the fictitious gear that go out to divide a circle to go up in its is S а N to arc transverse tooth thickness, helix angle is β а , the tine number of fictitious gear and original gear, external diameter and root way are same, concern according to this calculable the other parameter that gives fictitious gear. The helix angle dividing a circle of fictitious gear is ′ of а of =D of ′ of Tg β а / а of β of D а Tg (1) ′ of а of the D in type -- fictitious gear divides round diameter, ′ of а of β of Z/cos of ′ of =mn of D а ′ enters era of D а ′ type (1) а of β of Tg of ′ of а of β of Cos of а of Z/D of ′ of =mn of ′ of а of the β that get Tg is arranged а of β of Ztg of ′ of =mn of ′ of Sin β а / Mn ′ of D а ＝ / . Pressure angle of round end panel of fictitious gear cent is ′ of N of а of α of =tg of ′ of S of Tg α а / ′ of Cos β а (diameter of basic circle of gear of 3) 　 hypothesis is ′ of S of а of α of Cos of ′ of а of Do ′ =D (transverse tooth thickness of circular arc of cent of gear of 4) 　 hypothesis is S а S ′ , can calculate piece with substitute the inclined variable that when hob machines gear, produces. 3.

The computational inclined variable of inclined variable is to point to the teeth shape error between fictitious gear and original gear, the purpose of computational inclined variable is to will substitute the teeth shape error that gear of hob treatment hypothesis and original gear produce quite is added in mill tine allowance, so that be eliminated when finish machining,substitute the teeth shape error that hob causes. Substitute the inclined variable that hob causes has the following 3 kinds of circumstances: (1) substitute the base pitch of hob and original gear base pitch are equal, right now inclined variable is 0, without teeth shape error, age formerly namely form of teeth of a cogwheel and fictitious gear tooth form are complete coincide, below this kind of circumstance substitute hob is most ideal. (2) substitute the base pitch of hob is more than original gear base pitch, right now fictitious gear will produce a root to cut, appear inclined variable. Graph 1 in solid line is original gear tooth form, dotted line is fictitious gear tooth form, its are inclined variable is Δ δ =Sin-Sin ′ (the Sin in 8) type -- ′ of Sin of 　 of 　 of transverse tooth thickness of Xiang Hu of round law of original gear root -- transverse tooth thickness of Xiang Hu of round law of fictitious gear root pursues Sin of 1 　 　 and Sin ′ can be in respectively original gear and fictitious gear are medium. The root circle transverse tooth thickness of original gear is Sin=Di [(Is of α of S-inv of а of α of S а N/mn)/z+inv] π of Is of α of Is- of α of Is=tg of α of Inv of 　 of 　 of 　 of Is=arccos(Do/Di) of the α in type of Cos β I (9) / а of β of Tg of а of I=arctg(Di/D of β of 　 of 180 　 　 ) the root of fictitious gear. (3) substitute hob base pitch is less than original gear base pitch, right now fictitious gear cuts generation top, also can appear inclined variable. Graph 2 in solid line is original gear tooth form, dotted line is fictitious gear tooth form, right now inclined variable is △ δ =Sen-Sen ′ (the Sen in 11) type -- ′ of Sen of 　 of wide 　 of top of former tine teeth of a cogwheel -- fictitious gear tine carries broad plan on the head ′ of Sen of 2 　 　 , Sen all is a law to the value, can part to be gotten in original gear and fictitious gear. Former tine teeth of a cogwheel is very wide it is Ses=De [(Es of α of S-inv of а of α of S а N/mn)/z+inv] (а of β of N/cos of а of Arctg(tg α of ＝ of S of а of α of 　 of 　 of 　 of E of β of the Sen=Sescos in 12) type) а of α of S- of а of α of S=tg of а of α of Inv of 　 　 　 . 4.

Root of fictitious gear generation is cut and carry the gear with cut particular to a parameter account on the head, in different pitch circle its pitch is different, the pitch circle that small pitch is in is lesser, the pitch circle that big pitch is in is bigger. Be more than when original gear base pitch substitute when hob base pitch, original gear base pitch also is more than fictitious gear base pitch. Count same gear to tine, its basic circle with big base pitch is big also, its basic circle with small base pitch is small also, namely right now original gear basic circle is more than fictitious gear basic circle. Because both external diameter is identical, former tine teeth of a cogwheel carries pressure angle on the head to be less than fictitious gear pressure angle, age the change of form of teeth of a cogwheel is less than fictitious gear dentiform to change formerly namely; Because original gear and fictitious gear are in,at the same time D а handles a way Xiang Hu transverse tooth thickness is equal, bounty of top of teeth of a cogwheel of former tine of because this is outer round place ages at fictitious gear very wide, fictitious gear produces a top to cut a phenomenon necessarily in tine top place. Manage together, be less than when original gear base pitch substitute when hob base pitch, the basic circle of fictitious gear is more than original gear basic circle, right now outer diameter place ages teeth of a cogwheel supports formerly wide be less than fictitious gear tine is very wide, fictitious gear does not produce a top to cut, and because transverse tooth thickness of fictitious gear arc is less than transverse tooth thickness of original gear arc,be in in root circle, because this hypothesis gear is in a round place,produce a root to cut a phenomenon necessarily. 5.

Substitute of hob treatment gear cut deep computation to substitute of hob cut deep the method that machines gear with the hob that uses identical modulus and pressure angle is basic and same, its computation formula cuts ＝ for H [(Mn ′ π - Δ - Δ δ - ′ of S а N - S а knife) / 2] / ′ of N of Tg α а + H knife (а knife of the S in 14) type -- substitute upper of hob section line, can decide mill is deep or mill is shallow. Can adjust Δ of mill tine allowance according to actual condition normally, in order to achieve original gear cut late demand. Using substitute when hob machines gear, if use fair normal to control working procedure dimension, the computational method of public law line is M mill = [(N-1)mn ′ π + ′ of S а N + ′ of S of а of α of Mn ′ Zinv] ′ of N of Cos α а (the parameter in 16) type all is fictitious gear parameter, n is the number that cross tine. The osculatory circle of public law line is Dm=2 (M mill / ′ of Cos β O) + 2Do ′ (′ of O of the β in 17) type, do ′ -- when the basic circle helix angle that is fictitious gear respectively and basic circle diameter are measured, can contact a circle to adjust the number that cross tine according to different fair normal, so that be in,aspirant travel measures good place. CNC Milling