Principle of gear of inclined tine small line segment

The development of modern industry is opposite foreword the demand of positive drive is higher and higher, and positive drive attributes solid drive, want to improve its drive performance, consider from 3 respects commonly: Material, tooth form reachs craft. With respect to tooth profile character, people did much research work. Gear of small line segment is we put forward a kind brand-new clench the teeth makes positive drive, consider to make clear, gear of small line segment has higher flexural strength and osculatory strength, and least tine number is less (3~4 ages) , can get used to the requirement with modern all-around to positive drive function industry well, especially the requirement of high speed, burden and miniaturization respect [2][3] . But the research that at present we make has in the light of gear of straight tine small line segment, because the circumstance of clench the teeth of straight gear is abruptly is entered at the same time along whole facewidth,clench the teeth is mixed exit clench the teeth, the power that gets on teeth of a cogwheel thereby is abrupt be added or discharge drops, the smooth stability of reason drive got be affected certainly, and the concussion with constant presence and noise, a when solve afore-mentioned problems efficient way uses helical gear namely, and, helical gear also must be used on certain gear-box product, the promotion application that accumulates to make gear of small line segment gets bedding face accordingly must have the research of gear of inclined tine small line segment. 2.

Standard tooth form -- the tooth form curve of method extent rack 2.

When 1 basic idea is machining gear with Fan Chengfa, it is to use countless straight line segment or plane to wrap curve of tooth profile of subsidiary channels in the human body through which vital energy or curved surface. Cut impossibly countless times as a result of cutting tool actually, the face joins and the tooth profile curve that forms finally consequently or curved surface are become by tiny linear Duan Huoping necessarily. Suffer this to inspire, we realise want straight line segment only or planar and enough small can use straight line segment or plane to construct tooth profile curve or curved surface. To facilitate with Fancheng the law is machined, use construct first basic rack, recycle Fan Chengyuan manages the means that gets gear tooth profile. The first pace of tectonic and basic rack is tectonic theoretic successive and 2 but small curve, of course, this curve is by a lot of paragraphs of curves " go all out " rise, next, alternate according to the scanning in graphics again principle, draw-out piece enough much dot, decide the form of tooth profile curve with these dots, we say call " curve of disperse dot tooth profile " , the interpolation principle in recycle CNC Machining, get what needing tooth profile with linear interpolation method. 2.

The construction of rack of 2 methods extent passes pair of current and commonly used gear to actor or actress defect is analysed, we offerred the train of thought of method extent rack of tectonic and basic rack and means: 1) should make contact intensity as far as possible big. Be about to come true this, be about to make two tooth profile are protruding, sunken contact or it is to make the same score the contact that faces plane. For this, we are in macroscopical on the tectonic method that used gear of double circular arc, in microcosmic place implementation makes the same score the contact that faces plane. 2) should make flexural strength as far as possible big. Because age the root curves stress and tine root ply to having close connection, reason makes age the root is added when construction thick. 3) want slide to move coefficient as far as possible small. Slip coefficient is small, chafe wear away small, mechanical efficiency is tall. To come true this, we are when curve of tectonic tooth profile, ensure relatively slip in each small paragraph in finish, do not accumulate the next small paragraph. Foundation of science of * the Anhui province funds a project (01044104)4) should prevent a root effectively to cut. Age to make when number is lesser, do not produce a root to cut, when construction, should notice make affect " the root is cut " parameter is adjustable, when making sure tine number is less then, tine root curve also can share the work normally. According to above train of thought, the way that our construction gave rack of standard small line segment to tooth profile, it is open line essence clever join by very much small Duan Jian and into, the curvature center that every small Duan Jian opens on the line two end points is to be on the basic circle of different position, different radius, and these curvature centers all are on the section line of rack, if pursue,1 is shown. Detailed tectonic process and undermentioned formula (the derivation of 1) can refer to document [2][3] . Graph tooth form of rack of 1 small line segment 2.

The equation of tooth profile curve of 3 basic rack is in gear of small line segment, have 3 important parameter, they are respectively: 1) : Initiative pressure angle; 2) : Parameter pressure angle; 3) : Radius of initiative basic circle. These 3 parameter decided way of gear of small line segment the appearance to rack. Assume office to protruding tooth profile at 10 o'clock K, in the graph 1 shows coordinate to fasten O1x1y1 in, coordinate equation is: (1) in type (2) (3) for with about and the I that changes by rule of make choice of nods basic circle radius. 3.

Equation of general tooth flank 3.

The law arrow 0 o'clock is the random on rack of 1 the face that seek a way equation of the tooth flank that seek solution, answer to get the law arrow that contacts a dot first, but with type (1) beg the coordinate that those who go out is disperse dot only, for this, set the successive curve equation that nods through all disperse to be, be in K was in at 0 o'clock, have: Because be on a tooth profile of gear of small line segment,have tens of thousands of and even hundred thousands of at 0 o'clock, accordingly, two of photograph adjacent zero distances are very short, reason can think, have to was in at 0 o'clock arbitrarily, have so: (4) accordingly, the law arrow of K place was the random on method extent rack at 0 o'clock 3.

2 seek basic rack tooth form to tooth form by the law to derive fiducial rack tooth flank is equational, building two following coordinate is, if the graph shows 2 times: Graph the end panel of 2 basic rack and σ of department of method extent coordinate (T) -- end panel coordinate is, the coincide of an end panel of O(t)x(t)y(t) and basic rack; σ (N) -- method extent coordinate is, o(n)x(n)y(n) and coincide of extent of basic rack method, and with σ (the coordinate origin coincide of T) plane. Be equivalent to a graph 1 medium O1x1y1 coordinate is. The coordinate in setting tooth flank to assume office to was in is, in in coordinate is, in be in law arrow at this o'clock to be in, express to be, and in in can express to be, have: (5) (6) 3.

Of equation of 3 general tooth flank beg solution to machine a principle by Fan Cheng knowable, the tooth flank of gear of small line segment is the face including sth resembling a net of basic rack tooth flank, to undertake begging solving, building 3 coordinate is, if pursue,3 are shown. Graph the coordinate that place of equation of the 3 tooth flank that seek solution uses fastens σ (0) -- the space secures coordinate is, among them O(0)x(0)z(0) plane and coincide of rack section plane. σ (1) -- the coordinate that connects with rack solid is, among them the coincide of an end panel of O(1)x(1)y(1) plane and rack, o(1)x(1)z(1) plane and coincide of rack section plane, and when position of rest, σ (1) and σ (0) coincide. Here, σ (1) is equivalent to a graph 2 in σ (T) . σ (2) -- the coordinate that connects with gear solid is, among them on the rotational axes that O(2) dot is located in gear, the coincide of an end panel of O(2)x(2)y(2) plane and rack, and when position of rest, y(2) axis and Y(0) gross ril load close. Set rack shift speed to be V namely, the floating rate of gear is ω namely, the pitch circle radius of gear is R, when the mobile distance of rack is, the angle that gear has turned is, right now the M dot on tooth profile becomes a contact to nod. Have: (7) M dot is along with rack shift speed: ; (8) the speed that M dot moves along with gear is: (9) type (8) with type (9) decrease, and type (7) the opposite motion speed that era enters so that gear rack nods in M: (10) will (6) reach (10) era enters equation of clench the teeth to get: relation (5) take the place of to go up type gets: (11) : Coordinate is σ (1) and σ (the coordinate commutation type between 2) is again relation (5) take the place of to go up the tooth profile equation that type can gain gear: (12) to using formula (1) affirmatory random at 0 o'clock K() , usable type (4) , (11) affirmatory Zk and the relation between, enter its era type again (12) attainable with K is opposite at 0 o'clock an answering curve, ordinal change the position is attainable at 0 o'clock gear tooth profile. 4.

Afore-mentioned formula look computational example very troublesome, but have the aid of is calculated at computer process designing actually very convenient. The tooth flank that the author developed gear of small line segment of an inclined tine according to afore-mentioned principles makes software, calculate exemple gear to be generated to use it namely. Exemple: Foregone, modulus is 4mm, tine number is 20, facewidth is 10mm, helix angle is 15 ° , , initiative pressure angle, parameter pressure angle. Generated gear is shown 4 times like the graph. Graph if the 4 partial data that calculate earning of exemple gear computation to calculate exemple gear tooth profile express 1 to show. Express the 1 part that calculates exemple gear to count the side that occupy a law tooth flank of serial number of direction of serial number tooth flank nodded coordinate at 0 o'clock (tine coping is divided) tine noodle coordinate (tine root part) 5.

Conclusion (1) article place puts forward " successive curve, disperse nods a curve, interpolation " the method of the tooth profile that gains gear of inclined tine small line segment is correct and feasible, train of thought is novel; (2) on the foundation that ages in research gear of small line segment gains a success continuously, solved the main problem that gear of inclined tine small line segment designs successfully, for the farther promotion of gear of small line segment application laid solid foundation; (3) the formula that article formula machines dextral gear for Zun Xuan rack, same method can be pushed derive dextral rack machines formula of left gear wheel coming back; (4) the train of thought of the article and method are other the research of similar orgnaization offerred a new approach. CNC Milling CNC Machining