The tooth profile of columnar worm measures circular arc to be begged instead with parameter

Summary: Be based on worm of circular arc cylinder (ZC) tooth profile equation, the tooth profile that discussed worm of face of lines of this kind of melody measures principle and model of error numerical analysis. The tooth profile that when introducing to beg ZC1 worm parameter instead, involves is measured analyse a method with data. Gave out to measure the actual measurement outcome of tooth profile of worm of the ZC1 on machine in HCM320 column coordinate. Keyword: Tooth profile of worm of circular arc cylinder measures parameter to beg Reverse Solution Of Parameters Of ZC WormShi Zhaoyao Et AlABSTRACT of ＆ of Profile Measurement instead: Based On The Profile Equation, the Principle And Model Of Measuring The Profile Of ZC1 Worms Is Discussed. The Methods Of Measuring The Profile Of ZC1 Worms And Reverse Calculating Worm Parameters Are Presented. The Result Of Measuring The Profile Of A ZC1 Worm By A Cylindrical Coordinate Measuring Machine Is Given. Keywords: 　 of 　 of ZC Worm Profile Measurement Reverse Solution Of Parameter 1. Foreword presses GB10086-88 regulation, worm of circular arc cylinder (ZC) have 3 kinds of forms: Worm of cylinder of cirque biscuit sth resembling a net (ZC1) , torus columnar worm (ZC2) with worm of cylinder of tine of axial circular arc (ZC3) . The article basically introduces the measurement of ZC1 worm and relevant issue, the measurement of ZC2 and ZC3 worm and ZC1 worm kind with. ZC1 worm is worm of face of lines of a kind of grinding melody, appearance of its tooth flank depends on the geometrical parameter that machines emery wheel and installation position. Inside the axial plane of emery wheel, producing look line is the circular arc of a paragraph of protruding of torus mother circle; When grinding, emery wheel axes is opposite at worm axes deflexion γ of horn of lead of a worm, the axis of emery wheel is sectional the part of method extent tooth form of tooth form horn and worm is equal, if pursue,1 is shown. Its install parameter to be the ρ in type -- arenaceous axle is sectional R of 　 of 　 of radius of tooth profile circular arc -- An of 　 of 　 of radius of worm reference circle -- the law of worm reference circle to A of 　 of 　 of tooth form horn -- center of circular arc of emery wheel tooth profile arrives worm axes and emery wheel. Equation of ZC1 worm tooth flank is shown 2 times like the graph, set worm coordinate coefficient to be σ (O - Xyz) , coefficient of emery wheel coordinate is σ 1 (O - X1y1z1) . The Z that two coordinate fasten and Z1 crisscross, crisscross horn is γ of worm lead horn, most stone's throw is A, and X axis is on the official vertical line of Z and Z1. By document [1] knowable, below the condition of parameter of foregone emery wheel, equation of ZC1 worm tooth flank is the φ in type, θ -- the ψ of parameter 　 　 of emery wheel surface -- the P of corner 　 　 of the worm when grinding -- worm helix parameter, n -- worm head counts 　 (2) the ρ in type, a, γ , a, the meaning of D and (1) pattern is same. Graph the setting 　 that 2 coordinate fasten 3. Equation of tooth profile of ZC1 worm axial to worm axial tooth profile, y ＝ 0 hold water, reason by (2) the 2nd type with medium type gets ＝ of the υ in type (ρ Cos θ - α ) Sin γ - (D of ＋ of ρ Sin θ ) ＝ of ω of 　 of 　 of 　 of φ of Cos γ Sin (D of ＋ of ρ Sin θ ) Cos φ - A, can beg an equation of axial tooth profile, it is nonlinear surmount equation. In be being measured actually, give out normally a series of Xi (I ＝ 1, 2, ... , n) , benefit can beg solution to give corresponding Zi to be worth conveniently with the computer. 4. The measurement of worm tooth profile principle graph shows the tooth profile that is worm 3 times to survey principle plan. The linear setup measuring a head that has parallel reed orgnaization can be in at the same time X direction (worm is radial) with Z direction (worm axial) athletic measurement on slide. When the computer controls slide to move in X direction and Z direction, measure a head to be able to undertake scanning metrical along worm tooth profile. Among them the Z of slide to motion be great distance " thick " motion, the sensor measuring a head that has small displacement function is used at compensating the athletic error of slide, experience teeth shape error at the same time. The process is measured in scanning in, the span ground such as the displacement sensor of X direction issues sampling signal, undertake sampling to displacement sensor to measuring head sensor and Z. The either that goes up to actual tooth profile is measured to nod, each Xi all has the Z that answers relatively to it to be mixed to Li of displacement sensor reading I of δ of the reading that measure a head. Zai of actual axial coordinate is I of δ of ＋ of Zai ＝ Li (5) it is suppose on a tooth profile measure N place, actual tooth profile but the A of Σ of gather Σ A that token nods for these: ｛ (Xi, zai) ｜ I ＝ 1, 2, ... , n ｝ (6) graph 3 measure Xi of correspondence of principle sketch map, basis (3) type can beg a worm the corresponding Z on tooth profile is worth to academic coordinate, write down here for Zi, academic tooth profile but token is gather Σ Σ : ｛ (Xi, zi) ｜ I ＝ 1, 2, ... , n ｝ (7) 　 by (6) , (7) type can beg a worm to assemble in the teeth shape error of axial ERRERR: ｛ Err (I) ＝ Zai - ＝ of Zi ｜ I 1, 2, ... , n ｝ (8) 　 if this worm measures M in all axial tooth profile, n of the sampling on each tooth profile dot, end up with teeth shape error is 　 in the computational formula of axial 5. Worm parameter is begged instead in producing practice, often encounter another kind of problem related to worm: Below the case that has worm in kind, the geometrical parameter that how obtains this worm and treatment install parameter. This is one begs project question instead. The parameter of ZC worm is begged instead than common the parameter of worm of straight grain face is begged instead, its complex part depends on how deciding the tooth profile parameter of ZC worm. Outside dividing tooth profile parameter, the other parameter of ZC worm all can adopt groovy measure or current capacity appearance is measured. The article emphasizes the affirmatory method that discusses parameter of ZC1 worm tooth profile. The tooth profile parameter of ZC1 worm begs instead dissoluble into two problems: (1) the basic information that how gets tooth profile, namely tooth profile measures an issue; (2) after obtaining tooth profile information, how to get tooth profile parameter, namely tooth profile information analyses a problem. Use on the measurement of section introduction principle, below the condition of parameter of sealed tooth profile, the key that implementation tooth profile measures depends on how controlling the athletic contrail that measures a head. Commonly used control strategy has two kinds: Dog measure law and section to approach a way. Dog measuring a way is to point to in measuring a process, change according to measuring the reading of the head, the computer is controlled in real time measure slide to be in Z to athletic speed, make measure the span that head reading changes around set value and does not measure head sensor more than, implementation measures a head to follow tooth profile appearance moves. The defect of this kind of method is to measure speed slower. Section approachs a way is to show tooth profile cent becomes a few paragraphs, every paragraphs are used go approaching point-blank, measure a head to make corresponding linear motion in every paragraphs, so that measure an implementation,scanning is measured. In the span that measure a head bigger case falls, tooth profile cent is two paragraphs to be able to satisfy a requirement. If the graph is shown 4 times, measure a graphic representation size with callipers or current capacity appearance, beg a Ci of coefficient of proportionality to regard control as the basis of skateboarding. Among them the good point that Ci approachs a way for section is tooth profile measures speed faster. Graph section of 4 tooth profile obtains worm after the A of coordinate gather Σ of actual tooth profile, the problem of parameter of the tooth profile that seek solution became a many variable actually to optimize a problem. Target function F is among them F is ρ , a, γ , the function of α N. Satisfy certain tie requirement, combine worm deputy effective demand, right (11) type undertakes optimizing handling, namely F → Min, can beg a tooth profile parameter and treatment installation parameter. 6. Measure example to measure the tooth profile that afore-mentioned principles and method use to measure ZC1 worm on machine in HCM320 column coordinate. The law of the worm that be measured is sectional like the graph 5 are shown, its parameter is: M ＝ 5. 2mm, 23 ° of α N ＝ , 10 ° of γ ＝ 03 ″ of 47 ′ , z ＝ 2. Way of Carlo of applied Monte 　 is right (3) type seeks solution, can gain the academic tooth profile of this worm conveniently. The axial tooth profile that the graph shows the right tooth flank that goes out to beg 6 times (scale 1 ∶ 10) ; The graph is shown 7 times for actual measurement result, it is in the sampling span of X direction among them 0.

05mm. For with larger proportion (1 ∶ 100) draw gives academic tooth profile and actual measurement tooth profile, so that can see both the difference between, graph 7a is the result after undertaking to academic tooth profile and actual tooth profile coordinate alternates; If graph 7b is curve of teeth shape error (1 ∶ 500) with measure an outcome. If be measured 5 times to the same tooth profile of this worm, its repeatability is 0.

8 μ M. When measuring tooth profile, what dot and worm axis space measure to be apart from actually since is the crucial factor that assures to measure precision certainly, for this, the null of calibration instrument answers when measuring. Graph 5 worm law is sectional graph tooth profile of 6 axial theory pursues curve of 7 tooth profile and 　 of teeth shape error 7. Article place narrates the last word the method that measures ZC1 worm tooth profile has rate fast, precision is advanced characteristic. This method also applies to ZK worm to wait for the tooth profile of worm of face of other melody lines to measure, it is academic tooth profile differs only. CNC Milling