【機(jī)械類畢業(yè)論文中英文對(duì)照文獻(xiàn)翻譯】包絡(luò)法的資產(chǎn)負(fù)債【word英文1611字6頁word中文翻譯2512字6頁】,機(jī)械類畢業(yè)論文中英文對(duì)照文獻(xiàn)翻譯,word英文1611字6頁,word中文翻譯2512字6頁,機(jī)械類,畢業(yè)論文,中英文,對(duì)照,對(duì)比,比照,文獻(xiàn),翻譯,包絡(luò),資產(chǎn)負(fù)債,word,英文,中文翻譯 英文原文 A Envelope Method of Gearing Following Stosic 1998, screw compressor rotors are treated here as helical gears with nonparallel and nonintersecting, or crossed axes as presented at Fig. A.1. x01, y01 and x02, y02are the point coordinates at the end rotor section in the coordinate systems fixed to the main and gate rotors, as is presented in Fig. 1.3. Σ is the rotation angle around the X axes. Rotation of the rotor shaft is the natural rotor movement in its bearings. While the main rotor rotates through angle θ, the gate rotor rotates through angle τ = r1w/r2wθ = z2/z1θ, where r w and z are the pitch circle radii and number of rotor lobes respectively. In addition we define external and internal rotor radii: r1e= r1w+ r1 and r1i= r1w? r0. The distance between the rotor axes is C = r1w+ r2w. p is the rotor lead given for unit rotor rotation angle. Indices 1 and 2 relate to the main and gate rotor respectively. Fig. A.1. Coordinate system of helical gears with nonparallel and nonintersecting Axes The procedure starts with a given, or generating surface r1(t, θ) for which a meshing, or generated surface is to be determined. A family of such gener-ated surfaces is given in parametric form by: r2(t, θ, τ ), where t is a pro?le parameter while θ and τ are motion parameters. r1 =r1(t, θ)=[ x1,y1,z1] =x01cosθ-y01 sinθ, x01 sinθ+ y01 cosθ,p1θ] (A,.1) = (A.2) (A.3) (A.4) (A.5) The envelope equation, which determines meshing between the surfaces r1 and r2: (A.6) together with equations for these surfaces, completes a system of equations. If a generating surface 1 is de?ned by the parameter t, the envelope may be used to calculate another parameter θ, now a function of t, as a meshing condition to define a generated surface 2, now the function of both t and θ. The cross product in the envelope equation represents a surface normal and ?r2 ?τ is the relative, sliding velocity of two single points on the surfaces 1 and 2 which together form the common tangential point of contact of these two surfaces. Since the equality to zero of a scalar triple product is an invariant property under the applied coordinate system and since the relative velocity may be concurrently represented in both coordinate systems, a convenient form of the meshing condition is de?ned as: （A.7） Insertion of previous expressions into the envelope condition gives: (A.8) This is applied here to derive the condition of meshing action for crossed helical gears of uniform lead with nonparallel and nonintersecting axes. The method constitutes a gear generation procedure which is generally applicable. It can be used for synthesis purposes of screw compressor rotors, which are electively helical gears with parallel axes. Formed tools for rotor manufacturing are crossed helical gears on non parallel and non intersecting axes with a uniform lead, as in the case of hobbing, or with no lead as in formed milling and grinding. Templates for rotor inspection are the same as planar rotor hobs. In all these cases the tool axes do not intersect the rotor axes. Accordingly the notes present the application of the envelope method to produce a meshing condition for crossed helical gears. The screw rotor gearing is then given as an elementary example of its use while a procedure for forming a hobbing tool is given as a complex case. The shaft angle Σ, centre distance C, and unit leads of two crossed helical gears, p1 and p2 are not interdependent. The meshing of crossed helical gears is still preserved: both gear racks have the same normal cross section pro?le, and the rack helix angles are related to the shaft angle as Σ = ψr1+ ψr2. This is achieved by the implicit shift of the gear racks in the x direction forcing them to adjust accordingly to the appropriate rack helix angles. This certainly includes special cases, like that of gears which may be orientated so that the shaft angle is equal to the sum of the gear helix angles: Σ = ψ1+ ψ2. Furthermore a centre distance may be equal to the sum of the gear pitch radii :C = r1+ r2. Pairs of crossed helical gears may be with either both helix angles of the same sign or each of opposite sign, left or right handed, depending on the combination of their lead and shaft angle Σ. The meshing condition can be solved only by numerical methods. For the given parameter t, the coordinates x01 and y01 and their derivatives ?x01?t and ?y01?t are known. A guessed value of parameter θ is then used to calculate x1, y1, ?x1 ?t and ?y1?t. A revised value of θ is then derived and the procedure repeated until the difference between two consecutive values becomes sufficiently small. For given transverse coordinates and derivatives of gear 1 pro?le, θ can be used to calculate the x1, y1, and z1 coordinates of its helicoid surfaces. The gear 2 helicoid surfaces may then be calculated. Coordinate z2 can then be used to calculate τ and ?nally, its transverse pro?le point coordinates x2, y2 can be obtained. A number of cases can be identi?ed from this analysis. (i) When Σ = 0, the equation meets the meshing condition of screw machine rotors and also helical gears with parallel axes. For such a case, the gear helix angles have the same value, but opposite sign and the gear ratio i = p2/p1 is negative. The same equation may also be applied for the gen-eration of a rack formed from gears. Additionally it describes the formed planar hob, front milling tool and the template control instrument.122 A Envelope Method of Gearing (ii) If a disc formed milling or grinding tool is considered, it is suffcient to place p2= 0. This is a singular case when tool free rotation does not affect the meshing process. Therefore, a reverse transformation cannot be obtained directly. (iii) The full scope of the meshing condition is required for the generation of the pro?le of a formed hobbing tool. This is therefore the most compli-cated type of gear which can be generated from it. B Reynolds Transport Theorem Following Hanjalic, 1983, Reynolds Transport Theorem de?nes a change of variable φ in a control volume V limited by area A of which vector the local normal is dA and which travels at local speed v. This control volume may, but need not necessarily coincide with an engineering or physical material system. The rate of change of variable φ in time within the volume is: (B.1) Therefore, it may be concluded that the change of variable φ in the volume V is caused by: – change of the speci?c variable in time within the volume because of sources (and sinks) in the volume, dV which is called a local change and – movement of the control volume which takes a new space with variable in it and leaves its old space, causing a change in time of for ρv.dA and which is called convective change The ?rst contribution may be represented by a volume integral:. (B.2) while the second contribution may be represented by a surface integral: (B.3) Therefore: ( B.4) which is a mathematical representation of Reynolds Transport Theorem. Applied to a material system contained within the control volume V m which has surface A m and velocity v which is identical to the fluid velocity w, Reynolds Transport Theorem reads: (B.5) If that control volume is chosen at one instant to coincide with the control volume V , the volume integrals are identical for V and Vm and the surface integrals are identical for A and Am , however, the time derivatives of these integrals are different, because the control volumes will not coincide in the next time interval. However, there is a term which is identical for the both times intervals: (B.6) therefore, (B.7) or: (B.8) If the control volume is ?xed in the coordinate system, i.e. if it does not move, v = 0 and consequently: (B.9) therefore: (B.10) Finally application of Gauss theorem leads to the common form: (B.11) As stated before, a change of variable φ is caused by the sources q within the volume V and influences outside the volume. These effects may be proportional to the system mass or volume or they may act at the system surface. The ?rst effect is given by a volume integral and the second effect is given by a surface integral. (B.12) q can be scalar, vector or tensor. The combination of the two last equations gives: Or: (B.13) Omitting integral signs gives: (B.14) This is the well known conservation law form of variable . Since for = 1, this becomes the continuity equation: ?nally it is: Or: (B.15) is the material or substantial derivative of variable . This equation is very convenient for the derivation of particular conservation laws. As previously mentioned = 1 leads to the continuity equation, = u to the momentum equation, = e, where e is speci?c internal energy, leads to the energy equation, = s, to the entropy equation and so on. If the surfaces, where the fluid carrying variable Φ enters or leaves the control volume, can be identi?ed, a convective change may conveniently be written: (B.16) where the over scores indicate the variable average at entry/exit surface sections. This leads to the macroscopic form of the conservation law: (B.17) which states in words: (rate of change of Φ) = (inflow Φ) ? (outflow Φ) +(source of Φ)