Hydraulic changes quadrature implement group of broad sense equation reachs emulation computation

332GENERAL EQUATIONS OF TORQUEConVERTER AND SIMULATIONCALAULATIONSun Xuguang Han Decai (Yanshan University) Abstract According To The Newton ' S Law And The Conservation The General Components Equationes And General Engery Equation Of Torque Converter Are Given.

These Are Significant For The Dynamic Processes Of Torque Converter Or The Control Systems Which Transmision Power Chain Contins Torque Converter.

A Kind Of Dynamic Process Is Also Simulated By The Numerical Method.

Key Words: A of symbol of Torque Converter Generalized Elementary Equations Simulation -- shed area Q -- H of circular bulk discharge -- head loss β -- relative speed and M of horn of U Xiang Ga -- V of component motive moment of force -- R of velocity of flow -- impeller radius Ω -- ξ of component integral region -- J of local loss efficiency -- moment of inertia: 1 -- entrance 2 -- exit 0 -- stable state U -- U direction L -- liquid P -- impeller T -- turbine D -- dynamic M -- edge Cheng J, local 0 preface serve as a kind of important transmission, hydraulic changes quadrature implement got applied extensively in transmission domain. In addition, it is used as equipment of a kind of adjusting control also have particular case [1, 2]  . Come for years, be opposite domestic and internationally change quadrature implement research great majority is in centrally denounce treat of to perfect its respect of static job theory. However, in transmission and circumstance of adjusting control application, include in transmission catenary change quadrature implement dynamic job process still cannot undertake analyse and emulation computation reasonably at present. As a result of academic inadequacy, use change quadrature implement static job theory will consider to change with the analysis quadrature implement the method of dynamic job process has been used actually [3] , of its method be not being perfected is apparent. Be built accordingly and be over capricious quadrature implement the analytic computation of dynamic job process is to have actual project value and academic sense theoretically, at the same time it also is a newer research field. Change quadrature implement it is the loop inside the complex liquid that comprises by impeller, turbine and guide pulley hydraulic transmission. Traditional static job theory is to build on foundation of Ou Lafang Cheng, but in this basic equation in dynamic job process already no longer applicable. Accordingly, research changes quadrature implement a of dynamic job theory main base works even if from the most fundamental analysis proceed with builds reasonable fundamental equation. 1 change quadrature implement pitching moment equation sets component liquid trends change quadrature implement inside working fluid is not to have agglutinant ideal fluid, pass to aleatoric instantaneous change quadrature implement turbine (in graph 1) small Dw is in yuan of body the analysis in department of coordinate of Z, U, R, use Newtonian law to have a plan 1 small yuan of body Dzdudr of γ of power of quality of oversight of analysis getting power, think current is axial symmetry is mixed shed noninterference of the each other between the layer, arrange and the type on integral can be gotten [4] (1) notices impeller and turbine is the component that each other goes against, will go up type right is multiplied - 1 have (2) 　 by type (1) , (2) can see, action the liquid trends moment of force at the component is decided by two. The first is by instantaneous parameter Q and roll decision of place of product of U of  of Rv of fast difference Δ , it is place of corresponding instantaneous parameter moment of force of denotive stable state; The 2nd those who be dynamic moment of force is add, it by circumferential cent fast the integral place decision after differential Vu/t multiplies radius R, this Xiang Kegen reachs according to the particular form of impeller definite parameter expression; If this posture turned oversight into Europe,pull equation. In addition, change to what the axis sheds turbine quadrature implement foliaceous bar has R of ＝ of R2 ＝ R1, accordingly (the auspicious Nuo equation of the moment of force of hydraulic turbine trends that the type on 3) 　 ever mentioned in a few data namely [5] . 2 change quadrature implement equation of component trends moment of force sets what what study to change quadrature implement for the commonnest 3 element afferent turbine changes quadrature implement (graph 2) , have a plan by speed triangle 2 change quadrature implement ω of R of ＝ of structural diagram Vu + Q/A.

Tan β will go up type generation enters type (1) or type (the dynamic and add moment of force of 2) is conveyed in have notice D ω / Dt ＝ ω / T+ ω / S.

Q/t+q/s of ＝ of Dq/dt of 　 of 　 of Ds/dt 　 　 .

　 of Ds/dt 　 　 and 0 　 of ＝ of Q/t ＝ Q/s arrange type to have pair of turbine: To impeller: Will above two posture and moment of force of corresponding stable state   [6]  takes the place of respectively type (1) , (2) has (the Atl in 3) (4) type, apl -- annulus, the area coefficient Jpl of eddy impeller, jtl -- liquid of the job in impeller, turbine is inertial volume coefficient Lp, lt -- inside round meridional plane of loop of impeller, turbine Ap of intermediate streamline length, at -- in impeller, turbine perpendicular the annulus at intermediate streamline shed an area to be opposite impeller rotor and turbine rotor, by pitching moment balance relation can get 　 (the Jp in 5) (6) type, jt -- impeller, turbine is inertial Mdp of quadrature 　 　 , mdt -- moment of force of trends of the load outside impeller, turbine by type (5) , (6) can see, of impeller and turbine action outside dynamic moment of force is equal to corresponding the sum of dynamic and add moment of force that at dynamic parameter place moment of force of denotive stable state reachs place of rotate speed change to cause at discharge change. Below stable state circumstance, the differential in type for 0, posture degrades to change quadrature implement the expression of stable state moment of force of the action on the component. 3 change quadrature implement equation of broad sense energy changes quadrature implement in dynamic job process, also want to abide by principle of conversation of energy. Can put forward to change according to this principle quadrature implement in dynamic job process its input ω of P-Mdt of ω of energy ∑ Mdp completely T and its the difference of Hmc of ∑ of Hcj+ of ∑ of Q of γ of total loss energy is equal to the equation of conversation of energy of 0, change to common 3 element quadrature implement (graph 1) can convey ＝ of Hmc of ∑ of Hcj+ of ∑ of Q of γ of T- of ω of Mdp ω P-Mdt as follows 0 　 　 (energy of total loss of energy of output of turbine of energy of input of the impeller in 7) type goes to afferent turbine quadrature implement, concussion loss efficiency is general and desirable for 1, considering have Rt1 of radius Rp2 ＝ commonly, rp1 ＝ Rt2, rt2 ＝ Rd1, rp1 ＝ Rt2, shed At1 of area Ap2 ＝ , ap1 ＝ At2, at2 ＝ Ad1 has Hj of the ∑ in type, ∑ Hm -- change quadrature implement total impact and M of ξ of 　 of 　 of loss of edge Cheng head -- loss efficiency of edge Cheng head will above analytic type generation enters equation of conversation of energy (7) arranges 　 having 　 (8) type is medium 4 change quadrature implement broad sense is basic. This equation group was described change quadrature implement the mutual connection between T of ω of Mdt of Mdp of the discharge Q below dynamic motion curve, moment of force, moment of force, rotate speed and P of rotate speed ω . When the differential in equation group posture take 0, equation group turns into to change commonly quadrature implement group of stable state equation, it shows next changing to group of equation of this broad sense describes trends already quadrature implement motion curve, also described quadrature changes below stable state implement motion curve. Because this calls its hydraulic to change quadrature implement group of broad sense equation, and equation (8) and (5) , (6) says respectively to change quadrature implement equation of broad sense energy and equation of generalized force quadrature. The Chang Wei of linear of gets dispute of group of broad sense equation separates equation group, ask its are analytic solution is very difficult, but the numeric solution that the method that can use numerical analysis will come to to beg its to have project value. There are T of 5 variable Q, Mdp, Mdt, ω and ω P in equation group, the case that because this is specific and numeric,tries the load that sees this equation group still need a basis to be linked together actually and drive is compensatory and additional equation. In addition, also can make to this equation group small disturbing linearization analysis, seek the analytic solution that gives it, this kinds of method is to control a domain to seek the academic means building a model that takes control system model commonly usedly. Beg solution and test and verify to change for convenient numerical value quadrature implement group of broad sense equation, one kind is used to change here quadrature implement special process of flying car trends (change quadrature implement the job is nodded in job of some stable state, the drive that will be linked together suddenly with impeller and turbine and load change loosely quadrature implement) of dynamic change process, see a picture 3, dynamic to this process has compensatory equation to pursue as follows 3 change quadrature implement process of flying car trends takes the place of compensatory equation to change quadrature implement group of broad sense equation is attainable 3 Chang Wei of 3 time variable divide equation. This differential equation group but numerical value seeks solution, ＝ of the T in equation group the 0 stable state parameter when are decided by stable state equation. Computation changes quadrature implement parameter is as follows: ＝ of Cot β P1 - 0.

0 　 of ＝ of P1 of β of Cot of 280 　 　 ＝ of T1 of 　 Cot β 1.

＝ of T2 of β of Cot of 　 of 121 　 - 1.

＝ of D1 of β of Cot of 611 　 　 - 0.

＝ of D2 of β of Cot of 569 　 　 2.

＝ of Rd1 of ＝ of Rt2 of ＝ of Rp1 of 145 　 　 0.

＝ of Rd2 of ＝ of Rt1 of ＝ of Rp2 of 059436m 　 　 0.

＝ of Apl of 059436m 　 　 - 0.

＝ of Atl of 000331m2 　 　 - 0.

Jpl+Jp ＝ of ρ of 001090m2 　 　 0.

0107608kg.

Jtl+JT ＝ of ρ of M2 　 　 0.

0292638kg.

M2. Use library of case of 4 rank dragon to amount to methodological numerical value to seek solution this trends process can get a picture 3, graph midpoint is test result. Can see emulation result and test result be identical are better. 5 conclusion set out by basic law, derived change quadrature implement equation of generalized force quadrature. From this equation is knowable, change quadrature implement of component action outside dynamic moment of force is equal to corresponding at dynamic parameter place moment of force of denotive stable state the dynamic and add moment of force that creates at discharge change and rotate speed change the sum. And what traditional Ou Lafang Cheng and auspicious Nuo equation just derive change quadrature implement a kind of of moment of force of component liquid trends special situation. (2) is defended by energy judge law sets out, put forward and built change quadrature implement equation of broad sense energy. (3) puts forward and built a description to change quadrature implement of motion change quadrature implement group of broad sense equation. Group of equation of this broad sense described next dynamic changing quadrature implement motion curve, and quadrature changes below stable state implement motion curve is a kind of below trends special situation only. Came true to changing quadrature implement the numeric emulation computation of dynamic process, emulation result accords with actual condition. CNC Milling CNC Machining