The permeance - Курсовая работа

ABSTRACT Object of investigation - direct current electromagnet. Aim of the work - to get skills of electromagnet calculation. Method of investigation - empirical formulas. The calculation of dc-current electromagnet was made. The course project consists of four parts. In the first part the so-called direct problem is solved and the magnetic-moving force is found. In the second part the winding is calculated and the pure MMF of the coil is found. The third part includes the so-called inverse problem, the magnetic flux is being determined. And the last, the fourth part includes defining of the actuation time of the electromagnet. DC ELECTROMAGNET, AIR-GAP, WINDING, ACTUATION TIME, MAGNETIC MOTIVE FORCE, INDUCTION. INTRODUCTION This course design is intended for getting skills on calculation of electromagnets. In this work next problems are solved: - direct problem. Condition of the work of electromagnet: the armature is in open stage. Here such parameters are calculated: permeances of the air-gaps, magnetic fluxes, magnetic potential drops in metal and, as a result, magnetic motive force; - calculation of winding. Here such parameters are calculated: diameter and cross-section of wire, resistance of wire, current, flowing in wire and precise value of magnetic motive force; - inverse problem. Conditions of the work: armature is in closed stage. Here such parameters are calculated: permeances of air-gaps, magnetic flux, inductance of metal and magnetic intensity; - calculation of dynamic characteristics of electromagnet. Here such characteristics are found: moving, pick up, actuation time and electromagnetic force for actuation of calculated electric apparatus. Nowadays special computer programs are made for computing electromagnets and their characteristics. But the importance of this work is to understand and to learn the stages of finding one or another thing during calculation of contacting electric apparatus. 1. MMF determination 1.1. Initial data A dc electromagnet with next parameters is given on Figure 1.1: a=10 mm; d=25 mm; d2=20 mm; l=250 mm; h=80 mm; dп=10 mm; d2=0.25 mm; dк=0.2 mm; induction at d=dп, B=0.1 T; winding power voltage U=36 V; magnet circuit material is steel of quality 50HXC. Figure 1.1. - Calculated electromagnet The tasks are: - to determine MMF of electromagnet winding; - to design electromagnet winding; - to define electromagnetic forces; - to find actuation time of the electromagnet. 1.2. Completing of the equivalent circuit The first step is to set up equivalent magnetic circuit without taking into account reluctance of iron subcircuits. The scheme is represented on the Figure 1.2. The MMF that is produced by flowing current through the coil is drawing as the source of power. The magnetic resistances of operating and parasitic air gaps are drawn as resistors. Rm1 is the magnetic resistance of the operating air-gap. Rm2 and Rm3 are the magnetic resistances of the parasitic air-gaps. Figure 1.2. - Equivalent circuit 1.3. The permeance of the air-gaps determination The permeance of the operating air-gap is determined according to the method of probable flux passes. The fluxes in this air-gap are shown on the Figure 1.3. Figure 1.3.1. - Fluxes flowing between core and armature (1) and between yoke and armature (2) The magnetic permeances of the operating air-gap by the method of probable fluxes can be calculated where µ0 - is magnetic constant, or vacuum permeability, ; δп - is the value of the operating air-gap, m. where δп - is the value of the operating air-gap, m. Determination of the steel magnetic potential drops Now let’s find the magnetic potential drops of the magnetic circuit by the method of leakage ratio. The division of the electromagnet is shown on the Figure 1.5.1 At first the core is divided by 5 equal parts (x) equaled to Figure 1.5.1. - Dividing of a magnetic circuit on subcircuits Now the leakage ratios of every subcircuit must be defined: where xi - is the length from the top of the core to the middle of the investigated subcircuit; λS - is the specific permeance; in this case this is the specific permeance of coaxial cylinders: . After that, the total permeance ΛδΣ is found: ; ; , where Λδ, Λδ1, Λδ2 - are the permeances of the air-gaps, H. Then, the calculations for the first subcircuit are made. The bulging coefficient σX1 is found , where λS - is the specific permeance, ; in this case this is the specific permeance of coaxial cylinders; ΛδΣ - is the total permeance, H. Then the magnetic flux through the first subcircuit is made: ; , where Фδ - is the magnetic flux through the circuit, Wb; σX1 - is the bulging coefficient of the subcircuit.