Simulate the single-throw electric upcut shears operation in Mathcad

. The relevance of sheet processing technology, which finds increasing application, is given. Efficient equipment for sheet metal processing and sheet mounting is justified and proposed. This article deals with upcut shears’ operation. The solution to the mathematic model of manual upcut shears using Mathcad is provided.

Portable shears have a higher upcut speed, do not give material to chip, but they provide a length of strips only from the edges, bending them somewhat.
Nibble shears are made by upcut the sheet in an arbitrary place with a minimum upcut radius, which ensures their use for upcut holes of various shapes in smooth and corrugated sheets.
In this case, the equivalent mechanical drive system can be represented as a single-mass system with a mass driven, for example, to the motor shaft. In this case, the rotation angle of the motor α will be the generalized coordinate of the system. Total moment of engine inertia and reduced mass I = Imot + Ipr. In the transient mode of the drive operation, the equation of its motion will take the form: where Md(ω)is the moment of the engine determined by its mathematical model or by the available mechanical characteristic; Mс(ω)is the moment of resistance forces determined by the type of work operation performed and characteristics of the processing object; = / =̇is a shaft rotation speed; Mdyn-defines the dynamic moment ensuring change of engine rotation speed. Depending on moment of inertia I (Iconst I = I(α)) value Mdyn will be defined differently. If If I = I(α), it is characteristic, in particular, for the drives with crank-rod and eccentric converter mechanisms, value Mdyn we define from the Lagrange equation of the second kind in the form: where А = ( )( 2 /2)is the kinetic energy stored by the mechanical part of the drive.
Having differentiated, we get: The equations (1) and (2) or (1) and (4), along with the specified initial conditions, give a complete description of the drive with rigid kinematic constraints. In steady state operation ( = 0) the equation of the drive motion will be: Based on the given dependences, we obtain the equation of motion of the drive of vibration-type hand shears with an eccentric conversion mechanism (r is the eccentricity value) and analyse it. Let us choose the value of the eccentric shaft rotation angle -α as the generalized coordinate. We will take the extreme right position of the eccentric shaft as the starting point. From here we will count the positive x coordinate of the slider translational movement. In this case, the connection between them is as follows: The value of the machine drive parts' inertia, reduced to the eccentric shaft axis: Where Iрis the eccentric shaft drive inertia moment reduced to the axis of the armature-rotor; mis the mass of the translationally moving parts of the drive. The moment of resistance forces, reduced to the axis of the eccentric shaft, Where Pis the force generate don the tool when performing the working process of upcut or punching; η1is an efficiency of the conversion mechanism.
Depending on the type of excitation winding (serial, parallel) of collector single-phase electric motors, their external mechanical static characteristic can be written by the corresponding expressions ) (9 b) Where a0, a1, b0, b1 -are the constant coefficients. Let us take Mmot (̇) in the form (9b), where b0 = M0is the moment of the "inhibited" enginethe conditional point of intersection of the linearized characteristic with the axis of moments; b1 -the tangent of the slope of the characteristic to ̇.
For the convenience of performing dynamic analysis, we rewrite the obtained equation of the drive motion relative to the generalized coordinate x, assuming ̇= -constand taking Р=сх+ḃ (сis the reduced stiffness of the stationary working body holder and a sheet of metal; bis the coefficient resistance), in the form: where msl is the drive mass reduced to the slider; φis the phase shift angle between the displacement and the driving force; F0is the force amplitude in the slide ℎ = /(2 , );0 ;<ω0/√2; >ω0 /√2.

Discussion
To create a mathematical model of Portable shears driven by an AC collector motor, we set the function of the moment of inertia brought to the shaft for the motion system J(φ) according to (7), as well as the function of the resistance moment Mс(φ) according to (8): The reduced moment of inertia Jis the moment of the rotor inertia for the engine itself, kg m 2 ; Jredshaft, kg m 2 ; m --the angular coordinate of the rotor of the engine, I am glad; iredgear ratio of reduction gear box.
The given moment of resistance (the blade coordinates are counted from the middle position, the upper dead point is located on the positive position, and the lower -on the negative axis) can be set as Ccutis the stiffness of fixed blade holder, N/m; Pcutis upcut power, N; ηis an actuator efficiency; ris an eccentricity value, m; his the thickness of metal to be cut, m. At the same time: relation Pcut/ Ccutis the maximum holder deformation, m; (h + Pcut/ Ccut r)is the blade coordinate at which the blade contacts the metal to be treated (the deformation process of the holder begins); m; (hr)is the blade coordinate, at which the holder deformation is maximum (the metal separation process begins), m. Auxiliary operator: Since the blade coordinate is proportional to sin (a), the following replacement is true:

Summary
The following is a simulation of the single-throw shears operation in the MathCAD system. -moment of eccentric shaft inertia kg, m 2 r:=0.003 -eccentricity m ir:=3 -gear ratio η:=0. 8 -conversion mechanism efficiency ratio Pcut:=1800 -upcut force Н Ccut:=900000 -rigidity of the fixed blade holder and the metal being processed N/м h:=0.001 -metal thickness, m