Control of Accuracy of Forming Elastic-Deformable Shafts with Low Rigidity

Analysis of Typical Structures of Dynamic Systems of Machining of Elastic-Deformable Shafts With Low Rigidity

“…Analysis of the equation of movement of the pneumatic element shows that its dynamic properties can be approximately described by means of an operator transmittance of the aperiodic element as: (2) where the equivalent time constant T np − depending on the initial position of the piston of the pneumatic actuator equals 0,01-0,02 s. The increase of elastic deformations relative to coordinate Y was analysed in relation to the initial coordinate of the object when supplying a unit step-wise signal on its input, taking into account the inertia of the actuator. The operator transmittance of the object is equal to: (3) Based on earlier research [19,20] it was concluded that the time constants in the numerator and the denominator of the operator transmittance of the object have similar values, and thus its dynamic properties are similar to the properties of the proportional element, i.e. the transitional process at step-wise signal supplied to the input of the actuator is most frequently determined by the properties of that element (Fig 4).…”

“…In the case under consideration, the elasticity coefficients of the elastic system relative to coordinate X are determined primarily by the elastic properties of the machine tool − h xx =3·10 -7 m/N, and relative to coordinate Y − by the elastic properties of the part. The calculations were performed following the 4 relations given in [20], in the case when the machining force, applied at the centre point of the part, determines the initial value of elastic deformations of the part g y0 = 0,11·10 -3 m, h yy = 1,2·10 -6 m/N. The values of coefficients B 0 and В are equal to B 0 = 0,18, В = 0,17.…”

“…Typical structures of dynamic systems of forming elastic-deformable shafts with low rigidity at various force-type regulatory effects, for which typical transmittances of the object of control gains coefficients relative to those effects have been determined in accordance with the relationships given in [20,21], are presented in Fig. 2.…”

“…The conventional methods of achieving accuracy of machining low-rigidity shafts, based on multi-pass machining, reduced machining parameters, steadies, and hand lapping, cause a significant lowering of efficiency, are uneconomical and inefficient, and preclude the automation of the process of machining [20,21,24]. This causes the necessity of developing new theoretical (e.g.…”