accuracy forecasting disks manufacturing of axial power machines considering the forces at the industrial process system

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 152 (2016) 487 – 492 International Conference on Oil and Gas Engineering, OGE-2016 Accuracy forecasting disks manufacturing of axial power machines considering the forces at the industrial process system Nesterenko G.A *, Nesterenko I.S., Lysenko E.A Omsk State Technical University, pr Mira, 11, Omsk, 644050, Russian Federation Abstract The paper provides information on the axial displacement calculation of the hydraulic pump non-rigid disk when their dimensional processing The radial forces accounting actions method by means of equivalent axial force has been offered The ability of the proposed replacement was proved with experimental studies The boundary conditions for the calculations for various disc fixing schemes during processing are presented © 2016 Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license © 2016 The Authors Published by Elsevier Ltd (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-reviewunder underresponsibility responsibility of the Omsk State Technical University Peer-review of the Omsk State Technical University Keywords: disk, engineering process, processing accuracy, the form error Introduction While manufacturing disks of axial power machines which are used in the chemical and oil industry, the central issue is the ability to forecast and control the errors originated in the course of their processing The clearest and the most frequent example is the example of processing error resulting from the axial displacement of the processed disc body relative to the rim As a result of considering the mechanism of this error the conclusion has been made that it is necessary to consider a set of factors that affect the disk body Z deflection Some of these factors are the forces in the industrial process system Study subject The study subject was to establish the dimensional errors forming patterns of axial power machines non-rigid disks considering the simultaneous action of all the forces in the industrial process system * Corresponding author Tel.: +7(908)107-17-06; E-mail address: nga112001@list.ru 1877-7058 © 2016 Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Omsk State Technical University doi:10.1016/j.proeng.2016.07.630 488 G.A Nesterenko et al / Procedia Engineering 152 (2016) 487 – 492 Turning to the consideration of these forces it should be noted that the deflection value is inextricably linked with the stability of the disk body We understand stability as the disk body ability to counteract the forces aiming to bend it in the axial direction As it is known, the deflection of the disk body is the most strongly influenced with force of cutting Р, namely its component Ру applied axially to the disk body The action of this force component can be measured both qualitatively and quantitatively using approaches and methods of the theory of elasticity When assessing the action of the cutting force it is also necessary to consider that its value is a variable depending on the mode used for processing (cutting speed v, cutting depth t, supply s), the value of the tool wear hз for its back surface As the permissible errors for the manufacture of the disc body in the axial direction are of 0.01 - 0.05 mm to evaluate the effect of cutting forces on the processed disc a mathematical model based on the equations of the initial parameters method (IPM) was developed The IPM equation for calculating will be the following: ω (Dω  r M ψ  r M ψ  P r 2ψ )/D r0 ωr θ0 ωq y ωp (1) where Z0 is deflection at the inner radius of the disk body (determined from the boundary conditions); Мr0, MT0 are moments acting on the inner radius in the radial and tangential directions, respectively, they are determined from the boundary conditions; r is the current radius, the deflection is calculated using it; \Zr, \ZT, \ZP are maintainig functions [1]; Ру is a component of the cutting force; D is cylindrical rigidity: D Eh3 12(1 μ ) , (2) Е is modulus of elasticity; P is Poisson's ratio; h is the thickness of the disk body To determine Z0, Мr0, МT0 is necessary to determine them with boundary conditions Depending on the crosssection of the disc body different schemes may be regarded Such schemes and boundary conditions are shown in Table In addition to cutting force the deflection is affected with the values of fastening force Fastening forces Рfо, acting in the axial direction, can be assessed with increment of the argument to the power factor function in equation (1), whereupon it takes the form: ω (Dω  r M ψ  r M ψ  (P r 2ψ  P r 2ψ ))/D r0 ωr θ0 ωq y ωp fо ωp , (3) Fastening forces Рfр, acting in the radial direction effect disk body resistance to deflection during processing The influence of such forces may be different: they both reduce resistance and increase it We consider the worst of these cases, when stability decreases (Fig 1) This condition arises from the effects of compressing of fastening forces applied to the rim of the disc or to the outer radius of the disk body, and the tensile forces applied to the hub or to the inner radius of the disk As long as the fastening forces value does not exceed the critical values (till the stability loss), their action is possible and must only be regarded together with the cutting force (Fig 2) The action of radial fastening forces with simultaneous cutting forces component action is proposed to be considered as the action of the axial force РE, which is determined from expression [2]: 489 G.A Nesterenko et al / Procedia Engineering 152 (2016) 487 – 492 Ρ E 64 ˜ S ˜ Е ˜ h ˜ D ˜ ( ε  ε  ˜ μ ˜ ε ˜ ε ) θ r r θ , r ˜ r ˜ (1  в )2 d r d (4) where εr, εθ are relative deformations; ε θ ˜ (P  μ ˜ Р ); ε fr r E ˜ h fθ ˜ (P  μ ˜ Р ); fθ E ˜ h fr (5) Рfr, Рfθ are radial and tangential efforts the processed disk fastening forces; rin, rout are inner and outer radii of the disk body Рfr, Рfθ are radial and tangential efforts the processed disk fastening forces; rin, rout are inner and outer radii of the disk body 490 G.A Nesterenko et al / Procedia Engineering 152 (2016) 487 – 492 ω, mm – Titanic alloy ОТ-4 0.25 – Steel – St 1’ 0.20 0.15 2’ 0.10 0.05 30 20 10 60 50 40 70 r, mm b) Fig The disk deflection values under cutting forces action РУ = 10Н (1, 2) and with combined cutting forces action РУ = 10Н and the outer compressing fastening force Рfр = 200Н, acting in the radial direction (1’, 2’); а – disk without rims, b – disk with rims Р fр Р fр 1 РУ Ру 1 РУ Ру Р fр Р fр Р fр Р fр Р fр 3 2 Р fр Fig The scheme of combined action of cutting forces РУ and fastening forces Рfр, acting in radial direction while disks processing: - chisel, – fixed disk, – bearing support 491 G.A Nesterenko et al / Procedia Engineering 152 (2016) 487 – 492 When calculating the disk deflection value from the combined action of cutting forces and radial efforts of fastening forces using IPM equations one uses equation (2), where the component Рfо is substituted into РE from expression (3) and the equation will look like this: ω (Dω  r M ψ  r M ψ  (P r 2ψ r P r 2ψ ))/D r0 ωr θ0 ωq y ωp E ωp , (6) The sign (+) is selected in the calculation of the deflection from the compressive forces, and (-) - when calculating the strain efforts of fastening Results and discussion T The results of experimental studies and calculations have shown that this method of calculation can be used at the stage of process engineering (PE) to calculate the expected error from non-rigid disks processing of power machines The error between the calculated and experimental data is - % Table The boundary conditions for the calculation of the processed disc body deflection Cross-section Calculation scheme R Boundary conditions Z(R)=0 r a) M(R)=0 Z(r)=0 M(r)=0 a) R, rare outer and inner disc body radii b) b) Z(R)=0 M(R)=0 R R Z(R)=0 M(R)=0 M(r)=0 r 492 G.A Nesterenko et al / Procedia Engineering 152 (2016) 487 – 492 R Z(R)=0 a) М(R)=0 r M(r)=0 a) b) Z(r)=0 b) References [1] A.N Podgorny, G.A Marchenko, V.I Pustynnikov, Fundamentals and methods of the elasticity theory, Kiev, Vyshcha School, 1981, 328p [2] G.A Nesterenko, Influence of technological congenital stresses and efforts of non-rigid disks GTD processing errors, Applied mechanics problems, Proceedings, Omsk, Publishing House OmSTU, 1999, pp.152 – 155  ... for the manufacture of the disc body in the axial direction are of 0.01 - 0.05 mm to evaluate the effect of cutting forces on the processed disc a mathematical model based on the equations of the. .. from the effects of compressing of fastening forces applied to the rim of the disc or to the outer radius of the disk body, and the tensile forces applied to the hub or to the inner radius of the. .. be used at the stage of process engineering (PE) to calculate the expected error from non-rigid disks processing of power machines The error between the calculated and experimental data is -