Energy saving design of the machining unit of hobbing machine tool with integrated optimization

doi:10.1007/s11465-022-0694-2

Front. Mech. Eng.

2022, Vol. 17

Issue (3) : 38 https://doi.org/10.1007/s11465-022-0694-2

RESEARCH ARTICLE

Energy saving design of the machining unit of hobbing machine tool with integrated optimization

Yan LV¹, Congbo LI¹(

), Jixiang HE², Wei LI¹, Xinyu LI³, Juan LI¹

¹. State Key Laboratory of Mechanical Transmission, College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China
². Department of Process Technology, Sichuan Aerospace Fenghuo Servo Control Technology Corporation, Chengdu 611130, China
³. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

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Abstract

The machining unit of hobbing machine tool accounts for a large portion of the energy consumption during the operating phase. The optimization design is a practical means of energy saving and can reduce energy consumption essentially. However, this issue has rarely been discussed in depth in previous research. A comprehensive function of energy consumption of the machining unit is built to address this problem. Surrogate models are established by using effective fitting methods. An integrated optimization model for reducing tool displacement and energy consumption is developed on the basis of the energy consumption function and surrogate models, and the parameters of the motor and structure are considered simultaneously. Results show that the energy consumption and tool displacement of the machining unit are reduced, indicating that energy saving is achieved and the machining accuracy is guaranteed. The influence of optimization variables on the objectives is analyzed to inform the design.

Keywords energy saving design energy consumption machining unit integrated optimization machine tool

Corresponding Author(s): Congbo LI

Just Accepted Date: 28 April 2022 Issue Date: 31 October 2022

Cite this article:

Yan LV,Congbo LI,Jixiang HE, et al. Energy saving design of the machining unit of hobbing machine tool with integrated optimization[J]. Front. Mech. Eng., 2022, 17(3): 38.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0694-2
https://academic.hep.com.cn/fme/EN/Y2022/V17/I3/38

Fig.1 Flow chart of the energy saving design of the machining unit.

Fig.2 Structure and force diagram of the machining unit.

Tab.1 Main technical parameters of the machine tool and gear

Tab.2 Parameters used for the calculation of energy consumption

Fig.3 YS3118CNC5 hobbing machine tool and its machining unit.

Fig.4 Schematic of tool displacement of the hobbing machine tool.

Fig.5 Tool post support plate of the machining unit.

Fig.6 Distribution of sample points of the design variables in the LHS experiment. DoE: design of experiment.

Fig.7 Finite element model of the hobbing machine tool.

Tab.3 Dataset of the LHS experiment

Tab.4 Descriptive statistics of the dataset of the LHS experiment. The number of samples for each parameter was 60

Fig.8 Test results of the surrogate models of (a) tool post support plate mass and (b) tool displacement.

Algorithm setting	Symbol	Value
Particle dimension	Dim	11
Initial population number	Nip	100
Maximum iteration number	Mit	300
Learning factor	c₁	2
	c₂	2
Inertia weight	$ω i n i$	0.9
	$ω e n d$	0.4

Tab.5 Relevant parameters of the MOPSO

Tab.6 Solutions selected from the Pareto frontier. They have the same parameters, i.e., P_N1 = 3000 W, n_N1 = 800 r/min, P_N2 = 1500 W, x₂ = 100 mm, x₃ = 50 mm, and x₄ = 30 mm

Fig.9 Pareto frontier of the optimization results of the MOPSO algorithm.

Tab.7 Comparison of variables and objectives before and after the optimization

Fig.10 Tool displacement simulation result of the original value.

Fig.11 Sensitivity analysis of (a) energy consumption and (b) tool displacement.

Fig.12 Influence trend of the variables on the energy consumption: (a) P_max1 and P_N1, (b) P_max1 and P_max2 ,(c) n_N1 and n_N2, (d) x₄ and x₅, (e) x₃ and x₂, and (f) x₂ and x₁.

Fig.13 Influence trend of the variables on the tool displacement. (a) x₁ and x₅, (b) x₁ and x₂, (c) x₅ and x₂, and (d) x₄ and x₃.

a	Distance between the two sliders
a_p	Cut depth
A	Surface area of the motor core
B	Equivalent viscous friction damping coefficient
B_sm	Servo motor damping coefficient
c₁, c₂	Learning factors
d_h	Hob outer diameter
Dim	Particle dimension
E	Energy consumption of the machining unit
E_k	Kinetic energy of mechanical transmission components
f_BA	Basic frequency of the inverter
f_c	Coulomb friction force
f_i	ith order natural frequency of the machine tool after optimization
[f_i]	ith order natural frequency before optimization
f_v	Viscous friction force
f_z	Axial feed of the hob
F_c	Cutting force
F_cz	Cutting force on the slide plate
F_f	Friction force between the sliding plate and the vertical guide rail
F_N	Normal force on the guide rail
F_t	Slide plate load force
g	Gravitational acceleration
h	Heat dissipation coefficient
J_l, J_s, J_sm	Moments of inertia of the coupling, ball screw, and servo motor, respectively
J_s^*	Moment of inertia equivalent to the motor shaft of the transmission system
K₁, K₂, K₃	Coefficients associated with the materials, hardness, and helical angle of the gear, respectively
l₁	Distance between the barycenters of the slide plate and the axis of the ball screw
l₂	Distance between the barycenters of the tool post and the axis of the ball screw
l₃	Distance between the barycenters of the main gearbox and the axis of the ball screw
l₄	Distance between the barycenters of the additional component and the axis of the ball screw
l₅	Distance between the barycenters of the hob and the axis of the ball screw
L_b	Ball screw lead
m	Normal modulus of the hob
M, M_a, M_c, M_h, M_k, M_t	Masses of the machining unit, additional components, main gearbox, slide plate, tool post shell, and tool post support plate, respectively
M₀	Equivalent nonload Coulomb friction moment
Mit	Maximum iteration number
n^*	Initial speed before the motor is accelerated
n_gm	Hob speed
n_N	Rated speed of the motor
n_N1, n_N2	Rated speeds of the main and servo motors, respectively
n_sm	Servo motor speed
N_i	Motor speed under working condition i
Nip	Initial population number
N_s	Number of samples
p	Number of pole pairs of the motor
P	Power of the machining unit
P_ad-i	Additional loss power under working condition i
P_c	Cutting power
P_Cu	Peak copper loss power
P_Cu-i	Copper loss power under working condition i
P_e	Peak eddy current loss power
P_e-i	Eddy current loss power under working condition i
P_h	Peak hysteresis loss power
P_h-i	Hysteresis loss power under working condition i
P_loss	Peak loss power of the motor
P_loss-i	Motor loss power under working condition i
P_m-i	Mechanical loss power under working condition i
P_max	Peak power of the motor
P_max1, P_max2	Peak powers of the main and servo motors, respectively
P_mec	Mechanical loss power
P_mo	Main motor output power
P_n-i	Motor input power under working condition i
P_N	Rated power
P_N1	Rated power of the main motor
P_N2	Rated power of the servo motor
P_sm	Servo motor output power
P_o-i	Motor output power under working condition i.
P_SA	Motor acceleration power
P_SR	Motor shaft rotation power
sgn(·)	Symbolic function
t	Operation time of the machine tool.
t^*	Duration of the rotation acceleration
t_A	Acceleration time of the inverter
t_r	Limit value of temperature rise
T_b	Frictional moment generated by the bearing preload
T_i	Motor output torque under working condition i
T_l	Coupling output torque
T_sm	Servo motor output torque
T_t	Output torque of the ball screw
T_z	Input torque of the ball screw
Τ	Output threshold vector
v_c	Cutting speed
V_z	Axial feed speed of the moving components along the Z axis
x	Sample data set
x_i, x_j	Sample points
x₁, x₂, x₃, x₄, x₅	Structure parameters of the tool post support plate
$y^$	Fitting expression of y
Z	Tooth number of the workpiece
α	Load factor of the mechanical transmission system
α^*	Motor angular acceleration
γ_i	ith observed value
$γ i ?$	ith predicted value
$γ ˉ i$	Mean value of the ith observed value
δ	Tool displacement
?(·)	Global prediction polynomial
Θ(·)	Random error
κ(·)	Radial basis function
η_b	Bearing transmission efficiency
η_m, η_sm	Motor efficiencies of the main and servo motors, respectively
η_z	Ball screw transmission efficiency
η(i)	Motor efficiency under working condition i
μ_c	Coulomb friction coefficient
μ_v	Viscous friction coefficient
χ	Center of κ(·)
$ω$ ^*	Angular velocity of the motor
$ω e n d$ , $ω i n i$	Final and initial values of the inertia weight, respectively
$ω m$	Angular velocity of the spindle motor shaft
$ω s m$	Servo motor output angular velocity
ξ₀, ξ_i, ξ_ij	Undetermined coefficients of the RSM model
?(·)	Linear polynomial function
?²	Variance of Θ(·)
Ξ(·)	Correlation function
?_k	Related parameter determined by the maximum likelihood estimation
?_i	Adaptability weight coefficient
?_50×1	Synaptic weight matrix
\|\|·\|\|	Euclidean norm

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