Understanding energy consumption of hydraulic press during drawing process

Abstract

Prediction of manufacturing equipment’s energy consumption plays an important role in selecting appropriate process parameters for energy saving. However, it is difficult to model the energy consumption of metal forming equipment during the drawing process characterized by variable process parameters and dynamic loads. In this paper, a model was developed to quantify the energy consumption of a typical hydraulic press during the drawing process under a range of operating conditions. The hydraulic press studied consists of two different circuits and two controllable parameters, i.e., punch velocity and blank holder force can be set for drawing processes performed. To start, the energy flow during the drawing process was analyzed by using the energy conversion mechanism and components’ specifications to understand the detailed energy characteristics of each circuit. Then, orthogonal experiments including these two parameters at three levels were designed and carried out to find significant parameters. Finally, the contribution of each parameter, which was obtained from the analysis of variance (ANOVA) of the experimental results, was used to simplify energy flow modeling efforts. Consequently, a model of the press was established and used to predict the energy consumption of the drawing processes with different parameters. Good agreement with the experimental results was observed. The model can be used to identify parameters for minimal energy consumption, while the approach could be adapted to develop an energy consumption model for different hydraulic equipment.

Appendices

Appendix 1

Table 8 Observable responses for the drawn part with the drawing depth of 15 mm, 20 mm, 25 mm, and 30 mm respectively

Appendix 2

Based on the energy flow analysis in Section 2 and the principle summarized in relevant references, the main power losses included in ES1 and ET1 are listed as follows.

Table 9 Power losses of pipe and valves, pump, and motor in ET1 and ES1

Considering the relationship between the frequency and the punch velocity, the fitted curve for frequency versus punch velocity is shown in Fig. 19.

Based on the ANOVA results that factor B can be neglected when simplifying the model, the total losses of ES1 and ET1 can be simplified and expressed as Eq. (27) by combining items with the same order.

Fig. 19

Fitting for frequency versus the punch velocity.

$$ {E}_{\mathrm{CC}}={\sum}_{i=1}^5{b}_i{v}_{\mathrm{p}}^{4-i}, $$

(27)

where b = [b₀, b₁, b₂, b₃, b₄, b₅] is the vector of the coefficients for the total losses.

Appendix 3

Since the described BH circuit working in status S₂ in Section 2.3, the pressure and flow of the circuit employed in this experiment can be illustrated in Fig. 20.

The pressure and flow at the outlet of the pump can be expressed as

$$ {\displaystyle \begin{array}{c}{p}_{\mathrm{ET}2}={p}_{\mathrm{BH}}^{\mathrm{load}}+\Delta {p}_{\mathrm{BH}}\\ {}{q}_{\mathrm{ET}2}={q}_{\mathrm{ET}2-1}+{q}_{\mathrm{ET}2-2}\end{array}}. $$

(28)

where q_ET2-1 and q_ET2-2 are the flow through the pressure relief valve and reducing valves, respectively.

Substituting the specifications of the employed pressure-reducing and relief valves as shown in Fig. 20, and considering Eq. (15), Eq. (28) can be expressed as

$$ {c}_2+{c}_3{q}_{\mathrm{ET}2-1}={c}_0+{c}_1{F}_{\mathrm{BH}}+{c}_4{\left({q}_{\mathrm{ET}2}-{q}_{\mathrm{ET}2-1}\right)}^2. $$

(29)

Therefore, the BH force and the power consumption changing with the BH force can be expressed as Eq. (30).

$$ \left\{\begin{array}{c}{F}_{\mathrm{BH}}=-\frac{c_4}{c_1}{\left({q}_{\mathrm{ET}2-1}\right)}^2+\frac{c_3+2{c}_4{q}_{\mathrm{ET}2}}{c_1}{q}_{\mathrm{ET}2-1}+\frac{1}{c_1}\left({c}_2-{c}_0-{c}_4{\left({q}_{\mathrm{ET}2}\right)}^2\right)\\ {}{P}_{\mathrm{BH}}={p}_{\mathrm{ET}2}{q}_{\mathrm{ET}2}/{\eta}_{\mathrm{ES}2}={c}_5+\sqrt{c_6+{c}_7{F}_{\mathrm{BH}}}\end{array}\right., $$

(30)

where

$$ {\displaystyle \begin{array}{c}{c}_5=\frac{q_{\mathrm{ET}2}}{2{c}_4{\eta}_{\mathrm{ES}2}}\left(2{c}_2{c}_4+{c}_3^2+2{c}_3{c}_4{q}_{\mathrm{ET}2}\right)\\ {}{c}_6=\frac{c_3^2{q}_{\mathrm{ET}2}^2}{4{c}_4^2{\eta}_{\mathrm{ES}2}^2}\left({c}_3^2+4{c}_2{c}_4-4{c}_0{c}_4+4{c}_3{c}_4{q}_{\mathrm{ET}2}\right),\\ {}{c}_7=-\frac{c_1{q}_{\mathrm{ET}2}^2{c}_3^2}{c_4{\eta}_{\mathrm{ES}2}^2}\end{array}} $$

(31)

Note that c₀, c₁, c₂, c₃, and c₄ are the corresponding coefficients, and c = [c₅, c₆, c₇] and the vector of power consumption for the BH circuit. The energy efficiency of ES2 can be deemed as a constant since the power consumption of the motor varies in a small range. Considering c₁ and c₄ are both positive, c₇ will be negative in Eq. (31).

Fig. 20

BH circuit analysis and performance of the employed valves (pressure relief valves [43] and reducing calves [44])