**Mingmao Hu 1, Yu Sun 1, Qingshan Gong 1,2,\*, Shengyang Tian <sup>1</sup> and Yuemin Wu <sup>1</sup>**


Received: 3 August 2019; Accepted: 4 December 2019; Published: 18 December 2019

**Abstract:** Grinding is widely used in mechanical manufacturing to obtain both precision and part requirements. In order to achieve carbon efficiency improvement and save costs, carbon emission and processing cost models of the grinding process are established in this study. In the modeling process, a speed-change-based adjustment function was introduced to dynamically derive the change of the target model. The carbon emission model was derived from the grinding force using regression. Considering the constraints of machine tool equipment performance and processing quality requirements, the grinding wheel's linear velocity, cutting feed rate, and the rotation speed of the workpiece were selected as the optimization variables, and the improved NSGA-II algorithm was applied to solve the optimization model. Finally, fuzzy matter element analysis was used to evaluate the most optimal processing plan.

**Keywords:** grinding optimization; low carbon; low cost; improved NSGA-II; fuzzy matter element

### **1. Introduction**

In the production and processing of an enterprise, the grinding process induces a small amount of cutting, and the post-processing surface roughness of the parts are very low and is mainly used for precision and ultra-precision machining of parts. The high-speed rotation of the grinding wheel and the long processing time can lead to large carbon emissions from the machine tool, and this can be accompanied by a high processing cost and greater use of cutting fluid in the process. According to the analysis of the energy consumption of the grinding process [1–3] and the mathematical model of CNC (computer numerical control machine tools) [4–9], a grinding parameter optimization model based on carbon emissions and cutting costs is established.

Many scholars have carried out research on the optimization of the manufacturing process or system, and discussion on the connotation of energy efficiency of manufacturing systems [10–16]. Cai et al. [17,18] proposed a new concept of entitled, lean, energy-saving, emission reduction and fine energy consumption allowance. Greinacher S. et al. [19] focused on the identification of a cost-optimized combination of lean and green strategies with regard to green targets. Cai et al. [20] measured the eco-environment loss caused by industrial solid waste. Researchers have studied the model of green CNC machining. Feng Ma et al. [21] established the multi-objective, laser-sintering forming process optimization model, with minimum energy consumption and material cost. Jiang et al. [22] proposed a method to predict the remanufacturing cost based on dates. Lin et al. [23] proposed a method to directly quantify carbon emissions during the entire turning process and established a low-carbon, efficient turning model. Yan et al. [24] built a model to improve the thermal efficiency of the arc welding process, reducing energy consumption as a result. Bustillo et al. [25] took into account the

optimization of the process by requiring calibration of the main input parameters in relation to the desired output values.

Grinding forces are key parameters in the grinding modeling process; however, most studies were based on the analysis of grinding motion and individual abrasive forces. Shen et al. [26] analyzed the characteristics of the non-circular grinding movement of special-shaped parts and established an empirical model of grinding force during the processing of special-shaped parts. Li et al. [27] considered the microscopic interaction between abrasive particles and workpieces at different processing stages and proposed a detailed cutting force model. Zhang et al. [28] proposed that the aggregate force was derived through the synthesis of each single-grain force, based on material-removal and plastic-stacking mechanisms.

For the analysis of the results of green manufacturing, many scholars have proposed many assessment and decision-making methods of energy efficiency [29–34]. Cai et al. [35] proposed energy performance certification to manage energy consumption and improve energy performance. Jia et al. [36] developed an energy consumption evaluation method for the activities related to machine tools and operators. Green manufacturing processing steps can also be evaluated by the general principles of fuzzy matter evaluation [37], and carbon emissions from it can be evaluated by aggregating the unit process to form a combined model [38].

In a comprehensive analysis of the above research, although the optimization of the machining process is discussed, the influence of the optimization variables on the dynamic changes of the multi-objective model is rarely considered. In order to improve the accuracy of the model, the dynamic modeling method needs to be studied. During the actual processing, the use of a single abrasive force to establish a theoretical model would cause errors, and few researchers dynamically fit the model at each stage of the process through experimental data. In the analysis of the results, each target of the multi-objective optimization model is incompatible. So, using the theory of fuzzy matter-element to evaluate Pareto front-end could improve the efficiency of evaluating incompatible problems in reality. Methods to improve the accuracy of the models and the results require further research.

#### **2. Establishment of a Multi-Objective Optimization Model for the Grinding Process**

#### *2.1. Optimization Variable*

Cutting speed *vc*, feed rate *f*, and depth of cut *ap* are three important variables in the machining process. For the outer circle cutting of the grinding process, the main motion is the rotary motion of the grinding wheel. The cutting speed is the linear speed *vs* of the outer circle of the grinding wheel. The feed rate and the depth of cut are determined by the cutting feed rate *vr* of the grinding wheel, and the rotation speed of the workpiece is *vw*. The optimization variable is

$$
\mathcal{U} = \begin{pmatrix} \upsilon\_{\mathfrak{s}\_{\prime}} \upsilon\_{\mathfrak{r}\_{\prime}} \upsilon\_{\mathfrak{w}} \end{pmatrix}^{\mathrm{T}} \tag{1}
$$

#### *2.2. Carbon Emission Model in the Grinding Process*

The operation process of the CNC grinding machine is generally divided into start-up, standby, no-load, cutting, and retracting stages. The energy-consuming components of each stage are relatively fixed. Therefore, the power jump corresponding to each stage is relatively stable. The carbon emission during the grinding process is mainly composed of non-cutting and cutting. Non-cutting parts include carbon emissions from auxiliary systems such as standby, air cut, and cooling. The cutting part is mainly the overall carbon emissions of the machine tool during the material removal process. With the start-stop process of the CNC grinding machine as the aim, the energy consumption characteristics of each component are individually analyzed, and an energy-based carbon emission model is established.

With energy consumption as the basic input and greenhouse gas (GHG) as the output, the corresponding carbon emissions in this process are converted through the carbon emission coefficient of various energies [39]. ξ is the carbon emission coefficient of the energy type (e.g., fuel, electricity). δ is the environmental impact, such as the time of production and the area where the workshop is located. μ is the influence of the auxiliary process, such as the cooling of the processing environment, etc. The carbon emissions' factor *W* can be defined as

$$\mathcal{W} = \xi (1 + \delta + \mu) E \tag{2}$$

According to the study of Li et al. [40], the relationship between cutting speed and carbon emissions should follow the curve shown in Figure 1. When the cutting speed is increased in Area 1, the cutting power is also increased, but as processing time decreases, the energy consumption reduced by the time reduction is greater than the energy consumption increased by the increase of the spindle load, that is, the carbon emission is reduced. In Area 3, when the cutting speed is increasing and the power is increased, the energy consumption of the spindle load is greater than the energy consumption reduced by the time reduction, so the carbon emissions increase. There is an optimum cutting speed in Area 2 that minimizes carbon emissions.

**Figure 1.** Cutting speed-carbon emission curve

When the grinding machine power is turned on, the lighting system, operation panel, machine tool frequency converter, servo driver, and other components are turned on. The time is short and the power fluctuation is large, so the start-up energy consumption is ignored. The standby power of the machine *P*<sup>1</sup> consists of the power of the auxiliary system, the motor and the servo power. The time for standby preparation and input of the program before processing is *t*1. When the *Z*-axis starts to rotate, the spindle's no-load rotation power is *Pz*<sup>1</sup> . No-load standby power is *P*<sup>s</sup> = *P*<sup>1</sup> + *PZ*<sup>1</sup> , and no-load standby time is *t*s. Then the energy consumption *Es* after the machine is turned on can be expressed as

$$E\_s = \int\_0^{t\_1} P\_1 dt + \int\_0^{t\_s} P\_s dt\tag{3}$$

The empty cutting energy consumption of the cylindrical grinding machine includes the movement of the X-axis of the head frame and the movement of the Z-axis of the grinding wheel. The X-axis rotation and the Z-axis movement power are respectively *PX*, *PZ*<sup>2</sup> . Therefore, the energy consumption of air cut can be expressed as

$$E\_{\rm air} = \int\_0^{t\chi} P\_{\rm X} dt + \int\_0^{t\chi\_2} P\_{Z\_2} dt + \int\_0^{t\chi + t\chi\_2} P\_{\rm s} dt \tag{4}$$

In order to ensure the surface roughness of the parts and avoid the quality problems such as grinding burns, the flow rate and consumption of the cutting fluid change with different grinding wheel linear speeds and table feed speeds, and the wear amount of the grinding wheel also changes, resulting in dynamic changes of the model. For the change of the linear speed of the grinding wheel and the feed rate of the table, the adjustment function is defined as

$$
\psi\_i = a\_i(\Delta v\_s)^2 + \beta\_i(\Delta v\_r)^2 + \gamma\_i(\Delta v\_w)^2 (i = 1, 2) \tag{5}
$$

where α*i*, β*i*, γ*<sup>i</sup>* are the adjustment factors, ψ<sup>1</sup> is the cooling adjustment factor, and ψ<sup>2</sup> is the grinding wheel wear adjustment function. The energy consumption of the auxiliary system includes the energy consumption generated during the cutting time *tm* by the power of the filtration and cooling system *Pc*, and the energy consumption generated during the standby time *tch* of the machine tool in the process of loading and unloading parts, so the auxiliary energy consumption of each part processing can be expressed as

$$E\_{\rm as} = \psi\_1 \int\_0^{t\_m} P\_{\rm c} dt + \int\_0^{t\_{\rm ch}} P\_1 dt \tag{6}$$

Non-cutting process carbon emissions can be expressed as

$$\mathcal{W}\_1 = \mathcal{Z}(1+\delta+\mu) \cdot (E\_\mathfrak{s} + E\_{\text{air}} + E\_{\text{as}}) \tag{7}$$

As shown in Figure 2, the grinding force of the grinding wheel is divided into the normal grinding force *Fn* and the tangential grinding force *Ft*. The machining power of the grinding *P*<sup>m</sup> is mainly determined by the tangential grinding force and the linear velocity.

$$Pm = Ftr\text{vs}75 \times 1.36 \times 9.81kW \tag{8}$$

**Figure 2.** Grinding wheel force analysis

The speed of the wheel is recorded as follows:

$$
\upsilon\_s = \pi d\_0 \cdot n\_0 / (60 \times 1000) \tag{9}
$$

where *d*<sup>0</sup> is the diameter of the grinding wheel, and *n*<sup>0</sup> is the grinding wheel speed.

The tangential grinding force is an important parameter for power calculation. The index in the empirical formula is calculated by experimental data to obtain the actual tangential force of this kind of grinding wheel. The mathematical formula of the cylindrical grinding force is *Ft* = *Fpvx s v y r vz <sup>w</sup>*, and *Fp* is an experimental variable based on different processing environments. The experimental value of the grinding force of the grinding wheel is taken as the natural logarithm, and the regression equation is shown as follows:

$$\ln F\_{l} = \ln F\_{p} + \mathbf{x} \ln \upsilon\_{s} + \mathbf{y} \ln \upsilon\_{r} + \mathbf{z} \ln \upsilon\_{w} \tag{10}$$

$$y = b\_0 + b\_1 \mathbf{x}\_1 + b\_2 \mathbf{x}\_2 + b\_3 \mathbf{x}\_3 \tag{11}$$

The data of grinding consumption obtained in the experiment were coded, the large value is +1, the small value is −1, and the four coefficients *b*0, *b*1, *b*2, and *b*3, of the regression equation are calculated according to the data of the grinding force. In the grinding, *Fi* is the *i*-th grinding variable, *F*<sup>1</sup> is the grinding wheel linear speed *vs*, *F*<sup>2</sup> is the grinding wheel cutting feed amount *vr*, *F*<sup>3</sup> is the workpiece

*Processes* **2020**, *8*, 3

rotation speed, and *fij* is the *j*-th experimental value of the *i*-th grinding amount. Then find the three values in the regression equation:

$$\alpha\_{i} = \frac{2(\ln F\_{i} - \ln f\_{i\text{jmax}})}{\ln f\_{i\text{jmax}} - \ln f\_{i\text{jmin}}} + 1 = \frac{2}{\ln f\_{i\text{jmax}} - \ln f\_{i\text{jmin}}} \ln F\_{i} + \frac{-\ln f\_{i\text{jmax}} - \ln f\_{i\text{jmin}}}{\ln f\_{i\text{jmax}} - \ln f\_{i\text{jmin}}} \tag{12}$$

Assuming that *Ai* = <sup>2</sup> ln *fij*max−ln *fij*min ,*ai* <sup>=</sup> <sup>−</sup>ln *fij*max−ln *fij*min ln *fij*max−ln *fij*min , then *xi* <sup>=</sup> *Ai* ln *Fi* <sup>+</sup> *ai*. Substitute it for *xi* in the regression equation.

$$\begin{aligned} y &= b\_0 + b\_1(A\_1 \ln F\_1 + a\_1) + b\_2(A\_2 \ln F\_2 + a\_3) + b\_3(A\_3 \ln F\_3 + a\_3) \\ &= (b\_0 + b\_1a\_1 + b\_2a\_2 + b\_3a\_3) + b\_1A\_1 \ln F\_1 + b\_2A\_2 \ln F\_2 + b\_3A\_3 \ln F\_3 \end{aligned} \tag{13}$$

$$F\_t = \mathfrak{e}^{\left(b\_0 + b\_1 a\_1 + b\_2 a\_2 + b\_3 a\_3\right)} \mathfrak{v}\_{\mathfrak{s}}^{b\_1 A\_1} \mathfrak{v}\_{r}^{b\_2 A\_2} \mathfrak{v}\_{\mathfrak{w}}^{b\_3 A\_3} \tag{14}$$

Substitute *b*0, *b*1, *b*2, and *b*<sup>3</sup> with their values in Equation (14) to calculate the *Ft*, and the actual tangential force is determined according to different depths of cut, wheel speeds, and table feed speeds. The processing energy consumption model takes the form of integral, and the power from 0 to *tm* is integrated to obtain the energy consumption value. The *Em* expression of grinding energy consumption is

$$E\_m = \int\_0^{t\_m} \frac{F\_t v\_s}{75 \times 1.36 \times 9.81} dt\tag{15}$$

Then total carbon emissions from the grinding process are

$$\mathcal{W} = \xi (1 + \delta + \mu) \cdot (E\_{\text{sf}} + E\_{\text{air}} + E\_{\text{as}} + E\_{\text{ll}}) \tag{16}$$

#### *2.3. Cost Model in the Grinding Process*

The processing cost of a single part increases with the increase of processing time. The grinding cost is mainly divided into two aspects: processing cost and loss cost. With the part affected by the optimization variable taken into consideration, the grinding process cost model is established. The processing cost includes standby, empty cutting, energy consumption cost of cutting operation, the labor cost during processing time and the use cost of auxiliary equipment, and thus the processing cost expression for each process is shown as follows:

$$\mathcal{C}\_{m} = (M\_{\varepsilon} + M\_{as}) \times (\frac{t\_1 + t\_s}{Q} + t\_{air} + \frac{a\_p}{v\_r} + t\_{ch}) \tag{17}$$

where *Cm* is the grinding cost (yuan), *Me* is the electricity cost (yuan/s), and *Mas* is the labor cost and the use cost of auxiliary equipment (yuan/s); *tair* is the empty cut time (s); *ap* is the depth of cut (m) at which the grinding load is generated and it can be known based on processing requirements; the number of processing batches is *Q*.

Loss costs include wheel loss and cutting fluid consumption, and multiple wheel dressings are required during machining of the part until the wheel is reduced to the minimum diameter. The cost of the grinding wheel *Closs* is

$$\mathcal{C}\_{\text{loss}} = M\_a \cdot \psi\_2 \cdot \frac{\pi r^2 b - [\pi (r - a\_p)^2 b]}{G} \tag{18}$$

where *Ma* is the grinding wheel cost (yuan/mm3); *b* is the wheel width; *r* is the workpiece radius; *G* is the grinding ratio.

The consumption of cutting fluid consists of the portion of the machined surface that rises in temperature and evaporates into the air, the portion taken away by the chip, and the portion deposited on the surface of the part. Cutting fluid consumption cost *C*lub (yuan) is

$$C\_{\rm lub} = M\_l \times \left[ \psi\_1 \cdot \left( \frac{a\_p}{\upsilon\_r} \cdot l\_{\rm lub} \right) \right] \tag{19}$$

where *Ml* is the unit cost of cutting fluid consumption (yuan/L); *l*lub is the cutting fluid flow rate (L/s).

The total cost of grinding is

$$\mathcal{C} = (M\_{\rm c} + M\_{\rm as}) \times \left(\frac{t\_1 + t\_s}{Q} + t\_{\rm air} + \frac{a\_p}{v\_{\rm r}} + t\_{\rm ch}\right) + M\_{\rm a} \cdot \psi\_2 \cdot \frac{\pi r^2 b - \left[\pi (r - a\_p)^2 b\right]}{G} + M\_l \times \left[\psi\_1 \cdot \left(\frac{a\_p}{v\_{\rm r}} \cdot l\_{\rm hlb}\right)\right] \tag{20}$$
