This section describes the deterministic energy consumption model of SLS. For estimating the energy consumption of any AM process, it is necessary to have proper information on different energy consuming components of a 3D printing machine. A brief description of SLS is provided in Chapter 3. There are several machinery components in SLS machine that consumes energy. Table 6.1 lists the energy consuming elements of SLS. All the energy consuming components are described in the next subsections.
Table 6.1 Energy consuming components of SLS Energy consuming components Purpose
Laser system Sintering of powder in layer-by-layer manner Heater system Maintaining the chamber at an elevated temperature
and heating the powder
Rotating roller Supplying and levelling the powder in bed
Pistons in the movable platform One piston for lowering of the powder bed and the other piston for supplying the powder in front of the roller
6.2.1 Energy consumed by laser system
The energy consumed by the laser beam during the sintering of the powder is dependent on laser parameters, geometrical parameters of the part as well as material properties. The estimation of the energy requirement by the laser system considering all parameters simultaneously by an analytical model is a tedious task. Franco and Romoli (2012) analysed the effect of different laser parameters on the energy requirement for polyamide polymer powder, which is also considered as a raw material in this study. The interaction of laser beam and the powder is characterised by a basic parameter, viz., the energy density. The energy density (Ed) is given by
l ,
d s l
E P
v d (6.1) where Pl is the power rating of the laser, vs is the scan velocity of the laser and dl is the diameter of the laser beam. Franco and Romoli (2012) conducted experiments on an SLS machine and provided data to estimate laser energy consumed per unit mass based on different values of Ed. Based on those data, the laser energy consumption can be estimated.
6.2.2 Energy consumed by heater system
The heater system is composed of an infrared heater and a resistive heater (Gibson et al.
2014). The closed chamber is maintained at a high temperature by the infrared heater. On
the other hand, the resistive heater is used to maintain an elevated temperature of the build platform throughout the fabrication of the part. The energy consumed by the infrared heater (Eir) is given by (Metreyer et al. 2014)
ir build ,
ir
ir
E P t
(6.2) where Pir is the power rating of the infrared heater, tbuild is the time involved in warming up the machine chamber and building the part and ηir is the efficiency of the infrared heater.
On the other hand, a resistive heater is required to heat the powder in the build platform for proper sintering to occur. The energy is required in the form of heat. It depends on the powder material properties. The heat input (Qr) to maintain the elevated temperature of the powder during building of the part is given by
,r p p f i
Q m c T T (6.3) where mp is the mass of the powder, cp is the specific heat of the powder, Tf is the final attainable temperature of the powder and Ti is the initial temperature of the powder. The heat input is provided by the resistive heater and its energy consumption (Erh) is given by
r ,
rh r
E Q
(6.4) where ηr is the efficiency of the resistive heater. The total energy consumed by the heater system (Eheater) is given by
heater ir rh.
E E E (6.5) 6.2.3 Energy consumed by roller
The roller spreads the powder and forms a layer in the machine bed. The mechanical energy of the roller is estimated as per the kinematic profile shown in Figure 6.1.
Figure 6.1 Velocity versus time diagram of the roller
The energy spent in portion AB (E1) is given by the change in kinetic energy and work done against powder:
2 2
1
2 2
1
1 1
2 2
1 1 1
2 2 2 ,
r r r r r ab
r r r r r r
E m v I F s
m v I F v t
(6.6)
where mr is the mass of the roller, vr is the maximum attainable translational velocity by the roller, Ir is the moment of inertia of the roller about its centre and ωr is the maximum attainable angular velocity by the roller. The term Fr is the resistive force provided by the powder to the roller, sab is the distance travelled by the roller from point A to B and t1 is the time spent by the roller to reach the point B. The roller is considered to be a solid cylinder. Its moment of inertia is given by
1 2
2 ,
r r r
I m r (6.7) where rr is the radius of the cylindrical roller. During travelling of the roller, it is assumed that rolling takes place without slipping that satisfies the relation
r r r.
v r (6.8) At point B, the roller attains its maximum velocity and continues to move until point C.
The energy spent in portion BC (E2) is given by
2
2 1 ,
r bc r r
E F s F v t t
(6.9) where t2 is the time required by the roller to reach point C. From point C, the roller decelerates and comes to rest at point D. For bringing the roller to rest, it requires some amount of kinetic energy. However, during this period, the powder also offers resistance.
Hence, the energy spent in portion CD (E3) is less than the energy spent in portion AB. E3 is given by
2 2
3
1 1
2 r r 2 r r r cd,
E m v I F s (6.10) where scd is the distance travelled by the roller from point C to D. The total energy spent (Er) is given by
1 2 3
2 2 2 2
1 1 1 1
2 2 2 2 .
r
r r r r r ab r bc r r r r r cd
E E E E
m v I F s F s m v I F s
(6.11)
However, sab = scd, hence
2 2
1 2 .
r r r r r r r
E m v I F v t t (6.12) The study conducted by Nan et al. (2020) revealed that the roller force is approximately 20 times the total weight of the heap of powder generated in front of the roller. This heap of powder is generated approximately up to the half the diameter of the roller (Haeri et al. 2016). The diameter of the roller is evaluated based on the size of the polymer powder. In SLS, the size of the roller is related to the size of the powder particle as (Haeri et al. 2016)
500,1000 ,
roller powder
d
d (6.13) where droller and dpowder are diameters of the roller and powder, respectively, and square bracket contains interval number. Overall, the energy required by the roller is provided by a motor. Hence, the energy requirement by the motor to operate the roller (Eroller) is given by
r
,
roller m
E E
(6.14) where ηm is the efficiency of the motor.6.2.4 Energy consumed by the movable platform
The part fabricated in a build platform moves in the downward direction according to the prescribed layer thickness. Apart from this, a powder delivery platform is also present on the other side that supplies the powder in front of the roller. Both the platforms are controlled by piston. The piston moves and stops repeatedly according to the number of layers present in the part. Assuming that no energy is required in stopping, the mechanical energy of the piston (Eps) is given by the summation of potential and total kinetic energy:
1 2
2 ,
ps ps ps ps ps l
E m gh m v N (6.15) where mps is the mass of the piston, g is the acceleration due to gravity, hps is the total height travelled by the piston, vps is the velocity of the piston and Nl is the number of layers present in the part. Similar to the energy required by the motor, the energy required by the piston (Episton) is also provided by the motor:
ps ,
piston m
E E
(6.16) where ηm is the efficiency of the motor.
Apart from the energy consumption mentioned in Sections 6.2.1–6.2.4, some additional energy is also consumed by the computer, workstation and some amount of energy are also lost during the process. This extra amount of miscellaneous energy (Emisc) is considered to be 5% of the total energy:
0.05 .
misc laser heater roller piston
E E E E E (6.17)