#### 2.1. The Jetting System Structure

Figure 1 shows the structure of the solder paste jetting system, which consists of the piezoelectric actuator, lever, needle-to-nozzle distance control sleeve, pressure control unit, needle, and nozzle. The difference with the traditional nozzle-needle-system is that a miniscule gap exists between the nozzle and needle instead of the needle hitting the nozzle directly, and it can be adjusted by the sleeve. The principle is shown in

Figure 2.

The working principle of the solder paste jetting system is shown in

Figure 2.

1. As shown in

Figure 2a, the piezoelectric stack is powered on, and the needle is in suspension under the combined effect of the lever and the force of the spring. A miniscule gap exists between the nozzle and needle. The supply pressure acting on the solder paste is off, and viscous force and surface tension can prevent the solder paste flowing out.

2. As shown in

Figure 2b, the needle raises up under the restoring force of the spring when the piezoelectric stack is powered off. At the same time, the supply pressure acting on the solder paste is activated. The relation between the supply pressure and piezoelectric power shows in

Figure 3.

3. The needle moves down when an electric field is applied to the piezoelectric stack. The solder paste at the nozzle is forced by the inertial force pressured by the needle to remove the tensile viscous force and surface tension and then jets out from the nozzle orifice so as to produce a drop. The needle does not touch the nozzle during the solder paste jetting process (

Figure 2c).

#### 2.2. Theoretical Analysis of Jetting

The solder paste at the nozzle is forced by the inertial force pressured by the needle, the tensile viscous force, and surface tension. The tensile viscous force

${F}_{\eta}$ can be expressed as

where

d is the nozzle diameter, and

${P}_{n}$ is the tensile stress, which can be expressed as

where

${\eta}_{n}$ is the extensional viscosity.

${\stackrel{\cdot}{e}}_{n}$ is the strain rate, which can be expressed as

where

L is the length of the droplet, and

v is the droplet velocity.

Thus, the tensile viscous force

${F}_{\eta}$ can be expressed as

We assume that the diameter of the solder paste droplet departed from the nozzle is the nozzle diameter

d. The inertia force generated by the impact of the needle can be expressed as

where

ρ is the solder paste density. Thus, the necessary condition to eject the fluid is

where

${F}_{b}$ is the surface tension.

As the solder paste jets through a small nozzle orifice, the Weber number can be calculated by

where

σ is surface tension coefficient. It is approximately 0.49 N/m.

When the nozzle diameter

d is 0.1 mm, the solder paste density

ρ = 7400 kg/m

^{3}, the droplet velocity

v = 1.5 m/s, and the

We = 3.39 > 1. Thus, the effect of surface tension can be ignored.

From (8), in order to achieve the injection of the solder paste, it must ensure that the solder paste velocity exceeds a critical value v.

Assume the pressure pressed on the solder paste in the nozzle orifice during the impact process as

F, viscous resistance at the nozzle orifice as

T. Under the action of the two forces, solder paste began to flow down, according to the Newton's second law:

where

$V$ is the volume of solder paste.

Viscous resistance T can be expressed as

where

A is the area of the solder paste contact with the wall of nozzle orifice, and

$\tau $ is the shear stress.

However, the solder paste is Bingham plastic. The shear stress

$\tau $ can be expressed as

where

τ_{0} is shear yield stress, and

η is the solder paste viscosity.

Based on (9)–(11), the following formula can be obtained:

At the initial state, the solder paste is static, e.g.,

υ_{(t)} = 0. Therefore, the solder paste velocity calculated from (12) can be expressed as

From (13), the solder paste velocity is critically influenced by the pressure pressed on the solder paste F and the nozzle diameter d.