The variation of air pressures P
1, P
2 of the parts (1), (2) of the cylinder of a spot welder operated through compressed air, as well as the velocity ν and displacement z
1 of the piston are calculated under the assumption that the pressure of the air source is maintained constant at the value P
H at the inlet (1), Fig. 1.
The results are shown in Figs. 2-5 and in Table 1, in which Fig. 2 is the case when the effect of moving mass M is assumed to be zero and Fig. 6 is the case when the gravity effect is taken into consideration.
With the time constant T
a2 as defined in equ. (1), variations of P
1, P
2, v and z
1 are related to time t in dimensionless forms as shown in the figures, the parameters being the dimensionless acceleration (equ. (9)), and the ratio of the effective sectional areas S
1. S
2 of air circuits (1), (2). The boundary conditions are shown in the figures, V
10 being the initial volume of (1) and V
0 the sum of volume of (1) and (2) : V
0=V
1+V
2=V
10+ V
20.
When the piston moves at the velocity ν
0 as defined in equ. 5, the pressure P
2 does not vary, and the air in (2) is discharged through S2 at sound velocity (See equ. (7)). This velocity is taken as the denominator of the dimensionless velocity.
It is interesting to note that the accelerating force, which is proportional to (P
1-P
2) or (γ
1-γ
2) in dimensionless expression, decreases when J (or M) is decreased, and the time t
m required for the piston to reach the bottom (i.e. V
1=V
0, z
1=z
0) varies only in small range even when j (or M) is changed in wider range.
Calculation was made by the step-by-step method, i.e. dγ
1, dγ
2, dν/ν
0, dz1/z0 corresponding to dt/ T
a2 were calculated from equ. (11), (12) and (18).
It is assumed that equation (6) holds true for the whole range of P
2.
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