4.0 NUMBER OF CAVITY CALCULATIONS
4.1 Introduction
Numbers of cavities in mould depend on
1. Production requirement to meet target.
2. Machine’s capacity
· shot
· plasticizing
· clamping
3. Max. Size of component and the mould that can fit into the moulding machine between tie rods.
4. Max. Injection pressure required to flow and fills the particular plastic into mould
4.2 Shot capacity
Plunger machine is often rated in terms of maximum shot weight (g) with PS. The rating can be determined from the following relations
Shot capacity with material “A” = Shot capacity of with material “B” times density of “A” over density of “B” times bulk factor of “A” over bulk factor of “B”
Density of A Bulk factor of A
= shot capacity with material “A” x ------------------ x --------------------
Density of B Bulk factor of B
Where
“A” = plastic material used for specifying the rating of injection moulding machine (polystyrene)
“B” = Plastic material actually to be used.
The screw type machine is normally rated in terms of swept volume of the injection cylinder (cm3)
Shot capacity (g) = swept volume x density x a constant ( C ). Only 85% of the value will be taken for safety. “C’ is taken as 0.85 for the crystalline material and 0.93 for the amorphous material.
4.3 Plasticizing capacity:
Plasticizing capacity is expressed in kg/f of plasticized Polystyrene. Plasticizing rate of material “B” is equal to the plasticizing rate of material “A” times specific heat capacity of “A” over specific heat capacity of “B” times moulding temperature of “A” over moulding temperature of “B”.
Specific heat capacity of “A” moulding temp. of “A”
= plasticizing rate of material “A” x ------------------------------------ x -----------------------------
Specific heat capacity of “B” moulding temp. of “B”
Or plasticizing rate of material “B” = Plasticizing rate of material “A” x QA/QB
Where, Q - Total heat content, “A” - Polystyrene, “B” - Material to be used.
Plasticizing rate = Mass of moulding (kg) x number of moulding cycle per hour. Only 85% of the capacity to be used for calculation.
4.4 Clamping capacity:
Clamping force is calculated by multiplying projected area with injection pressure. Usually 33 to 50% injection pressure is considered for calculation and normally 63 KN/m2 is considered as the cavity pressure and may be substituted in place of injection pressure. Maximum injection pressure can be obtained from machine manufacturer’s data sheet.
4.5 Cycle time:
The cycle time also can be calculated when moulding machine is limited by plasticizing capacity. It is calculated by multiplying mass of the shot with 3600 and divided by plasticizing capacity.
Cycle time Tc= m x 3600/ P
Where, Tc = minimum cycle time obtainable
M = mass of the shot
P = Plasticizing capacity of the machine with the particular polymer being moulded (kg/h)
4.6 Number of cavity calculation:
The number of cavities in injection moulds is determined in most cases by the machine performance, but sometimes by the moulding shape or the mould locking pressure.
It is determined by three ways
- Determined by shot capacity
- Determined by plasticizing capacity and
- Determined by clamping capacity.
Once all the three are found, select the least number of cavities. If it is in decimal, round of to minimum size
Determined by shot capacity based on 85% of rated shot capacity
0.85 W
Ns = ---------- (W = swept volume x density x constant)
M
Determined by plasticizing capacity based on 85% of rated plasticizing capacity.
0.85 P x Tc
Np = ----------------
3600 m
Determined by clamping capacity based on 85% of rated capacity
C
Nc = -------------
Pc x Am
Where
Ns = number of cavities based on shot capacity
W = rated shot capacity for particular polymer (kg or g)
m = mass of moulding per shot
Np = Number of cavities based on plasticizing capacity
P = Rated plasticizing capacity for polymer
Tc = Overall cycle time
Nc = Number of cavities based on clamping capacity
C = Rated clamping capacity
Pc = Cavity pressure (normally 63 Mpa)
Am = Projected area of moulding including feed system
Polystyrene is taken as the base material for the calculation of number of cavities in the mould for the following reasons
Practically there is no latent heat produced while melting
The density is almost one and
The is the earliest material invented among the commonly used material.
4.6 Example:
Following are the data available for the calculation
Component to be produced per day = 5000
Effective production time per shift = 7 hours
Total number of shifts = 2
Component data:
Material -------------------------------------- = polypropylene
Density--------------------------------------- -= 0.9 gm/cc
Wall thickness------------------------------- = 2.0mm
Weight of one component--------------- -= 3.6 gm
Weight of feed system---------------------= 0.9 gm
Max. projected area of component-----= 12.5 cm2
Projected area feed system--------------= 2.5 cm2
Cycle time-------------------------------------= 30 sec
Heat content of PS--------------------------= 57
Heat content of PP-------------------------= 130
Machine date:
Machine----------------------------------------= SP 30 Windsor
Injection pressure----------------------------= 1950 kg/cm2
Swept volume---------------------------------= 44 cm3
Plasticizing capacity-------------------------= 15 kg/hour
Calculations:
The safe number of cavities to utilize optimum capacities of machine and also to meet the daily production is calculated as shown below.
Machine’s safe shot capacity = Vs x Xp x C x n
Where
Vs = Swept volume
Xp = Density of plastic in gm/cm3
C = Material constant (0.85 for crystalline & 0.93 for amorphous)
N = Efficiency of machine (85%)
Hence safe shot capacity of m/c = 44 x 0.9 x 0.85 x 0.85
= 28.6 gm/shot
Weight of one component + feed system = 3.6 + 0.9 = 4.5 gm
Hence no. of cavities as per shot capacity = 28.6 / 4.5
= 6 cavities
M/c safe plasticizing capacity(PP) = Pl. capacity of PS x Qps/Qppx n
= 15 kg/hr x 57/130 x 0.85
= 5.6 kg/hr
With cycle time of 30 sec., no. of shots/hr = 3600/30 = 120
Hence no. of cavities as per plasticizing capacity = (5.6 x 1000) / (120 x 4.5)
= 10 cavities
Clamping tonnage = number of cavities x proj. area x cavity pressure
For PP, injection pressure recommended is 700 to 1400 kg/cm2
Wall thickness being 2mm, inj. Pressure (Pi) can be taken as 800kg/cm2
Cavity pressure = ½ or 1/3 of injection pressure
Since PP is easy flow material, cavity pressure = ½ x 800 kg/cm2
There fore clamping tonnage = N x 15 x 400/1000 tones.
Equating to machines safe clamp tonnage of 30 x 0.85, then
N x 15 x 400/1000 = 30 x 0.85
N = 30 x 0.85 x 1000/ 15 x 400
N = 4 cavities.
The least number of cavities is 4, out of the three capabilities selected.
There fore the number of cavities = 4.Check for production rate per day,
Total productive time per day = 2 x 7 hours
Cycle time being 30 sec, number of shots/hours = 120
Therefore production / day = 14 x 120 x 4 = 6720 components.
So the number of cavities of 4 is alright.
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