The size of an injection moulding machine
Tat Ming Technology Co. Ltd.
January 2001
Summary
Three traditional ways of sizing of an injection moulding machine are discussed. Three new measures of the injection unit power suited to selection for thin-wall moulding are introduced and explained.
1. Shot weight
The oldest method to size an injection moulding machine is by its shot weight. In Hong Kong, shot weight in ounces is still often used. That shot weight is chosen to size an injection moulding machine is understandable. Amoulder has an article to be moulded. The shot weight of the machine must be sufficient toinjection mould the article in an n-cavity mould. If one machine does not have a sufficientshot weight, select a bigger model that can do the job.
1.1 Short comings An injection moulding machine has a clamping unit and an injection unit but shot weightonly indicates the size of the injection unit. To be more specific, it only indicates the shotweight capable of this machine using a particular screw.
Many injection moulding machines could be fitted with more than one screw. An example isa 125-ton machine with a 39 mm diameter standard screw. To get a higher injection pressure,a 35 mm diameter screw could be chosen, but the shot weight is reduced. To get a higher shotweight, a 43 mm diameter screw could be chosen, but at the expense of injection pressure. Inshort, shot weight is screw diameter dependent.
Another short coming of shot weight is its dependence on resin density although most shotweights are specified using PS (S.G. = 1.05 at room temperature). Please refer to Equation (1)below. To be correct, the S.G. of PS at its melt temperature should be used, but this was notknown to be used.
Furthermore, due to the backward movement of the non-return valve at the beginning ofinjection, and the compressibility of the melt, the actual shot weight is less than thetheorectical value calculated from swept volume times S.G. Manufacturers have used a factorvarying from 0.8 to 1, making comparison among models inaccurate.
w = k * 1.05 * v (1)
v = 3.1416 * i * d2/4 (2)
where
w = maximum shot weight in g,
k = factor from 0.8 to 1,
v = maximum swept volume in cc,
d = screw diameter in cm,
i = maximum injection stroke in cm.
2. Clamping force At present, clamping force is commonly used to characterize the size of an injectionmoulding machine as could be seen in its use naming a machine model. In Hong Kong andJapan, the unit used is metric ton. A metric ton is 1000 kgf.
In the U.S., short ton is used. A short ton is 2000 lbs, which is about 10% less than a metricton. A 20 metric ton machine has a clamping force of 22 short tons.
In Europe, kN (kilo Newton) is used. A kN is about 0.1 kgf. To be exact, one kN is 1/9.807kgf = 0.102 kgf. A 20 metric ton machine has a clamping force of about 200 kN.
3. Injection unit capacity
At present, injection unit capacity is commonly used to characterize the size of an injectionunit in Europe.
I = p * v (3)
where
I = injection unit capacity, p = the maximum injection pressure of a screw in kbar,v = the maximum swept volume in cc of the same screw.
At first sight, using Equation (3) to size an injection unit seems puzzling. After some analysis,however, its use is found to be very logical.
3.1 Relationship to shot weight Since both shot weight and injection unit capacity measure injection unit size, they are relatedby their dependence on v, but there the resemblance ends. Injection unit capacity is a bettermeasure because
a. it accounts for injection pressure,
b. it is independent of screw diameter,
c. it is independent of resin density,
d. it does not use the not-so-standard factor k. Injection unit capacity is most useful when comparing among models from differentmanufacturers. Unfortunately, not all manufacturers have included this metric in theirspecification. It, however, could be calculated using Equation (3).
3.2 Accounts for injection pressure In section 1.1, we saw the trade off between screw diameter and injection pressure. Ifinjection pressure is not accounted for, as shot weight is, one could increase the screwdiameter to increase shot weight up to a point when injection pressure is too low for aparticular resin and mould to injection mould successfully. We conclude that shot weightwithout accounting for injection pressure is not as useful.
Injection unit capacity explicitly involves injection pressure in its definition. If injectionpressure is bigger at the same maximum swept volume (akin to the same shot weight), onehas a more capable injection unit.
3.3 Independence of screw diameter For simplicity, assume the injection unit is operated by a single injection cylinder. FromFigure 1, the maximum injection pressure is given by
p = P * A / (3.1416 * d2/4) (4)
where
P = hydraulic system pressure
A = injection piston area (head end)
d = screw diameter
Put Equation (2) and (4) into Equation (3),
I = P * A * i (5)
which is independent of screw diameter.
Equation (4) also shows why maximum injection pressure decreases with (the square of)
screw diameter.
Figure 1
In Figure 1, the cylinder marked by dotted line is the maximum swept volume.
3.4 Interpreting injection unit capacity From Figure 1, P * A is seen to be the force pushing the injection piston (and screw) forward.During injection, this force is displaced by an amount up to i. Hence injection unit capacity isthe maximum work done during injection. The more work is done, the higher capacity is theinjection unit.
As defined in Equation (3), injection unit capacity has a unit of 100-Joule, or a tenth of a kJ.
3.5 Increasing injection unit capacity From Equation (5), one can see there are three ways to increase injection unit capacity.At present, a hydraulic system pressure of 140 kgf/cm2 is common. In the last few years,machines with 160 – 175 kgf/cm2 have appeared. In Europe, system pressure up to 210kgf/cm2 has been used.
One rationale for increasing P is to reduce cylinder size, i.e. A, while keeping force the same. One could of course increase P and A at the same time. There is a consideration to increasingA: as A is increased, the piston velocity is reduced at the same pump flow rate. This leads usto define another metric in Section 5 which takes into account injection velocity.
The maximum injection stroke i could also be increased but only up to a certain extent. Ausually adopted limit on i is 5 * d, five times the screw diameter. Increasing i has the effect ofreducing the effective L/D (length to diameter) ratio of the screw.
Effective L/D = L/D – i/(2d) (6) As the screw rotates during plasticizing, it retracts up to a distance i. On average, therefore,the screw length is reduced by i/2 during plasticizing. This is reflected in Equation (6).
3.6 Using injection unit capacity Although injection unit capacity is a better measure of injection unit size than shot weight, itis not very often used, most probably because it was not popularized. Furthermore, itsdefinition is mathematical (p*v).
Its interpretation as the maximum work done duringinjection may help.Another reason is it does not answer a moulder’s question of whether the injection unit is bigenough for the job, where shot weight excels.
Injection unit capacity is best used when selecting an injection unit (or injection mouldingmachine) from among different manufacturers. As a ‘supplementary’ parameter, shot weightis consulted to determine whether the article could be moulded.
If a machine specification does not show injection unit capacity, it could be calculated fromEquation (5). If injection pressure is provided in kgf/cm2, use I = p * v /1020 (7)where p is the maximum injection pressure of a particular screw in kgf/cm2,v is the maximum swept volume using the same screw in cc.
If injection pressure is provided in bar, use I = p * v /1000 (8) wherep is the maximum injection pressure of a particular screw in bar,v is the maximum swept volume using the same screw in cc.
If injection pressure is provided in psi, use I = p * v /884 (9) where p is the maximum injection pressure of a particular screw in psi,v is the maximum swept volume using the same screw in in3. The three equations help compare among machines from Hong Kong/Japan, Europe andU.S.A.
4. EUROPMAP size Most injection moulding machines from Europe have a EUROMAP size containing twofigures: the clamping force in kN followed by injection unit capacity, separated by a -. Thecombination of course contains size information of the clamping unit and the injection unit.
5. The power of an injection unit It was mentioned in Section 3.5 that injection unit capacity does not account for injectionvelocity. Injection unit capacity could be increased by increasing A, but this is at the expenseof injection velocity. In thin-wall moulding, a high injection velocity is important to get themould filled before the melt froze in the cavities.
The power of an injection unit Po is defined to supplement where injection unit capacity isnot sufficient. It is given by Po = p * r (10) where Po = the power of an injection unit in tenths of kW,p = the maximum injection pressure of a particular screw in kbar,r = the maximum injection rate of the same screw in cc/s.Going through a similar analysis that gives rise to Equation (5), we can show that Po = P * A * vel (11) where vel = the maximum injection velocity of the screw/piston in cm/s.
In fact, by referring to Figure 1, it can be seen that Q = A * vel (12) where Q = the maximum flow rate of hydraulic fluid into the injection cylinder. If an injection unit is operated without an accumulator, Q is the maximum flow rate of thepump. Otherwise, it is the combined maximum flow rate of the accumulator and the pumpduring injection, assuming both the accumulator and the pump are driving. Usually, the flowfrom an accumulator is 2 to 3 times that of the pump. The combined flow is therefore 3 to 4times that of the pump alone.
Substituting Equation (12) into Equation (11), we get Po = P * Q (13)which is a measure of the power of the injection unit. Without accumulator, Po is the same asthe maximum power delivered by the hydraulic pump.
5.1 Most suited to thin-wall moulding We recommend using the power of an injection unit in making selection in thin-wallapplications. Po is not intended to replace injection unit capacity but to supplement it.
Furthermore, maximum injection velocity and rate, maximum acceleration and deceleration,sampling rate, etc. are also useful data in such a selection. Please refer to Section 7.
If a machine specification contains maximum injection rate, Po could be calculated fromEquation (10).
If only the maximum injection speed is available, maximum injection ratecould be calculated from r = vel * 3.1416 * d2/4 (14) In thin-wall moulding, both maximum injection pressure and maximum injection rate need to be high. Both are accounted for in Equation (10). Note that the definition uses maximum injection rate, not maximum injection velocity. Maximum injection rate tells us how fast a cavity or cavities can be filled. Maximum injection rate is screw diameter dependent.
Maximum injection velocity is not screw diameter dependent. If r is screw diameter dependent, could we increase the power of an injection unit byincreasing the screw diameter? The answer is no. Everything else the same, increasing thescrew diameter would decrease the maximum injection pressure by the same amount, as theinjection force P * A is divided by a bigger screw cross sectional area. In short, Po staysconstant irrespective of screw diameter.
5.2 An example Two brands of injection moulding machines of roughly the same clamping force arecompared. Their specifications are shown in Table 1.
Brand A Brand B Brand B with
accumulator
EUROMAP size 800-290 750-258 750-258
Injection unit
Screw diameter (mm) 36 33 33
L/D ratio 20 22 22
Max. injection stroke (mm) 145 150 150
Max. swept volume. (cc) 147 128 128
Max. shot weight (g) (PS) 132 115 115
Max. injection pressure (kgf/cm2) 2014 2057 2057
Max. injection velocity (cm/s) 12.4 37
Max. injection rate (cc/s) 78 106
Clamping unit
Clamping force (tons) 80 75 75
General
Hydraulic system pressure
(kgf/cm2)
145 160 160
Pump flow rate (l/min) 82 82
Motor power (kW/hp) 15/20 15/20 15/20
5.2.1 Shot weight Despite the shorter injection stroke of Brand A, its bigger screw gives a higher swept volumethan that of Brand B. Brand A and B both use the same factor k of 0.85. The shot weight ofBrand A is therefore also higher.
5.2.2 Clamping force
Brand A has a higher clamping force than Brand B.
5.2.3 Injection unit capacity Brand A has a more capable injection unit than Brand B (290 vs 258). Brand B withaccumulator has the same injection unit capacity as Brand B without accumulator.
5.2.4 Effective L/D
For Brand A,
Effective L/D = 20 – 145/(36 * 2) = 18.
For Brand B,
Effective L/D = 22 – 150/(33*2) = 19.7. Brand B uses a bigger maximum injection stroke to increase injection unit capacity. Thereduction in L/D (to effective L/D) is more than compensated for by a longer screw(L/D=22).
5.2.5 EUROMAP size
Brand A has a bigger EUROMAP size than Brand B.
5.2.6 Injection unit power Po
For Brand A,
Po = 2014 * 78 / 1020 = 154.
For Brand B,
Po = 2057 * 106 / 1020 = 214. Due to both a higher maximum injection pressure and a higher maximum injection rate,Brand B has a more powerful injection unit, despite its smaller injection unit capacity. Po isan independent attribute from I.
For Brand B with accumulator, according to Equation (14),Po = 2057 * 37 * 3.1416 * 3.32 / (4 * 1020) = 638.
Once again, we see that Po is increased while I stays the same.
Since pump flow rate is available from Brand B’s specification, according to Equation (13),
Po = (160 / 1020) * (82 * 1000 / 60) = 214
which agrees with the previous value of Po for Brand B.
5.2.7 Pump flow rate Brand A does not have a pump flow rate in its specification. However, it could be calculatedfrom Equation (13) using the known value of Po and its hydraulic system pressure of 145kgf/cm2.
Pump flow rate of Brand A = 154 * (1020 / 145) * (60 / 1000) = 65 l/min.
5.3 Motor power implications of Po For linear motion, power is defined as force * velocity. From considering the power demandby various motions during an operation cycle, we see that the injection motion needs thehighest power. Please refer to Table 2. As a result, the electric motor driving the pump issized for the injection stroke.
Note that power is different from work done. Due to the usually longer duration ofplasticizing versus injection, it is plasticizing that consumes most of the energy of anoperation cycle. This is why a hybrid (hydraulic and electric driven) injection mouldingmachine uses an electric screw motor to economize on energy usage.
5.3.1 No accumulator Without an accumulator, Equation (13) may lead us to think that Po is the power rating of theelectric motor driving the pump as the pump power comes from the motor. This is not so asthe three-phase induction motor could be overloaded (torque increased) to two times its rated power for a short duration. Most machine maker would overload the motor from 0% to itslimit. One manufacturer even resort to cool the motor by water, so as to obtain an even higheroverload. As a result, comparing injection unit power by comparing electric motor rating isnot conclusive.
5.3.2 Motor overload example Both Brand A and Brand B use a 15 kW motor. Due to the higher hydraulic system pressureand pump flow rate of Brand B, the Brand B motor has a higher overload than the Brand Amotor. To be exact,pump power in kW = pump pressure in kgf/cm2 * pump flow rate in l/min * 98.07/60000.Motor overload = (pump power / motor power) – 1.
For Brand A,
motor overload = (145 * 65 * 98.07/(60000 * 15)) – 1 = 2.7%.
For Brand B,
motor overload = (160 * 82 * 98.07/(60000 * 15)) – 1 = 43%.
A higher motor overload is used to increase the injection unit power of Brand B.
5.3.3 With accumulator With an accumulator, injection unit power is further removed from electric motor rating. Inthis case, the size of the accumulator is important in determining Po.For the Brand B machine, the increase of injection unit power from Po = 214 to Po = 638 byadding an accumulator comes from storing away the motor-generated energy in the form ofpotential energy which is released in a burst during injection. An accumulator is a device tostore such energy, usually during the cooling stage after plasticizing has stopped.
5.4 Electrical drive implication of Po As no hydraulic pressure and flow are involved, Equation (10) also applies to an electricdriven injection unit.At present, fully electric driven injection moulding machines are limited to the smaller sizes.Furthermore, injection velocity and acceleration/deceleration are inferior to those of ahydraulic driven injection unit. There are a few reasons for this.
Heat dissipation is the main constraint. To improve speed of response, the servo motor rotor diameter is optimized. This reduces thearea through which the overloaded motor could dissipate heat. This is in contrast to a muchbigger induction motor driving the injection unit through a pump and a servo valve.
Furthermore, accumulator could increase the injection velocity by up to four times that usingthe pump alone. No such energy reservoir is available to the servo motor. Until such a devicecould be devised, electric machine is not expected to outperform hydraulic machine ininjection power.
Table 3 displays the specification of three fully electric injection moulding machines in the 85 to 102 tons clamping force range.
Table 3 All three machines have smaller injection unit capacities than their hydraulic counterpartsshown in Table 1. The power of their injection units are bigger, but not as big as that of BrandB with accumulator.
For Brand C,
Po = (2000/1020) * 128 = 251.
For Brand D,
Po = (2000/1020) * 20 * 3.1416 * 3.22 /4 = 315.
For Brand E,
Po = (2150/1020) * 154 = 325. Among the three, Brand C has the least powerful injection unit. This could be understand ableas it is also a smaller machine in terms of clamping force.
Brand D has a smaller maximum injection pressure but a higher maximum injection rate thanBrand E. Their injection units are comparable in power. It is the combination of maximuminjection pressure and maximum injection rate that determines injection power.
6. The rates at which power is delivered by an injection unit The power of an injection unit Po as defined by Equation (12) is the rate of change version ofI as defined by Equation (3). We could apply the rate of change idea one more time to comeup with the acceleration power Pa and the deceleration power Pd of an injection unit.
Pa = p * (3.1416 * d2/4) * acc (15)
where
acc = the maximum acceleration of the screw in cm/s2.
Pd = p * (3.1416 * d2/4) * dec
(16)
where
dec = the maximum deceleration of the screw in cm/s2. Like I and Po, both Pa and Pd are screw diameter independent. This is so despite theappearance of d in Equations (15) and (16). The reasoning is the same as that in Section 5.1.The bigger is d, the smaller is p such that p * d2 stays the same.
The way Pa and Pd are defined reflects the fact that most machine makers publish theirmachine’s linear acceleration and deceleration but not volumetric acceleration anddeceleration.
6.1 What affects acceleration and deceleration? In getting to up speed, the injection piston in Figure 1 is resisted by the pressure at the screwtip as well as the mass to be accelerated. From Newton’s Second Law of Motion,
F = m * acc,
where
F = pushing force = P * A,
m = mass to be accelerated, we see that for a given force, the smaller the mass, the higher is the acceleration. The designof the injection unit determines the mass to be moved. The minimum mass is that of the screw,the piston rod and the piston combined. If the screw motor also moves during injection, theacceleration is reduced.
The same mass accelerated during start up is also decelerated at the velocity-to-pressuretransition. The restraining force during deceleration is smaller since the hydraulic systempressure now acts on the rod end where the area is reduced by the cross section of the pistonrod. Please refer to Figure 1. This does not mean deceleration is smaller. On the contrary, it isbigger in magnitude than acceleration since deceleration is helped by the resistance force atthe screw tip.
Acceleration is related to energy build up; deceleration to energy dumping. A driver couldappreciate a car could brake from a cruising velocity in a shorter time than it could acceleratefrom rest to the same velocity. We conclude that there is a need to distinguish betweenacceleration power from deceleration power.
6.2 Significance of acceleration power An injection velocity of 100 cm/s is considered very high. If the screw starts from rest,acceleration tells us how soon this high velocity could be attained. An acceleration of 5000cm/s2 means this speed could be attained in 0.02 s. Such acceleration could only be obtainedusing accumulator-driven hydraulic power. 0.02 s is also the state-of-art response time of aservo valve.
In a multi-stage injection, injection velocities change between stages. Acceleration anddeceleration are again called for.
Pa is not merely acceleration, but acceleration against a resistance force at the screw tip: p *(3.1416 * d2/4). Naturally, if an injection unit can attain the same acceleration against ahigher resistance force, it is more powerful, as measured by acceleration power Pa.
6.3 Significance of deceleration power If one considers injection as the stage for filling the mould, injection ends when the cavitiesare completely filled. At this point, injection transitions to holding pressure, which is thestage to make up for part shrinkage. This point is known as the velocity-to-pressuretransition.
Before this transition point, velocity is controlled. Injection pressure is not controlled and isdetermined by melt viscosity and cavity cross section at that particular injection velocity.
After this transition point, injection pressure (now called holding pressure) is controlled.Injection velocity is not controlled and is determined by the rate of shrinkage of the parts inthe cavities, which in turn is determined by the rate of cooling of the mould. Compared to thehigh injection velocity commonly associated with thin-wall moulding, the injection velocity during holding could be considered as zero.
The screw needs to decelerate from the last injection stage velocity to zero at the transition‘point’. During deceleration, the screw travels a distance before stopping, compressing themelt in the cavity. This is called the packing stage, after which the holding stage sets in.
Proper packing gives the part its necessary density.If deceleration is low, the cavities will be overpacked by the advancing screw. Overpacking ischaracterized by a cavity pressure peak (observable if a cavity pressure sensor is installed).
An overpacked part has a higher part weight, a higher built-in stress, and in the extreme case,flashes the mould. Neither do we want underpacking which gives a short shot in the extremecase. A high deceleration or a high deceleration power avoids irregular packing.
Repeatability/part stability is guaranteed.
7. Electronic control and other factors Many design details make an injection moulding machine more suited to thin-wall mouldingthan another machine. Po, Pa and Pd only characterize the injection unit of a machine.
A modern injection moulding machine is invariably controlled by a digital computer. Onecharacteristic of digital computer is that measurements are not made continuously but only atfixed intervals, called scan intervals or sampling interval. At a scan interval of 1 ms, a screwtraveling at 100 cm/s could have traveled 1 mm. Variation of 1 mm in shot stroke gives rise toirregular packing just as low deceleration power does. There are two solutions.
The simple solution is to reduce the scan interval. This may necessitate using a morepowerful microprocessor which is the brain of the computer. Alternatively, an analog circuitis incorporated to continuously compare the set transition point with the actual value(injection distance, hydraulic pressure or cavity pressure). Once the set transition point isreached, an interrupt is generated to notify the microprocessor which then starts thedeceleration and transition to holding pressure control.
Platen deflection affects parts dimensions, which is more critical in thin-wall moulding. Inthe extreme case, platen deflection flashes the mould. Rigid platen is a requirement inthin-wall moulding.
A thin-wall part does not need a lot of shot weight. A small injection unit as measured byshort weight is suitable. Otherwise, residence time would be increased which causes resindegradation. The rule-of-thumb is to use an injection unit two sizes smaller. A 90-tonconventional machine has a 100 g shot weight, a thin-wall machine of the same tonnage has a20 g shot weight.
8. Experiments The claim that Po, Pa and Pd characterize an injection unit’s suitability in thin-wall mouldingis theoretical and mathematical (time rate of change). Experiments are to be performed tobear this out. So far, such experiments have not been carried out. The interested readers areencouraged to do so.
9. Conclusion The traditional measures of an injection moulding machine size are shot weight and clampingforce.
Injection unit capacity I was shown to be a better measure than shot weight. In fact, Itranscends the notion of size. It measures the capability of an injection unit. I is most usefulwhen selecting injection units from different manufacturers.
In thin-wall moulding applications, three measures of injection unit power were found to berelevant.
Po is the power delivered to the injection unit. If the injection unit is driven by a hydraulicpump, Po is the power delivered by the pump. If the injection unit has an accumulator, Po isthe power delivered by the accumulator and the pump.
I was shown to be independent of Po. Po is more relevant than I in thin-wall moulding. Pa is acceleration power. It tells us how much power is available e.g. to start the screwmoving from rest. It determines how closely the set velocities could be attained duringinjection.
Pd is deceleration power. A high deceleration power reduces variation in overpacking. Both Pa and Pd determine the repeatability of the shot or the stability of the product. They aredifficult to achieve in thin-wall moulding. Experiments are to be performed to verify highvalues of Pa and Pd improve product stability.
Other factors affecting the selection of an injection moulding machine for thin-wall mouldingincludes scan interval, incorporation of analog comparator, platen deflection and in fact alsoshot weight.
Table 4 summaries the characteristics of the different attributes of an injection unit.
a = cross section area of the screw
Table 4
Copyrighted by Tat Ming Technology Ltd., Jan 2001
Unit 919, Tower A, Regent Centre,
63 Wo Yi Hop Road,
Kwai Chung, NT, Hong Kong.
Tel: (852) 2790-4633, Fax: (852) 2797-8774
Email: tatming@netvigator.com
Web site: http://www.tatming.com.cn
|
