CHAPTER 3 THE STC DESIGN MODEL VALIDATION
3.4 Experimental Results
3.4.2 Second stage validation
1. After modifying the discharge port dimension and tuning the locations of P2~P5 of the piezoelectric pressure transducers, the over-compression and interlaced phenomenon are minimized such as Fig. 3.6 shows.
2. Based on above calibrations, Fig. 3.6 also depicts the comparison of pressure versus crankshaft rotation angle between predicted results and measured results of which the STC is operated at ARI conditions, that condition No. 1 of Table 3.5 shows. The acceptable deviation of results between computer simulation and testing measurement is shown as Table 3.5.
3. From Fig. 3.6 shows, the deviation of pressure versus crankshaft rotation angle between predicted results and measured results is very small. Meanwhile, Fig. 3.7 also shows the 18 temperature measurements data at six different operation conditions, which indicates the laboratory STC prototype has stable thermal distribution within the compressor housing. This measurement data is extremely valuable when used in predicting STC performance with the developed STC simulation package.
4. As Table 3.5 shows the results, the maximum deviations of cooling capacity, power consumption and COPel between calculated results and real measured results are 1.31%, 2.89% and 3.89%, respectively.
3.5 Conclusions
The study results in this section are summarized below:
(1) A practical computer estimation package of STC has been constructed to evaluate
overall performance of STC in detail.
(2) Using an on-line data acquisition system combined with experimental measurement techniques, the pressures and temperatures during the compression process can be captured to understand the details as the scrolls operate during the compression process. Meanwhile, from the detecting data at first stage, the experimental system has been calibrated accurately.
(3) After the calibration of temperature and pressure measurements, the validation between calculated results and real measured data has been carried out. Finally, the deviation of the verified STC’s performance between predicted results and experimental measured results, are under 4%. It means the validated STC simulation package that this study developed, can be used in the STC practical design works.
(4) Based on the research results and technical facilities, the other validations about the temperature distribution on scrolls and the distribution of the thermal deformation on scrolls have been approached continuously by Lin et al. (2005) and given a practical reference for the developed STC simulation tool.
Table 3.1 The items and functions of measuring components and instruments.
Items & Functions Photos
1. T-type thermocouples and connectors:
Max. pressure rating is 400psi,
Operating temp. is – 45 ~ 150ºC
2. PCB 111A20 Dynamic pressure transducers:
Pressure measuring range:
(1) PCB 111A21: ~125psi, (2) PCB 111A26: ~500psi
3. Bently Nevada 7200 proximity transducer system:
(1) High-pressure feed through:
Max. pressure rating is 400psi, Operating temp. is – 45 ~ 121ºC (2) Proximity probe:
Power: -17.5 ~ -26VDC,
calibration range: 2mm (80Mils), Scale factor: 200MV/Mil,
Operating temperature: -34~177ºC (3) Proximitor:
Operating temperature: -51~100ºC, Power: -17.5~-26VDC,
Scale factor: 200MV/Mil 4. PC based monitor system:
Personal computer with 200Hz CPU, PCB 482A10 Amplifying power unit,
HP 54602B digital scope operated at 150MHz, HP 3852A Data acquisition system with 20channels.
HP 82341D HP-IB interface card.
5.Others:
OMEGA Feed through: Max. pressure is 2000psi
Table 3.2 The measuring points of temperatures
Symbols Measuring points Notes
T1 Discharge port of scroll set
T2 Discharge port at isolating member T3 Pressing members of axial sealing
mechanism
To measure the accurate discharge temperature after compression
operation
T4 Back plate of fixed scroll To monitor the fixed scroll temperature variations T5 Orbiting scroll plate To monitor the orbiting scroll
temperature variations T6 Inside hole of motor stator
T7 Upper side of motor stator coils T8 Middle side of motor stator coils T9 Lower side of motor stator coils
To monitor the motor temperature variations
T10 Lower journal bearing
T11 Upper side of isolating member T12 Moddle side of isolating member T13 Lower side of isolating member T14 Suction inlet of scroll set
To measure the accurate suction temperature before inlet to suction port
of scroll set
T15 Driving bushing T16 Main journal bearing T17 Upper side of motor stator T18 Oil sump
To measure each bearing temperature variations and to monitor the oil
supply status
Table 3.3 The specifications of calorimeter used for measuring STC performance.
Items Specifications General description of system According to ISO 917, this equipment is designed
for fully automatic measurements Compressor loop refrigerant R22
Capacity measuring range 1500W~12000W
Measuring method and required accuracy
(1) The equipment is employed for the secondary refrigerant system and liquid flow meter system.
(2) The value of the estimated error for the cooling capacity from the secondary refrigerant system calculated should be lower than liquid flow meter system.
(3) The deviation of cooling capacity and COPel
measuring results between the secondary refrigerant and liquid flow meter system should be within ± 4%.
(4) The accuracy of refrigerant flow-measuring instruments should be within ±1%
(5) The accuracy of speed-measuring instruments should be within ±0.75%
(6) Repeatability ≤ 1%
The background noise of
compressor chamber ≤ 40dBA when Fan is closed
Control items Range Stability
Compressor discharge pressure 10~30 kg/cm2 ± 0.1 kg/cm2 Compressor suction pressure 1.67~9.28 kg/cm2 ± 0.15 kg/cm2
Compressor suction temperature -25~50℃ ±0.5℃
Table 3.4 The operating conditions used for the first stage calibration.
Condition No.
Discharge pressure (kgf/cm2)
Suction pressure (kgf/cm2)
Motor operating frequency (Hz)
1 10 2 40
2 10 2 60
3 20 4 60
4 20 5 60
5 20.86 5.36 50
6 20.86 5.36 60
Table 3.5 The comparisons between simulations and experimental measurements.
Operating Conditions
Cooling Capacity (W)
Power Consumption (W)
COPel
(W/W) No. Evap.
Temp.
Cond.
Temp. Comput. Real Error
(%) Comput. Real Error
(%) Comput. Real Error (%) 1 7.2℃ 54.4℃ 9244.22 9247.59 -0.04 3347.1 3329.4 0.53 2.76 2.78 -0.84 2 5.0℃ 40.0℃ 9890.50 9938.53 -0.48 2493.7 2567.8 -2.89 3.98 3.87 2.70 3 5.0℃ 50.0℃ 9010.92 9007.90 0.03 3008.3 3038.4 -0.99 3.00 2.97 1.18 4 5.0℃ 60.0℃ 7948.99 7846.18 1.31 3659.0 3751.1 -0.02 2.17 2.09 3.89
Fig. 3.1 Experimental apparatus for STC model validation in this study
(a) 18 thermocouple locations for temperature measurements
(b) 6 piezo sensor locations for pressure measurements
Fig. 3.2 Temperatures and pressures measuring locations for experimental validations
T12 T11
Fig, 3.3 Experimental schematic for measuring STC instantaneous pressures
Crankshaft rotation angle 30.0
20.0
10.0
0
360º
Digital oscilloscope Piezoelectric
transducers
Magnetic Proximity transducer
Crankshaft rotation angle 30.0
20.0
10.0
0
360º
Digital oscilloscope Piezoelectric
transducers
Magnetic Proximity transducer
(a) Laboratory STC assembly (b) Laboratory STC located in test bench
(c) Testing feature
Fig. 3.4 Photos of laboratory STC used for validation test in this study
(a) The results of operating conditions 1 and 2
(b) The results of operating conditions 3 and 4
(c) The results of operating conditions 5 and 6 Fig. 3.5 The experimental results at first stage validation
360º
Fig. 3.6 The comparison between calculated results and measuring results Crankshaft rotation angle
(Pd =20.86kgf/cm2, Ps =5.36kgf/cm2, operated at 60Hz) 360º
30.0
(Pressure (kgf/cm2 )
20.0
10.0
0
calculation measurement
Crankshaft rotation angle
(Pd =20.86kgf/cm2, Ps =5.36kgf/cm2, operated at 60Hz) 360º
30.0
(Pressure (kgf/cm2 )
20.0
10.0
0
calculation measurement
1 2 3 4 5 6 ps/pd kgf/cm2 2/10 2/10 4/20 5/20 5.36/20.86 5.36/20.86
fm Hz 40 60 60 60 50 60
T1 ℃ 74.00 75.21 103.20 96.11 104.60 105.56
T2 ℃ 68.11 70.22 92.10 84.33 91.50 92.11
T3 ℃ 58.89 60.12 79.01 72.11 78.09 78.89
T4 ℃ 67.33 72.23 89.20 81.56 89.10 89.78
T5 ℃ 51.72 52.12 58.20 55.72 59.30 60.44
T6 ℃ 63.89 65.41 83.20 72.78 84.00 85.00
T7 ℃ 44.44 45.12 61.01 57.22 61.80 62.78
T8 ℃ 62.78 63.12 80.21 71.11 81.21 82.22
T9 ℃ 44.44 45.12 55.21 50.00 57.22 57.22
T10 ℃ 43.44 43.89 51.20 50.33 51.92 53.94
T11 ℃ 58.89 61.12 79.12 72.11 78.10 78.89
T12 ℃ 53.67 54.18 65.78 60.56 65.01 65.56
T13 ℃ 48.22 49.20 53.12 51.22 54.12 55.39
T14 ℃ 33.67 33.91 35.01 34.44 35.89 36.67
T15 ℃ 55.28 56.10 60.21 59.89 64.21 64.94
T16 ℃ 48.72 49.11 51.50 53.33 56.41 57.44
T17 ℃ 43.39 44.17 51.20 48.78 52.12 53.22
T18 ℃ 42.78 43.12 50.20 49.61 51.91 53.22
Condition No.
Units Symbols
Fig. 3.7 The 18 temperatures measurement data at 6 operating conditions 30.00
40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00
T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18
Condiiton No.1 Condition No.2 Condition No.3 Condition No.4 Condition No.5 Condition No.6
18 Thermocouples location symbol of Fig. 3.2 depicted
℃
CHAPTER 4
STC FAMILY DESIGN WITH OPTIMIZATION METHOD
One critical problem in the mass production of commercial STC is that their key components—including fixed scroll, orbiting scroll, Oldham ring, mainframe and crankshaft—all require the use of very high precision machining skills. To help in lowering the complexity, cost and lead-time of product development, a systematic design method with optimization for developing a family of STC is proposed. Such a family design needs to meet two goals: (i) a series of STC with multi-specified cooling capacities should have the same outside shell diameter and use common key parts or casting molds, (ii) the performance of each specified capacity of the developed STC should meet market requirements.
In addition to using the general design optimization model which includes multi-variable, direct search and inequality constraints, both interactive session and discrete variable design optimization skills have also been employed in this study. Meanwhile, based on the balance between cost, manufacturing effectiveness and product performance, the STC family design used for a series of air-conditioners, has been carried out, and the STC family with a range of 5200W~9800W in four models has been implemented. The performance of each model is also verified and satisfies the required objectives.
4.1 Literatures review
From a technical point of view, Etemad and Nieter (1989) provided a simple and easily understood optimization design approach to evaluate the effect of three relevant
physical parameters on manufacturing, design limitations and energy losses for STC.
Ooi (2005) presented a design optimization algorithm coupled with a mathematical model of the rolling piston compressor by employing multi-variables, direct search and constrained optimization technique. Although these two studies could provide some guides for STC optimization design algorithm and design procedure, the details of optimum design to put in practice were not demonstrated.
Kota et al. (2000) has introduced the use of commonality components in product family design to help in lowering the complexity, cost and lead-time of product development. In addition, Hernandez et al. (2001) described a mathematical decision model to carrying out a family design evaluation for absorption chiller development that provided a guideline for the systematic design of a product family.
This paper proposes a family design procedure that combines with the optimization method (Arora, 2004) and the STC simulation package that this study developed to use in STC commercial product development.
4.2 Description of the design process
Fig. 2.9 lists the cross section and major components of a hermetic STC used in this study. This STC’s structure consists of a low-pressure-shell design with a solid axial compliance mechanism. The details of the STC design structure and the design model, have been described in Chapter 2 of this dissertation.
In STC family design, the first decision of the design process is to select a common outside diameter for the main shell of the STC. This selection is made based on the inside space constraints of specified air-conditioners and the motor size that can meet the torque requirements for the developed STC.
After the decision is made on the common outside diameter, the most important
design process is to define the objective functions for the optimization approach. In this study, the requirement is to obtain the maximum coefficient of performance based on electrical power input (COPel) for each model of the developing STC family.
Therefore, the COPel is selected as the objective function and defined as the ratio of useful cooling capacity, Q&c, to the overall power consumption of the motor, Pmotor:
motor el c
P COP Q&
= (4-1)
The next process is to define the design variables and related constraints, and then evaluate the feasible dimensions and performance for each specified STC to meet these requirements. To realize the controllable design variables and the constraint functions, the following steps are carried out.
Step 1: Define the design variables that have the most effect on the cooling capacity,
Q&c, and the overall power consumption of the motor, Pmotor.
{ }
Because the refrigerant properties, operation conditions and suction paths can allbe specified in the same family, the cooling capacity, Q&c, can be evaluated from four major design variables: φr, pt, t and he. In the meantime, the journal bearings and the Oldham coupling used in the developed STC family are the same, so it should be noted that this model makes it possible to obtain the motor efficiency and compressor speed. Several work losses and the overall power consumption, Pmotor, can all be evaluated while the design variables of pt and t are defined.
Step 2: Set up the design constraints in order to meet the practical requirements of the scroll wrap manufacture and STC assembly.
To communicate with the engineering experts, three constraints should be considered. The rigidities of the scroll wrap and the cutting tool are the constraints for scroll wrap manufacturing, and the outside diameter limits of the scroll is the constraint for STC assembly. The correlations between design variables and constraints are defined respectively as follows:
t From involute spiral definition (Ikegawa et al., 1984), the outmost curve
coordinates that define the minimum required outside diameter Dob_min of the orbiting scroll are formulated as
[ ]
From Morishita et al.’s (1984) derivation and Eq. (2-12), the roll angle of the scroll wrap is roughly obtained as
o o
where the built-in volumetric ratio vr can be derived from the polytropic operation conditions depicted in Table 4.1 and Fig. 2.11. The polytropic index n can be measured by the laboratory experiment (DeBlois and Stoeffler, 1988), which 1.11 is selected for this study.
Eqs. ((4-4) to (4-11)) clearly define the constraints of φr, pt, t and he for the STC family design.
Step 3: Select a proper and robust optimization algorithm to perform detailed simulation and iteration, and to obtain the optimum solutions for practical applications.
Summarize the Eq. (4-2) ~ Eq. (4-9), the objective function requirement can be defined as: and subjected to the constraints:
s Since the objective function and constraints are non-linear, the suitable optimization technique was a direct search method (Ooi, 2005). Meanwhile, the design variables must monitor the progress and be selected from a given set of values with practical experience. An algorithm combined with interactive session and discrete variable design optimization (Arora, 2004), has been employed in the current study. Fig. 4.1 depicts the optimization process.
Interactive design optimization algorithms are based on utilizing the designer’s input during the iterative process. They must be implemented into an interactive environment to report the status of the calculation results and then the designer can specify what needs to be done depending on the current design conditions. In this study, an analysis module of STC simulation package and graphical display to draw conclusions play a part in the decision making during the interactive optimization process. Fig. 4.2 shows the basic simulation flowchart of the developed STC computer package.
A design variable is called discrete if its value must be selected from a given finite set of values to meet the parametric design requirements, fabrication limitations and cost effectiveness. Therefore, φr, pt, t and he of the four design variables is given as discrete variables to put in practice. In the meantime, the Equal Interval Search technique (Arora, 2004) is used in this approach.
By using the optimization algorithm combined with the graphical solution method, the feasible region of each design variable can be identified. Finally, the optimum solutions for this family design are obtained.
4.3 Case study of STC family design
The required operation conditions and specifications used in the case study of STC family evaluation are given in Tables 4.1 and 4.2. The design constraints, defined in Table 4.3, are based on the facility limitations and capabilities of manufacturing and assembling STCs. An outside diameter of 139 mm for the motor stator is selected as the design base.
4.3.1 Initial design
First, the motor performance data must be collected from the motor supplier or from experiments using the dynamometer. Under the specified operational conditions (as defined in Table 1), the R22 refrigerant properties can be obtained from REFPROP 6.01 (1998). Thereafter, the theoretical pressure ratio, mass flow rate and displacement can be roughly calculated from Eqs. ((2-1) to (2-3)). Based on the suggestion of the scroll manufacturer, t=2.5mm and φr =1050o are selected as initial design values. Given the limitations of the outside motor diameter and assembly tolerance, 100 mm is selected as the maximum outside diameter of the scroll set.
Table 4.4 shows the initial design data in this STC family development. The four design variables can be evaluated from the equations outlined above using an iterative process.
4.3.2 Search direction approach
The optimization approach used in this study first requires is that a search direction for the multiple design variable variations should be identified. Figs. 4.3 and 4.4 illustrate the direction of the scroll wrap height, the sizes resulting from the different steps in the search direction approach to meet cooling capacity requirements under the constraints of Do_max,Gw and Gc based on the initial design data of
mm
t =2.5 and φr =1050o. These results underscore three important outcomes of using this approach:
(1) On the basis of one set of thickness t and a roll angle φ of the scroll wrap r selections, Eq. (4-2), subjected to a change in the search direction of scroll height he matched with pitch pt of the scroll wrap, can fit to each required cooling
capacity requirement. The allowances are listed in Table 4.4.
(2) For a specified cooling capacity requirement, increasing he, Gw and Gc will increase, but Dob_min reduce. To meet the constraints of
5 . 2 ,
5 . 8 ,
max 100
_ min
_ ≤ o ≤ w ≤ c ≤
ob D mm G G
D , the feasible region of he can be
given. In this initial design case, the feasible region of he is between 16 mm and 21.3 mm. Fig. 4.3 has presented the approach results clearly.
(3) At specified cooling capacity, increasing he can improve COPel as Fig. 4.4 shows.
4.3.3 Optimization process
Once the search direction of the four design variables of φr, pt, t and he have been tuned to meet the objective requirements for each specified cooling capacity with interactive process, the optimization approach with a detailed simulation and iteration is carried out.
1. First phase evaluation:
In the first-phase evaluation, the basic data variations of t are 2.5mm ~ 3.3mm with a step size of 0.05mm ~ 0.1mm, and φ is 1050°~1250° with a step size of 20°r
~50°, respectively. As shown in Table 4.4, by individually applying a search direction approach to each specified set of t and φ , a maximum COPr el can be arrived at for every required cooling capacity subject to practical design limits. Fig. 4.5 shows the simulation data and depicts the following optimum results:
(1) Except in the case of 5200W, the maximum COPel of each required cooling capacity in this STC family occurs at φr =1150o, despite various thicknesses of scroll wrap. Moreover, even though the maximum COPel for 5200W is located at
1120o r =
φ , the COPel deviation between 1120º and 1150º is within 0.1%.
(2) The optimum points of scroll wrap thickness are 3.2mm, 3.3mm, 2.6mm and 2.6mm for 9800W, 8100W, 6800W and 5200W, respectively. Nevertheless, for 8100W, the COPel deviation between 3.3mm and 3.2mm is within 0.1%. Table 4.5 shows the detailed design variable data for achieving the maximum COPel. (3) As a result of the above data, two thicknesses of scroll wrap are proposed to meet
the objective function requirements—2.6mm for 5200 and 6800W, 3.2mm for 8100W and 9800W. At the same time, 1150° of roll angle is selected as the optimum value. Thereafter, only the two design variables he and pt need to be tuned continuously.
2. Second phase evaluation
As already discussed, increasing he can improve the COPel at specified t and φ , but r Gw and Gc will limit the increment of he. In addition, the orbiting radius
of p t
ror = t −
2 must also be considered because the r will influence the decision or on the crankshaft dimension. Therefore, the following two approaches are carried out in this second-phase evaluation for this STC family design:
(1) The first approach uses the same orbiting radius for the STC family. Under a maximum height of scroll wrap with Gw, Gc constraints (see Table 4.6(a) for the solutions), the COPel cannot meet the objective requirement of 5200W.
(2) The second approach opens the restraint of the orbiting radius by drawing on the two thicknesses defined in the first-phase evaluation to propose two types of orbiting radius for this STC family. As Table 4.6(b) shows, all result data can satisfy the COPel objective requirements under specified constraints and present the final optimum solutions for this study.
4.3.4 Prototyping and experimental validations
Subsequent to finding the optimum solutions for the STC family, this study implements four family prototypes. A calorimeter with a semi-anechonic chamber (a background noise of 40dBA) and a sound level meter are used to measure the cooling capacity, COPel and noise level of the developed STC series under investigation.
Table 3.3 has presented the specifications and measuring method of this calorimeter.
Fig. 4.6 shows one hermetic sample of the developed STC family prototype and its major components. Figure 4.7 shows the comparisons of cooling capacity and COPel between the experimental and calculated results. The maximum deviations for cooling capacity and COPel are under 2.53% and 1.69%, respectively, suggesting that the research has successfully achieved its desired results.
Table 4.7 illustrates the common sharing of each major component in this STC series. In all, 58% of shared components are identical, with a total cost share of
Table 4.7 illustrates the common sharing of each major component in this STC series. In all, 58% of shared components are identical, with a total cost share of