CHAPTER 4 STC FAMILY DESIGN WITH OPTIMIZATION METHOD
4.4 Results and Discussion
This study has demonstrated a systematic and practical process for optimization of STC family design that allows the COPel for each specified capacity to meet the objective requirements of commercialization. Seven important aspects of this research are summarized below:
(1) The study implemented a practical optimization algorithm combined with interactive session and discrete variables techniques. Meanwhile, the developed
STC simulation package and graphical display method play a part in the decision making during the interactive optimization process.
(2) This investigation selected as its design variables the four geometrical factors of scroll wrap—φr, pt, t and he—that can define the major dimensions of the developed STC family.
(3) Based on manufacturing and assembling expertise input, and after the COPel was defined as the objective function, one case study of an STC family was developed.
The calculated COPel for each specified capacity of this STC family are 3.027, 3.173, 3.230, 3.296 for 5200, 6800, 8100, 9800W, respectively.
(4) All STC models developed for this study met the target requirements and performance objectives. Comparisons between measured and calculated results show that the maximum deviation of cooling capacity and the COPel deviation are below 2.53% and 1.69%, respectively.
(5) Two sets of scroll wrap thickness are designated, 2.6mm for 5200W and 6800W and 3.2mm for 8100W and 9800W, but the dimension of the outside diameter for each specified STC in this family is identical.
(6) A common share percentage of over 80% is achieved for major components in this family design, and only 16% of components are wholly different for each specified STC.
(7) As the case study results of STC family development proved, by following the design procedure and considering the manufacturing constraints, the STC products with good performance, can be developed logically and easily.
Table 4.1 Compressor operation conditions Condensing
temperature
Evaporating temperature
Degree of Subcooling
Degree of Superheating 54.4℃ 7.2℃ 8.3℃ 27.8℃
Table 4.2 Specifications of the STC family used in this study
Refrigerant R-22
Input power 220V, single phase
Lubricants Mineral oil
Shell type Low pressure
Compliant mechanism type Solid axial compliant mechanism
Motor outside diameter (mm) 139
Specified capacity (W) 5200 6800 8100 9800
Objective of COPel(W/W) 3.00 3.10 3.15 3.20
Table 4.3 Design constraints
Item no. Design constraint Notes
1 Dob_min ≤Do_max ≤100 mm
mm mm D
a motor o
40
_ 139
≈
= δ
2 1≤Gw ≤8.5 From finite analysis of stress deflection and wrap machining capability
3 1≤Gc ≤2.5 From cutter catalog and machining expertise
Table 4.4 Initial data definitions in this STC family
Required cooling capacity (W) 5200 6800 8100 9800 Displacement volume (cc) 25.4 32.3 37.4 45 Motor operating torque (N·m) 3.8~4.8 4.8~5.8 5.5~6.7 6.5~8.2
Motor efficiency (%) 87 88 89 90
Cooling capacity allowance ±2%
Motor operating speed (rpm) 3490
Theoretical compression ratio 3.43
Polytropic exponent 1.11
Initial design data t=2.5mm, φr =1050o
Table 4.5 Optimum results of first-phase evaluation.
Required cooling capacity (W) 5200 6800 8100 9800
Objective of COPel (W/W) 3.00 3.10 3.15 3.20
Calculated cooling capacity (W) 5224.73 6689.15 8151.13 9817.72 Calculated COPel(W/W) 3.093 3.172 3.253 3.292
Thickness of scroll wrap t (mm) 2.6 2.6 3.3 3.2
Height of scroll wrap he (mm) 22.0 22.0 25.6 26.8 Pitch of scroll wrap pt (mm) 11.730 12.629 13.596 14.135 Orbiting radius of crankshaft ror 3.265 3.714 3.635 3.867 Roll angle of scroll wrap φ ( º ) r 1120 1150 1150 1150
min _
Dob 73.083 80.784 86.972 90.416
t h
Gw = e/ 8.462 8.462 7.758 8.375
) /(p t h
Gc = e t − 2.41 2.19 2.49 2.45
Table 4.6 Second-phase evaluation results.
(a) Used with the same orbiting radius
Calculated cooling capacity (W) 5273.15 6697.32 8181.60 9813.60
Objective of COPel (W/W) 3.00 3.10 3.15 3.20
Calculated COPel (W/W) of first-phase 3.093 3.172 3.253 3.292 Calculated COPel (W/W) 2.999 3.149 3.230 3.296
Thickness of scroll wrap t (mm) 2.6 2.6 3.2 3.2
Roll angle of scroll warp ( º ) 1150
Height of scroll wrap he (mm) 16.524 20.952 22.605 27.2 Pitch of scroll wrap pt (mm) 12.860 12.860 14.061 14.061
Orbiting radius ror = pt /2−t 3.83
min _
Dob 73.083 80.784 84.880 90.416
t h
Gw = e/ 6.355 8.059 7.064 8.500
) /(p t h
Gc = e t − 1.61 2.04 2.08 2.50
(b) Final optimum solutions used with two types of orbiting radius
Calculated cooling capacity (W) 5266.15 6688.37 8181.60 9813.60
Objective of COPel (W/W) 3.00 3.10 3.15 3.20
Calculated COPel (W/W) of first-phase 3.093 3.172 3.253 3.292 Calculated COPel(W/W) 3.027 3.173 3.230 3.296
Thickness of scroll wrap t (mm) 2.6 2.6 3.2 3.2
Roll angle of scroll warp ( º ) 1150
Height of scroll wrap he (mm) 17.427 22.100 22.605 27.200 Pitch of scroll wrap pt (mm) 12.608 12.608 14.061 14.061
Orbiting radius ror = pt /2−t 3.704 3.830
min _
Dob 80.651 80.648 89.946 89.944
t h
Gw = e/ 6.703 8.500 7.064 8.500
) /(p t h
Gc = e t − 1.74 2.21 2.08 2.50
Table 4.7 Common sharing status of each major component of this STC family.
Component items Common
sharer Cost share Notes
Top cover include
outlet port ˇ 3.74% One type for this series of compressor Check valve
mechanism ˇ 1.50% One type for this series of compressor Oldham ring ˇ 1.50% One type for this series of compressor Main frame ˇ 11.97% One type for this series of compressor Driving bushing ˇ 0.15% One type for this series of compressor Main journal bearing ˇ 0.22% One type for this series of compressor Terminal ˇ 0.15% One type for this series of compressor Bottom frame ˇ 2.24% One type for this series of compressor Lower journal
bearing ˇ 0.15% One type for this series of compressor Oil pump ˇ 2.24% One type for this series of compressor Bottom cover ˇ 2.99% One type for this series of compressor Back pressure
mechanism and isolating member
Δ 5.24%
One type of casting mold but different hole diameter for different back pressure required
Fixed scroll Δ 20.19% Two types of scroll wrap but used with same outside diameter
Orbiting scroll Δ 19.45% Two types of scroll wrap but used with same outside diameter
Main shell include inlet port and suction
baffle
Δ 13.46% One type of pressing mold but different length with different capacity required Motor Δ 3.74% One type of pressing mold but different
stack height with different capacity
Upper balancer X 0.30% Different type for each specified capacity
Crankshaft X 10.47%
Same shaft diameter with two types of orbiting radius and a different length for each specified capacity
Lower balancer X 0.30% Different type for each specified capacity
Notes:
1. “ˇ” means this series of STC family uses the same component.
2. “Δ” means the dimension of this component has been somewhat modified.
3. “X” means this component is different for each specified STC.
Fig. 4.1 The optimization process used in this study
Make decisions with practical experience
Change search direction &
step size of design variables Collect data to describe the developing STC system:
(1) Motor performance at operating conditions (2) Friction coefficient estimation of each contact
surface in STC moving parts
(3) Suction superheat degree & leakage clearance estimation from experiment measurement (4) Oil viscosity vs. temperature
Estimate the initial values of design variables from the required cooling capacity & specified operating conditions
2.Analysis module
Check the constraints
Does the design satisfy
Convergence Criteria ? Input Data
YES Identify:
(1)Objective function: COPelto be maximization (2)Design variables:
Make decisions with practical experience
Change search direction &
step size of design variables Collect data to describe the developing STC system:
(1) Motor performance at operating conditions (2) Friction coefficient estimation of each contact
surface in STC moving parts
(3) Suction superheat degree & leakage clearance estimation from experiment measurement (4) Oil viscosity vs. temperature
Estimate the initial values of design variables from the required cooling capacity & specified operating conditions
2.Analysis module
Check the constraints
Does the design satisfy
Convergence Criteria ? Input Data
YES Identify:
(1)Objective function: COPelto be maximization (2)Design variables:
Fig. 4.2 The design flowchart of STC simulation package used in this study
Boundary conditions &
operating requirements
Find the values of design parameters and basic dimensions of scroll set
Simulation results Basic mechanism dimensions
of STC (sealing mechanism, bearing data, etc.)
Refrigerant properties Oil properties
Motor performance
Various chamber areas &
volumes calculation
Suction gas mass flow model Heat transfer model
Leakage model Gas heating model Mass & Energy balance Forces & Moments of parts Bearing loads
Dimensions of moving parts Frictional loss
Boundary conditions &
operating requirements Boundary conditions &
operating requirements
Find the values of design parameters and basic dimensions of scroll set
Simulation results Basic mechanism dimensions
of STC (sealing mechanism, bearing data, etc.)
Refrigerant properties Oil properties
Motor performance
Various chamber areas &
volumes calculation
Suction gas mass flow model Heat transfer model
Leakage model Gas heating model Mass & Energy balance Forces & Moments of parts Bearing loads
Dimensions of moving parts
Frictional loss
Fig. 4.3 Search direction approach (I) based on the initial design data
Min. outside diameter of 9800 W Min. outside diameter of 8100 W Min. outside diameter of 6800 W Min. outside diameter of 5200 W
Gw of 9800 W Gw of 8100 W
Gw of 6800 W Gw of 5200 W
Gc of 9800 W Gc of 8100 W
Gc of 6800 W Gc of 5200 W
Min. outside diameter of scroll (mm)
Gwfeasible region
Gcfeasible region Do_max feasible region
Height of scroll wrap, he, (mm) Gwupper limit
Gcupper limit
GwGc
Min. outside diameter of 9800 W Min. outside diameter of 8100 W Min. outside diameter of 6800 W Min. outside diameter of 5200 W
Gw of 9800 W Gw of 8100 W
Gw of 6800 W Gw of 5200 W
Gc of 9800 W Gc of 8100 W
Gc of 6800 W Gc of 5200 W
Min. outside diameter of scroll (mm)
Gwfeasible region
Gcfeasible region Do_max feasible region
Height of scroll wrap, he, (mm) Gwupper limit
Gcupper limit
GwGc
Fig. 4.4 Search direction approach (II) based on the initial design data.
Cooling capacity of 8500kcal/h Cooling capacity of 7000kcal/h Cooling capacity of 5800kcal/h Cooling capacity of 4500kcal/h COPel of 8500kcal/h COPel of 7000kcal/h
COPel of 5800kcal/h COPel of 4500kcal/h
Cooling capacity (kW) COPel
Height of scroll warp, he, (mm)
Cooling capacity of 8500kcal/h Cooling capacity of 7000kcal/h Cooling capacity of 5800kcal/h Cooling capacity of 4500kcal/h COPel of 8500kcal/h COPel of 7000kcal/h
COPel of 5800kcal/h COPel of 4500kcal/h
Cooling capacity (kW) COPel
Height of scroll warp, he, (mm)
3.000 3.050 3.100 3.150 3.200 3.250 3.300 3.350
1050 1080 1100 1120 1150 1180 1200 1250
Roll angle of scroll
COPel
t=2.5 t=2.6 t=2.7 t=2.8 t=2.9
t=3.0 t=3.1 t=3.2 t=3.3
(a) 9800W
3.000 3.050 3.100 3.150 3.200 3.250 3.300 3.350
1050 1080 1100 1120 1150 1180 1200 1250
Roll angle of scroll
COPel
t=2.5 t=2.6 t=2.7 t=2.8 t=2.9
t=3.0 t=3.1 t=3.2 t=3.3
(b) 8100W
Fig. 4.5 Optimization results in the first-phase evaluation
3.000 3.050 3.100 3.150 3.200 3.250 3.300 3.350
1050 1080 1100 1120 1150 1180 1200 1250 Roll angle of scroll
COPel
t=2.5 t=2.55 t=2.6 t=2.65 t=2.7
(c) 6800W
3.000 3.050 3.100 3.150 3.200 3.250 3.300 3.350
1050 1080 1100 1120 1150 1180 1200 1250 Roll angle of scroll
COPel
t=2.5 t=2.55 t=2.6 t=2.65 t=2.7
(d) 5200W
Fig. 4.5 Optimization results in the first-phase evaluation (continued)
(a) Hermetic STC family sample
(b) Major components of the STC family prototype
(c) Scroll family of four models Fig. 4.6 The sample of the developed STC
Fig. 4.7 The comparisons of cooling capacity and COPel between the experimental and calculated results
5133.13
5200W 6800W 8100W 9800W
2.500
Maximum deviation is 1.69%
Maximum deviation is 2.53%
5133.13
5200W 6800W 8100W 9800W
2.500
Maximum deviation is 1.69%
Maximum deviation is 2.53%
COPel COPel
CHAPTER 5
VARIABLE-SPEED STC DESIGN WITH OPTIMIZATION
Based on the required specifications of the developed STC family in this dissertation, one variable-speed STC is investigated. At different specified rotation speed, the variable-speed STC can supply various definite cooling capacities required to cover the developed STC family. It means the developed variable-speed STC combined with inverter-fed controller can replace a series of constant-speed STC such as the four models of the STC family that this study implemented.
Three types of variable-speed motor, which are the three-phase AC induction motor, the brushless DC motor with surface permanent magnet (SPM) and the interior permanent magnet synchronous motor (IPMSM), are used with the same scroll mechanism to implement the prototypes. Meanwhile, the performance comparison between these three types of variable-speed STC, has been observed.
While developing the IPMSM in this study, a patent survey and innovative skill have been used to create a new configuration as Appendix 1 presents in this dissertation. In the meantime, a new IPMSM patent that this study innovated has been granted in Taiwan, mainland China and United States of America, respectively.
5.1 Literatures review
Twenty-five years ago, Danfoss Group, the biggest compressor manufacturer in Europe, presented the first paper about hermetic piston-type compressors used with brushless DC motor in small refrigerators (Sorensen, 1980). In 1982, Toshiba Corp., the most famous rotary compressor manufacturer in Japan, depicted the study of a
frequency-controlled compressor used with AC two-poles and three-phases induction motor in air-conditioner applications (Itami et al., 1982). According to the experimental results, it shows that when equipped with the frequency-controlled compressor, the COPel of air-conditioner can be improved by 20% ~ 40% in comparison to the general ON/OFF controlled (constant-speed) compressor. Daikin Industries Ltd., the other world-class compressor manufacturer in Japan, introduced other research results in 1998, that based on the same size of variable-speed motor applied for air-conditioners, the IPMSM can be derived to larger torque and operate at higher efficiency than AC induction motor and brushless DC motor as Fig. 5.1 shows (Igata et al., 1998).
Some papers have presented the performance and experimental analysis of scroll compressor varying its speed when applied for air-conditioners, heat-pumps and water chilling systems (Ishii et al., 1990; Morimoto et al., 1996; Kim et al., 1998; Park et al., 2001; Li et al., 2002; Cho et al., 2002; Aprea et al., 2006). But up to now, very few papers in the world have conducted research related to the variable-speed STC design with scroll geometrical evaluation.
Therefore, based on the minimum design change, the optimum design process and STC design model that this dissertation developed, one variable-speed STC to meet the specification requirements of the original STC family with constant-speed as Chapter 4 introduced, has been implemented. Meanwhile, the performance comparisons between the STC family with a constant speed motor, the variable-speed STC with AC induction motor and permanent magnet (PM) motor, have also been evaluated in this study.
5.2 Design Simulation
For commercialization purposes, the required operation conditions, specifications and basic design constraints are given as Tables 4.1, 4.2 and 4.3. The other required constraint is used with the same orbiting radius for the developing scroll set so that the crankshaft and Oldham ring of the STC can be the same also. Therefore, the major work will focus on the design changes of fixed scroll and orbiting scrolls only.
Five steps are carried out in the design evaluation to search for the optimum design data of this variable-speed STC as follows:
(1) Initial design: define the related specifications for this developing variable-speed STC from original STC family requirements with constant-speed and engineering decisions
(2) First-phase design approach: Based on the original scroll geometrical data and motor operating efficiency that Chapter 4 developed for STC family with constant-speed, reduce the scroll height only to meet the rated cooling capacity requirement and evaluate the design parameters availability.
(3) Second-phase design approach: fixed on the two types of orbiting radius that the STC family used, the optimization algorithm combined with a graphical solution method to search the maximum COPel for the developing variable-speed STC is calculated. Set in the same design base, the motor efficiency is also assumed the same as the STC family with constant-speed in this phase approach.
(4) Prototyping: combined with above optimum approach results and practical engineering experience, the prototypes that include three type of motors, two controllers and one variable-speed STC will be implemented and the operating performance will be measured at specified conditions also.
(5) Performance evaluation: the comparisons between measured results and
calculated results have been discussed. In advance, the STC simulation package receives the real motors operating efficiency and recalculates the operation performance for the STC to perform in variable-speed conditions. Thereafter, the deviation between recalculated results and measured results has been introduced.
Finally, the performance evaluation between constant-speed STC family prototypes and variable-speed prototypes is discussed to make sure the optimum design process meets the practical engineering requirements.
5.2.1 Initial design
The initial design for this developing variable-speed STC has been defined as Table 5.1 and summarized as below:
(1) The rated cooling capacity, 7700W, which is operated at 3600rpm, and is decided from the mean-value of four capacities of the STC family required as Table 4.4 shows. The allowance of cooling capacity is also ±2%.
(2) Based on the same compression ratio, the displacement can be roughly calculated from Eqs. ((2-1) to (2-3)) as 34cc, and the Polytropic exponent selected as the same value, 1.11.
(3) Because the rotation speed of the variable-speed STC can be controlled exactly by inverter-fed controller, the required cooling capacities of the original STC family supplied can be met easily from different rotation speeds.
(4) The motor operating torque and efficiency in different required cooling capacity is defined as the same between constant-speed and variable-speed STC. At the rated cooling capacity requirement of 7700W, the motor efficiency is defined as 89%
because the operating torque is near 8100W.
(5) Table 4.6 has depicted two sets of scroll wrap thickness and orbiting radius that
have been designated in the developed STC family, they are mm
r mm
t =2.6 , or =3.704 for 5200W and 6800W, and
mm r
mm
t =3.2 , or =3.83 for 8100W and 9800W, respectively. For minimum design change requirements, the scroll geometry parameters should follow these two scroll sets data as the design base.
5.2.2 First-phase design approach
Table 5.2 shows the comparison between original STC family data and the first-phase evaluation results and underscore two important outcomes:
(1) On the basis of scroll parameters, t =2.6mm, ror =3.704mm, φr =1150° , subjected to a scroll height he =22.1mm, can fit to rated cooling capacity 7700W.
But GW =9.116 is over the design constraint of GW ≤8.5. It means this original STC model, t =2.6mm, ror =3.704mm, φr =1150°, can not meet the required variable-speed STC by tuning the wrap height only.
(2) On the other scroll parameters, t =3.2mm, ror =3.83mm, φr =1150°, subjected to a scroll height he =20.55mm, can fit the rated cooling capacity of 7700W and all data is under the design constraints. Table 5.2 shows the calculated COPel of required cooling capacities with various rotation speeds as Table 5.1 defined. For 5200W and 6800W, the calculated COPel are higher than the original data, but for 8100W and 9800W, the calculated COPel are lower than the original data.
Moreover, the calculated COPel of 9800W can not meet the objective requirement.
Therefore, tuning scroll height only from the original scroll design parameters can not satisfy this study’s required target, so the following approach should be carried out with an optimization algorithm to develop the optimum variable-speed STC in this study.
5.2.3 Second-phase design approach with optimization
Since only one set of variable-speed STC has been developed to cover the cooling capacity range, which is not same as the STC family with constant-speed that develops a series of STC models to meet the required specified range of cooling capacity by using more common components as investigated in Chapter 4. Therefore, the discrete variables optimization approach has some differences, but the optimization algorithm combined with a graphical solution method, such as Chapter 4 described, is the same.
The newly approach process is introduced as.
The objective function requirement is also defined as Eq. (4-12) and subjected to the constraints as Eq. (4-13):
) , , , (
maximize COPel = f φr pt t he (4-12) s
UpperLimit D
G G s
LowerLimit ≤ w, c, o_max ≤ (4-13) The other major design consideration in this design approach is the orbiting radius that also sets as a restraint in two types: (1)ror =3.704mm, (2)ror =3.83mm, so that the crankshaft can be the same as the original STC family. Meanwhile, each motor efficiency at a specified rotation speed, is assumed the same as the STC family with constant-speed.
1. First-stage simulation:
This stage focuses on developing a variable-speed STC to operate at 3600rpm and with a cooling capacity of 7700W to search for the maximum objective function (maximum COPel) by drawing on the variation of scroll thicknesses from 2.6mm to 3.2mm. Table 5.3 and Fig. 5.2 depict the simulation results.
(1) As the orbiting radius is fixed, the basis of one set of thickness t with pitch pt
of the scroll wrap, from Eq. (4-2) can be subjected to a change of scroll height he
matched with a roll angle, φ , which fit the required cooling capacity requirement. r (2) As Chapter 4 introduced, increasing he can improve the COPel at specified t
and φ , but r Gw and Gc will limit the increment of he. Therefore, selecting 5
.
=8
Gw , means increasing he to the limit value, as researched in this study.
(3) Based on the above decisions, to increase wrap thickness, the pitch and the wrap height are increased, and the roll angle is reduced. Finally, the calculated cooling capacity can fit the defined data with a small variation and the COPel is higher than 3.2 and over the objective target.
(4) The maximum COPel occurs at t =2.9mm, φr =1077.694°, he =24.65mm and the orbiting radius is the type 1, ror =3.704mm. The calculated cooling capacity is 7728.26W and the COPel is 3.309. Moreover, at t =2.8mm, φr =1119.40°,
mm
he =23.80 the orbiting radius is the same as 3.704mm, the COPel is 3.308 and the calculated cooling capacity is 7746.57W. These two points all meet the object requirement, and the deviation between the two points is very little.
(5) Based on the type 2 orbiting radius, ror =3.83mm, the maximum COPel is located at t =2.7mm, φr =1118.49°, he =22.95mm. The calculated cooling capacity is 7752.45W, and the COPel is 3.299, which is lower than the optimum point of type 1 of orbiting radius, but the deviation is within 0.3%.
(6) As a result of the above data, the optimum value can be searched at t=2.9mmin mm
ror =3.704 , but the simulated variable-speed STC is operated at 3600rpm only.
Furthermore, in the range of operating speed as defined in Table 5.1, the optimum searching point should be approached and evaluated continuously.
2. Second-stage simulation:
Subsequent to finding the optimum solutions for the variable-speed STC in the