NISTIR 7560

Carbon Weight Analysis for 

Machining Operation and Allocation 

for Redesign 

Gaurav Ameta 

Mahesh Mani 

Sudarsan Rachuri 

Shaw C. Feng 

Ram D. Sriram 

Kevin W. Lyons 
NISTIR 7560

Carbon Weight Analysis for 

Machining Operation and Allocation 

for Redesign 

Gaurav Ameta 

Mechanical and Materials Engineering 

Washington State University 

Mahesh Mani 

Sudarsan Rachuri 

Shaw C. Feng 

Ram D. Sriram 

Kevin W. Lyons 

Manufacturing Systems Integration Division 

Manufacturing Engineering Laboratory 

 

 December 2009 

U.S. Department of Commerce 

Gary Locke, Secretary 

National Institute of Standards and Technology 

Pat Gallagher, Director
Table of Contents 

Abstract................................................................................................................................1 

1. Nomenclature.................................................................................................................2 

2. Introduction....................................................................................................................2 

3. Related Literature...........................................................................................................4 

4. Carbon Weight Tolerancing Approach..........................................................................5 

5. Case Studies...................................................................................................................9 

Case Study 1: Part Level CW ..................................................................................9 

Case Study 2: Assembly Level CW.......................................................................12 

6. Carbon Weight Allocation/Synthesis...........................................................................14 

Assembly Level CW Allocation ............................................................................15 

Process Level CW Allocation................................................................................16 

Redesign Methodology ..........................................................................................17 

7. Conclusion and Future Work.......................................................................................18 

References..........................................................................................................................19 

Appendix A: Worst Case and Statistical Case CW Computations....................................21 
List of Figures 

Figure 1: Methodology for utilizing CWTA....................................................................... 6 

Figure 2: Carbon Weight Tolerancing Approach ............................................................... 7 

Figure 3: Test part 1............................................................................................................ 9 

Figure 4: Assembly........................................................................................................... 13 

Figure 5: (a) Original and (b) redesigned Part A of the assembly (coupling) in Figure 4.15 

Figure 6: Multi-level Form Material and Process Optimization (FMPO) based allocation 

of CW and redesign .......................................................................................................... 17 

List of Tables 

Table 1: Computation of energy and CW from the specific energy................................. 10

Table 2 Computation of energy and CW from the process parameters............................ 11

Table 3: Energy Calculations Part A ................................................................................ 13

Table 4: Energy Calculations Part B................................................................................. 14

Table 5: CW allocation based on 20% reduction in CW for the assembly....................... 15

Table 6: CW values based on material and shape redesign for Part A of the assembly in 

Figure 4 ............................................................................................................................. 15

Table 7: Percent contribution for the process level CW example in section 5.1.2 All CW 

values are reported in X 10-3 metric Tonne ....................................................................... 16
Carbon Weight Analysis for Machining Operation 

and Allocation for Redesign 

Abstract 

The objective of th is research is to explore and develop a new methodolog y for 

computing carbon weight (CW ) - often referred to as carbon footprint, in manufacturing 

processes fr om the part leve l to a ssembly le vel. In this in itial stud y we focused on 

machining operations, specifically turning and milling, for computing the CW. Our initial 

study demonstrates that CW can be computed using either actual measured data from 

process level information or from initial material and manufacturing process information. 

In mechanical design, tolerance analysis prin ciples extend from design to manufacturing 

and tolerances accumulate for parts and proces ses. By extending this notion to CW, we 

apply mechanical tolerancing prin ciples for computing worst case and statistical case 

CW of a product. We call this the CW To lerance Approach (CWTA). Two case studies 

demonstrate the computation of CW. Base d on toleran ce alloca tion concepts ; CW 

allocation is also dem onstrated through specific redesign examples. CWTA helps in 

identifying carbon intensive parts/processes and can be used to make appropriate design 

decisions. 

Keywords: Carbon footprint, Carbon Weight Analysis, Machining, Re-design 

1 
1. Nomenclature 

CW Carbon Weight, unit: metric Tons 

E Energy, unit: kWh 

E variation of Energy (E)

F force, unit: N 

v surface speed, unit: m/s 

t cutting time, unit: s 

 tF net force acting on the tool at a given time t, 

ΔF(t) variation of F(t) 

 tv surface speed of the tool at a given time t 

Δv(t) variation of v(t). 

f conversion factor (0.620 Metric Tons/MWh) for transforming energy E to CW 

∆CW variation of Carbon Weight (CW) 

ut specific energy, unit: W-s/mm3 

Vs volume of the stock, unit: mm3 

Vp volume of the final part, unit: mm3

Vr total removal volume, unit: mm3 

Vri removal volume for each process, unit: mm3 

Pri Process rate for each process (the material removal rate), unit: mm3/sec

k constant ( ) for converting energy from W-s to kWh. 7 107778.2  

2. Introduction

In recent years, sustainable manufacturing has become a strategic move as industries 

began to seek novel ways for resource efficiency, ensure compliance with regulations 

related to environment and health, and enhance the marketability of their products and 

services. Energy is utilized at each stage of a product life cycle. Energy production from 

fossil fuels results in green house gas (GHG) emission. Hence minimization or efficient 

use of energy and resources are critical for reducing environmental effects of a product or 

process. 

2 
Awareness, investments and efforts towards reducing greenhouse gases by 

industry, government and environmental organizations have increased in the last decade. 

The Kyoto Protocol, an international agreement linked to the United Nations Framework 

Convention on Climate Change, binds developed nations to a cap and trade system1 for 

the emission of six major greenhouse gasses. Emission quotas were agreed by each 

participating country, with the intention of reducing their overall emissions to 1990 levels 

by the end of 2012. Under the agreement, for the 5-year compliance period from 2008 

until 2012, nations that emit less than their quota will be able to sell emissions credits to 

nations that exceed their quota. In 2006, the European Union ETS (Emissions Trading 

Scheme) market traded 1,101 MtCO2e, Millions of tons of carbon dioxide equivalent. 

The carbon market grew in value to an estimated US$30 billion in 2006 [27]. Therefore, 

a method to quantify green house gas emissions in products and process, especially CO2, 

is needed. At the G8 Summit which concluded in July 2008, the participating nations 

have pledged to move towards a low-carbon society and target the goal of at least 50% 

reduction in greenhouse gases by 2050 [1]. 

In this paper, we propose a methodology for computing Carbon Weight (CW), 

also called carbon footprint, as the metric for quantifying the CO2 emissions. Carbon 

footprint is defined as "a measure of the exclusive total amount of carbon dioxide 

emissions that is dir ectly and indirectly caused by an ac tivity or is accum ulated over the 

life stages of a product" [2]. In this preliminary study, we make an attempt to quantify the 

amount of CO2 emitted (in metric tons) from energy use in machining a part and compute 

the CW for the assembly, using mechanical tolerancing principles. 

The paper is organized as follows: section 3 presents a related literature review. 

Section 4 presents the main concepts, assumption and proposed methodology. Section 5 

presents two case studies, one at part level and the other at assembly level. Section 6 

demonstrates the allocation methodology. Section 7 presents our conclusions and scope 

for future work. 

 

1

an administrative approach used to control pollution by providing economic incentives for achieving 

reductions in the emissions of pollutants 

3 
3. Related literature 

Standardized guidelines for assessing the environmental impacts, called life cycle 

assessment (LCA), have been developed by International Organization for 

Standardization (ISO) [3]. By including the impacts throughout the product life cycle, 

LCA provides a comprehensive view of the environmental aspects of the product or 

process. LCA has also been attributed with some drawbacks [4-8] related to (a) system 

boundaries issues, (b) data issues and (c) methodology issues such as weighing methods, 

aggregation methods and comparison across indices. Moreover, LCA only provides 

methodology for assessing the environmental impacts and does not provide any 

guidelines for reducing the impacts. 

During a product’s life cycle, energy is consumed at most of the stages; design, 

production, use and disposal. Energy use varies throughout a products life cycle and is 

different for different products. Energy accounting and reduction during product use (use 

phase) is governed by standards such as Energy Star [9], which supports a number of 

industries. Energy Star does not include the energy consumption during the 

manufacturing phase of a product life cycle. In this paper we present a methodology for 

accounting manufacturing phase energy and an initial attempt towards reducing the 

energy utilization during manufacturing. 

Various studies [10; 11] at the Department of Energy (DoE) focused on 

accounting the energy usage and emissions in different manufacturing industries. A study 

conducted by the National Association of Manufacturers (NAM, www.nam.org) 

speculated possible savings of about 19 billion dollars with development of new energy 

efficient technologies [12]. Further details of energy-related carbon dioxide emissions in 

U.S. manufacturing were studied by Schipper [13]. 

Environmental impacts of different manufacturing processes have been 

extensively studied by Gutowski’s research group [14-17]. They identify environmental 

impacts by accounting for the exergy of the manufacturing process. Exergy is defined as 

the potential of a system to cause a change as it achieves equilibrium with its 

environment (heat reservoir) [18]. When the environment is used as heat reservoir, 

exergy is the energy that is available to be used. Although exergy contains more 

information regarding energy losses to the environment, it is the use of energy during 

4 
production that should be computed and then reduced for individual parts/component. 

Therefore, we choose to account for energy use instead of exergy. Moreover, Gutowski’s 

research group focused mainly on identifying process related energy requirements and 

not energy specific to products. 

Product related CO2 emission accounting has been reported by Jeswiet [19]. 

However, the author generalized the computation of CO2 factors from electricity 

requirements and did not consider the variability of different manufacturing processes. 

Jeswiet [19] also does not provide any extension to statistical analysis and utilization of 

CW analysis for the redesign of parts/assemblies. Furthermore, there is little work done 

on applying tolerancing scheme to CW calculations for machining an assembly of parts. 

4. Carbon Weight Tolerancing Approach 

In the proposed CW Tolerancing Approach (CWTA), we focus on the CO2 emissions 

based on the amount of energy consumed for manufacturing a part. Energy consumption 

is related to the power used due to the amount of removed volume, for specific material 

and associated manufacturing process. 

Figure 1 presents the flow diagram for the methodology used in CWTA. The 

input is an assembly of parts with candidate material and manufacturing processes. In this 

current work we have not included the computation of CW for assembly processes, for 

example, welding, fixtures, transport, etc. We compute the amount of energy used in 

manufacturing a part based on the removed volume, material and manufacturing process. 

Due to variability associated with specific manufacturing environments and related data, 

energy consumption can only be computed as a range. If the range is quite large, based on 

the availability of the data, the computed CW range may not facilitate environmentally 

benign decisions. Therefore, in such cases, further investigation is needed for reducing 

the range. In this paper we are not investigating the range, but demonstrating the 

computation of CW assuming data availability is not an issue. The range of energy 

consumption can then be converted into the range of CW by using conversion tables 

provided by the Department of Energy (DOE) [20]. 

5 
 

Assembly = {Parts (1...n) } 

(With material and candidate 

manufacturing processes) 

Compute energy consumption from 

material, manufacturing process and 

removal volume 

Convert energy to Carbon 

Footprint (CW) 

Report Energy, CW in the Bill 

of Materials (BOM)

Based on the actual 

measured data 

Based on generalized 

material, process 

information 

Carbon Weight Tolerancing Approach 

Carbon Weight Allocation 

Figure 1: Methodology for utilizing CWTA. 

The assembly level CW is computed using mechanical tolerancing principles, in terms of 

worst case and statistical scenario (Figure 2). The worst case CW reports the maximum 

and minimum carbon footprint for the assembly, while the statistical case reports the 

measured (or predicted) value of uncertainty for the range of the carbon footprint. For 

further details about computations related to worst case and statistical case CW, please 

refer to Appendix A. The purpose of CWTA is to include CW information about the 

assembly and parts in the bill of materials (BoM), thus creating a bill-of-carbon (BoC). 

This BoC, in conjunction with CW requirements, will then be utilized to improve the 

allocation of CW across the assembly (Figure 2) based on any functional requirements on 

the amount of CW for the given product. The CW allocation could be performed using 

percentage contribution or sensitivity of individual parts/features towards the total CW.

CWTA would therefore help in identifying carbon intensive parts/processes and can be 

used to make appropriate design decisions. In future, we hope to extend CWTA for 

information exchange between CAD/PLM tools to LCA tools and this allowing 

integration of environmental aspects into product design and development. 

6 
Assembly 

Parts, Material, 

Mfg Process 

Assembly 

Part1 Part2 ...... PartN

Material1 & Material2 & ...... MaterialN &

Mfg Process1 Mfg Process2 ...... Mfg ProcessN

CW1 CW2 ...... CWN

CW

Energy1 Energy2 EnergyN

BOM with CW

CW Tolerancing Approach

CWworst-case = CWmax and CWmin

CWstatistical-case = CWmean and VarianceCW

Analysis

Allocation

 Redesi

gn 

%Contribution, 

Sensitivity, 

etc. 

Assign CW 

CW 

Requirements

Design 

Requirements

Figure 2: Carbon Weight Tolerancing Approach

We now present generalized CWTA computations for a part; (a) based on the 

actual process level measured data (experimental) and (b) based on the initial material 

and manufacturing process information. 

a) CWTA computation based on the actual process level measured data 

If process parameters, namely cutting forces, surface speeds, process time, etc., from 

actual machining operations are available, they can be utilized to compute the energy 

consumed. Energy can be computed using the force, surface speed and cutting time as 

   

1

0

*

t

t

dttvtFkE ....................................... (1) 

Please refer to the nomenclature section for the meanings of the symbols used. Since all 

measuring instruments have variability in the measured values, the measured F and v

would be range of values. Therefore, the resultant energy E would also be computed as a 

7 
mean and variation. The variation in energy E due variation in the measurement of 

force and surface speed can be computed as: 

  ...............................(2)   

1

0

))((*))((

t

t

dttvtvtFtFkEE

A precision machining center has very good control on velocity, so Δv(t) is very small 

and can be neglected. The CW of the machining process can then be computed as 

    EEfCWCW )( ..............................................(3) 

Basically CW is proportional to E and the proportionality factor is f. Energy Information 

Administration (EIA) under the U.S. Department of Energy (DOE), have reported a 

methodology and related tables for computing factor f [20]. For Maryland the value of f is 

0.620 Metric Tons/mWh. EIA reports CO2 emission in terms of metric tons. 

Ivester et al. [21] at NIST have earlier provided characterization and optimization 

of specific manufacturing processes and provided useful data based on their test part, not 

an assembly of parts. In this study we use the experimental data from [21]. 

b) CWTA computation based on the initial material and manufacturing process 

information 

In the absence of specific process parameters, generalized energy consumption for cutting 

operation, given by Kalpakjian [22], in the form of specific energy will be utilized. The 

specific energy is energy per unit time required for removing a unit volume from a given 

material. By obtaining the total removal volume, energy will be obtained as 

t  kVuE ...........................................................(4) 

For a given machining process, based on the machine, tool, material, stock and removal 

volume we will estimate the amount of energy utilized for producing a part. CW will then 

be computed using equation (2). 

8 
5. Case Studies 

To demonstrate the CWTA methodology, we present two case studies, one at the part 

level and the second at the assembly level. In both cases we first compute the removal 

volume, then calculate the energy consumed and finally convert the energy to CW. In the 

subsequent subsections we present the CW computations for the individual cases based 

on the two methods discussed in the previous section. 

Our assumptions specific to the CWTA case studies are: 

 Turning and milling have been selected as the candidate manufacturing 

processes. 

 Only rough estimates for CO2 emissions, based on energy use during 

manufacturing, will be provided. 

 Stock is always assumed to be properly rounded (for turning operations). 

5.1 Case study 1: Part Level CW 

We choose test part 1 (Figure 3) specifically to demonstrate the CW computation using 

the two approaches mentioned in the previous section. The experimental data for the 

turning operations has been taken from Ivester et al. [21]. The reported material is AISI 

1045 Steel and all experiments were performed on a 22 kW lathe by Ivester et al. [21]. 

Figure 3: Test part 1 

We have adopted the specific energy data for cutting operations from [22] and 

have also compared with the data from [15]. The data available in [15] is not specific to 

particular material and is an average data for 1000 hrs of machine run. 

9 
5.1.1 CW based on material and manufacturing process information 

Table 1 summarizes the available data and the computed results for the test part shown in 

Figure 3. Subtracting the volume of the stock (Vs) and final part (Vp) gives the removal 

volume (Vr). The specific energy (ut) range as reported in [22] for the given material is 

2.7-9.3 W-s/mm3. As reported in [22], the value of specific energy is for dull tools and 

80% efficient drive motor. Therefore, we also report a modified specific energy data for 

sharp tools and fully efficient motor as 2.16-7.44 W-s/mm3

. The specific energy data from 

[15] is also shown. 

Table 1: Computation of energy and CW from the specific energy

Volume of the Stock (Vs, mm3) 581266 

Volume of the Part (Vp, mm3) 145397 

Removal Volume (Vr, mm3) Vs - Vp = 435869 

From [22] From [22], 

corrected for sharp 

tools 

From [15] (Total 

energy, material 

independent) 

Specific energy (ut, W-s/mm3) 

2.7 - 9.3 (2.16-7.44) 3.5-15 

Energy Consumption (kWh) 0.3269-1.1260 0.2615-0.9 0.4237-1.8161 

CW X 10-4,( metric Tons) 2.02678-6.9812 1.6214-5.5849 2.627-11.26 

Now utilizing equation (3) and the data from Table 1, energy consumption and CW (for 

turning the part shown in Figure 3) is computed as shown in the last two rows of Table 1. 

5.1.2 CW based on experimental data 

We approximate the process time (ti) by computing the removal volume (Vri) for each 

process and the material removal rate (Pri) given by Ivester et al. [21]. Due to lack of 

information regarding the time dependent variation of force (F), surface speed (v) and 

material removal rate (Pri), we assume these process parameters to be constant. Therefore, 

we drop the integration in equation (2) and approximate it as shown in equation (5). 

ri

ri

P

V  )()( vFFkvtFFkEE ..................................(5) 

10 
Utilizing the assumptions and equation (5) we compute the energy and the CW of 

the part as shown in Table 2. 

Table 2 Computation of energy and CW from the process parameters

Operation F (N) v 

(m/sec) 

Process

 Rate

(mm3

/sec) 

Power (W) t(sec) Nominal 

Energy 

(KWH) 

CW

10-4 

Rough OD 

(Outer 

Diameter) 

742±5 3.11 989.50 2307.62±15.55 294.64 0.1889 

0.1171±0.0008 

Rough 

Grooves 

204±4 4.26 426.67 869.04±17.04 61.21 0.0148 

0.0092±0.0002 

Rough 

Contour 

221±3 2.16 216.67 477.36±6.48 250.32 0.0332 

0.0206±0.0003 

Finish OD 

(Outer 

Diameter) 

 36±2 3.16 63.33 113.76±6.32 236.98 0.0075 

0.0046±0.0003 

Finish 

Grooves 

 74±2 3.33 100.00 246.42±6.66 268.48 0.0184 

0.0114±0.0003 

Finish 

Contour 

 76±2 1.83 55.00 139.08±3.66 402.08 0.0155 

0.0096±0.0003 

The total energy and CW can be computed by adding the energy and CW of 

individual process, respectively. The total energy consumed is 0.2782±0.0033 (see 

Appendix A for further details regarding this calculation) kWh and the total CW is 

(1.7251±0.0208) X10-4 metric tons of CO2. 

5.1.3 Comparison 

The data from [15] represent the specific energy during the entire manufacturing process 

including machine idle energy, coolant flow energy, etc. This data is not specific to a 

material and is only based on process information. The data from [22] also represents the 

specific energy during the entire manufacturing process including machine idle energy, 

coolant flow energy, but is specific for a particular material. The data from [21] 

represents the specific cutting energy and does not include idle energy, coolant flow 

11 
energy, etc. The data from [15], [22] and [21] follows from a general to a specific level of 

detail. Thus, the CW computed using the data from [15] should form an upper bound to 

the computed CW value using the data from [21]. The value of CW computed using data 

from [21], (1.7 X10-4), is well below the value of CW, (2.6 X10-4), computed using the 

data from [15]. 

 Moreover, the data in [22] assumes normal cutting operations, viz., blunt tools 

and 80% efficiency of the drive motor. Since, the experimental data provided by Ivester 

et al. [21] was measured using specific and sharp tools (to maintain the required surface 

roughness), a valid comparison can only be made if the data from [22] is corrected for 

sharp tools. The third column in Table 1 shows the computation using the corrected data 

for sharp tools. The range of CW (1.6214-5.5849) X10-4 computed from the corrected 

data now bounds the CW value (1.7251±0.0208) X10-4 computed using the data from 

[21]. Therefore, we can conclude that the data provided in [22] can be used to 

approximate CW values at the initial design stages. 

The relative closeness in range between the two approaches indicates the potential 

application of the proposed methodology for CW calculation, subject to the availability 

of reliable data. This initial experiment identifies a need to characterize the processes so 

that accurate CW can be computed. 

5.2 Case study 2: Assembly Level CW

In this case study we present the application of CWTA for an assembly based on material 

and manufacturing process information. The function of the assembly is to provide torque 

transfer and alignment between two rotating components. Figure 4 presents the assembly 

(coupling) and exploded view of the assembly used in the case study. The function of the 

coupling is to align two rotating shafts and to transmit the motion from one shaft to 

another. Tables 3 and 4 present the removed volume based on the machining operation 

for the individual parts of the assembly. The pins are assumed to be supplied by a 

supplier; therefore the energy consumed in producing the pins is ignored. We assumed 

AISI 304 Steel as the part material and hence the corresponding specific energy range is 

3.0 to 5.2 W-s/mm3

 [22]. 

12 
 

Assembly 

Part A 

Part B

Pins 

Figure 4: Assembly 

Table 3: Energy Calculations Part A 

Stock Volume to be 

removed 

Removed 

Volume 

Sawed surface Final part A 

368155.39 3 mm 3 232061.50 mm 3 mm 109343.04 122718.46 3 mm 136093.89 3 mm

Utilizing equation (4), the energy consumption for each of the parts can be 

computed. Energy consumption for Part A = 0.0820 - 0.2824 kWh. This energy can be 

converted to CW by using equation (3) as a range from 0.0508 X 10-3 to 0.1751 X 10-3

metric tons of CO2. Similarly, energy consumption for Part B = 0.0556 - 0.1917 kWh and 

this energy can be converted to CW by using equation (3) as a range from 0.0345 X 10-3

to 0.1188 X 10-3 metric tons of CO2. 

From equations (A-1) to (A-4) in Appendix A, the worst-case CW range for the 

assembly can be computed as 0.0853 X 10-3 – 0.2939 X 10-3 metric tons of CO2. From 

equations (A-1) and (A-5) in Appendix A, the statistical case CW mean and standard 

13 
deviation for the assembly can be computed as 0.1896 X 10-3 metric tons of CO2 and 

0.0347, respectively. Note that while computing the CW for the statistical case, due to the 

lack of data, we choose normal distribution as a candidate distribution over the range of 

CW on individual parts. We limited ourselves to normal distribution to simplify the 

computations. In future other distributions can also be explored and validated [23]. 

Table 4: Energy Calculations Part B 

Stock Volume to be 

removed 

Removed 

volume 

Sawed surface Final part B 

235619.45 3 mm 152759.94 3 mm 74220.13 mm3 78539.81 3 mm 82859.51 3 mm

6. Carbon Weight Allocation/Synthesis 

For an eco-friendly product, reduction in the CW of the individual parts and assembly is 

desired. To begin with, a reduction of, say, X% can be targeted for the whole assembly. 

The target CW for the assembly can then be allocated to individual parts/features, and 

later utilized for redesign of individual parts/assembly. For allocation of CW to 

individual parts, percent contribution or sensitivity of the CW of individual parts/features 

can be utilized. The percent contribution of individual parts/features should be computed 

while CWTA is completed. The basic idea is to identify carbon intensive 

parts/components and make appropriate design decisions and we may not need detailed 

design – we could use data from similar products. 

In the subsequent section we would demonstrate the application of CW allocation 

for redesign of assembly and manufacturing process. A methodology is suggested for 

redesign based on CW allocation. 

6.1 Assembly Level CW Allocation

14 
As an example of assembly level CW allocation, Table 5 shows the allocated 

values of CW for individual parts from the assembly in Figure 4. For demonstration, 

allocation is done based on a 20% reduction in CW for the assembly. The allocated 

values can then be used to redesign an eco-friendly product. The reduced value of CW 

can later potentially used in an eco-label. Figure 5a and b shows the original design and 

one of the redesign choices available for Part A. 

Table 5: CW allocation based on 20% reduction in CW for the assembly 

Initial CW (X 10-3 metric Tonne) % Cont. Allocated CW(X 10-3 metric Tonne) 

Min Max Min Max 

Part A 2.8631 4.9624 59.542 2.2904 3.9699 

Part B 1.9454 3.3691 40.457 1.5563 2.6952 

Assembly 4.8085 8.3315 100 3.8468 6.6652 

The redesigned Part A as shown in Figure 5(b), a) consists of closed slots, instead 

of open ones and b) has material around the rim that has not been machined. The 

function of the assembly in Figure 4, is to align two rotating shafts and to transfer the 

motion of one shaft to another. The new design (Figure 5(b)), does not affect the function 

of the assembly. The redesign solution, shown in Figure 5(b), is solely intended to 

demonstrate the methodology for CW allocation. Actual selection of a particular redesign 

would require additional considerations like function, material requirements, strength, 

cost, general assembly, etc. 

(a) (b)

Figure 5: (a) Original and (b) redesigned Part A of the assembly (coupling) in Figure 4.

Table 6: CW values based on material and shape redesign for Part A of the assembly in 

Figure 4

Calculations 

15 
16 

Geometry For open slots For closed slots 

Volume of the Part 136093.89 3 mm 180659.33 3 mm

Removed Volume 109343.04 3 mm 64777.60 3 mm

Material Steel Aluminum Steel Aluminum 

Energy for Machining (kWh) 0.0820 - 0.2824 0.0121-0.0334 0.0485-0.1673 0.0071-0.0197 

Carbon Weight 

(X 10-3 metric Tons) 

0.0508 – 0.1751 0.0075-0.0207 0.0301-0.1037 0.0044-0.0122 

Table 6 shows the values of CW and energy for the redesigned Part A. CW for 

two choices of material is also compared for the original and redesigned Part A. The 

sample calculations in Table 6 and the redesigned Part A in Figure 5b shows the choices 

that can be provided to the decision maker based on CW. As earlier mentioned, the final 

selection of a particular design would further involve a multi-constraint optimization 

scheme based on different requirements. 

6.2 Process Level CW Allocation 

CW allocation can also be extended to a manufacturing process level, for process level 

optimization. Table 7 shows a machining example for the process level allocation based 

on 80% reduction in CW from the example discussed in section 5.1.2. 

Table 7: Percent contribution for the process level CW example in section 5.1.2 All 

CW values are reported in X 10-3 metric Tonne 

Operation CW Process % contribution Allocated CW based on 20% 

reduction in CW 

Rough OD 0.1171 67.88405797 0.09368

Rough Grooves 0.0092 5.333333333 0.00736

Rough Contour 0.0206 11.94202899 0.01648

Finish OD 0.0046 2.666666667 0.00368

Finish Grooves 0.0114 6.608695652 0.00912

Finish Contour 0.0096 5.565217391 0.00768

Total 0.1725 100 0.138

For sample calculations in Table 7, equal weights were for each individual process 

(roughing, finishing, etc). Different weights can actually be utilized for the actual process 
optimization based on the requirements for individual steps. A process optimization 

scheme as discussed in [21] could potentially utilize such allocated values of CW. 

6.3 Redesign Methodology

Figure 6 demonstrates a framework for utilizing CW in redesign of an assembly at 

different levels, viz., form, material and process. Redesign at these three levels flows 

from top down. Any change in form would require changes in material and 

manufacturing processes for satisfying the design requirements. Any change in material 

may require changes in manufacturing processes. 

Redesign 

Assembly 

Parts, Material, 

Mfg Process 

BOM with CWAllocation

%Contribution,

Sensitivity, 

etc. 

Assign CW 

CW 

Requirements 

Design 

Requirements 

 Form 

Shape 

Size 

 Material 

 Process 

Optimization

Figure 6: Multi-level Form Material and Process Optimization (FMPO) based 

allocation of CW and redesign 

In the methodology shown in Figure 6, form redesign implies changes in shape 

and size of the design. Material redesign could indicate either selecting different material 

or designing new material to meet the design requirements. Manufacturing process 

redesign would indicate changes in process, setups, operations, tools, fixture etc. 

17 
Therefore, redesign based on CW allocation would require a multi-level form, material 

and process optimization. 

7. Conclusions and Future Work 

In this research, we have utilized and extended the mechanical tolerancing 

principles of assembly level analysis for computing a product’s carbon weight (CW). 

Such CW estimates can be utilized during the design evaluation stages of a product to 

make environmentally friendly decisions both regarding the product and the 

manufacturing process. This research work is a first step towards demonstrating the 

CWTA and the corresponding computations. The presented case studies indicate CWTA 

as a potential application for CW calculation. 

In future we would like to demonstrate CWTA for CW allocation through 

software application. Furthermore, we would like to investigate the data issues and 

metrology concepts (measurement methods, uncertainty, calibration, etc.) for CW. 

Identification of scopes for practical application and best practices for CW tolerance 

analysis and synthesis at successive stages of design will also be pursued in the future. 

8. Acknowledgements 

We wish to express our thanks to Dr. Alkan Donmez for participating in our earlier 

discussions and offering valuable insights to this research. 

9. DISCLAIMER 

No approval or endorsement of any commercial product by the National Institute of 

Standards and Technology is intended or implied. 

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Appendix A: Worst Case and Statistical Case CW Computations 

In this appendix we extend the ideas from tolerance analysis to CW analysis in 

assemblies. The basic ideas borrowed from tolerance analysis will be explained in the 

subsequent paragraphs. For further details, specifically about tolerance analysis and the 

mathematics discussed in this section, please refer to [24; 25]. 

20 
The worst case implies that if all the parts are within their given CW range, then all 

the assemblies comprising of these parts will fall in the computed worst case CW range. 

Statistical case CW analysis can take advantage of statistical averaging over assemblies 

of parts, allowing the allocation of larger range for CW (compare CW from equation 

(A-7) and (A-8)). 

The nominal value for the assembly level CW can be computed by adding the 

nominal values of CW of individual parts, as shown in equation (A-1). 

a   CWCWCW  CWN ..... 1 2 .......................................(A-1) 

where CWa represents the nominal value of assembly level CW and CWi for i=1...N

represents CW for part 1 to N. The maximum and minimum value (i.e. range) of the 

assembly level CW for the worst case can be obtained as shown in equations (A-2) and 

(A-3). 

max max1 max2 max ..... CWa  CW  CW  CWN ..............................(A-2) 

min min1 min2 min ..... CWa  CW  CW  CWN ..............................(A-3) 

where CWamax and CWamin are the maximum and minimum CW for the assembly, 

respectively. Similarly CWimax and CWimin for i=1...N represents the maximum and 

minimum values of CW for part 1 to N. By subtracting equation (A-3) from equation (A2), the worst case variation in the assembly level CW can be obtained as shown in 

equation (A-4). 

 

CWa    CWCW  CWN ..... 1 2 .................................(A-4) 

where ∆CWa represents the amount of variation in the CW value of the assembly from its 

nominal value. Similarly ∆CWimax and ∆CWimin for i=1...N represents the amount of 

variation of CW for part 1 to N. 

21 
 Statistical case CW analysis can be computed by assuming normal distributions to 

the range of CW for individual parts, with the mean being the nominal value and x

standard deviations spanning the range of CW. Such an assumption of normal 

distribution in manufacturing environment is justified because of the central limit 

theorem. For further details please refer to [26]. The mean and the standard deviation of 

the assembly level CW can be obtained as shown in equation (A-1) and (A-5), 

respectively. 

 

............................................(A-5) 2 2

2

2

1

2 ... a   N

Equation (A-5) represents the standard deviations of the CW distribution for the assembly 

if the individual CW of the parts are independent of each other. In case they are not 

independent, a correlation (12, 23, etc.) between each of them would need to be 

computed. The standard deviation of the assembly CW would then be computed from 

equation (A-6). 

 

 ..................................(A-6) 









ji

Nj

Ni

a N jiij

..1

..1

2 2

2

2

1

2 ... 

When allocating CW, for the worst-case allocation, consider equation (A-4). If all the 

CWi’s are assumed to be equal but unknown values, then each CW can be found from 

a given assembly CWa as 

CW = CWa/N.................................................(A-7) 

For statistical-case allocation, consider equation (A-5). As an example, assume that all 

the CWi’s are equal and unknown. Since the CWi’s are equal, their standard deviations 

are also equal, let’s say CWi = 6. Then, the value of CW can be obtained from a 

given assembly CWa by substituting i (=CWi/6) and a (=CWa/6) values in 

equation (A-5) as shown in equation (A-8). 

22 
23 

N

CW CW

CWNCW

a

a

 

 222

...............................................(A-8)