Yuta Tsukii , Libo Zhou2,b, Hirotaka Ojima2,c, Jun...

Development of wireless dynamometer for rotary infeed surface grinding

Yuta Tsukii1,a*, Libo Zhou2,b, Hirotaka Ojima2,c, Jun Shimizu2,d,

and Teppei Onuki2,e

1Graduate School, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Japan 316-8511

2School of Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Japan 316-8511

[email protected], [email protected], [email protected], [email protected],

[email protected]

Keywords: grinding force, dynamometer, rotary infeed surface grinding machine, grinding

Abstract. Many functional materials like Si, SiC, α-Al2O3, GaN fall in wafer form. For such wafer

manufacturing, rotary infeed surface grinding (RISG) is used. However, RISG dynamics, in which

both grinding wheel and wafer rotate around their own axes, is different from that of the conventional

reciprocating surface grinding. For this reason, the conventional wired dynamometers are not able to

be applied in RISG. Consequently, the material removal mechanism of RISG is not sufficiently

clarified. In this research, we have developed a wireless dynamometer to measure grinding force in

RISG. The dynamometer consists of an aluminum octagonal ring, 2 × 4 strain gages, Wheatstone-

bridge circuits, operational amplifiers, a 12bit AD converter, a Bluetooth transmitter and an internal

data storage. The dynamometer is installed in one segment of grinding wheel, can measure the

grinding force components (𝐹𝑡, 𝐹𝑛 ) in both tangential and normal directions during the contact

between the wheel segment and wafer. The estimated measurement range and resolution of the

dynamometer are 1~100[N] and 0.05[N] respectively. In addition, the dynamometer can measure the

distribution of grinding force along the wafer radical distance. The dynamometer was then applied

in silicon wafer grinding. 𝐹𝑡, 𝐹𝑛 and 𝐹𝑛/𝐹𝑡 are evaluated. Both d𝐹𝑡 and d𝐹𝑛 are linearly proportional

to the wafer radius. 𝐹𝑛/𝐹𝑡 is found to be about 2.

Introduction

Wafer formed functional materials are often used as substrates by semiconductors in

manufacturing ICs and LEDs. In recent years, due to high integrity and miniaturization of electronic

devices, the demand for thin wafers is increasing. For such wafer processing, rotary infeed surface

grinding (RISG), as shown in Fig. 1, is often used. RISG dynamics, in which both grinding wheel

and wafer rotate around their own axes, is different from that of the conventional reciprocating surface

grinding. Our knowledge on conventional grinding dynamics is insufficient to cover RISG. When

the grinding force is concerned, which is an important factor of elucidation of the material removal

mechanism, the conventional wired dynamometers are not able to be applied in RISG. As the

grinding force affects damage and warpage during thinning process of wafer [1~3], it is therefore

essential to develop a dynamometer which is able to measure the grinding force components in RISG.

Although similar wireless systems have been proposed by M. Sakakura and M. Shindou to measure

the temperature in cylindrical plunge grinding and end-milling [4~5], in this article, we have

developed a wireless dynamometer for RISG, as illustrated in Fig. 1, and evaluated the change of

grinding force during the contact zone with silicon wafer.

Wireless dynamometer development

The outline of the system of developed wireless dynamometer is shown in Fig. 2. The

dynamometer consists of an aluminum octagonal ring, 2 × 4 strain gages, two Wheatstone-bridge

circuits, operational amplifiers, a 12bit AD converter, a Bluetooth transmitter and an internal data

storage. Octagonal ring has two sets of 4-straingages affixed, in which A1~A4 strain gages constitute

Wheatstone-bridge circuit to measure normal grinding force (𝐹𝑛) while B1~B4 strain gages constitute

905

Proceedings of the 20th International Symposium on Advances in Abrasive Technology 3-6 December, Okinawa, Japan

mailto:[email protected]



mailto:[email protected],

Wheatstone-bridge circuit to measure tangential grinding force (𝐹𝑡). A built-in battery powers the

system.

The resistance of strain gages in each circuit changes proportionally to the deformation of

octagonal ring in either normal or tangential direction, which is in turn proportional to 𝐹𝑛 or 𝐹𝑡 respectively [6]. The Wheatstone-bridge circuits would then output response voltages corresponding

to 𝐹𝑛 or 𝐹𝑡 [8]. The output voltages are first amplified by × 200~1000, then converted into a digital

signal by a 12-bit AD converter at sampling frequency of 2 kHz. The digitized signals can be either

sent out by the Bluetooth transmitter or saved into the internal data storage [9]. The specifications of

developed dynamometer are listed in Table 1.

The calibration results of the developed dynamometer are shown in Fig. 3, in which the

amplification factor was fixed at × 500. It was found both response voltages are linearly proportional

to grinding force components 𝐹𝑛 and 𝐹𝑡 within the full range of 3.3 volts. The cross-talk of each

component was negligible.

Fig.1 Overview of rotary infeed surface grinding and wireless dynamometer

Fig.2 Configuration of developed wireless dynamometer

Table 1 Specifications of developed dynamometer

Amplification 200 ~ 1000

AD converter 12 bit (LPC1768) [7]

Bluetooth device RN-42XVP

Resolution [N] 0.05

sampling frequency [kHz] 2

Measurement range [N] Up to 100

wafer

Wireless dynamometer

Grinding wheel segment

n1

n2

f

Strain gage

Octagonal

Dynamometer

A2 A3A1

B2

A2A2

B4B3

B1

1. Power supply

2. Amplifier

3. ADC

4. Bluetooth transmitter

5. Data storage

Grinding

segment

Wafer

A1

A4A2

A3

B1

B4B2

B3

Fn

Ft

Bridge circuit A

Power supply

Bridge circuit B

Amplifier

Amplifier

ADC

Bluetooth

transmitter

PC

906

Advances in Abrasive Technology XX

The developed dynamometer is able to measure both 𝐹𝑛 and 𝐹𝑡 simultaneously in real

grinding time. As the segment moves across the wafer, the developed dynamometer also records the

distribution/variation of grinding force along the cutting path of wheel segment traced.

Installation and test

The developed dynamometer is installed as one of wheel segments, as shown Fig. 4. The

octagonal ring together with SD1000 underneath is fixed to the wheel spindle by a designed jig. The

size of SD1000 attached to the dynamometer is 4 × 5 mm2. Grinding test was performed on a Si

wafer while the forces were measured by using the developed dynamometer. The grinding conditions

are shown in Table 2.

Fig. 5 records the typical grinding force (a) at wheel speed 𝑉1 = 200 m/min while (b) at 𝑉1 =400 m/min, for two turns of wheel rotation. When the wheel revolution speed is doubled, it is found

that both grinding interval and grinding forces become halved.

Fig.3 Calibration of developed dynamometer

Vt = 0.1467Ft + 0.546

Vn = -0.0344Fn + 3.0503

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30 35

Outp

ut

Volt

age

V

n, V

t(V

)

Force Fn , Ft (N)

Ft

Fn

Ft

Fn

Fig.4 Implementation of developed wireless dynamometer

Table 2 Grinding conditions

Wheel segments, size (mm2) SD1000M, 4 × 5

Wheel rotation speed (m/min) 200, 400

Wafer rotation speed (min-1) 25

Wheel down-feed rate (µm/min) 2

Coolant Dry

907


Results and discussion The wafer volume removed in one wheel revolution in RISG is illustrated in Fig. 6 (a), in

which, the wafer is constantly removed in a spiral manner. At the stable state of grinding, therefore,

the depth of wheel engagement is given as;

∆=𝑓

𝑛2 (1)

where 𝑓 is the feed rate and 𝑛2 is the wafer revolution. The wafer can be considered as a bunch of

aggregated concentric annulus with different radical distance. The engagement between the wheel

and the annulus located at the wafer radical distance [𝑟2, 𝑟2 + d𝑟2 ] is zoomed up in Fig. 6 (b). The

side surface area 𝑆2 removed in one wheel revolution is express in Eq. (2).

𝑆2 = 2𝜋𝑟2𝑛2𝑛1∆= 2𝜋𝑟2

𝑓

𝑛1 (2)

During one revolution of wheel, the number of cutting edge passing through that side surface

𝑆2 is given as 𝐿 ∙ 𝑊 ∙ 𝑁𝑒/cos𝜃, where 𝐿,𝑊 are the length of wheel circumference and wheel width

and 𝑁𝑒 is the density of effective cutting edge in a specific area. Therefore, the average cross-

sectional area cut by an individual grain at the wafer radical distance 𝑟2 is calculated as below;

𝑎𝑔(𝑟2) =𝑆2cos𝜃

𝐿 ∙ 𝑊 ∙ 𝑁𝑒=2𝜋

𝐿

cos𝜃

𝑊 ∙ 𝑁𝑒

𝑓

𝑛1𝑟2 (3)

It is obvious that the average cross-sectional area of chip is proportional to the in-feed rate 𝑓,

reversely propotional to the wheel revolution speed 𝑛1. Also, 𝑎𝑔 increases as an increasing in the

wafer radical distance 𝑟2. The cutting force can be considered as the product of the specific removal

energy 𝐶𝑝 and chip cross-sectional area 𝑎𝑔. Therefore, the grinding force created by an individual

cutting edge at the wafer radical distance 𝑟2 is expressed as;

{

𝑓𝑡 = 𝐶𝑝 ∙ 𝑎𝑔(𝑟2) =2𝜋𝐶𝑝

𝐿

cos𝜃

𝑊 ∙ 𝑁𝑒

𝑓

𝑛1𝑟2

𝑓𝑛 = 𝜇 ∙ 𝑓𝑡 =2𝜋𝜇𝐶𝑝

𝐿

cos𝜃

𝑊 ∙ 𝑁𝑒

𝑓

𝑛1𝑟2

(4)

where 𝜇 is the force component ratio of 𝐹𝑛/𝐹𝑡. Within wafer radical distance [𝑟2, 𝑟2 + d𝑟2], the total

number of grains simultaneously engaged into the wafer is given as 𝑁𝑒 ∙ 𝑊 ∙ d𝑟2/cos𝜃. The grinding

force generated at [𝑟2, 𝑟2 + d𝑟2] is therefore calculated as;

(a) 𝑉1=200 (m/min) (b) 𝑉1=400 (m/min)

Fig.5 Recorded grinding force

-1

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6

Gri

nd

ing

forc

eF

n, F

t(N

)

Grinding time t (s)

Fn

Ft

n

t

-0.5

0

0.5

1

1.5

2

2.5

0 0.05 0.1 0.15 0.2 0.25 0.3

Gri

nd

ing

forc

eF

n, F

t(N

)

Grinding time t (s)

Fn

Ft

n

t

908


{

d𝐹𝑡 = 𝑁𝑒 ∙ 𝑊 ∙ 𝑑𝑟2

cos𝜃∙ 𝑓𝑡 =

2𝜋𝐶𝑝

𝐿

𝑓

𝑛1𝑟2d𝑟2

d𝐹𝑛 = 𝑁𝑒 ∙ 𝑊 ∙ 𝑑𝑟2

cos𝜃∙ 𝑓𝑛 =

2𝜋𝜇𝐶𝑝

𝐿

𝑓

𝑛1𝑟2d𝑟2

or

{

𝐹𝑡 =𝜋𝐶𝑝

𝐿

𝑓

𝑛1𝑟22

𝐹𝑛 =2𝜋𝜇𝐶𝑝

𝐿

𝑓

𝑛1𝑟22

(5)

(a) Wafer removal in one revolution of wheel (b) Detailed engagement at 𝑑𝑟2

Fig. 6 Wheel/wafer interference

(a) Force component 𝐹𝑛

(b) Force component 𝐹𝑡

Fig. 7 Change of grinding force along wafer radial distance

0

1

2

3

4

5

6

0 20 40 60 80 100

Gri

nd

ing

fo

rce

F

n(N

)

Wafer radical distance r2 (mm)

Measured V1=200 (m/min)


Analyzed V1=200 (m/min)






0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100

Gri

nd

ing

forc

eF

t(N

)

Wafer radical distance r2 (mm)









909


d𝐹𝑡,𝑛 stands for the distribution of grinding force along the wafer radical distance, while 𝐹𝑡 is

the total grinding force generated across the whole wafer. It is found that both d𝐹𝑡,𝑛 and 𝐹𝑡,𝑛 are

proportional to the in-feed rate 𝑓, reversely propotional to the wheel revolution speed 𝑛1. However,

d𝐹𝑡,𝑛 is proportional to 𝑟2, but 𝐹𝑡,𝑛 is proportional to the squares of 𝑟2.

Fig. 7 plots two sets of grinding force as a function of the wafer radical distance 𝑟2; one is

measured in actual grinding experiment as shown in Fig.5, the other is analyzed via Eq. (5). They

well agree one to another, for two different wheel speeds. The force components ratio 𝐹𝑛/𝐹𝑡 is found

to be about 2. However, the experimental results were slightly larger than analyzed data at the wafer

radical distance of 40 ~60 mm. This difference mainly attributes to that the initial wafer surface was

not flat enough to keep the depth of wheel engagement consistent. It can be therefore concluded that

the developed dynamometer is functional correctly and accurately in RISG.

Summary

In this paper, a wireless dynamometer is designed and developed to monitor the grinding force

in RISG. The obtained results can be summarized as below:

1) The wireless dynamometer is able to measure grinding force components (𝐹𝑡, 𝐹𝑛 ) in both

tangential and normal directions in RISG dynamics.

2) Not only the total grinding force but also the distribution of grinding force in the wafer radical

direction can be measured correctly and accurately as compared with analyzed results.

3) The grinding force is funded to be proportional to the wafer radical distance and the in-feed rate

𝑓, reversely propotional to the wheel revolution speed.

Acknowledgement

This research was financially supported by JSPS KAKENHI, Grant-in-Aid for Scientific Research

(A) (No. 15H02213), and Exploratory Research (No. 15K13840).

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