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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 06, June 2019, pp. 323-332, Article ID: IJMET_10_06_028
Available online at
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
THE EFFECTS OF BOLT PRELOAD ON
VIBRATION AMPLITUDE OF GANTRY CNC
ROUTER
Nguyen Huu Loc, Tran Van Thuy
Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology,
VNU-HCM (HCMUT)
ABSTRACT
The joint prop

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perties signiﬁcant affect on the dynamic performance and spindle
vibration of gantry CNC router structure. This paper presents the relationship
between the vibration amplitude of the spindle nose of a gantry CNC router and a bolt
pre-tightening force. The dynamic model from machine structures with bolt joints was
developed to consider the impact of a bolt pre-tightening force to spindle vibration of
CNC router structures and dynamic behavior. Based on the dynamic model, harmonic
analysis is conducted to specify the spindle nose’s displacement corresponding to the
different bolt pre-tightening force. The FE analysis results indicate that bolt pre-
tightening forces have great influence on the spindle nose vibration amplitude and
when the pre-tightening force of bolt joints was increased, the dynamic stiffness of the
spindle also increases while the vibration amplitude decreases. The accuracy and
effectiveness of the model have also been confirmed by experimental results. The
achieved result will enhance the rigidity, improve the vibration resistance of the
machine structure to improve the reliability as well as machining precision, and attain
the best surface quality
Key words: Pre-tightening force, FE analysis, vibration amplitude, harmonic analysis,
dynamic stiffness, CNC router.
Cite this Article: Nguyen Huu Loc, Tran Van Thuy, The Effects of Bolt Preload on
Vibration Amplitude of Gantry CNC Router. International Journal of Mechanical
Engineering and Technology 10(6), 2019, pp. 323-332.
1. INTRODUCTION
In the modern furniture industry, gantry CNC router are widely utilized, especially when high
quality of products and flexibility of the manufacturing process are expected. The dynamic
behaviors of the gantry CNC router involve to its capacity to prevent the vibrations in the
manufacturing. The CNC router is consists of many parts, for example, the welding, the guide
rail, the bolt connection, etc. The continuity of the machine structure is demolished due to the
existence of different joints in the machine structure. Hence both components and dynamic
properties of joints could have an influence on its dynamic properties (Lee et al., 2006; Liang
et al., 2013). Studies indicate that about 90 percent of the total damping and approximately 60
The Effects of Bolt Preload on Vibration Amplitude of Gantry CNC Router
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percent of total dynamic stiffness (G. P. Zhang et al., 2003). It is important to research how
the dynamic parameters of joint influence the dynamic properties of a CNC router.
Investigates about the joints concentrated on joint parameters identification, the dynamic
modeling of the dynamic and the joints behaviors of a whole gantry CNC router ( Li et al.,
2010; Mao et al., 2010). Based on the vibration experiment and the finite element simulation,
the linear guide slides joint influence the dynamic parameter in the column and spindle of the
machine. Its dynamic properties have been improved while the preload of the guide is
increased (Lin et al., 2010). To investigate the dynamic properties of guides influenced by
preload of joints, contact stress was introduced and used shear/normal stiffness to the contact
elements of the FE model. At the overall stage of machine design, a model of the whole
machine is set up. The components include a mass beam, a distributed lumped mass, and
joints to predict the dynamic characteristics. According to the dynamic values of the joints on
machine structure, the dynamic equations with this synthesis have been established. (G.
Zhang et al., 2001).
One of the most important operating parameters of CNC machines is the preload on the
joint. Studies show that preloads have a major impact on damping and stiffness of the
machine joints (Li et al., 2010; Mao et al., 2010). In other studies, a preload technology of
roller bearings for machine spindle has been extensively analyzed (Cao and Altintas, 2004;
Hwang and Lee, 2010b; Jiang and Mao, 2010). Various devices rely on electromagnetic and
centrifugal forces are proposed to control the preload of the rolling spindle bearing (Hwang
and Lee, 2009, 2010a). It is important to research a relationship between the preload of joints
on machine structures such as bolts, bearings, ball screws, linear guides, and dynamic
stiffness, the vibration amplitude of spindle head. Accurate analysis of such relationships is
useful in applying an appropriate preload
This paper aims to explore the effect of pre-tightening force on vibration amplitude of the
spindle nose of gantry machine structure. For this, this paper proposes the FE model of the
gantry CNC router with the integration of bolt joints model. With FEM, stiffness and
vibration amplitude under different pre-tightening forces are predicted. Results indicate that
bolt pre-tightening forces on CNC router have a significant impact on the stiffness and spindle
head vibration amplitude.
2. DYNAMIC CHARACTERISTIC OF BOLT JOINT
The gantry CNC router of 800x800x320 mm was designed. The machining operation speed of
12000 rpm and accuracy of 0.05mm were predicted as the capability of this machine. The
CNC router model is illustrated in Fig. 1.
Figure 1 Model of the gantry CNC router structure
Nguyen Huu Loc, Tran Van Thuy
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There are four types of joints in the gantry CNC router, which are respectively bearing,
bolt joint, linear guide and a ball screw (Mi et al., 2012; Shulong, 2010). The article is
primarily interested in determining the dynamic characteristics of bolt joints and create their
dynamic models.
A typical type of fixed joint is a bolt joint that is widely available in the gantry CNC
router structure. The analysis indicates that the dynamic properties of bolt joints depend on
many components, some of which
are material, appearance, pressure, geometry shapes, etc.
(Li et al., 2010; G. P. Zhang et al., 2003).
In Fig. 2. illustrates a typical bolt joint of CNC
router structure including bolts, nuts, details A and B.
Figure 2 Modeling of bolt joint
The simulation of joint characteristics with high precision conditions is a complex
problem. The gantry CNC router is divided into several independent parts. Where the
connection of face-to-face are ignored, the joints of these parts are associated with damping
and spring.
To tighten the bolt with pre-tightening force V, it is necessary to have a pre-tightening
moment TV on the bolt body with the torque acting on the thread Tr to prevent the bolt from
rotating in Fig. 3. Then:
V f rT T T (1)
Where Tf is the friction moment between two surfaces of detail A and nut. Tf, Tr are
calculated by Eq. (2) and Eq. (3).
0 0
f
D dVf
T
2 2
(2)
r t 2 2T 0.5Fd 0.5Vd tan ' (3)
Figure 3 Load conditions of bolt joints
The Effects of Bolt Preload on Vibration Amplitude of Gantry CNC Router
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Substituting the expressions for defining Tr and Tf in Eq. (1). Eq. (1) can be rewritten as:
'tan
2
5.0
2
00
2 f
d
dD
VdTV (4)
Where, d0, d2, D0, f, ’ represent the pitch diameter of the threaded hole, the average
diameter of the thread, the nut diameter, the friction coefficient between the surface of detail
A and the nut, the lead angle and the equivalent friction angle respectively.
For every joint of the bolt, the dependence between pre-tightening force V and pre-
tightening moment TV are described as Eq. (5).
KVdTV
310 (5)
Where the tightening coefficient is K, the nominal bolt diameter is d. This coefficient
depends on the bolt thread, surface friction, size and material and is described as Eq. (6).
'tan
2
5.0
2
002 f
d
dD
d
d
Vd
T
K V (6)
The bolt joint pressure is shown as Eq. (7).
A
dD
dD
fD
T
P V
2
0
2
0
3
0
3
0
3
2'tan
2
(7)
Where D and A are the nut nominal diameter and area of bolt joints
In many cases, there are many bolts in the bolt joint. Assuming that the applied force is
the same for each bolt (Mi et al., 2012), the pressure is described as Eq. (8).
AN
dD
dD
fD
T
P V
2
0
2
0
3
0
3
0
3
2'tan
2
(8)
Where the number of bolts is N.
Dynamic stiffness of the bolt joints can be calculated by Eq. (9) (Xu et al., 2012).
dxdyRfSPkK ii ,,, (9)
Where S is the joints surface area, f is the frequency of load, P is the bolt joint pressure,
and ki is obtained from the identification of joints .R relates to the machining method of
surface and the properties of the material.
From Eq. (9), it is found that the stiffness of Ki bolt joints depends on the tightening
pressure of the bolt joints. Besides, structure stiffness depends greatly on the stiffness of bolt
joints. Consequently, it can be concluded that the tightening pressure of the bolt joints greatly
affects the stiffness of the whole CNC router. In this way, the stiffness of the whole CNC
router is confirmed by FEM, and compared with the experimental method.
3. FINITE ELEMENT ANALYSIS
Using ANSYS Workbench performs finite element analysis and solid elements to create a
mesh for machine structure model. The material of all bodies is steel with E = 2.06×10
11
Pa
with ρ = 7850 kg/m3 (density) and ν = 0.3 (Poisson’s ratio). Alloy structural steel made the
M8 bolts with elastic modulus E = 2×10
11
Pa with ρ = 7830 kg/m3 (density) and ν = 0.32
(Poisson ratio). The FEM of the gantry CNC router is illustrated in Fig. 4.
Nguyen Huu Loc, Tran Van Thuy
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Figure 4 The FEM of the CNC router structure
Application of finite element method performs the modal and harmonic analysis for CNC
router structure. The modal analysis determines the dynamic performance of gantry CNC
machines such as mode shapes and natural frequencies. With natural frequencies, the gantry
CNC router can dodge resonant frequency in the manufacturing process. The results of the
natural frequencies analysis of machine are described in Fig. 5. At the first natural frequency
of 200.71 Hz, the headstock has twisted vibration around the X-axis as described in Fig. 5a.
At frequency 294.44 Hz, the headstock and cross beam has a swaying movement in the YZ-
plane as described in Fig. 5b. At the frequency 352.83 Hz, the column has bending vibration
in the XZ plane as described in Fig. 5c. At the frequency 433.88 Hz, the cross beam has
bending vibration in the XZ-plane as described in Fig. 5d. At the frequency 610.88 Hz, the
cross beam and headstock have twisted vibration around the X-axis as described in Fig. 5e. At
the frequency 696.91 Hz, the headstock has a twisted vibration around the Z-axis as described
in Fig. 5f.
(a) ( b) (c)
(d) (e) (f)
Figure 5 The natural frequency and vibration modes obtained from FEM
The Effects of Bolt Preload on Vibration Amplitude of Gantry CNC Router
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Harmonic analysis is carried out to specify vibration amplitude and response of spindle
head of gantry CNC router structure based on the external excitation force. The analytical
results are illustrated in Fig. 6.
(a) X Direction FRF (b) Y Direction FRF
(c) Z Direction FRF
Figure 6 Results of harmonic response analysis
4. THE INFLUENCES OF PRE-TIGHTENING FORCE ON THE
VIBRATION AMPLITUDE OF SPINDLE
Maximum cutting parameters valued as follows: cutting speed n = 6000 rpm, feed rate s =
6000 mm/min and cutting depth t = 3 mm. With the maximum cutting parameters, calculate
the cutting force as follows direction X and direction Y: FX = FY = 390N. The harmonic
analysis was performed with bolt joint under different pre-tightening forces and the external
excitation force FX = FY = 390N as shown in Table 1.
Table 1 Harmonic analysis results
N
0
Pre-tightening
force, kN
Vibration amplitude of spindle
head, mm
ux uy
1 5.0 0.057 0.069
2 5.5 0.045 0.062
3 6.0 0.039 0.056
4 6.5 0.033 0.047
5 7.0 0.029 0.038
6 7.5 0.025 0.031
7 8.0 0.021 0.027
8 8.5 0.016 0.024
9 9.0 0.013 0.020
10 9.5 0.012 0.018
Nguyen Huu Loc, Tran Van Thuy
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The analytical results indicate that with each of pre-tightening force values, it is possible
to determine the vibration amplitude value of spindle nose in the directions of X and Y
respectively. Also, when pre-tightening force value of bolt joints increased, the vibration
amplitude value of spindle nose in the directions of X and Y decreased respectively.
5. EXPERIMENTAL SETUP
The experimental setup is illustrated in Fig. 7. Experimental devices include the system of
Multi-Channel NI SCXI-1000DC, accelerometer sensor PCB 603C01, sensitivity 10.2 mV/g,
PCB Group, and the NI Signal Express software. The experiments were carried out at the
spindle nose in the machine structure. Machining materials are fir wood. The NI SCXI-
1000DC vibration analysis is connected to a computer and acceleration sensor; the
acceleration sensor was connected to the spindle nose of a CNC machine. The measured data
is analyzed and processed on NI Signal Express software.
Figure 7 Experimental setup
Performing ten experiments with different pre-tightening forces, every test was performed
seven times. The average findings of the measurement of vibration amplitude are illustrated in
Table 2
Table 2 Experimental results
N
0
Pre-tightening
force, kN
Vibration amplitude of spindle head, mm
Harmonic analysis
method
Experimental method Relative error
%
ux uy xu yu %ux %uy
1 5.0 0.057 0.069 0.065 0.077 12.30 10.4
2 5.5 0.045 0.062 0.050 0.068 10.00 8.82
3 6.0 0.039 0.056 0.045 0.064 13.33 12.50
4 6.5 0.033 0.047 0.038 0.055 13.16 14.55
5 7.0 0.029 0.038 0.034 0.044 14.70 13.64
6 7.5 0.025 0.031 0.029 0.036 13.78 13.89
7 8.0 0.021 0.027 0.024 0.031 12.50 12.90
8 8.5 0.016 0.024 0.018 0.028 11.11 14.29
9 9.0 0.013 0.020 0.015 0.023 13.33 13.04
10 9.5 0.012 0.018 0.014 0.021 14.29 14.28
The accuracy of the simulation method is proposed in the article has been tested by the
experimental method. Comparison of the vibration amplitude of the spindle head using the
simulation method and experimental method with the same input conditions illustrated in
Table 2. The greatest relative error in the vibration amplitude of the spindle head is less than
The Effects of Bolt Preload on Vibration Amplitude of Gantry CNC Router
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15%. The difference between the experimental method and the simulation method are
associated with the geometry simplifications, relatively coarse mesh and damping coefficient.
(a) X direction ( b) Y direction
Figure 8 The effects of bolt preload on vibration amplitude
Regression model for X direction:
Simulation method: Y1 = 0.1721 - 0.03081V + 0.001470V
2
Experimental method: Y2 = 0.1899 - 0.03337V + 0.001561V
2
Regression model for Y direction:
Simulation method: Y3 = 0.2080 - 0.03561V + 0.001636V
2
Experimental method: Y4 = 0.2160 - 0.03505V + 0.001515V
2
Following the Fig.8, the dependence of the spindle nose vibration amplitude on a pre-
tightening force. It is shown that the vibration amplitude decreases with increasing the pre-
tightening force.
6. CONCLUSIONS
This article studies the significant influences of the vibration amplitude of the spindle nose
based on bolt pre-tightening force. The FEM of the whole gantry CNC router about the effects
of joints is created. This model exactly predicts and simulate the dynamic properties of the
gantry CNC machine. Effects of various bolt pre-tightening forces on the machine structure
are careful analyzes. It indicates that pre-tightening force on the joint of the gantry CNC
router has a relationship to the vibration amplitude of the spindle nose. The simulation and
experimental results indicate that when bolt pre-tightening force was increased, the dynamic
stiffness of spindle also increases while the vibration amplitude of the spindle head decreases.
According to the above results, some frequencies of dynamic stiffness decrease and thus
decline the dynamic performance in the gantry CNC router. The accuracy of the simulation
method proposed in the current study has been tested through experimental method. The error
between the experimental results and the simulation are less than 15%. The difference
between the experimental method and the simulation method are associated with the
simplifications of geometry, relatively coarse mesh and damping coefficient.
ACKNOWLEDGEMENT
This research is funded by Vietnam National University - Ho Chi Minh City (VNU-HCM)
under grant number B2016-20-04.
Nguyen Huu Loc, Tran Van Thuy
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