Thermal investigations on CNC lathe fitted with dynamically enhanced steel reinforced epoxy granite bed

doi:10.21203/rs.3.rs-1531804/v1

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Thermal investigations on CNC lathe fitted with dynamically enhanced steel reinforced epoxy granite bed

https://doi.org/10.21203/rs.3.rs-1531804/v1

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Polymer concrete or epoxy granite is now becoming more popular for beds, bases, and other structures of precision machine tools, owing to its excellent damping characteristics. In order to realize the same static rigidity as that of the cast-iron structures, steel-reinforced epoxy granite (SREG) structures are being used. The vast differences in the thermal properties of steel and epoxy granite (EG) are likely to cause higher magnitudes of thermal error. The objective of this work is to investigate the thermal behavior of a CNC lathe built with an SREG bed and compare its performance with the lathe with cast iron bed. Experimental and numerical investigations have been carried out under cross feed drive (CF) idle running conditions to determine the TCP deformation. The results reveal that the thermal error in the CNC lathe with SREG bed is 1.68 times that of the lathe with CI bed at 20ºC and 1.8 times at 40ºC environmental temperature variation chamber (ETVC) conditions. It could be identified that the heat generated in the CF is conducted to the steel guideways embedded in the SREG bed, but further heat transfer to the EG portion of the bed is impeded and hence the heat accumulation that occurs in the guideways leads to higher magnitude of thermal error. The experimentally validated numerical model is used to extend the investigations to study the effect of the idle running of the longitudinal feed drive (LF), and combined cross and longitudinal feed drives, on the thermal behavior of the lathe.

Precision machine tools

thermal error

steel reinforcement

epoxy granite

Machining accuracy is a crucial parameter in the development of precision machines. Since machine tool performance is governed by static, dynamic, and thermal stability, designers must contemplate these aspects at every stage of development. Different materials with desired properties are used for various machine tool components. Cast iron is commonly used as a material for base or bed since they are important parts that hold all the other parts together and also has the functionality of absorbing shocks and vibrations [1], [2]. Instead of cast iron, mineral castings such as tailor-made polymer concrete materials have gained popularity in recent years for use in high performance and high-speed machine tools to ultra-precision machines and metrology applications, due to their excellent damping characteristics [3]–[5].

Mineral castings are light in weight and necessitate lower development and handling costs. A wide range of polymers and particulates have been used to develop custom-made polymer concrete for machine tool structures[6], [7]. Epoxy granite (EG) is a type of tailor-made material that belongs to the polymer concrete group[8]. EG has a very high damping capacity, seven to ten times that of the conventional cast-iron but has a low modulus of elasticity[3], [9]–[11]. EG can be used as a machine tool structural material to achieve better dynamic performance, by improving the stiffness by the application form design principles and the use of metal reinforcements[12]–[14].

When a machine tool structure made of cast iron is to be replaced with one made of EG material in an existing machine tool, the footprints of the conventional CI bed have to be maintained to meet assembly requirements. In such cases, rather than adopting form design modifications, metal reinforcements have to be employed to increase the static rigidity significantly [15]. S. Chinnuraj et al. [15] presented the static and dynamic characteristics of CNC lathe with CI bed and SREG bed. Experiments revealed that the dynamic performance of the lathe with SREG bed improved considerably compared to that of the lathe with CI bed.

Another advantage of EG is that its thermal conductivity is very low which aids in maintaining thermal stability under different climatic conditions associated with environmental temperature variations[16], [17]. But it is vital to investigate the total machine tool's thermal behavior and the thermal error under the influence of heat generated internally due to friction in bearings, guideways, and other moving assemblies. Thermal error accounts for 30–70% of overall error in machine tools[18], [19]. Although EG is thermally stable, since it is reinforced with steel whose thermal conductivity is much higher than that of EG, a bi-material effect can arise as the temperature of the machine tool rises and heat flows through the reinforcement in epoxy granite structures, resulting in thermal inaccuracies. The objective of this work is to study the influence of the bi-material effect (different thermal properties) of steel and EG on the thermal behavior of the lathe, in comparison to that of the lathe with the existing cast iron bed. In this work, investigations on the thermal behavior of a CNC lathe built with an SREG bed have been carried out as a continuation of the static and dynamic investigations of this lathe presented by S. Chinnuraj et al. [15]. The methodology of the proposed research work is presented in Figure.1. The thermal error associated with SREG structures must be investigated in order to reap the full benefits of the thermally inert, high damping tailor-made EG material. Some feasible methods of reducing thermal error have prompted the use of EG material in precision machine tools. According to I.Tanabe and K. Takada [20] heat sources should be kept separated from polymer concrete structures in machine tools in order to reduce large thermal gradients.

Neugebauer et al. [21] reduced thermal error in a machine tool built with a mineral casting bed by isolating heat sources by providing a composite layer of different materials with different thermal expansion coefficients. Weidlich D et al. [22] studied thermal deformations in polymer concrete bed caused by local temperature gradients and provided additional steel fixings in linear guideways to improve heat conduction; investigations on such a method revealed a 30% reduction in deformation.

In this paper, to highlight the benefits of SREG structures for machine tools, brief insights on the static and dynamic analysis of lathe bed, VMC base, and VMC column have been explained in section-2. Experimental investigations on the thermal behavior of CNC lathe with CI and SREG beds have been presented in section-3. The development and validation of the numerical model have been discussed in section 4. The validated numerical model has been used to determine thermal error under the idle running of longitudinal feed drive and idle running of both cross and longitudinal feed drives and conclusions have been made and presented in section-5 and section-6 respectively.

Cutting forces induce twisting as well as bending on the machine tool structures, hence the machine tool bed/base/column must be rigid against both bending loads and twisting moments. This section contains an overview of the literature on the use of steel reinforcement to obtain equal stiffness for EG machine tool structures.

S. Chinnuraj et al. [15], P. R. Venugopal et al.[23], [24]carried out investigations on the application of SREG structures to CNC lathe and VMC. Static and dynamic investigations have revealed that the use of SREG structures in machine tools will enhance the static and dynamic performance of the machine. The authors developed numerical models of the structures and validated the same through experimental modal analysis; these validated models aid in the iterative design of steel reinforcements and the EG structure. Based on the numerical investigations, the best reinforcement design was chosen from among several proposed designs. SREG structures for CNC lathe and VMC with the best design configuration have been fabricated and tested for static stability and modal frequencies. Results revealed that the SREG structures have higher stiffness and natural frequencies than the respective CI machine tool structures, with significantly lesser mass. The material properties of steel, cast iron, and EG are represented in Table.1.

Table.1. Machine tool structures material properties

Property \ Material	Steel	Cast	Epoxy granite [15]
Density, kg/m³	7890	7890	2300
Modulus of elasticity, GPa	100	110	30
Poisson ratio,	0.27	0.24	0.25
Compressive strength, MPa	250	600	110
Flexural strength, MPa	380	450	36
Split tensile strength, MPa	-	-	24
Damping factor	0.0001	0.001	0.0176
Thermal conductivity, W/m^oC	50	50	0.5-1.5
Thermal expansion coefficient, /^oC	12x10^-6	6x10^-6	12x10^-6
Heat capacity, kJ/kg-K	400	400	700

The results of the static and dynamic analysis carried out on the SREG structures of the CNC lathe and VMC, with the finalized reinforcement configuration are presented in Table 2. The boundary and loading conditions applied to the CI structures were used for the respective SREG structures also. Torsional rigidity, natural frequency, and mass of the machine tool bed/base/column made up of CI and SREG are compared in Table 2.

Table.2 Static rigidity and modal parameters of CI and SREG structures

Reference

Measurement in respective machine tool structure

Static performance

First natural frequency (Hz)

Average damping ratio of structure

Mass

(kg)

SREG

Steel

S. Chinnuraj et al. [15]

Torsional rigidity of the lathe with different beds

7.32

(Nm/arc sec)

11.7

(Nm/arc sec)

258

276

0.0007

110

P. R. Venugopal et al. [23]

Deformation along y-direction in VMC base

18.8 µm

12.1 µm

133

370

0.0013

890

1041

P. R. Venugopal et al.[24]

Deformation at the spindle nose in VMC column

76.8 µm

75.2 µm

0.001

660

542

161

S. Chinnuraj et al. [15] developed five design configurations for the steel reinforcement and developed the SREG with Design configuration 5, shown in Figure 2, due to its improved torsional and significant positive shift in natural frequencies and 22% mass reduction as compared to CI bed. The torsional rigidity of the SREG bed was found to be 3.3 times that of the original CI bed. The developed SREG bed was fabricated and the numerical model was validated by conducting static and modal testing.

Even though the static and dynamic characteristics of the SREG bed developed have been proved to be superior to those of the original CI bed, the behavior of the SREG bed to thermal loads needs to be investigated. There is a possibility of bi-material thermal effect due to large changes in their operating conditions, ranging from extremely heavy loads encountered in rough machining cycles to extremely light loads encountered in finishing cycles. The results will aid in reconfiguring the reinforcement design to enhance heat transfer, thus reducing thermal error.

As shown in Figure.3, a CNC lathe was taken up for investigations on its thermal behavior. Length (L) and breadth or width (W) of the bed fitted in the machine tool is 975 mm and 344 mm. The distance from the bed bottom to the top surface is 405 mm. The dimensions of the machine tool are shown in Figure.3. Firstly, the experiments were carried out on the lathe which was originally built with a cast iron bed, under the cross feed drive idle running. Secondly, the studies were repeated on the lathe with the cast iron bed replaced with the newly developed SREG bed. To provide the same datum for measuring, pre-experiment adjustments and corrections must be made precisely; also, appropriate conditions as per standards and environmental temperature control should be maintained. The following assumptions are considered in the thermal behavior analysis.

As per ISO 230-3 standards, idle running of the machine tool feed drive is recommended, where the effect of machining is not considered since a large amount of cutting liquid is required in the machining process; thermal deformation between the cutting tool and parts being machined is ignored [25].
Since machining is not considered, the effect of chips is not factored.
The offset errors of the ball screws are already corrected by the controller parameters.
Since the experiments are carried out in a closed environment chamber, the environmental impact, such as magnetic field, humidity change, and vibration, is ignored since the primary objective of the research is to identify the discrepancy in CNC lathe performance with different beds.

Since TCP on the lathe turret is primarily associated with the moment of feed drives, the thermal behavior of feed drive has been considered separately to analyze its impact on the use of SREG bed on TCP, which is prompted by axis thermal growth of the feed drive. Methods for a systematic examination of the thermal behavior of machine tools are provided by the International Organization for Standardization (ISO). The ISO standard adhered to in this research is ISO 230-3 [26]. The loading cycle considered for thermal analysis is three minutes running and one minute idle. Temperatures at various locations and deformation at the TCP from the feed drive side were measured during machine run time from t=0 to t=360 min. (6 h.).

The different machining operations carried out on the machine tool demand fluctuating load cycles[25]. As per standards [26], the feed drive should run for 6 hours at the specified load cycle. The drive system's feed is to idle run at a maximum speed of 20 m/min for three minutes and stop for one minute. The load cycle is used to investigate the transient temperature variations in the machine structure as a result of intermittent and repeated machining circumstances.

Temperature, deformation measurement, and data extraction

Temperature sensors, RTD Pt100 are used for temperature measurement by gluing to different critical machine elements. Since major heat sources are in motion during experimentation, inaccessibility of all the locations, few sensors were mounted at critical locations as shown in Table 3. A laser interferometer (Make: Renishaw XL80) is used to measure x-axis thermal growth measurement. The XL- 80 environmental compensation unit is attached to the sidewall surface of the machine tool casing as shown in Figure 5 in order to minimize the influence of temperature and air pressure variation in laser interferometer measurement. Temperature data was taken from six distinct places, with details on the sensor locations provided in Table.3. The location of temperature and deformation sensors are represented in Figure 4. Temperature data is collected every one minute and deformation is collected every 15 minutes from the data acquisition system (DAQ).

In order to make a meaningful comparative study of the effect of using the SREG bed against the CI bed in CNC lathe, the thermal deformation of structures arising due to ambient temperature variations has to be eliminated by conducting the experiments under identical controlled environments. To maintain the desired environmental conditions, the entire test setup, along with the machine tool was kept in ETVC (Environmental Temperature Variation Chamber- Temperature variation range: 10°C to 65°C). The chamber was custom built by Kaladascope Climatic solutions to control temperature. Experimental investigations were carried out to measure thermal error at the TCP of the feed drive of the CNC lathe with cast iron and SREG beds by maintaining the temperature of the ETVC at 20^oC and 40^oC, to simulate typical operating conditions, below and above room temperature.

For conducting the thermal investigations, the complete machine tool is shifted to the chamber as shown in Figure.5. First, the lathe with CI bed was tested for thermal behavior at 20ºC and 40ºC ambient temperatures. After this, the complete machine tool was dissembled and assembled again with an SREG bed instead of CI bed. The soaking time required for the lathe with CI and SREG beds was found to be nearly the same, which is 4 hours for 20ºC and 7 hours for 40ºC environmental conditions. The machine tool has two feed drives: cross feed drive (CF) and longitudinal feed drive (LF). Since the standard testing procedure for the lathe with the original CI bed involves conducting experiments under cross feed drive idle running, the lathe with the SREG bed is also run with the cross-feed drive idle running.

Throughout the loading cycle, due to friction, several structures such as bearings, lock-nut, guideways tend to produce heat in 3 minutes of the running stage and tend to natural convection in one minute of rest. Electromagnetic losses from the drive motor will produce heat during functioning in the loading cycle. Due to motion, the lead screw and the structures seated on the feed drive are subjected to self-forced convection which is responsible for more heat dissipation. The heat generation in bearings, lock nut, guideways, and motor throughout the loading cycle will tend to generate heat. The heat from the heat sources is conducted to the surrounding structures, thus causing a thermal gradient in the machine tool structures. In such cases, the developed non-uniform temperatures could lead to expansion of structures resulting in thermal error. In Figure 5, notations +X and -X refers to distances away from and towards the operator respectively.

Analysis of thermal behavior under cross-feed drive idle running

The temperature measured from experiments at various sensor locations glued on the lathe with the CI bed and the SREG bed at 20^oC and 40^oC is depicted in Figure 6 and Figure 7 respectively. T1 represents the ambient temperature and the variation of the same is limited to 0.5 ^oC. Similarly, T2, T3, T4, T5, T6 represent the temperatures at LM block, drive motor, bed center, ball screw housing, and turret. Since T2 and T3 represent the temperature in the vicinity of heat sources, they are found to be higher in magnitude in all the experiments.

Deformation in the feed direction can be regarded as linear positioning error. Transient variation of X-axis thermal growth can be considered as a measure of thermal error. Transient variation of feed drive drifts in the lathe with CI bed and SREG bed at 20ºC and 40ºC environment temperatures are analyzed and the same is depicted in Figure 8. The trend of variation of the x-axis growth observed under 20ºC and 40ºC environment temperature conditions show the behavior of the machine tool typically at temperatures below and above room temperature. Since the difference from 20ºC to room temperature and 40ºC to room temperature is not similar, a slight difference with a similar trend in the opposite direction has been observed in the lathe with both the CI bed and SREG bed.

Thermal analysis of the lathe with CI bed at 20^oC and 40^oC ETVC

From Figure 7(a), at 20^oC from 0 min. to 360 min, the temperature difference of 8^oC, 11^oC, have been observed at T2, T3 respectively. From Figure 7(b), at 40^oC from 0 min. to 360 min, the temperature difference of 7.5^oC, 8^oC have been observed at T2, T3 respectively. The change in temperatures of the structures is a higher magnitude of temperature difference observed at 20^oC than 40^oC which refers to the rate of heat transfer being higher at 20^oC as compared to 40^oC.

From the temperature profile, a maximum temperature difference has been observed in the drive motor and LM block locations in the first 120 min. From 120 min to 360 min. the rise in temperature is less which reflects a low-temperature difference. hence the variation in x-axis thermal growth from 120 min to 360 min is low. The temperature of structures in the lathe with CI bed, from T2 to T6 reached steady-state reached after 120 min, whereas at 40^oC ETVC the steady-state has been identified after 300 minutes. From Figure 7 (b), the temperature profile of lathe with CI bed at 40^oC, the temperature rise among T2 to T6 locations increased gradually.

The temperature difference of all structures at 40^oC is less than the temperature difference of structures at 40^oC, hence the cumulative expansion of all structures at 40^oC will be lesser than the cumulative expansion of the same structures at 40^oC. At 20ºC chamber conditions, the thermal growth at TCP is in the negative direction (towards operator), the trend followed was identical to the that reported by the authors (L.Ruijun et al.[27], Z.Z. Xu et al. [28]). At 40ºC chamber conditions, the thermal growth at TCP is in the positive direction (away from operator), the trend followed was identical to the observation in experiments conducted by the authors (Y.Li et al. [29]).

Thermal analysis of the lathe with SREG bed at 20^oC and 40^oC ETVC

From the results, the temperature rise of the EG portion in the SREG bed is found to be low owing to its very low thermal conductivity. Higher temperature rise has been observed in the lathe with SREG bed than that in the lathe with CI bed, except in the bed itself.

Thermal analysis of the lathe with CI and SREG bed at 20^oC

From Figure 8, the x-axis growth in the lathe with the SREG bed is found to increase from 0 µm to 17 µm (towards operator side) in the time span of 0 min. to 150 min. Further, in the time span of 150 min. to 225 min. the x-axis thermal growth is found to remain unaltered, and then reversed from -18 (µm to -14.8 µm in the time span of 225 min. to 360 min. The start of the reverse trend is deemed as a sign of development of re-initiation of unsteady-state due to non-uniform temperature.

At 20ºC ETVC, the linear x-axis thermal growth at 360. min. in the lathe with CI bed is limited to 8.8 µm, whereas for the lathe with SREG bed, it is -14.8 µm. Due to more heat accumulation in the steel reinforcement, which is reflected as temperature rise in the lathe with SREG bed, more nonuniform temperature distribution leads to more thermal error than in the lathe with CI bed at 20ºC.

Thermal analysis of the lathe with CI and SREG bed at 40^oC

From Figure 8(a), the x-axis thermal growth in the lathe with CI bed from 0 min to 340 min. gradually increased from 0 µm to 9 µm. Further, from 340 min. to 360 min. there exist not much variation in the x-axis thermal growth. The x-axis thermal growth in the lathe with SREG bed from 0 min to 360 min. gradually increased from 0 µm to 17.8 µm. Since the lathe with CI bed took 340 min. to reach steady-state, there is the possibility of taking more than 360 min. to reach steady state for the lathe with SREG bed at 40 ºC. The linearity for the x-axis thermal growth of the lathe with SREG bed at 40ºC has not been observed in a time span of 0 min. to 360 min. Finally, the linear axis growth at 360 minutes of idle run in the lathe with CI bed is limited to 9 µm, whereas in the lathe with SREG bed is 17.8 µm.

From the experiments, the lathe with SREG bed exhibits 1.68 times higher thermal error at 20ºC and 1.88 times higher at 40ºC environment temperature than the thermal error in the lathe with CI bed. The higher thermal error in the lathe with SREG bed is due to the more heat accumulation in steel reinforcement. According to Weidlich D et al., the thermal deformations in a machine tool with a polymer concrete bed is higher, and such deformations are reduced by improving heat conduction with the help of additional steel fixings. The measurements of temperature and deformations at required locations under different conditions and the analysis of the same are possible with validated finite element modal. The development of FE model is presented in section-4.

A numerical model is developed to investigate the thermal behavior of the CNC lathe with CI bed and SREG bed, under the influence of idle running of cross-feed drive. To perform the analysis, the following assumptions were made:

Internal heat generation is given as heat input for bearings and ball screw.
Heat flow is given as input for frictional heat generation in guideways.
Heat generated by air friction loss can be ignored because it is insignificant in comparison to other heat sources
Small system structures such as nuts, holes, and so on are omitted
Heat transfer through radiation is not considered
On the bottom of the machine tool there exist no thermal deformation in the x, y, or z directions

4.1 Modeling of heat sources by analytical heat calculations

Since it is practically impossible to measure temperatures at locations of heat sources to serve as input data for numerical analysis, analytical models are used to estimate the generated heat and convection. The heat transfer mechanism from sources to other structures undergoes conduction, contact conduction, free convection, and forced convection. Figure 9 represents the method of modeling heat for various heat sources with analytical equations. Based on the above assumptions, the heat sources of the guideways were divided as follows:

1. Heat produced due to the sliding of the carriage relative to the guide block.

2. Heat generated by the bearings

3. Heat generated by the lock nut

4. Feed drive motor electromagnetic heat losses

The model is considered to have an initial preload which is further considered as radial load (F_r) and axial load (F_a) on the angular contact bearing are 477.34 N, and 500 N respectively. The feed rate is 20 m/min.

Heat generation in bearings

The torque and frictional heat due to friction in the bearings is calculated by the given Eq. (1)

𝐻_𝑏 = 1.047 ∗ 10⁻⁴∗𝑛𝑀_𝑏 (1)

Here, M_b is total frictional torque acting on bearing and n is shaft rotational speed, Total frictional torque, 𝑀_𝑏 = 𝑀₁ + 𝑀₂. Here M₁ is load related frictional torque and M₂ = Viscosity related frictional torque.

𝑀₁ = 𝑓₁∗𝐹_𝑏∗𝑑_𝑚 (2)

$${where, f}_{1}=0.001{\left(\frac{{P}_{0}}{{C}_{0}}\right)}^{0\cdot 33}$$

𝐹_𝑏 = 1.4𝐹_𝑎 − 0.1𝐹_𝑟

𝑃₀ = 2.3𝐹_𝑟𝑡𝑎𝑛𝜃 + 𝐹_𝑎

M ₂ = 10^− 7 f₀($\nu$₀n)^2/3d_m³, $\nu$₀n ≥ 2000 (4)

M ₂ = 160 $\times$ 10^− 7 f₀d_m³, $\nu$₀n ≤ 2000 (5)

𝑓₀ = 2𝑎𝑛𝑑𝑓₁ = 0.00043 are the parameters related to the type, the structure, the force and the lubrication of bearings. Kinematic viscosity (𝑣) of lubricant is 35 cSt, Rotational speed (𝑛) is 3000 rpm. The diameter of the pitch circle 9(𝑑_𝑚) is 33.75 mm. The calculated internal heat generation in the bearing is 453211.60 W/m³.

Heat generation in ball screw nut

The frictional heat generation between the moving nut and the ball screw is another important heat source. The efficiency of the screw nut (𝜂) is 95%, the diameter of the screw nut (𝐷_𝑚) is 20 mm Parameters 1(angle 𝛿) and 2 (angle 𝛼) in Eq. 7 are 28 ^º and 8.53^º respectively. Rotational speed(𝑛) is 3000 rpm.

H _s = 0.01πnM_s (6)

𝑀_𝑠= Total frictional torque of the ball screw system

𝑀_𝑠= $\frac{(1-\eta )W tan(\alpha +\delta )Dm}{2}$ (7)

Heat Generation in screw nut (H_s) is 170283.48 W/m³.

Heat generation in Guideways

Heat generation in guideways H _g = µF_aV (8)

The coefficient of friction (µ) is 0.12, the normal force acting on the guideway (F_g) is 500N, moving velocity (V) is 20 m/ min. Thus, H_g =20W. Motor heat losses are considered as 50W, and the same is given as heat flow to the surface of the drive motor. For free convection around stationary surfaces, the convection coefficient (h) is considered as 10 W/m² °C[19]. Average self-forced convection on rotary and reciprocating surfaces at the specified feed has been calculated as 35W/m² °C and 27 W/m² °C respectively. Boundary conditions are applied to the lathe model in transient thermal analysis in ANSYS workbench. Later, for thermo-mechanical analysis, transient thermal analysis is coupled with static structural analysis. In experiments, throughout the 6 h time span, the temperature and x-axis thermal growth for the lathe have been collected. Similarly, for numerical transient analysis, total time span of 21600 sec. (6 hr.) was considered and heat input values were provided at locations of heat sources as per the loading cycle. In addition to the analytical heat calculations, joint contact resistance between steel reinforcement and epoxy granite structures has been evaluated and provided as joint contact conductance in the simulation.

Thermal Contact Conductance Between Steel Reinforcement And Epoxy Granite Material

Contact conductance depends on the geometry, surface roughness, mean interface pressure, and joint temperature. Contact conductance is the inverse of thermal contact resistance developed in the joint. Eq. 12 is an analytical model developed by Bahrami et al. [30] for estimating the thermal contact resistance between metal and polymer and is considered in this work. Joint resistance is a summation of the thermal constriction/spreading resistance through the micro contacts (${R}_{s})$ and bulk resistance of the polymer$\left({R}_{b}\right)$. The heat transfer to the EG portion from reinforcement by considering joint contact resistance will be different in the condition without considering joint contact resistance as depicted in Fig. 10.

$${R}_{J}={R}_{s}+{R}_{b}$$

$${ R}_{S}=0.565{H}_{m}\left(\sigma /m\right)/\left({k}_{s}F\right)$$

$${R}_{b}=\left({t}_{0}\left(1-\left(P/{E}_{P}\right)\right)/\left({A}_{a}{k}_{p}\right)\right)$$

$${R}_{J}=\left(0.565{H}_{m}\left(\sigma /m\right)/\left({k}_{s}F\right)\right)+\left({t}_{0}\left(1-\left(P/{E}_{P}\right)\right)/\left({A}_{a}{k}_{p}\right)\right)$$

Equivalent thermal conductivity of polymer and steel (${ k}_{s})$is considered as $\left(\left(2{k}_{m}{k}_{P}\right)/\left({k}_{m}+{k}_{p}\right)\right)$ (W/m. K). Polymer characteristics considered for epoxy are micro hardness $({H}_{m}$) is 0.15 GPa, Combined surface roughness$({\sigma }$) is 0.5 µm, $(m$)surface asperities slope is 0.14 µm/m, Thermal conductivity of steel$({k}_{m}$) is 50 W/m. K, Minimum thickness of the polymer throughout the reinforcement $({t}_{0}$) is 5 mm. Contact pressure $\left(P\right)$ is 0.1 MPa, Modulus of elasticity of the polymer$({E}_{P}$) is 20 GPa. Thermal conductivity of the polymer ${(k}_{p})$ is 1.5 W/m. K. From the analytical equation, the joint contact resistance is estimated as 12.5 m²ºC /W, the joint contact conductance value which is inverse of joint contact resistance is found to be 0.08 W/m²ºC.

4.2 Numerical Thermal Investigations On Ci And Sreg Cnc Lathe

The developed CAD model has been used for transient thermal Finite Element Analysis (FEA) at 20^oC and 40^oC environmental temperatures for CNC lathe with CI and SREG beds. During analysis, calculated heat values were provided at the heat source locations in FE model. Convection (free air circulation) has been applied at the exposed boundaries.

Except for the bed, a converged mesh with a 20 mm element size was used, and the hex dominant technique was used. The bed geometry at different locations has dimensions less than 20 mm, and automatic mesh generation technique was used. The step size (time of each step) and number of iterations has a significant impact on the time taken for solving transient thermal analysis. Since there are more time steps and iterations involved, it usually takes more than 30 hours for one analysis. Figure 11 (a), Fig. 11 (c) depicts the temperature distribution, F Fig. 11 (b), and Fig. 11 (d) depicts the deformation under idle running of cross feed drive for lathe with CI and SREG bed at 20 ºC, ETVC condition.

Table.3. Temperature at sensor locations

	Sensor location	Lathe with CI bed at 20ºC			Lathe with SREG bed at 20ºC			Lathe with CI bed at 40ºC			Lathe with SREG bed at 40ºC
	Sensor location	Exp.	FEA	% dev	Exp.	FEA	% dev	Exp.	FEA	% dev	Exp.	FEA	% dev
T 1	Ambient temperature	20	20	0	20	20	0	40	40	0	40	40	0
T 2	Top right LM block	24	25	4.2	26	27	3.8	43.5	46	1.2	46	48	4.3
T 3	Drive motor	29	29.2	0.6	32	33.3	4.1	48	51	6.2	49	52	6.1
T 4	Bed center	23	22.5	2.2	22	21.5	2.3	43.5	43	1.2	42	41.5	1.2
T 5	Ball screw housing	24	25	4.2	25	26	4	44	45	2.3	44	45	2.3
T 6	Below turret	22	24	9.1	24	24.5	2.1	42	45	2.4	43.5	45.5	4.6

The differences in temperature of various structures are responsible for deformation. The cumulative deformation of all structures is responsible for deformation at the TCP. Lead screws of both longitudinal and cross feed drives have significant temperature rise since nearer to the heat sources. The rise in temperature in all structures except the bed in the lathe with SREG bed is higher than the lathe with CI bed.

The effect of resistance causes a temperature rise in all locations, but in the case of the SREG bed, the temperature is less because of its lower thermal conductivity Although, there is not much temperature rise at TCP, the deformation at various structures causes a considerable deformation at TCP. The major structures contributing to TCP deformation are saddle, cross slide, bearing hub, bearings, cross feed drive guideways, and turret. The temperature obtained from the different sensor locations in the experiment and temperature from same locations obtained from FEA are compared in Table 3. Deformation (X-axis growth at TCP) from experiments and FEA are compared in Table 4. Results from the FE analysis and experiments have been consolidated in Table 3 and Table 4.

Table 4. Comparison of experimental and FEA results

Chamber temperature (^oC)	Deformation measurement location	Deformation in lathe with CI bed (μm)			Deformation in lathe with SREG bed (μm)
Chamber temperature (^oC)	Deformation measurement location	Exp.	FEA	Deviation (%)	Exp.	FEA	Deviation (%)
20	TCP	8.8	9.5	7.9	14.8	16	8.1
40	TCP	9	9.4	4.5	17	17.2	3.4

There is a good correlation between the results and the numerical model developed is deemed validated. Further, the validated simulation FEM model can be used for further analysis. The temperature and deformation in lathe with CI bed and SREG bed from the simulations results are depicted in Fig. 11. Below the cross feed drive bearing hub, saddle, structures in LF and the SREG bed are stationary. Structures above the cross feed drive, viz., cross rail, turret, etc. are subjected to motion.

These moving structures dissipate more heat due to self-forced convection. Hence, the surface temperature of the top structure is less due to more heat dissipation. Temperature in the structures below the cross feed drive is higher due to more heat conduction from nearby heat sources and less heat dissipation from these stationary structures. Even though the bottom structures experience higher temperature rise, they are constrained from expanding; the higher thermal growth of the top structures can be attributed to their free expansion at the top. The transient state temperature and the thermal expansion from simulations at different locations are depicted in the Fig. 11. From the figure, it can be seen that at the locations P2, P3, P7, P8, P10, temperature increases slowly at the start and gradually saturates to the steady state temperature when the amount of heat generation balances with the heat dissipation into the atmosphere. The total heat generated at the left and right bearings is the same but for the temperature of the right bearing is much higher than that of the left bearings due to the reason that the right bearing is near to the motor.

From Fig. 12, it is observed that the temperatures of the bed and steel reinforcement are not continuous and there are temperature drops due to thermal contact resistance. This can be attributed the high thermal contact resistance, which can also be referred to as low thermal contact conductance between steel reinforcement and EG. Motor deforms along the negative direction since it is exposed to convection and is free to expand in other directions, overhanging due to self-weight. Each of the two transits per period (one while moving downwards, one while moving upwards) leads to an increase in temperature, followed by a more gradual decrease due to heat diffusion.

Motor temperatures in the lathe with SREG bed are 3ºC higher than the temperature at the same location in the lathe with CI bed. The temperature of the structures namely, saddle, guideways of LF, and CI bed are the same, there is no temperature gradient, which refers to steady-state heat flow throughout the structures, whereas, the same structures in the lathe with SREG bed have the following temperatures at different locations: P11- 25.5 ºC, P 12 is 24 ºC and at P13 is 21 ºC. The steel reinforcement and EG structures are bonded together during fabrication, the heat flow from top structures to the bed is not possible due to the difference in thermal characteristics of both materials. Due to this reason, a large temperature difference in bed and reinforcement has been noticed. In the SREG bed, the EG portion and steel reinforcement are bonded together and the reinforcement is provided till the bottom end of the bed. Temperature rise and expansion of EG in SREG bed is low but it could be seen from the simulation result that the deformation of the EG is more than that of the CI bed which is due to expansion of corresponding bonded steel reinforcement.

The x-axis thermal growth value due to cross feed drive will have a direct influence on the depth of cut during turning operation and hence will be directly responsible for the misleading cut in turning operations. Similarly, for internal and external threading operations, a moment of longitudinal feed drive (LF) is much more important. A combination of machining operations associated with feed and depth of cut will also be responsible for a moment of both longitudinal and cross feed drives. Hence, the validated numerical model is used to analyze the thermal behavior of the lathe with SREG bed under idle conditions of the longitudinal feed drive (Case II) and both longitudinal and cross feed drives (Case II). The testing standards adopted for Case I are used for Case II and Case III also. The temperature and deformation simulations plots of lathe with SREG bed are depicted in Fig. 13.

For all the three cases, the temperature and deformation have been simulated and the results are depicted in Fig. 13. From the results, analysis of heat transfer in machine tool associated with CF, heat dissipation due to self-forced convection, LF and its impact in another have been studied. In Case I, temperature rise and deformation of structures below and above the CF show that there is heat transfer both towards the bed and towards the TCP, whereas in Case II, the temperature of the EG bed remains low due to its low thermal conductivity and high specific heat. In this case, the temperatures of all the structures except the bed are found to be higher compared to the corresponding temperatures in Case I. Figure 13 depicts the temperature and the deformation under the three cases. Temperature of the structures above cross feed drive, namely saddle, turret, TCP are subjected to similar temperature in Case II as that observed in Case I, due to the increase in self-forced convection area.

Even though the self-forced convection area in Case II is higher than that in Case I, which is responsible for more convection, the thermal error at TCP is higher than that is Case I. Idle running of CF and LF has resulted in 17 µm and 23 µm of x-axis thermal growth at TCP. Hence, under similar operating conditions, idle running of LF results in 26% higher thermal error than the idle running of CF. Further, simultaneous idle running of both CF and LF has been found to result in a thermal error of 33 µm which is 1.4 times higher than the thermal error in Case II, and 1.9 times higher than that in Case I. A similar trend has been observed in simulation results of feed drive with SREG bed at 40^oC. From temperatures and deformation of structures, it is clear that there is a more heat accumulation in steel reinforcement, which lead to higher thermal error in Case II and Case III as compared to case I. In Case I the heat generated in the cross feed drive flows towards the structures above as well as below the drive, thus resulting in gradual increase in temperature of the steel reinforcement. In case II, since the heat sources are nearer to the SREG bed, due to more accumulation of heat in one side heat can flow from bottom to top. Due to this reason, there exists higher slope in temperature profile of steel reinforcement at the beginning as shown in Fig. 14. Similarly, in Case III, there exist one side heat flow from bottom to the top but same self-forced convection area as like case II.

From the Fig. 14, it can be noted that the temperature of steel reinforcement in Case III is higher than that in Case I and Case II. Idle running of LF will lead to more heat accumulation in steel reinforcement than in Case I, but after three hours, the temperature has been found to attain a steady-state. No significant temperature rise was observed in EG in all the cases. Simultaneous idle running of both CF and LF has been found to result in a thermal error of 33 µm which is 1.4 times higher than the thermal error in Case II, and 1.9 times higher than that in Case I. A similar trend has been observed in simulation results of feed drive with SREG bed at 40^oC. From temperatures and deformation of structures, it is clear that there is more heat accumulation in steel reinforcement, which leads to higher thermal error in Case II and Case III as compared to Case I.

SREG beds and bases are employed to replace cast iron in precision machine tools due to their promising rigidity and damping characteristics designed with equal or greater rigidity. A systematic approach for thermal analysis for the idle running of the cross-feed drive system of a CNC lathe with CI and SREG bed is presented in this article. Experiments were conducted as per ISO 230-3, with 3 minutes running and 1-minute idling load cycle for 6 h. in closed ETVC conditions at 20ºC and 40ºC. Results reveal that the lathe with SREG bed exhibits a thermal error which is 1.68 times that of the lathe with CI bed at 20ºC and 1.8 times at 40ºC ETVC conditions. The thermo-mechanical FE model of the machine was developed, and boundary conditions such as heat generation, self-forced convection due to motion, and natural convection have been applied. In addition, thermal contact resistance between the steel reinforcement and the epoxy polymer has been estimated by the analytical model and applied the same. The load cycle considered for experiments have been used for the transient thermal analysis and later coupled with static structural analysis. There was a high level of agreement when the measured and simulated results were compared. Thermal analysis of the CNC lathe with SREG bed reveals that it is more susceptible to thermal error than cast iron machines since more heat is accumulated in steel reinforcement and as a result bi-material expansion/effect occurs. Further, with validated numerical model, thermal analysis by simulation for idle running of CF, LF and both CF and LF have been conducted. Simulation results revel that idle running of LF develop 1.3 times higher thermal error than thermal error in idle running of CF. Idle running of both CF and LF develop 1.9 and 1.4 times higher thermal error than thermal error under idle running of CF and LF respectively.

Acknowledgments

The authors acknowledge M/s Galaxy Machinery, India, Pvt Ltd, for the support and technical contributions. Authors’ sincere thanks to AICTE-New Delhi, for providing fellowship through NDF program (National Doctoral Fellowship). Author’s sincere thanks to PSG College of Technology-Coimbatore, for providing constant support in this research work. Authors wish to acknowledge the Advanced Machine Tool Testing Facility (AMTTF) for providing a thermal chamber to perform experiments.

Author contribution

Authors have been personally and actively involved in substantial work leading to the paper, and will take public responsibility for its content.

Funding

The authors gratefully acknowledge the financial support for this research work by the Office of the Principal Scientific Adviser to the Government of India [Project sanction no. F.No.: Prn.SA/DRDP/MT/2010(G)].

Conflicts of interest/Competing interest Not applicable.

Availability of data and materials Not applicable.

Code availability (software application or custom code) Not applicable.

Ethics approval: Not applicable

Consent to participate: All authors have been actively involved in research work and manuscript preparation, and will take public responsibility for its content.

Consent for publication: All author(s) are agreed for publication

Competing interests: The authors declare no competing interests.

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Thermal investigations on CNC lathe fitted with dynamically enhanced steel reinforced epoxy granite bed

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Abstract

Figures

1. Introduction

2. Literature Review On Steel-reinforced Epoxy Granite Machine Tool Structures

3. Experimental Investigations On The Thermal Behavior Of Cnc Lathe With Ci And Sreg Beds

4. Development Of Numerical Model For Feed Drive Of Cnc Lathe With Ci And Sreg Bed

Heat generation in bearings

Heat generation in ball screw nut

Heat generation in Guideways

Thermal Contact Conductance Between Steel Reinforcement And Epoxy Granite Material

4.2 Numerical Thermal Investigations On Ci And Sreg Cnc Lathe

5. Numerical Simulations Under Idle Running Of Longitudinal Feed Drive And Both Feed Drives

6. Conclusions

Declarations

References

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