^{1}

^{2}

^{2}

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^{1}

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The disadvantages of the common current thermal error modeling methods for CNC machine tool feed drive systems were analyzed, such as the requirement of many temperature sensors to reach high accuracy and poor applicability of different moving states. A new robust modeling method based on the heat transfer theory is proposed, and the procedure of the thermal tests for a feed drive system is presented. Multiple regression method and robust modeling method based on the heat transfer theory were, respectively, used to establish a thermal error model, and a pointer automatic optimizer was used to optimize the parameters in the robust model. A compensation simulation was conducted under five different moving states using these two modeling methods, and the advantages of the robust modeling method were proved. Finally, the compensation effect of the robust modeling method was verified under a random moving state on a vertical machining center.

Currently, mainly two methods are used to reduce CNC machine tool thermal errors: error prevention and error compensation [

Many studies have developed compensation schemes to counteract the thermal deformation of a feed drive system. Some studies have established thermal error models using the multiple linear regression method [

Some machine tool builders have applied thermal error compensation on CNC machine tools such as OKUMA’s thermofriendly technology and MAZAK’s intelligent thermal shield. However, most of them compensate the thermal errors caused by ambient temperature variation and spindle rotation. For the thermal errors caused by ball-screw friction, ball screw or nut cooling is used instead of error compensation.

According to the current studies and applications of thermal error compensation, a new robust modeling method based on the heat transfer theory is proposed. In this modeling method, the thermal errors caused by ambient temperature variation and ball-screw friction were calculated separately. Based on the heat production, heat conduction, and heat convection theory, the ball-screw temperature field at any time can be obtained to predict ball-screw thermal errors. Finally, the developed method was compared with the multiple regression modeling method through simulation and experiment.

The thermal errors of a feed drive system were investigated on the

Two temperature sensors, whose tolerance is ±0.1°C (5–45°C), were placed on the nut and base near the bearing block [

Placement of temperature sensors on the machine tool.

Thermal errors were investigated using a dual-frequency laser interferometer XL80 system, as shown in Figure

Investigation of thermal errors using a laser interferometer.

The tests were conducted under five moving states, and the test parameters are shown in Table

Parameters of thermal error tests.

Speed |
Range | |
---|---|---|

State 1 | 8000 | 210–490 |

State 2 | 6500 | 210–490 |

State 3 | 15000 | 210–490 |

State 4 | 8000 | 0–210 |

State 5 | 8000 | 0–700 |

For example, the procedure of thermal tests in state 1 is described as follows:

Test the positioning error of

Let

Stop moving. Test the positioning error, and record the values of temperature sensors 1 and 2.

Repeat steps (2) and (3) until

Let

Based on the above tests, thermal error curves (Figure

Thermal error curves of

Temperature curves of

Tests were conducted under states 2–5 in the same manner.

The multiple regression model is a multiple-input-single-output system. The multiple regression method has some advantages such as a simple modeling procedure. When the moving state of a machine tool is constant, a relatively high compensation accuracy can be obtained. The thermal error model established with the multiple regression method can be described as follows:

The thermal error

The screw is discretized into

Discretization of the screw.

In general, the change in ambient temperature is slow. Therefore, the change in ball-screw temperature caused by the change in ambient temperature is also slow. Therefore,

The temperature distribution of each point in an object is known as temperature field, which is not only the function of position but also the function of time [

For a certain segment

For

If the nut moves on ^{2};

For

If the nut moves on ^{2};

The thermal change of ball screw is a dynamic process; therefore, the temperature field of the ball screw also changes dynamically. For

Therefore, ball-screw thermal errors caused by movement at a certain time

Combining (

A robust modeling method based on the heat transfer theory considers the dynamic process of a feed drive system’s temperature field; therefore, even if the moving state of the feed drive system changes, an excellent compensation result can still be obtained.

In the robust model, some parameters are difficult to determine such as heat capacity

The compensation results of the multiple regression model and robust model based on the heat transfer theory were compared using Matlab R2014a.

A positioning error compensation was also included in these two models considering the existing positioning errors. The positioning error compensation was used to compensate 0 min errors using the following:

In a multiple regression model,

The multiple regression models were established based on the data of states 1 and 5. M1 is the model established based on the data of state 1, and M5 is the model established based on the data of state 5.

The compensation results of M1 for state 1 and M5 for state 5 are shown in Figure

Simulation results of M1 for state 1 and M5 for state 5.

The compensation results of M1 for states 2–5 are shown in Figure

Simulation results of M1 for states 2–5.

A robust model based on the heat transfer theory was established based on the data of state 1. The compensation results for states 1–5 are shown in Figure

Simulation results for states 1–5.

Figures

The advantages of the robust model based on the heat transfer theory were verified by simulation reported in Section

The reading of a feed drive system’s position from CNC and the writing of compensation values to CNC are needed for compensation experiments. Fanuc Open CNC API Specifications (FOCAS) was used to obtain these reading and writing functions, as shown in Figure

Diagram of data acquisition and error compensation.

The

Moving states in compensation tests.

Speed |
Range |
Time | |
---|---|---|---|

State 1 | 8000 | 0–280 | 6 |

State 2 | 5000 | 490–700 | 10 |

State 3 | 10000 | 240–450 | 5 |

State 4 | 12000 | 0–700 | 2 |

Position errors were investigated using a laser interferometer after each moving state, and the results are shown in Figure

Compensation effects of the robust model based on the heat transfer theory.

The simulation and test results in Figures

The disadvantages of existing thermal error models were analyzed, and a new robust model based on the heat transfer theory was proposed. Multiple regression and robust models were derived and used for simulations and experiments. The results show that the robust model based on the heat transfer theory has better accuracy and robustness and can satisfy the actual application. The advantages of this technology are as follows:

Only one temperature sensor is needed for a linear axis in real-time compensation, and the cost is low.

The manufacturing accuracy of a single workpiece can be improved.

The manufacturing consistency of the bulk of workpiece can be improved, and the rejection rate can be reduced.

Machines do not need to warm up before the machining. Thus, time and power costs can be saved.

Machines do not depend on a constant-temperature workshop, and construction and power costs can be saved.

Through the above analyses, it can be concluded that this technology has excellent potential.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This research was supported by National Science and Technology Major Project of People’s Republic of China (2013ZX04011011).